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U.S. DEPARTMENT OF COMMERCE National Technical Information Service
AD-A029 389
NCVA-2 - A Digital Computer Program for
Analyzing Nuclear Overpressure Effects
on Aircraft. Part 2. Computer Program
Koman AviDyne
August 1976
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254094 AFWL-TR-75-262, Pt. 2 AFWL-TR-
75-262 Pt. 2
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NOVA.2 — A DIGITAL COMPUTER PROGRAM FOR ANALYZING NUCLEAR OVERPRESSURE EFFECTS ON AIRCRAFT
Part 2 Computer Program
Kaman AviDyne Burlington, MA 01803
August 1976
r
Final Report
Approved for public release; distribution unlimited,
REPRODUCED BY
NATIONAL TECHNICAL INFORMATION SERVICE
U. S. DEPARTMENT OF COMMERCE SPRINGFIELD, VA. 22161
AIR FORCE WEAPONS LABORATORY Air Force Systems Command Kirtland Air Force Base, NM 87117
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AFWL-TR-75-262, Pt. 2
This final report was prepared b/ Katnan AviDyne, Burlington, Massachusetts, under Contract F29601-'/5-C-0032v Job Order 38090339, with the Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico. Mr. Geralo M. Campbell (SAT) was the Laboratory Project Officer-in-Charge.
When US Government drawings, specifications, or other data are used for any purpose other than a definitely related Government procurement operation, the Government thereby incurs no responsibility nor any obligation whatsoever, and the fact that the Government may have formulated, furnished, or in any way supplied the said drawings, specifications, or other data, is not to be regarded by implication or otherwise, as in any manner licensing the holder or any other person or corporation, or conveying any rights or permission to manufacture, use, or sell any patented invention that may in any way be related thereto.
This report has been reviewed by the Information Office (01) and is releasa- ble to the National Technical Information Service (NTIS). At NTI.S, it will be cvailable to the general public, including foreign nations.
This technical report has been reviewed and is approved for puolication.
GERALD M. CAMPBELL Project Officer
T^vz^ /?. Ztky^tJ^^ F0R7THE COMMANftfR
TERRYS. LAURITSEN PAUL J. DAILY ' Lt Colonel, USAF Colonel, USAF Chief, Technology and Analysis Branch /A^» Analysis Division
/
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DO NOT RETURN THIS COPY. RETAIN OR DESTROY. •\/
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UmASSIEIED SICURITY CLASSIFICATION Of THIS PAGB C^«" D«» Bnltrtd)
REPORT DOCUMENTATION PAGE
AFWL-TR-75-262, Pt. 2
READ INSTRUCTIONS BEFORE COMPLETING FORM
2. OOVT ACCESSION NO 3. RECIPIENT'S CATALOG NUMBER
4. TITLE rand 5u*tl(/«; S. TYPE OF REPORT i RERIOO COVERED
r!0VA-2 -- A DIGITAL COMPUTER PROGRAM FOR ANALYZING NUCLEAR OVERPRESSURE EFFECTS ON AIRCRAFT, Part 2, Computer Program
Final Report «. PERFORMING ORG. REPORT NUMBER
ja.TR-128 7. «uTHORf«;
William N. Lee Lawrence•Jr Mente
8. CONTRACT OR GRANT NUMBERC*)
F29601-75-C-0032
9. PECIFORMiNG ORGANIZATION NAME ANO ADDRESS
Kaman AviDyne ^ A Division of Kaman Sciences Corporation Burlington. MA 01803
10. PROGRAM ELEMENT, PROJECT, TASK AREA * WORK UNIT NUMBERS
62601F 88090339
11), CONTROLLING OFFICE NAME ANO ADDRESS
Air Force Weapons Laboratory (SAT) Kirtland Air Force Base. NM 87117
12. REPORT DATS
August 1976
14. MONITORING AGENCY NAME A AOORKSSO« dllltnnl 'ram Con(ro<(/n« Olticm)
13. NUMBER OF PAGES
IS. SECURITY CLASS, (ot Ihl» nport)
UNCLASSIFIED IS«, OECLASSIFICATION/ OQWNGRAüING
SCHEDULE
16. DISTRIBUTION STATEMENT (al Ihi» Rmpori)
Approved for public release; distribution unlimited.
17. DISTRIBUTION STATEMENT (ol'th» abmtruel uifrmd In Block 30, II dllltrtnt Inm Riport)
18. SUPPLEMENTARY NOTES
This report consists of two parts. Part 1, Theory, includes the front matter, Sections I through V, pages 1 to 196. Pan 2, Computer Program, includes Section VI and the references, pages 197 to 348.
19. KEY MOROS 'Canllnua on rortto «id» // nocofary tid idontlly iy block numbtr)
Aircraft aerodynamic loading Aircraft vulnerability Digital computer program Elastic-plastic material behavior Ground reflection effect
Nuclear blast Overpressure effects Structural response of beam
and panel elements
20. ABSTRACT fContlnum an r«v«r«« $id9 If n«c»«««fy and identity by block numbmr)
N0VA-2 (Nuclear Overpressure Vulnerability Analysis, Version 2) is an updated version of NOVA, a F0RTRAN-IV digital computer program for calculating the respor.cc of individual structural elements of aircraft, such as stringers, frames and panels, exposed to the transient pressure loading associated with the blast wave from a nuclear explosion. The updated version extends the capability of NOVA to analyze rib elements, frames with variable cross section, and offers a clio'ce of clamped, simply supported or free edoe boundary (over)
DO , :°:M73 1473 EDITION OF 1 NOV «S IS OBSOLETE UNCLASSIFIED S£CURlTY CLASSIFICATION OF 'HIS 3ACE Whan Dmta Entefd)
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UNCLASSIFIED SECURITY CLASSIFICATION Of THIS PAGErWian Dmim Snlmnd)
ABSTRACT (cont'd)
conditions. For inelastic structural response, a plastic model for material behavior is provided, the REFRA near-ground reflections model for blast still provides the overall capability to analyze ; panel elements exposed to a steady-state subsonic dynamic preload, followed by a dynamic blast wave range is automatically determined in an iteration (specified on a probabilistic basis) are compared response.
much improved elastic Also added to NOVA is wav*?. The program
nu I ti1ayered beam and or supersonic aero-
. A critical slant where damage criteria with the structural
/' UNCLASSIFIED SECURITY CLASSIFICATION a F THIS P»GEr»7i»n D«r« Enfrad)
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SECTION VI
PROGRAM DESCRIPTION AND OPERATION
The NOVA Computer program can be divided Into three distinct sets
of routines, identified as NOVA, DEPROB and DEPROP. DEPRQB is respon-
sible for the structural response of beam elements, DEPROP is similarly
responsible for panel elements, and NOVA contains the aerodynamics, the
blast routines, the vulnerability iteration routines, and controls the
program as a whole. The specific routines associated with each program
are listed in table 15. A description of each routine follows in
subsection 6.1 and 6.2, along with the complete instructions for the
operation of the NOVA computer code in subsections 6.3 and 6.4.
6.1 DESCRIPTION OF ROUTINES
Table 15 lists the 103 routines which maka up NOVA, most of which
are described in this section. A brief description of the purpose is
given, followed by a list of routines it references, and which routines
reference it. In addition, flow diagrams of the major subprograms are
given. It should be noted that routines referenced by both DEPROB and
DEPROP are included in the NOVA group of routines, since such routines
belong, in a sense, to the program as a whole rather than to either
structural codt.
Table 16 lists all of the labeled common blocks in the program, the
length of each common, and the subprograms which use each common block.
The underlined subprogram names in table 16 indicate the subprogram
which "owns" it in a recommended segmentation procedure to be discussed
in section 6.4.
-197-
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TABLE 15. LIST OF SUBPROGRAMS
iqpmani •MIIMMII
NOVA DEPROP DEPROB
NOVA WFDZR DEPROP DEPROB BLOCK WELL BOLT COMP1 IODUM WFPRMT DSET1 COMP2 SEC WFVZR DSET2 COMSET NIN WFVRMT DSET3 CYCLE NEWSL AIR DERV2 DAB NOVSUM WFPKOP DTSTEP DEFORM RITC REFRA HIM DPUR RITER OPT1 LEGEND EQUILr
CSETUP 0PT2 LIST1 EQUILX INTP OPT3 LIST2 FB PINIT ADVANC RELAXP FBCTL SOLVE BISH SIGMA FBSET BLAST READ FINAL XBLAST POSTAP FSOL HYDRA SKIP PRINT1 IOPT1 FPRES READ1 IOPT2 INTSLO RESD IOPT3 PFUSE RESET ATMOS PJUMP RLAXB MATM62 POSTW1 RLAXF SHOCK POSTW2 SLAY TPINT POSTW3 STRESS INT1 POSTW4 STRESX INT 2 P0STW5 STRN1 WFZR POSTW6 STRN2 WFPKOD P0STW7 STSET WFPR PRESS TSTEP WFPKV PREW VCS WFDRMT SETW
WPRES
1 i
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TABLE 16. COMMON BLOCKS AND SUBPROGRAMS USING THEM
Common Block
Length (Decimal) Subprograms
CNOVA
DNOVA
CTLX 2
CONSTC 15
SCALEC 5
WFRT 13
REFRAC
PW1
CBLK1
CBLK2
142
2858
7495
23
82
1990
NOVA*. NIN, NEWSL, NOVSUM, RITC, CSETUP, BLAST, XBLAST, PINIT, FPRES, PRESS, PREW, WPRES, DEPROP, DSET1, DSET2, DSET3, DERV2, DTSTEP, LIST1, LIST2, SIGMA, DEPROB, COMP1, COMP2, COMSET, CYCLE, DEFORM, EQUILP, EQU'XLX, FB, FINAL, PRINT1, READ1, STRESS, TSTEP.
NOVA, BLOCK, NIN, NEWSL, NOVSUM, RITC, BLAST, XBLAST, PINIT, FPRES, POSTW1, POSTW2, POSTW3, P0STW4, PCSTW5, POSTW6, POSTW7, PRESS, PREW, SETW, WPRES
NOVA. BLAST, REFRA, FPRES, WPRES
HYDRA. IOPT1, IOPT2, IOPT3
HYDRA. lom, IOPT2, IOPT3, SHOCK
SHOCK, V7FPK0D, WFPR, WFPKV, WFDRMT, WELL, WFPRMT, WFVRMT
REFRA, OPT1, OPT2, ADVANC, READ, SKIP
POSTW1, POSTW2, POSTW3, P0STW4, POSTW5, POSTW6, P0STW7, SETW, WPRES
DEPROP, BOLT, DSET1, DSET2, DSET3, DERV2, DTSTEP, LEGEND, LIST1, LIST2, SIGMA
DEPROP, BOLT, DSET1, DSET2, DSET3, DERV2, DTSTEP
Underlined routine owns that commoa block in segmentation setup.
-199-
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BLK3
BLK4
BLK5
BLK6
Table 16. (Concluded)
CBLK3 12
CBLK4 226
CBLK5 393
ci'T;: 12355
CBLK7 12
CBLK8 50
CBLK9 128
CBLK10 5776
CBLK11 12
CBLK12 6150
CBLK13 9
CBLANK 30056
CHIM 76 i
466
7216
21
2269
DEPROP, DSET1, DSET2, LEGEND, SIGMA
DSET3, DERV2,
DEPROP, DSET1, DSET2, SIGMA
DSET3, DERV2,
DEPROP, DSET1, DSET?, DSET3
DEPROP, DSET1, DSET2, LIST1, LIST2, SIGMA
DSET3, DERV2,
DEPROP, DSET1, DSET2, SIGMA
DSET3, LT.ST2,
DEPROP, DSET1, DSET2, DSET3, DERV2
DEPROP, DSET1, DSET2, LIST2
DSET3, LIST1,
DEPROP, DSET1, DSET2, LIST1, LIST2
DSET3, DERV2,
DEPROP, DSET1, DSET2, DSET3, DERV2
RELAXP
DEPROP, DSET1, DSET2, DSET3, DTSTEP
SIGMA
HIM
DEPROB, C0MP1, COMP2, COMSET, CYCLE, DAB, DEFORM, DPUR, EQUILP, EQUILX, FB, FBCTL, FBSET, FINAL, FSOL, PRINT1 READ1, RESD, RESET, SLAY, STRESS, STRESX, STRN1, STRN2, STSET. "..'STEP, VCS
DAB, DEFORM, DPUR, FSOL, RESD, RESET, STSET
RLAXB
RLAXF
COMP1, C0MP2, COMSET, DEFORM, F3, FBSET, PRINT1, STRESS, STRN1, STRN2
-200-
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6.1.1 NOVA
The NOVA routine is the master routine which controls the
logic of the overall program. It contains the subroutines for predict-
ing the aerodynamic flight loads, the blast pressure loads that are
applied to the lifting surfaces and fuselage during subsonic and super-
sonic flight, and the iterative technique for determining the slant
range at which a structural element incurs damage which has been speci-
fied on a probabilistic basis.
NOVA reads the input data associated with specific aircraft,
weapon, and structural element parameters which are outlined in para-
graph 6.3.1. Figures 66 and 67 present flow diagrams for NOVA and for
subroutine PINIT, respectively.
Fourteen of the subprograms comprising the 1-KT free-air blast
model are not described in detail here as they are the product of AFWL
(refs. 2 and 3). Subroutines HYDRA, I0PT1, I0PT2 and ATMOS wece written
to make the model consistent with earlier versions of HYDRA using the
data tape. The only changes to the AFWL functions were: 1) the sup-
pression of the two-dimensional fireball effect, 2) the lengthening of
common block. WFRT in certain routines to make them all equal length, and
3) the addition of an error message in function WFPKOD.
Similarly, the REFRA routines are not described in detail due
to the existing documentation (ref. 7). The ground reflection model is
a self-contained package, the only required change being the addition of
common block CTLX.
The following is a brL%f description oi all other routines
belonging to the NOVA group (listed alphabetically), including their
relationship with other programs:
NOVA
Main program, exercises entire vulnerability code. Calls ATMOS, BLAST, BLOCK, DEPROB, DEPROP, NEWSL, NIN, NOVSUM, PINIT, RITC.
-201-
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ATMOS
Calculates ambient atmospheric properties as a function of altitude. Calls MATM62. Called by NOVA, REFRA, XBLAST.
BLAST
Calls the appropriate blast oackage, depending on ground reflection option. Calls REFRA, XBLAST. " Called by NOVA, FPRES, NOVSIM, WPRES.
BLOCK
Sets up nominal direction cosines for 21 burst orientations. Called by NOVA.
CSETUP
Sets up constants related to damage criteria for use by DEPROB and DEPROP in determining ratio of maximum response to critical levels of response. Calls INT1. Called by DEPROB, DEPROP.
FPRES
Calculates times and associated flow conditions for fuselage points. Calls BLAST, PFUSE, PJUMP. Called by PINIT.
HYDRA
Responsible for obtaining free-air blast characteristics. Calls I0PT1, I0PT2, I0PT3, MATM62. Called by 0PT1, 0PT2, REFRA, XBLAST.
INTP
One-dimensional interpolation routine for time-pressure tables, where time is always increasing. Called by PRESS.
INTSLO
Performs one-dimensional interpolation and also calculates slope. Called by WPRES.
INT1
Performs one-dimensional interpolation. Called by CSETUP, XBLAST.
-202-
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INT2
Performs two-dimensional interpolation. Called by XBLAST,
IQDUM
Dunnny routine whose sole purpose is to cause the loading of all 10 sys- tem routines in the root level of segmentation setup. Necessary because of current problem with loader. Not referenced.
I0PT1
Finds free-air blast characteristics given time and distance from burst. Calls SHOCK. Called by HYDRA.
I0PT2
Finds incident shock wave position given time from burst. Calls WPKOP, WFPR. Called by HYDRA.
I0PT3
Finds time of arrival of incident shock wave given distance from burst. Calls WFPKOP, WFPR. Called by HYDRA.
NIN
Reads basic aircraft data and prints out description. Called by NOVA.
NEWSL
Reads aircraft data associated with each structural element and prints out description. Called by NOVA.
NOVSUM
Prints summary of results of entire NOVA run and selects critical element for each orientation. Called by NOVA.
PFUSE
Calculates steady-staf.c pressure on fuselage. Called by FPRES.
-203-
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PINIT
Assembler, pressure-time table and provides initial pressure for DEPROB or DEPFwP. Calls BPRES, WPRES. Called by NOVA.
PJUMP
Calculates jump in fuselage pressure at shock arrival. Called by FPRES.
P0STW1. P0STW2. P0STW3, P0STW4. P0STW5. P0STW6, P0STW7
Determine the post-blast aerodynamic loading on a lifting surface for seven different cases. The number in the subroutine name corresponds to NCASE, as determined i .1 subroutine SETW. Called by WPRES.
PRESS
Interpolates pressure for DEPROB or DEPROP. Calls INTP. Called by CYCLE (DEPROB), DERV2(DEPROP).
PREW
Determines preblast aerodynamic loading on a lifting surface. Called by WPRES.
REFRA
Determines blast characteristics, with or without near-ground reflection effects, as provided on data tape, file TAPE10. Calls ATMOS, HYDRA, 0PT1, 0PT2, 0PT3. Called by BLAST.
RITC
Controls range iteration as a function of structural response. Itera- tion is either along slant range or constrained to constant altitude. Calls RITER. Called by NOVA.
RITER
Calculates new trial range, making use of up to three previous trials, if possible. Checks to see if criterion is decreasing as range increases, and determines if iteration has converged on an acceptable range. Called by RITC.
SEC
Finds elapsed CP time. Calls system routine SECOND. Called by COMSET(DEPROB), FINAL (DEPROB) , DEPROP.
204
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SETW
Determines which post-blast subroutine is to calculate the aerodynamic loading. Sets up several quantities which are independent of time and position. Called by WPRES.
SOLVE
Solves a set of simultaneous linear algebraic equations. Called by RLAXB(DEPROB), RELAXP (DEPROP) .
TPINT -
Solves for intersection of shock wave with triple point path. Called by XBLAST.
WPRES
Calculates times and associated flow conditions for wing (lifting surface) points. Calls INTSLO, P0STW1, P0STW2, P0STW3, P0STW4, POSTW5, P0STW6, P0STW7, PREW, SETW, XBLAST. Called by PINIT.
XBLAST
Calculates blast characteristics using analytical curve fit for near- ground reflection effects. Calls ATMOS, HYDRA, INT1, INT2. Called by BLAST.
6.1.2 DEPROB
The DEPROB portion of the program contains the routines for
crnculating static and dynamic, elastic or inelastic response of air-
craft structures such as stringers, longerons, frames, ribs, and conical
or cylindrical shell sections which can be represented by a ring. The
method can also be applied in certain circumstances to panels with
sufficiently high aspect ratio.
DEPROB reads the input data described in section 6,3.2. Flow
diagrams of the major routines are presented in figures 68-71, and other
descriptive information is provided below.
-205-
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DEPROB
Executes the static and dynamic beam solutions. Calls C0MP1, C0MP2, COMSET, CSETUP(NOVA), CYCLE, DEFORM, FBSET, FINAL, PRINT1, READ1, STRN2, TSTEP. Called by NOVA.
C0MP1
Creates idealized model of cross section and stress-strain model. Calls SLAY, VCS. Called by DEPROB.
C0MP2
Sets up spanwise model of beam and locates origin at center of gravity. Writes major variables to file TAPE1. Calls STRN1. Called by DEPROB.
COMSET
Sets major program variables to values corresponding to static results. Reads from file TAPE1. Called by DEPROB.
CYCLE
Executes dynamic response, and performs numerical temporal integration. Calls EQUILP, FB, PRESS (NOVA), PRINT1, STRESS, STRN2. Called by DEPROB.
DAB
Calculates variables after a trial has been completed in iterative static solution process. Called by DEFORM.
DEFORM
Executes static analysis and writes major variables on file TAPE1. Calls DAB, DPUR, EQUILX, FBCTL, FSOL, PRINT1, RESD, RESET, RLAXB, SEC, STRESS, STRESX, STRN2, STSET. Called by DEPROB.
DPUR
Calculates variables after each perturbation in the static solution
process. Called by DEFORM.
■206-
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EQUILP
Calculates external forces and accelerations during dynamic response. Called by CYCLE.
EQUILX
Same as EQUILP, except is appropriate for the static solution. Called by DEFORM.
II Determines conditions near clamped edge boundaries through an iterative procedure. Calls RLAXF. Called by CYCLE, FBCTL.
FBCTL
Controls calls to FB during static solutior; process. Calls FB, FBSET. Called by DEFORM.
FBSET
Initializes variables for FB solution. Called by DEPROB, FBCTL.
FINAL
Compares accumulated n uximum response values with criteria at end of
dynamic response, and prints results. Calls PRINT1, SEC. Called by DEPROB.
FSOL
Assembles variables corresponding to final static solution. Called by DEFORM.
PRINT1
Prints most of the DEPROB output. Called by DEPROB, CYCLE, DEFORM, FINAL.
READ1
Reads input data for DEPROB and prints out description of data.
Called by DEPROB.
RESD
Computes residues In the iterative static solution process. Called by DEFORM.
-207-
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RESET
Resets variables during static solution process. Called by DEFORM.
RLAXB
Solves simultaneous nonlinear equations associated with static solution using relaxation procedure. Checks to see If solution Is converging. Calls SOLVE (NOVA). Called by DEFORM.
RLAXF
Solves simultaneous equations associated with clamped edge condition and checks to see if solution Is converging. Called by FB.
SLAY
Sets up mechanical sublayer stress strain model. Called by C0MP1.
STRESS
Determines strains, stresses and Internal moments and forces during dynamic response. Called by CYCLE, DEFORM.
STRESX
Same as STRESS, except Is appropriate for the static solution. Called by DEFORM.
STRN1
Calculates Initial lengths and angles corresponding to spanwise shape. Called by C0MP2.
STRN2
Calculates lengths and angles In the bar-mass representation for dynamic response. Called by DEPROB, CYCLE, DEFORM.
STSET
Sets up constants for static solution. Called by DEFORM.
TSTEP
Calculates an integration time step small enough to avoid numerical instabilities. Called by DEPROB.
-208-
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vcs
Sets up geometrical variables for beams of variable cross section. Called by C0MP1.
6.1.3 DEPROP
The DEPROP routines provide the static and dynamic, elastic
or Inelastic-response of aircraft skin panels, canopies, and radomes
that can be approximated by a cylindrical panel. The elastic option
applies to single and multllayered panels of Isotropie or orthotropic
material, and the elastic-plastic options apply to single layer (or
honeycomb) panels of Isotropie material.
Flow diagrams of the major routines are presented in figures
72-74. It should be noted that subroutine SIGMA is only needed for the
elastic-plastic option.
The following is a description of the routines belonging to
DEPROP:
DEPROP
Executes the static and dynamic panel solutions. Calls CSETUP(NOVA), DERV2, DSET1, DSET2, DSET3, HIM, LIST1, LIST2, RELAXP, SEC. Called by NOVA.
BOLT
Sets up W mode shapes for boundary conditions selected. Called by DSET1.
DERV2
Computes strains, displacements, and accelerations in the main Inte- gration loop. Calls LIST1, LIST2, PRESS, SIGMA. Called by DEPROP.
DTSTEP
Computes an integration time step small enough to avoid numerical Instabilities. Called by DSET2.
-209-
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T-»«»IIIH,P,^ i i|l^l! 1 ' 1 ' lll'll^|
DSET1
Reads DFPROP Input data and calculates constants. Called by DEPROP.
DSET2
Calculates constants used In DEPROP. Calls LEGEND, DTSTEP. Called by DEPROP.
DSET3
Calculates additional constants and writes out a description of input data. Calls BOLT. Called by DEPROP.
HIM
Numerical timewise integration routine. Called by DEPROP.
LEGEND
Sets up constants for Gaussian integration through the thickness for an elastic-plastic solution.
Called by DSET2.
LIST1
Output routine for the elastic-only option, accumulated and compared with allowables. Called by DEPROP, DERV2.
LIST2
Output routine for the elastic-plastic option, are accumulated and compared with allowables. Called by DEPROP, DERV2.
RELAXP
Maximum response values are
Maximum response values
Solves simultaneous nonlinear equations representing preblast conditions using a relaxation procedure. Calls SOLVE(NOVA). Called by DEPROP.
SIGMA
Computes stresses in the main integration loop for the elastic-plastic option. Is not needed for the elastic-only option. Called by DERV2.
-210-
iMMl''aMI*iMiai"1'' • - - mflügiiignigiii.
■n< "'I-TT'- mr"W~
NIN
NEWSL (I)
NCALL - 2
OEPROP
PINIT (0)
OEPROB
1 NOVSUM
C STOP )
NEWSL (2)
NCALL = 0 NOR -0
NOR:NOR + i >0
< 0
NTRIAL=NTRIAL+I
I
1.2
^ KTYPE >5
OEPROP OEPROB
Figure 66. Program NOVA Flow Diagram
■211-
•MOIMHi Ü -■"-
W v * w >■ mwm n i 1^1 i m^^^^m*
'- ■■i ■..>",■ ,,. , .
CALCULATE PREBLAST PRESSURE
C RETURN J
NO
WPRES
INTSLO
BLAST
PREW
SETW
POSTWI
POSTW7
CALCULATE POSTBLAST PRESSURE
Figure 67. Subroutine PINIT Flow Diagram
-21:
AMMMMMM
mptmprw-n »wiiii IUIIUWH in» ■.jui iii'»i»nnMwwTaii|TOlwpw^|j—''''^'■w'^"'—■ —^^mmw^ ^•^mmmmmmmmm
P< ^ ^ CSETUP KOAM
\ 2
[ " i
PRINT 1
E (""RETURN )
(INITIALIZE)
NCMP s NCALL
^ RETURN ^
C~(ETURN )
JTIM: JTIM+I
(STATIC) (DYNAMIC)
Figure 68. Subroutine DEPROB Flow Diagram
-213-
^ atMfctA*^J^^.-..-.-. -ri.,--.^.-.^.--.,..-^....,.. ..... .,■,.:.
^■iprngi—P.iHi i u M^ap;.!.i.,..»,—MM» "^•^^ri^pwpwH!«!« v^9li*ww*i*m
/
S
"'•affi<.*r,-.
^ ^N^ 2 RtTBI
> "
STRESS
EQUIUP
COMPUTE NEW
DISPLACEMENTS
PRINT I
(^ RETURN"*)
>0 PRINT I
~r" NERROR:2
( RETURN J
Figure 69. Subroutine CYCLE Flow Diagram
-214-
iMiMHtHaaM ■MM ^—m ii
tm^mm mwvwmsisiwmKmi
f RETURN 3
Figure 70, Subroutine DEFORM Flow Diagram
-215-
Ijggjlgj^-^^..... ......■-. w.-^ ..,..^:.... ,-....,■
11 m i ii iiMim —i 4
MPRINT
Q RETURN 3
PRINT PRINT INSTANTANEOUS PRINT
SUMMARY VALUES FOR MAXIMUM OF POSITIONS, VALUES
INPUT ACCELERATIONS, FOR DATA STRAINS,
ETC. RESPONSE
i i . i Q RETURN J ( RET URN } f RETURN )
Figure 71. Subroutine PRINT1 Flow Diagram
-216-
m^ii ilf ^liW*1' •
^■"f , ..'W"W t.. mqnwrnm ■i j lam i mpTi...'.^ ■:-w.:-^mmtmmmim
( RETURN }
LIST I
I | LIST 2 I
f RETURN ) Q RETURN ^
PRINT RESULTS
( RETURN } ^ RETURN ")
(INITIALIZE) (STATIC) (DYNAMIC)
Figure 72, Subroutine DEPROP Flow Diagram
-217-
■»M MM^MMHgUUM^
i i im
>o
COMPUTE OISPLACEMEIITS
DRESS
COMPUTE STRESSES
COMPUTE STRAINS
SIGMA
LIST I
COMPUTE ACCELERATIONS
7=rr f RETURN j
LIST 2
Figure 73. Subroutine DERV2 Flow Diagram
-218-
tmmmmmm^ a^yaijfliia^iM u iMlBiiM
m m ■"" ■ " i mm ^^^—^^^-m^^^^^^^^m^^^^^^^^^^^m^^^qn^^mimmm^m wmmm^mm
3,5,7...
ELASTIC UNLOADING
(STRESS-STRAIN)
SET UP CONSTANTS.
" INITIALIZE VARIABLES
ELASTIC EQUATIONS
(STRESS-STRAIN)
4,6,8,.
ELASTIC-PLASTIC EQUATIONS
(STRESS-STRAIN)
ELASTIC-PLASTIC RE-YIELDING
(STRESS-STRAIN)
>0
I f RETURN J
<r —
1 f*0
>
\ y ,>o
>
T<o
.> < « -
>
KY=KY + I | XY:KY-H >0 KY = KY + I
■ i
<
<£- >-n
KY:KY+ 1
1 ' > < - • ■ + i ■ . i
Figure 74. Subroutine SIGMA Flow Diagram
-219-
iMMU —■ — -'■-— ■ ■■' i i iriiiw^ar^" atii.iiir. i
jlllMtKMBimmimmmmimm.,..*. ^
6 Z DEFINITION OF MAJOR PROGRAM VARIABLES
The major program variables are defined In paragraphs 6.2.1, 6.2.2,
and 6.2.3 for the NOVA, DEPROB, and DEPROP routines, respectively. An
asterisk preceding a variable name Indicates that the variable Is input
as run data. The dimension of a variable Is given parenthetically after
the variable name. A numeric dimension Indicates the fixed amount of
storage required for the variable. There Is no need to hange the dlmen- [
sion of such a variable. However, other variables have variable dimen-
sions. As an example, the first doubly dimensioned vaixable listed In
paragraph 6.2.1 is FP(10,NMASS). The first dimension Indicates a fixed
amount of storage which is required regardless of changes that are made
in other dimensions. The second dimension is a variable, NMASS, which
represents the number of mass points in a structural element. This
dimension must be the largest number of mass points the user Intends
to employ in a solution involving a beam element. In the NOVA program,
this dimension is 40. If additional mass points are required, the
dimension of NMASS must be increased, thus increasing the dimensions
for all variables with the dimension, NMASS. Since the variable 11 repre-
sents the same quantity in the DEPROB routine as NMASS does in the NOVA
routine, the dimensions for all variables with the dimension N would also
have to be Increased. The current dimensions provided for the variables
in the NOVA, DEPROB and DEPROP routines are given in tables 17, 18, and
19.
Almost all of the variables which may require dimension changes
as indicated above are contained in the COMMON blocks for the three
routines. There arr a few exceptions and, in such cases, the subroutine
in which the variable is dimensioned is indic?.ted in the list of variables
or in table 20. If the dimensions are changed, certain additional
changes in the program may be required. These changes are also indicated
in table 20.
The axis system used in describing the program variables is described
in table 21 and illustrated in figure 75. It should be emphasized that
the aircraft axis system (AAS) must be centered at the center of gravity
of the aircraft.
-220-
üiMMMiMHMM m iumtm^mmammmimmim
RWff^l'^UW1^"'1 ||- " .iiiip^''»T^^^PWiffW
TABLE 17. DIMENSIONS OF VARIABLES FOR NOVA ROUTINE
VARIABLE DIMENSION
NEL 20
NFS 20
NLE 5
NLEHT 5 *
NLEVT 5
NLEW 5
NMASS 40
NORMAX 30
NORMAX*NEL 100
NTE1 5
NTEHT 5
NTEVT 5
NTEW 5
NTP1+1 1000
NLE must be largest of NLEHT, NLEVT, NLEW and NTE must be largest of NTEHT, NTEVT, NTEW
-221-
IMH ■—
iianii I ■ i.iiiM^i i mmmm
ttKmrmtrm
'■' "" '" ' I' «I ! mrnm W mmm^^^^m
/
^^^m
i TABLE 18. DIMENSION OF DEPROB VARIABLES
VARIABLE DIMENSION
NX1 10
N2 40
NL3 8
NLK 20
NSL 5
NSSC4 5
5 NSSCT 5
1 The program automatically assigns NX or fewer flanges to each layer, so NX should usually be four or six since the sum of all flanges must not exceed NLK.
2 NMASS in NOVA 3 For a uniform beam, the program may add one layer, so the actual
limit on input would ordinarily be seven. 4 The number of distinct slopes defined by NSSC and NSSCT, excluding
zero slope segments, must not exceed NSL.
-222-
— - ■ „«MHiMriMMHk
mm ww »II •"■■"I"III.IH*JJ ',i:.ii i Pffl ll1. "f"1- ■ wiRii|iiiifiii«j wm
TABLE 19. DIMENSIONS OF DEPROP VARIABLES
VARIABLE DIMENSION
LBAR 6
1 MB 7
MBAR 19
2 MBAR*NBAR*LBAR 1156
1 MG 7
NEAR 19
NL 8
1 Additional constraint: The total number of modes selected from the total possible (MB*MG) cannot exceed 25.
2 This constraint is only significant for an elastic-plastic run (NDERV«2). Three possible combinations using maximum dimensions are: (13x13x6), (15x15x5), (17x17x4).
-223-
■MMMMMMMa ■J-J-- -
/
TABLE 20. PROGRAM CHANGES REQUIRED BY DIMENSION CHANGES
When Changing the Dimensions Corre- sponding to:
Also Change the Fixed-Point Number in the Indi- cated Statement
Routine Subroutine Location
NORMAX NOVA NOVA 5-1
NORMAX*NEL NOVA NOVA 570+6
NTP1+1 NOVA WPRES 43-2
MG*MB*3 DEPROP HIM COMMON BLOCK
LBAR DEPROP LEGEND 300-11
MG*MB*3 DEPROP RELAXP 20+1
NL DEPROB C0MP1 SO"7
NSL*NLK*2*(N+l) DEPROB COMPl 50-6
NLK DEPROB COMPl 50-5
NSL DEPROB COMPl 50-4
N*2+2 DEPROB RLAXB 40+3
1 The location co de is read as follows: s refers to the nth line after statement number s.
-224-
r
TABLE 21. AXIS SYSTEMS USED IN DESCRIBING VARIABLES
AAS
HAAS
EFAS
LAS
Aircraft Axis System
Centered at aircraft center of gravity, X-Y plane parallel to plane of wing, X axis positive forward and forming an angle equal to the aircraft angle of attack with a horizontal plane, Y axis positive in ttfe direction of the right wing, Z axis posi- tive upward.
Horizontal Aircraft Axis System ,. , ,
Obtained from AAS by rotation about the Y axis such that the X axis becomes horizontal.
Earth-Fixed Axis System
Centered at burst point, X-Y plane horizontal, X axis parallel to aircraft velocity vector. The EFAS thus results by transla- tion of the HAAS.
Local Axis System
Used for DEPROB only. Axis system is two-dimensional (y,z) in plane of structural element. For a stringer, longeron or the directions of y and z may be chosen at the convenience of the analyst. For a frame or a radome, either of which is assumed to lie parallel to the Y-Z plane of the AAS, the y- axis, LAS, is parallel to the Y-axis, AAS (i.e., in the direc tion of the right wing); and the z-axis, LAS, is parallel to the Z-axis, AAS (i.e., positive upward).
rib
-225-
mili—MMi—iiii i i
II ■ ■ •mm ti^r 'wm
/
ZAk A
BURST ^VJ^ POINT ls<
v. xHA
Figure 75. Earth-Fixed Axis System (x , y , z ),
Aircraft Axis System (x , y , z ) and
Horizontal Aircraft Axis System
(XHA, yHA' ZHA)
-226-
— ■-■
•^^^WM mm^mm*r*m*
6.2.1 Major
*ALFAA
ALFAF
*ALT
*BAF
CORD
CRIT(5)
CO
*DELTIM
*DRDX
FP(10,NMASS)
GAMMA (NMASS+1)
HB
*HG
*HTINC
*TCOMP
*INOUT
*IUL
Program Variables for the NOVA Routine
Aircraft angle of attack, rad
Fuselage axis angle of attack, rad (set equal to ALFAA)
Aircraft altitude, ft
Bend angle of the fuselage, 3 (fig. 26), rad
Chord length, ft
Response criterion equal to unity at critical range. The most recent value in CRIT(l); previous points in CRIT(2) - CRIT(4). Dimensionless
Ambient speed of sound, ft/sec
Integration time interval, sec
Rate of change of radius of equivalent fuselage cross section with x, where x is the fuselage axis, positive forward, dimensionless
2 Pressure on fuselase point, lbs/in
Circumferential slope angle for fuselage frame or ring, rad
Height of burst above ground, ft
Height of ground above sea level, ft
Horizontal tail incidence, rad
Code designating aircraft component on which the structural element is located:
1, Wing 2, Fuselage 3, Horizontal tail 4, Vertical tail
Program output-option code: 0, do not print out input data 1, print out input data
Code designating side of lifting surface being considered:
1, Upper surface (for vertical tail, right side)
2, Lower surface (for vertical tail, left side)
-227-
ttmm* ■--- -- i ^-.—i-J—ai-Mitttfr^w.-,..., ,,J...,J,...
mii«:ri-;.k„ mmmmm
*KALT
*KB
Code designating whether iteration is at constant altitude:
0, no altitude restriction 1, iteration restricted to constant altitude
Code designating ground reflection model to be used: 1, REFRA tape based on REFLECT code. 2, Analytical model used in NOVA 1.
*KDAM Damage level code: 0, no permanent damage 1, catas';rophic damage 2, response run only
KDS
KERR
KF
*KGRD
KGRDO
KOK
Not used in NOVA.
Error Code: 0, no error 1, problem encountered in FPRES, WPRES,
DEPROB or DEPROP (Appropriate message is printed out)
Code associated with calling BLAST with option 2. 1, check first shock for lack of data. 2, check second shock for lack of data.
Control constant for ground reflection: 0, no ground reflection 1, include ground reflection
Original value of KGRD
Range iteration code: 0, try another range 1, finished iteration 2, error
*KTYPE Code designating structural type: 1, single-layer metal panel 2, single-layer plastic panel 3, honeycomb metal panel 4, honeycomb plastic panel 5, multilayer plastic panel 6, metal stringer or longeron 7, metal frame 8, metal ring 9, plastic ring
10, rib
-228-
■* ■ -' ■ -• -■-■
m/wrvt^^^^^^mirwmmemnm mmmm
NCALL
NCASE
NCHPT
*NDBUG
NEL
*NFP
*NFS
NLE
*NLEHT
*NLEVT
*NLEW
NMASS
*NOR
*NORMAX
NORT
NTE
*NTEHT
*NTEVT
*NTEW
Code for number of call to DEPR'»B or DEPROP: 0, ensuing calls, find dyr imic response. 1, second call, find preh.ast solution. 2, first call, read data
Number of cases run, considering each orientation
Not currently used.
Output debugging control constant: 0, no additional output 1, most additional output 2, all additional output
Number of the structural .element being considered
The number of the fuselage section at which pres- sures are desired
Number of fuselage sections used to describe fuse- lage geometry
Number of points used to define leading edge
Number of points used to define the leading edge of the horizontal tail
Number of points used to define the leading edge of the vertical tail
Number of points used to define the leading edge of the wing
Number of mass points in DEPROB structural element
Number of orientation to be considered
Number of last orientation to be considered
Total number of orientations considered.
Number ot points used to define trailing edge
Number of points used to define the trailing edge of the horizontal tail
Number of points used to define the trailing edge of the vertical tail
Number of points used to define the trailing edge of the wing
-229-
|MM ■ - ■■•■--^—iiini i - ^. ; .
wwwrpwpB^pwi ^^mm^mm^mmmm WW* ^•>ri\\t ii i im i iiiiiiiiäinn.^^ tmvam*
NTPl
NTRIAL
OUT(8)
PB(NMASS)
*PDAM
*PINT
PPP
PO
RCRIT(IOO)
*REST(NORMAX)
*RF(NFS)
RFR
RHOO
RTRIAL(5)
SL
SSPAN
ST
Number of times, minus one, at which pressures are calculated
Number of the present trial in iteration for the critical range
Storage for data returned from BLAST: 0UT(1) = material velocity, ft/sec OUT(2) =» pressure, lbs/in2« 0UT(3) - density, slugs/ft 0UT(4) ■ speed of sound, ft/sec 0UT(5) ■ ratio of specific heats, dimensionless OUT(6) * x component of material velocity, ft/sec 0UT(7) = y component of material velocity, ft/sec 0UT(8) = z component of material velocity, ft/sec
Net pressure acting on mass point for DEPROB, lbs/in2
Probability of exceeding specified damage level, expressed as a fraction, dimensionless
Input as internal pressure above ambient, changed by program to absolute internal pressure, lbs/in2
2 Net pressure acting on panel for DEPROP, lbs/in , net axial force acting on a rib for DEPROB, lbs
Number of time intervals between printouts (0.0 will give no printout), dimensionless
2 Ambient pressure, lbs/in
f .cal range for each element for each orienta- tion, ft
Estimated range at shock arrival L .ie, ft
Radius of equivalent fuselage, in
Radius of equivalent fuselage at section NFP, in
3 Ambient density, slugs/ft
Trial ranges (current trial range in RTRIAL(l), pre- vious values in RTRIAL(2) - RTRIAL(5)), ft
Slope of leading edge, dimensionless
Effective semispan, ft
Slope of trailing edge, dimensionless
-230-
MIHia *L*i*vi4LBlLL£4*iA*±...*.*---.< . ,, .■l.tfji
ri<>iTBin^.T»Bre»'3mg'¥il^^
TFP(10,NMASS)
*THETAR
TIME
*TITLE(20)
*TSTOP
TLX
TWP(NTP1+1)
*VEL
*WKT
WP(NTP1+1)
*XB(NFS)
*XBF
XCC(NFS)
XCW
XLE(NLE)
*XLEHT(NLEHT)
*XLEVT(NLEVT)
*XLEW(NLEW)
XLL
*XNOSE
Time corresponding to FP, sec
Angular location of the center of the structural element (panel, stringer, or longeron) on the circumference of the equivalent circular section for the fuselage and the point at which the pressures are applied (see Fig. 19), rad
Time, sec
Title card - description of aircraft, date, etc.
Time after-shock intercept at which computations are to stop, sec
Time corresponding to lasx> data on REFRA tape, sec
Time corresponding to WP, sec
Aircraft velocity, ft/sec
Weapon yield, KT
Pressure on lifting surface point (wing, horizontal tail, or vertical tail), lbs/in-
X coordinate (AAS) of fuselage section, in
X coordinate (AAS) of fuselage station at which bend angle, BAF, occurs (see fig. 26), in
X coordinate (HAAS) of ctrter of equivalent fuselage circular cross section, ft
Chordwise distance from leading edge to point at which pressure is desired, ft
X coordinate (AAS) of point used to define leading edge, in
X coordinate (AAS) of point used to define hori- zontal tail leading edge, in
X coordinate (AAS) of point used to define vertical tail leading edge, in
X coordinate (AAS) of point used to define wing leading edge, in
X coordinate (AAS) of leading edge at spanwise station YSW, ft
X coordinate (AAS) of nose of fuselage, in
-231-
mm ^^MM iMMiiiiriiiiiriK "•-"-■-■'■■ -■ ■■ ■--
i ■pppnm N i i i mmm mmmmn^m^f -muwrnvm ITTWI m
*XOSRO(NORMAX)
XOSRB(NORMAX)
*XP
XSA
XSCRIT(IOO)
*XTAIL
XTE(NTE)
*XTEHT(NTEHT)
*XTEVT(NTEVT)
*XTEW(NTEW)
XTL
YCC(NFS)
*YF
YLE(NLE)
*YLEHT(NLEHT)
*YLEW(NLEW)
*YOSRO(NORMAX)
X direction cosine (EFAS) of orientation, dimen- sionless (input only for orientation numbers greater than 21)
Original set of XOSRO's prior to range iteration.
X coordinate (AAS) of point at which pressure is desired, in
X component of vector from burst point to aircraft eg at shock arrival time (EFAS), ft
Critical value of XSA for each orientation and structural element, ft
X coordinate (AAS) of tail of fuselage, in
X coordinate (AAS) of point used to define trailing edge, in
X coordinate (AAS) of point used to define hori- zontal tail trailing edge, in
X coordinate (AAS) of point used to define vertical tail trailing edge, in
X coordinate (AAS) of point used to define wing trailing edge, in
X coordinate (AAS) of trailing edge at spanwise position YSW, ft
Y coordinate (HAAS) of center of equivalent fuselage circular cross section, ft
Y coordinate (AAS) of center of fuselage (YF will ordinarily be 0.0; it is included to accommodate external stores or nacelles), in
Y coordinate (Z coordinate for vertical tail) (AAS) of point used to define leading edge, in
Y coordinate (AAS) of point used to define hori- zontal tail leading edge, in
Y coordinate (AAS) of point used to define wing leading edge, in
Y direction cosine (EFAS) of orientation, dimen- sionless (input only for orientation numbers greater than 21)
-232-
•M^MMMM II !!■■ II
IJllMILPlllJllN.^^WlN""1.*!» W"«)"."."»»!! i VPHPi^pinp pi ^**^m*-*m^^m ^■■fip»"Pffirwpi^^wp»w
YOSRB(NORMAX)
*YP
YSA
YSCRIT(IOO)
YSW
YTE(NTE)
*YTEHT(NTEHT)
*YTEW(NTEW)
ZCC(NFS)
*ZF
*ZLEVT(NLEVT)
*ZOSRO(NORMAX)
ZOSRB(NORMAX)
*ZP
ZSA
ZSCRIT(IOO)
*ZTEVT(NTEVT)
ZZ1(9)
ZZ2(9)
Original set of YOSRO's prior to range iteration
Y coordinate (AAS) of point at which pressure is desired, in
Y component of vector from burst point to aircraft eg at shock arrival time (EFAS), ft
Critical value of YSA for each orientation and structural element, ft
Spanwise location of point at which pressure is desired, ft
Y coordinate (Z coordinate^ for vertical tail) (AAS) of point used to define trailing edge, in
Y coordinate (AAS) of point used to define hori- zontal tail trailing edge, in
Y coordinate (AAS) of point used to define wing trailing edge, in
Z coordinate (HAAS) of center of equivalent fuse- lage circular cross section, ft
Z coordinate (AAS) of fuselage axis, in
Z coordinate (AAS) of point used to define vertical tail leading edge, in
Z direction cosine (EFAS) of orientation, dimen- sionless (input only for orientation numbers greater than 21)
Original set of ZOSRO's prior to range iteration.
Z coordinate (AAS) of point at which pressure is desired, in
Z component of vector from burst point t;o aircraft eg at shock arrival time (EFAS), ft
Critical value of ZSA for each orientation and structural element
Z coordinate (AAS) of point used to define vertical tail trailing edge, in
Unused storage
Unused storage
-233-
- MMt mum** -MI' .....
TY"<:Frvir^---Tr"
6.2.2 Major Program Variables for DEPROB Routine
ACCNV(N+1)
ACCNW(N+1)
AFL(NL,W-2)
*AMP
ASRL(NSL,NL)
BAV(10,2)
BBV(10,2)
BIGM(N+1)
BIGMP(2)
BIGN(N+1)
*BIGR3
BMP1(2)
CCRIT(NL)
CEA(2)
CEZA(2)
CEZ2A(2)
CINST(3)
COSG(N)
C0ST(N+1)
C0STM(N+1)
Acceleration in the y direction (LAS), in/sec .
2 Acceleration in the z direction (LAS), in/sec .
2 Cross-sectional area of a flange, in .
Amplitude of initial lateral displacement (imperfec- tion) in rib element, in.
Area ratio of sublayer, c , in mechanical sublayer model, dimensionless.
Resultant internal axial force in clamped edge seg- ment , lbs.
Resultant Internal moment in clamped edge segment, in-lbs.
Resultant internal moment, in-lbs.
Resultant moment acting on end of clamped edge segment, in-lbs.
Resultant -'...lemal axial force, lbs.
Radius to center of cross section, in.
Previous value of BIGMP, in-lbs.
2 Critical compressive stress of layer, lbs/in .
Elastic axial force due to unit axial strain in clamped edge segment, lbs.
Elastic bending moment due to unit axial strain in clamped edge segment, in-lbs.
Elastic bending moment due to unit rotational strain . 9 in clamped edge segment, lb-in*-
, 2 Critical compressive instability stress, lbs/in
Average of COST for two adjacent links in undeformed state, dimensionless.
Cosine of the angle a bar makes with the y-z coordi- nate frame (LAS), dimensionless.
Value of COST after each trial in static solution.
-234-
ifcfri hia - ■--- ■-.^—^.-^-.-.-.. -■■.
CPTIM
CTET(11,2)
CTH2
CTP1(10,2)
CT1
CT2
C6(N+1)
DELTAS(N+l)
*DELTIM
DELTS(N+1)
DELTSM(N+1)
DELTS0(N+1)
DELTTi'N+l)
DELTTM(N+1)
DELTT0(N+1)
DELX(2N+2)
DEL3
DEN(2)
DIS(N)
DUMK
ECMXI(NL)
Accumulated computer (CP) time, sec.
Cosine of slope angle in clamped edge segment, dlmen- sicnless.
Cosine of angle last bar makes with perpendicular to plane of symmetry, set to 1.0 after rotation, dimen- slonless.
Average value of cosine of slope angle in clamped edge segment, dimenslonless.
Cosine of the angle the first end of the beam makes with the y-z coordinate frame (LAS), dimenslonless.
Cosine of the angle the aecoad end of the beam makes with the y-z coordinate frame (LAS), dimenslonless.
2 Inverse of the mass of a point, in/lb-sec .
Length of a bar joining two adjacent masses, in.
Integration time interval, sec.
Original average length of two adjacent bars, in.
Length of bar at the previous time, in.
Original length of bar, in.
Bend angle at mass point, rad.
Bend angle at mass point at the previous time, rad.
Original bend angle at mass point, rad.
Amount by which variables are perturbed in RLAXB, in. or rad.
Value of DELTTO(Nl), retained during static solution for KS-7, rad.
Elastic constant related to CEA, CEZA, and CEZ2A, (in-lb)2.
Absolute value of total displacement, in.
2 Equal to DELTIM squared, sec .
Maximum compressive strain in the innermost flange, in/in.
-235-
iüMlilll -~ - ■ — — :-■- ■ ■ ■ ■ - ■
««■»■flBWir«..."»!"!" i J i ppp^n ii in ■■
ECMXO(NL)
*EI(N)
*ELL
EPSILL(N+1)
EPSILU(N+1)
ER(3)
ERR
ERRR(2N+2)
ETMXI(NL)
ETMXO(NL)
FN(NSL,NLK,2N+2)
FNFL(NL)
FNX
FSKIN
FY(N+1)
FZ(N+1)
*H(NL,N+2)
HF(2)
HP1(2)
HT(N+2)
IL1(2)
Maximum compresslve strain In the outermost flange, in/In.
2 Stiffness of supporting longeron, El, Ib-in .
Length of supporting longeron. In.
Strain In the Inner layer. In/In.
Strain In the outer layer, In/In.
Error tolerance used in trial and error solution for clamped edge segment, lbs, lbs, ln-lbs.
Constant used In setting error allowed in the static solution, dimensionless.
Error In static solution. In or rad.
Maximum tensile strain in the Innermost flange, in/in.
Maximum tensile strain in the outermost flange, in/In.
2 Stress In each sublayer of each flange, lbs/in .
Number of flanges in a layer, dimensionless.
Equal to NX.
Inward acting spring constant normalized to skin thickness, taking into account membrane force of skin, lb/In2
Externally applied force in the y direction (LAS), lbs.
Externally applied force In the z direction (LAS), lbs.
Thickness of layer, in.
Horizontal force (parallel to end of beam) acting on end of clamped edge segment, lbs.
Previous value of HF, lbs.
Total thickness of cross section, in.
Lower limit of indices when looping on mass points; equal to 1 except for clamped or free edge, when it is 2.
-236-
cüMMMMMMMIMM
m^m^ff HV
IL2
IP(2N+2)
*IPROP(NL)
IU
IU1(2)
IU2
IY(N+1)
IY1
IY2
JTIM
KEL
*KEYB1
*KEYB2
*KEYRG
KFREE
Equal to IL1(2).
Working array in RLAXB.
Key as to whether the material properties are the same in tension and compression:
0, same 1, different
Upper limit on Indices during static solution.
Upper limit of indices when looping on mass points. Equal to M-except: N-l for clamped or free edge when computing BIGM; N+l for S.S. edge or free ring when computing BIGN. The first value corresponds to BIGN; the second to BIGM.
Equal to IU1(2)
Code as to whether link has yielded, equal to either IY1 or IY2.
Hollerith constant equal to a blank, signifying no yield.
Hollerith constant equal to an asterisk, signifying yield.
Number of integration steps which have elapsed.
Code as to whether run is elastic (1) or elastic- plastic (0).
Boundary condition code at first end: 1, free ring 2, clamped 3, simply supported 4, free
Boundary condition code at second end: 1, free ring 2, clamped 3, simply supported 4, free 5, symmetric
Key as to whether the structure is circular: 1, circular 2, not circular
Code as to whether the structure is completely free of any restraints:
0, not free 1, free
-237-
MMMi -. _.. . ._
>I|I.I|IIPII|I.HI ll|),IMI """""^■«•PtflPWII»
„nffi« ' • •■ 'smismr
*KIS
KMAX
KS
*KSUP
*KUNF
LMAX
LSCMXI(NL)
LSCMXO(NL)
LSTMXI(NL)
LSTMXO(NL)
MAXF
MAXLK
MAXSF
MMAX
Code as to definition of inner surface: 1, inner surface is on left when proceeding
from first end to second - corresponds to counter-clockwise direction for full ring, in local Y-Z coordinate frame (LAS). Repre- sents orientation consistent with that used in NOVA-1.
2, inner surface is on right.
Code designating where maximum strain occurred: 1, outer layer 2, inner layer
Code designating seven different boundary condition combinations solvable statically.
Support code for outstanding (inner) leg: 0, no outstanding leg 1, supported on one end 2, supported on both ends.
Code specifying whether beam is uniform in spanwise direction:
0, not uniform 1, is uniform
Link in which maximum response oi curred.
Number of the hex in which ECMXI occurred.
Number of the bar in which ECMXO occurred.
Number of the bar in which ETMXI occurred.
Number of the bar in which ETMXO occurred.
Equal to MAXSF*MAXLK*2*N1.
Maximum number of flanges the program is dimensioned for.
Maximum number of distinct stress-strain slopes the program is dimensioned for.
Code as to whether maximum response occurred in tension or compression:
1 , tension 2, compression.
■238-
-— -!'J ■ ■-'"1 m^LM
MPRINT
MTAPE
MYIELD
Ml
M2
*N
*NAY(N)
NCMP
NCOUND
Output code for subroutine PRINT1: 1, no output 2, summary of constants is to be printed 3, dynamic response is to be printed 4, summary of results from the dynamic response
is to be printed.
Logical file number used for output, equal to Tape 6,
Number of the integration step corresponding to the first yielding.
Printout Begins after Ml time intervals.
The dynamic response will be printed every M2th time step. 9- .••
Number of masses in model.
Mass point number corresponding to variable El at which elastic supporting element is attached.
Program flow code (equal to NCALL in NOVA): 0, dynamic response 1, static solution 2, read data and initialize code.
Number of the variable in RLAXF which has been per- turbed.
NCOUNT Number of the variable in RLAXB which has been per- turbed.
NEQ
NERROR
*NL
Number of variables (and residues) in RLAXB.
Code which terminates the program: 0, program continues 1, error in program 2, program stopped normally.
Number of layers in the cross section of the struc- tural element.
NIK
NM1
NPRINT
Total number of flanges used in model.
Equal to N-l.
Debugging code controlling printout during static solution (equal to NDBUG of NOVA)■
0, no printout 1, printout results of each trial 2, printout results of each perturbation and
each trial.
-239-
mmmm . - ,-.-,: .
^F!'■-.;*.. vnM««
*NSEL
NSKIN
NSL(NL)
*NSSC(NL)
*NSSCT(NL)
NTAPE
NTI(2)
NTR
NTRMAX
*NX
NYIELD
Nl
N2
PI
PRES(2N+2)
PX(2N+2)
Q(N+1)
RATIO(NL)
RES(2N+2)
RFY
Number of (elastic) supporting elements.
Code as to whether membrane force due to skin is appropriate (frames only)
0, not appropriate 1, is appropriate
Number of sublayers (stress-strain model).
Number of stress-strain segments used for compression.
Number of stress-strain segments used for tension.
Logical file number used for input, equal to five.
Number of trials quasi-static edge solution required at edge 1 or 2.
Number of trials which have elapsed in finding static equilibrium.
Maximum number of trials permitted in the static solution.
Maximum number of flanges in any layer.
Code which is responsible for printout of the dynamic response at the time when the structure first yields:
0, not first yielding 1, first yielding
Equal to N+l.
Equal to N+2.
Constant equal to IT.
Working array in RLAXB.
Printout interval (0.0 will give no printout), dimeu- sionless
Working array in RLAXB.
Internal shear force, lbs.
Quantity used in determining the number of flanges in a layer, dimensionless.
Residues used in the relaxation procedure for the static solution, in, rad, or in/sec^.
Rigid body force in y-direction (LAS), lb.
-240-
feWMM fc^U^ai -....„ ■ läniM
i i in ii iniiKinnm « ■ ■ 1 ' mm "' ^mm^umw^nm
RFZ
*RHO(NL)
RRES(2N+1)
SAV(10,2)
SAVP1(10,2)
SBV(10,2)
SBVP1(10,2)
SCM(NSL,NL)
SCMXI(NL)
SCMXO(NL)
SIGX(2N+2)
SING(N)
SINT(N+1)
SINTM(N+1)
SM(N+2)
SMASH (N+l)
SMASSF
SMASST
SSS(NL,NSSC+1)
SSST(NL,NSSCT+1)
STET(11,2)
STH2
Rigid body force In z-direction (LAS), lb.
2 4 Density of layer, lb-sec /in .
2 Base set of residues in RLAXB, in, rad, or in/sec''
Axial strain in clamped edge segment, in/in.
Previous value of SAV, in/in.
Rotational (bending) strain in clamped edge segement, rad/in.
Previous value of SBV, rad/in.
Fictitious compressive bceakftpint stress used in mechanical sublayer model, Ib/in^.
2 Stress corresponding to ECMXI for KDAM=0, lbs/in .
2 Stress corresponding to ECMXO for KDAM-0, lbs/in .
Working array in RLAXB.
Average SINT for two adjacent links in undeformed state, dimensionless.
Sine of the angle a bar makes with the y,z coordi- nate frame (LAS), dimensionless.
Value of SINT after each trial in static solution, dimensionless.
2 Mass of an individual point, lb-sec /in.
Working array in DEFORM.
2 Total mass, lb-sec /in.
Total mass, lbs
2 Stress-strain slope in compression, lbs/in"
2 Stress-strain slope in tension, lbs/in
Sine of slope angle in clamped edge segment, dimen- sionless
Sine of angle last bar makes with perpendii ular co plane of symmetry, set equal to 0.0 after otation, dimensionless.
-241-
--■■ m — --~>—«*—«
STM(NSL,NL)
STMXI(NL)
STMXO(NL)
STP1(10,2)
STBA(NSL,NLK,20)
*STRNA(NL, NSSC)
*STRNAT(NL,NSSCT)
*STRSO(NL,NSSC)
*STRSOT(NL,NSSCT)
ST1
ST2
SUMH(NL)
TCRIT(NL)
TEND1
TEND 2
TH
THETA(N+1)
*THETA1
Fictitious tensile breakpoint stress used in mechan- ical sublayer model, Ib/in^.
2 Stress corresponding to ETMXI for KDAM-0, Lbs/in .
2 Stress corresponding to ETMXO for KDAM-0, lbs/in .
Average value of sine of slope angle in clamped edge segment, dimensionless.
Stress in sublayer of flange in clamped end segment, lbs/in2.
Strain at break, point on the stress-strain curve for compression, in/in.
Strain at break point on the stress-strain curve for tension, in/in.
Stress at break point on the stress-strain curve for compression lbs/in2.
Stre s at break point on the stress-strain curve for te»•ion, lbs/in2.
Sine of the angle the first end of the beam makes with the y-z coordinate frame (LAS), dimensionlesa.
Sine of the angle the second end of the beam makes with the y-z coordinate frame (LAS), dimensionless
Quantity used in determining the center of gravity of the cross section, in.
2 Critical tensile stress for KDAM-0, lbs/in ; cri- tical tensile strain for KDAM=1, in/in.
Angle the first end of the beam makes with the y-z coordinate frame (LAS), rad.
Angle the second end of the beam makes with the y-z coordinate frame (LAS), rad.
Angle Last bar makes with perpendicular to plane of
symmetry, rad.
Angle locating a mass, measured from the negative z axis (LAS), rad.
Angle locating the first end of oeam, measured from the negative z axis (LAS), rad.
•242-
■MMM . .. . ... -..—^. ■■^^.-. ■■ ■..„ _. ---,.1.,-^..,
r^mmmmmm^^m^mim^m^ M^Fwva
*THETA2
TIME
TSCMXI(NL)
TSCMXO(NL)
TL'TMXKNL)
TSTMXO(NL)
*TST0P
*V(N+1)
VAR(2N+2)
VF(2)
VM(N+1)
V0(N+1)
VP1(2)
*V1
*V2
V2M
V20
*W(N+1)
WM(N+1)
W0(N+1)
*WR(NL,N+2)
WRAT(N+2)
Angle locating the second end of beam, measured from the negative z axis (LAS), rad.
Time from "he beginning of the dynamic response, sec.
Time corresponding to ECMXI, sec.
Time corresponding to ECMXO, sec.
Time corresponding to ETMX1, sec.
Time corve^pondlng to ETMXO, sec.
Time at which computations are to stop, sec.
Y coordinate (LAS) of a nassT'in.
Variables used in the relaxation procedure for the static solution. In. or rad.
Vertical force (perpendicular to end of beam) acting on end of clamped edge segment, lbs.
Y-coordlnate (LAS) of a mass at cti? previous time, in.
Y-coordlnate (LAS) of point corresponding to unde- formed state. In.
Previous value of VF, lbs.
Y-coordlnate (LAS) of the first end of beam, in.
Y-coordlnate (LAS) of the second end of beam, in.
Y-coordlnate (LAS) of second end of beam after each trial in static solution, in.
Y-coordlnate (LAS) of second end of beam as ini- tially specified.
7.-coordlnate (LAS) of a mass, in.
Z-coordinate (LAS) of a mass at the previous time, in.
Z-coordinate (LAS) of point corresponding to unde- formed state, in.
Width of layer, in.
Ratio of width of layer .o WT, dimensionless.
-243-
feBHHMMMMI MMM
npppn w^tmmmmm
*WT
*W1
*W2
W2M
W20
X(ll)
Y(ll)
XEH(NL)
XRES(2N+2.^:fZ)
XX(2N+2)
YCGO
YCGl(N+2)
ZETA(NLK,N+2)
ZETAL(N+2)
ZETAU(N+2)
Width of skin over which pressure acts for longerons, frames; effective loading depth for ribs, in.
Z-coordinate (LAS) of the first end of beam, in.
Z-coordinate (LAS) of the second end of beam, in.
Z-coordinate (LAS) of second end of beam after each trial in static solution, in.
Z-coordinate (LAS) of second end of beam as ini- tially specified, in.
Position of point on clamped edge segment measured perpendicular to wall, in.
Position of point on clamped edge segment measured parallel to wall, in.
Quantity used in defining the flanges in a layer, lbs/in.
Working array in RLAXB.
Working array in RLAXB.
Distance from the outer surface to the center of gravity of the cross section, in.
Algebraic difference between distance to center of cross section and distance to center of gravity of cross section, in.
Distance from the center of gravity of the cross section to a flange, positive inward for KIS=1. Positive outward for KIS=2, in.
Value of ZETA to outermost flange in cross section, in.
Value of ZETA to innermost flange in cross section, in.
-244-
i, n ...■!.. ■■■■ jMgnmiimjgggi
wjmiim^mn« w liiiyiiii^pipiiii ■■,!! ipw,i'n' w ■■"" —,—, ^»■(i.iii «■nilMimiljl.MI
6.2.3 Major Program Variables for DEPROP Routine
BETR(NBAR)
BTL(NL)
BXL(NL)
CCRIT(NL)
CCl(MG)
CC2(MB)
CC5(MG)
CC6(MB)
CINST(3)
CK(6)
CM11,CM12, CM22,CM33
CN10
CN11
CN6
CN7
CN8
CN9
COSB(MB*NBAR)
COSG(MG*MBAR)
Radius of the cylindrical panel, a, in. Is set equal to 1.0 for flat panel.
Integration positions in the beta-direction, rad.
k k k Constants used in elastic option, EQ/(l-v v.), psi.
k k k Constants used in elastic option, E /(1-v vn), psi.
Critical compresaive stress of layer, psi.
Constant, 2m-l, dimeasionj^fi^.
Constant, 2n-l, dimensionless.
Constant, 2m, dimensionless.
Constant, 2n, dimensionless.
Critical compressive instability stress, psi.
Constants, 1/k , l/kA, for the equations of motion, dimensionless.
Stiffness constants C used in elas'ic, multilayer
integration through the thickness, lb/in.
2 2 2 2 2 2 Constant, 21 R/TT a for elastic option, 21 /TT a for elastic-plastic option, dimensionless.
2, 2 2 2 Constant, i /6TT a R for elastic optic elastic-plastic option, dimensionless,
2 2 7 2 2 2 2 Constant, i /6TT a'R for elastic option, 21 /TT a for
Constant for elastic-plastic option, E/(l-v ), psi.
Shear moduxus for elastic-plastic option, E/2(H-v), psi.
2 2 2 Constant, i /TT a , dimensionless.
2 2 2 2 Constant, 2. /4TT a R , .jensionless.
Cosine functions of the bets, angles, cos (2nß.), dimensionless.
Cosine functions of the gamma angles, cos (2mY.), dimensionless.
•245-
jrttMM^i^f..^.^,.* ^.-^.y.-. .. -...,.. .-.^-■.
C0S2B(MB*NBAR)
C0S2G(MG*MBAR)
*DC
*DF.LTIM
DELX(3*MG*MB)
DM11, DM12, DM22, DM33
DPRT
DPRT1
DWB(MBAR,NBAR)
DWG(MBAR*NBAR)
DWO(MBAR*NBAR)
*EC
EL
*EM(NL)
*EP
EPBO(LMAX)
EPO
*EPSIF
Cosine functions of the beta angles, cos ((2n-l) 3.), dimensionless.
Cosine functions of the gamma angles, cos ((2in-l)Y.), dimensionless.
Core cell size, in.
Integration time interval, sec.
Working array in RELAX?, dimensionless.
Stiffness constants D.. used in elastic, multilayer
integration through the thickness, Ib-in.
Running time, in multiples of DPRT1, used to flag next printout, sec.
Time interval between printouts, sec.
Values for imperfection-related partial deriva- o
tive W , dimensionless P
Values for imperfection-related partial deriva- o
tives W , dimensionless. Y
o
Values for inperfection-related displacement W, dimensionless.
Core modulus of elasticity, parallel to core depth, psi.
Modulus of elasticity for elastic-plastic option, E, psi.
Modulus of elasticity for each layer for elastic- „k plastic option, E , psi.
StiTain hardening slope for elastic-plastic option, Et, psi.
Equivalent stress, squared, when response is still -2 2 4 elastic for the elastic-plastic option, a ,1b /in .
Equivalent yield strain corresponding to SIGO for elastic-plastic option, e , in/in.
Ultimate (fracture) strain for elastic-plastic option, £f, in/in.
-246-
nv.-ii .luMMmii
■'■ -"- ' jr.'Fi'.Fiiiii1'*!. > •rfr1 "w**:'**" '■
ERR(3*MG*MB)
*ET(NL)
ETT
*EX(NL)
Allowable error In displacement coefficients in the static preblast solution.
Modulus of elasticity in the theta-direction for
elastic option, £„ , psi.
Temporary value of strain, eoa , in/in.
Modulus of elasticity in x-direction for elastic
option, E , psi.
EXT m
Temporary value of strain, e fl, in/in.
EXX
*FG(MB,MG)
FM11, FM12 FM22, FM33
FP1, FP2, FP3, FP4, FP5, FP6
GAM(MBAR)
*GC
GX(LBAR)
*GXT(NL)
H
HBAR
HGO(LBAR)
*HM(NL)
IFIRST
Temporary value of strain,"e , in/in.
Modal displacement coefficients for the Initial imperfections, in.
Stiffness constants F used in elastic, multilayer
integration through the thickness, lb.
Spatial integration functions corresponding to the edge conditions selected, dimensionless.
Integration positions in tne y-direction, rad.
Shear modulus of core, psi.
Zeroes of the Legendre polynomial for the elastic- plastic Gaussian integration through the thickness, C., dimensionless.
Shear modulus, G A, psi. xö
Thickness of cross section for elastic-plastic option, in.
Distance from the inner panel surface to the coordi- nate surface, H, in.
Weighting factors for the elastic-plastic Gaussian integration through the thickness, H., dimension- less.
Distance from the inner panel surface to the outer surface of layer, h, in.
Code designating first pass through subroutine SIGMA, dimensionless.
-247-
m HMWMl -- turn imt*m\m
WT""^""""""-^"""?^
i
INZ(2)
IP(3*MG*MB)
JFIRST
KC
KDS
KSUMA(MBAR*NBAR)
KY(LMAX)
KZ
*LBAR
LMAX
*MB
*MJAR
*MG
MGM(MG)
MGMB
MGMB2
*MOUT(MG*MB)
MUSE(MB,MG)
Code designating the appropriate layer number corresponding to the two panel surfaces, dimen- sionless.
Working array in RELAXP, dimensionless.
Code which indicates if the panel has yielded for the elastic-plastic option.
Counter for determining whether strains should be compared with critical values. Values are only checked every tenth time step to save computer time.
Static-dynamic option code. Always 3 in NOVA,
Number of z points which have not yielded at each spatial station. Used only in elastic-plastic option.
Code in elastic-plastic response, indicating num- ber of times an integration point has yielded, unloaded, etc.
Code deciding whether the output routine should print, check maximum values, or both.
Number of integration points through the thick- ness. Is assumed to be one for elastic option.
Maximum number of integrated points being used. Equal to MBAR*NBAR*LBAR.
Number of beta modes to be incorporated into the solution.
Number of beta integration points to be used. For a symmetric boundary condition, only approxi- mately half as many points are required.
Number of gamma modes to be incorporated into the solution.
Gamma mode numbers.
Constant, equal to the total number of modal combinations used, MG*MB-NNOUT.
Constant, 2*MGMB.
Gamma modes not to be included, in combination with Che corresponding NOUT mode.
Code designating which modal combinations are to be used.
-248-
mmm mtM ^^^ttmmtmm
pwml ■PMiimippaaB ■«■■■i
*NBAR
NBN(MB)
*NBND
NBT
*NDERV
NELP
NGNB
NGT
*NL
NLZ(16)
*NNOUT
NOUT(MG*MB)
*NPLT
NREG
NSYMB
NSYMG
NTECO
NU
Number of gamma integration points to be used. For a symmetric boundary condition, only approxi- mately half as many points are required as other- wise.
Beta mode numbers.
Boundary condition code.
Same as NBAR.
Response code: 1-elastic (multilayer, orthotropic), 2-elastic-plrastic (single layer, Isotropie).
Respons) code for the clastic-plastic option: 1-keep solution elastic, 2yaliow solution to go elastic-plastic.
The spatial integration point number corresponding to the center of the panel.
Same as MBAR.
Number of layers.
Layer number corresponding to each layer's upper and lower surfaces.
Number of modal combinations (<MG*MB) to be elim- inated from the solution.
Beta modes not to be included, in combination with the corresponding MOUT mode.
Panel type code: 0-flat, 1 —curved.
Elastic plastic region number corresponding to the maximum response during an iteration run.
Symmetry code in the beta-uirection (depends on boundary conditions): 9-symmetric, 1-not symmetric.
Same as NSYMB, except in the gamma-direction.
Code indicating whether maximum response occurred in tension or compression on an iteration run: 1-tension, 2-compression.
Code indicating whether loading is spatially unifonn or not: 0-not unifonn, 1-uniform. In NOVA the loading is always assumed to be uniform.
•249-
mmtm
«■■■innmi mmm i' i">i 1 IPIUI » IP i rm IWIPMIR i
NUSE
NY2
NZP
P(MBAR*NBAR)
PI
PIMA(MBAR)
PINA(NBAR)
PP(NBAR,MBAR)
PR£S(3*MG*MB)
PX(3*MG*MB)
RHO
*RHOM(NL)
EIRES(3*MG*MB)
*SAC(NL)
*SAT(NL)
*SIGO
SIG02
SIGX(3*MG*MB)
SINB(MB*NBAIl)
SING(MG*MBAR)
SIN2B(MB*NBAR)
SIN2G(MG*MBAR)
Use code for the spatial Integration stations: 0-not used, 1-used for printout only, 2-used for Integration only, 3-both.
Constant, equal to 3*MGMB.
Number of z points to be checked for maximum response values on an iteration run.
Pressure at each spatial point, psl.
Constant, equal to IT.
Constants associated with the equation of motion and Simpson's Rule. Gamma-direction, in^/lb-sec .
Same as PIMA, only in the beta-direction.
Output frequency - integration steps per printout.
Pressure coefficients for nonuniform load, psi. Not used in NOVA.
Working array in RELAXP, dimensionless.
Working array in RELAXP, dimensionless.
2 4 Density of panel, lb-sec /in .
2 4 Density of layer, lb-sec /in .
Working array in RELAXP, dimensionless.
Compressive yield stresses for metal material, compressive ultimate stress for plastic material, psi.
Tensile yield stress.' for metal meterial, tensile ultimate stress for plastic material, psi.
Yield stress for elastic-plastic optijn, psi.
2 4 Constant, equal to SIGO squared, lb /in .
Working array in RELAXP, dimensionless.
Sines of beta functions, sin(2nß.).
Sines of gamma functions, sin(2nY.).
Sines of beta functions, sin((n-l)ö,).
Sines of gamma functions, sin((m-l)Y.).
-250-
i^MaaMM ^■fciil i
m***», ivi
SKTT(LMAX)
SKXT(LMAX)
Stress component, aQa, psi. 00
Stress component, a , psi. xo
SKXX(LMAX)
SMAX
STT(LMAX)
SXT(LMAX)
SXX(LMAX)
*THETAO
*THNU(NL)
TMAX
*TNU
*TSTOP
U(MBAR*NBAR)
UB(MBAR*NBAR)
UG(MBAR*NBAR)
UU(MB,MG)
U1(MB,MG)
V(MBAR*NBAR)
7B(MBAR*NBAR)
VG(MBAR*NBAR)
W(MB,MG)
VX0(3*MG*MB)
Sf -ess component, a , psi.
Critical response compared with allowable, dimen- sionless.
Stress component, o , psi. -- 00
m Stress component, a , psi.
Stress component, a , psi.
Total angle subtended by cylindrical panel, 6^, deg, or width of flat panel, b, in.
Poisson's ratio in the theta-direction, v , dimen- sionless.
Time at which SMAX occurs, sec.
Poisson's ratio for elastic-plastic option.
Integration stop time, sec.
Value of U, dimensionless.
Value of U , dimensionless. o
Value of U , dimensionless. Y
Displacement coefficient, U , dimensionless. mn
Displacement coefficients, U , representing the mn
preblast static conditions, dimensionless.
Value of V, dimensionless.
Value of V , dimensionless.
Value of V , dimensionless. Y
Displacement coefficients, V , dimensionless. mn
Initial velocity coefficients, always zero in NOVA, 1/sec.
151-
■MMHMMBMMa mtaammmmm
'-'"» •' ' ' '■ ^ '■ ■ '
V1(MB,MG)
W(MBAR*NBAR)
WB(MBAR*NBAR)
WBB(MBAR*NBAR)
WG(MBAR*NBAR)
WGB(MBAR*NBAR)
WGG(MBAR*NBAR)
WW(MB,MG)
W1(MB,MG)
XB(NBAR)
XG(MBAR)
XJ
XJ2
XJ3
XJ4
XJ5
XKTT
Displacement coefficients, V , representing the mn
preblast static condition, dlmensionless.
Value of W, dlmensionless.
Value of W , dlmensionless. p
Value of W , dlmensionless. CP
Value of W , dlmensionless.
Value of W „, dlmensionless.
Value of W , dlmensionless. YY
Displacement coefficients, W , dlmensionless. mn
Displacement coefficients, W , representing the
preblast static conditions, dlmensionless.
Integration positions in the beta-direction, inches for flat panel, degrees for curved panel.
Integration positions in the gamma-direction, inches.
Constant, J, equal to 180/9^ (dlmensionless) for
curved panel and n/b (inches) for flat panel.
2 Constant, J
Constant, J/L.
Constant, 2J.
Constant, 2J/L.
Temporary value of strain, e , in/in.
XKXT Temporary value of strain, £ ,, in/in.
XKXX
XL
*XLP
Temporary value of strain, e , in/in xx
Constant, ä/T, for flat panel (inches), i/ira for curved panel (dlmensionless).
Length of panel, I, inches.
2 Constant, 2L R.
■252-
M^MMaMHaMMiat| - —•-■■-■■■ -in
mP^BVW
XLP2
XL1
XL2
XL3
XL4
XL5
XL7
XRES(3*MG*MB)
XX(3*MB*MG)
*XXNU(NL)
XX1(3*MG*MB)
XU(MBAR*NBAR)
Constant, 2LR
Constant, 1/L.
2 Constant, L .
Constant, 2/L.
2 Constant, 2L .
2 Constant, 2L R.
Constant, I/L .
Working array in RELAX?, dimensionless.
Array composed of UU, W, and WW, dimensionless,
Poisson's ratio in the x-direction, v , dimen- sionless.
Working array in RELAX?, dimensionless.
Strain component, e , in/in.
X2A(MBAR*NBAR)
X3A(MBAR*NBAR)
X4A(MBAR*NBAR)
X5A(MBAR*NBAR)
Strain component, eQQ, in/in.
Strain component, e ., in/in.
Strain component, e , in/in.
Strain component, e,Q, in/in. do
X6A(MBAR*NBAR)
YY(3*MG*MB)
ZA(2)
ZB(2)
ZC(2*NL)
Strain component, e , in/in.
Array composed of acceleration coefficients, U , ? mn
V , W , 1/sec . mn mn
ZB aormalized with a, ZB/a, inches for flat plate, dimensionless for a curved panel.
z positions for determining critical strains for the elastic-plastic option, in.
z positions for determining critical strains for the elastic option, in.
•253-
r . ...... ,-. .^... ■■■^
"■-■ ■ ■■ • ---vT ■ ■- — "' im>j»;iini..Hwi i i I.II.I...H..II..|..W „ ,ii, I».»II»II I!..! ...ill IIIHHU. um i. mpini »,» u
ZF(6) ZH normalized with a, ZH/a, inches for a flat plate, dimensionless for a curved panel.
2 ZG(6) Gaussian station squared, £ , dimensionless.
ZHCö) z coordinates corresponding to the Gaussian integra- tion points through the thickness for the elastic- plastic option, in.
The following is a list of dimensioned variables used only in
subroutine SIGMA in conjunction with the elastic-plastic model in
DEPROP:
ETT1 (LMAX) EXT1 (LMAX) EXX1 (LMAX) SIGTT1 (LMAX) SIGXT1 (LMAX) SIGXX1 (LMAX) SIKTT1 (LMAX) SIKXT1 (LMAX) SIKXX1 (LMAX) TTNU (LMAX) XKTT1 (LMAX) XKXT1 (LMAX) XKXX1 (LMAX)
AKTT (LMAX) AKXT (LMAX) AKXX (LMAX) ALH (LMAX) ALXT (LMAX) ALXX (LMAX) BEI (LMAX) BE2 (LMAX) BE3 (LMAX) BE4 (LMAX) BE5 (LMAX) BE6 (LMAX) EPB (LMAX)
-25A-
*****ä—m*tt(iiiH ■ — -■■
1 ^«^>^P»pw
6.3 PROGRAM INPUT DATA SETS
The assessment by NOVA of the vulnerability of aircraft to over-
pressure effects depends, in part, on the selection of appropriate burst
orientations and structural elements. Those structural elements, in
turn, need to be converted into models which can be analyzed by DEPROB
and DEPROP. A few samples of this technique are presented in NOVA-1,
Volume 2 (ref. 50). An attempt has also been made throughout this
document, and particularly this section, to assist the analyst in the
preparation of appropriate da« for NOVA, DEPROB, and DEPROP.
The input data sets for NOVA, DEPROB and DEIROP are specified in
groups. Each group begins on a separate data^aTS; however, additional
cards may be required. The format corresponding to each data group is
given in parentheses and is always in fields of 12. Each parameter in
the data set is described and its units specified; also, the associated
variable name is given. Blank cards are used by the program to indicate
the beginning of the next data group or to initiate a logical branch.
Columns 73 through 80 may be useful to label the cards in the data sets
to facilitate assembly of the card deck and recognition of the variables
ir the data sets.
6.3.1 NOVA Input Data Set
The NOVA routine is the master routine which directs the over-
all program flow and provides the preblasc and blast-induced pressures.
The NOVA input data set includes data necessary for the performance of
these functions. The data for DEPROB and DEPROP are included in Group 31
of the NOVA input data set as appiopriate. The following comments apply
to the preparation of the NOVA date.:
Group 9 specifies wMch ground reflection model is to be used,
if any. If ground reflection is not deemed significant for the problem
of interest (KGRD-0), or if the analytical curve fit model is used
(KB-2), the REFRA data tape ia not required. Otherwise, it is required;
and unless the run is merely a response run (KDAM"2). the range itera-
tion must be restricted to constant altitude by specifying KALT«!, '«hen
an iteration is constrained to one altitude it means that the direction
■253-
■uMM^mte >^**mmmamt
Mlffl I III. »■«i« ■ ".•mmmjf.mnvsjmw . iii„,m. , n m tiiiinui.u, 1 | W l»ip ■■ ... ■w VB^HP
cosines associated with that orientation will not remain constant, as
shown in figure 76. Note that there also then exists a minimum range,
RMTN, except for orientations where burst and aircraft are at the sane
altitude. Twenty-two nominal burst orientations are presented in table
22 and figure 76. For the example shown i.i figure 76, the direction
cosines are related to $ by:
XOSRO ■ -cos*
YOSRO - 0
ZOSRO ■ -cos (|- - <j»)
Groups 12-24 describe the aircraft geometry. Note that the appro-
priate coordinate system is the aircraft axis system (AAS) which is cen-
tered at the aircraft center of gravity (table 21 and figure 75).
Groups 12-20 define the geometries of the lifting surfaces of the air-
craft for the aerodynamic routines. If a lifting surface has a straight
leading edge, then the coordinates of only two points are needed for
complete definition of that leading edge. If the leading edge has n
straight-line segments, then n+1 points are needed. The first point for
(a) Slant Range Iteration.
(KALT-0)
'MIN
» X
(b) Constant Altitude Iteration. (KALT-1)
Figure 76. Examples of the Two Range Iteration Techniques used in NOVA
-256-
MM mtmm
Table 22
DIRECTION COSINES DEFINING ORIENTATIONS
Orientation Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
tDirection Cosines
XOSRO YOSRO
•0.8660254
■0.5
0.0
0.5
0.8660254
1.0
0.8660254
0.5
0.0
•0.5
•0.8660254
•1.0
■0.8b60254
■0.5
0.0
0.5
0.8660254
0.0
0.0
0.0
0.0
-^~ .-^
o.c
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
-0.5
-0.8660254
-1.0
-0.8660254
-0.5
-0.5
-0.8660254
-0. 8660254
-0.5
ZOSRO
0.5
0.8660254
1.0
0.3660254
0.5
0.0
•0.5
■0.8660254
■1.0
•0.8660254
•0.5
0.0
0.0
0.0
0.0
0.0
0.0
0.8660254
0.5
•0.5
■0. 3660254
The direction cosines (XOSRO, YOSRO, ZOSRO) locate the aircraft vitn respect to tne nuclear ourst in the earth-fixed axis system (EFAS).
-257-
■^M
"I ■! ■ w^tvfHwmmmmmm
6 six
-N6- 17/Y^
16 •, s
1 ►x-o-
six 13
8s' / -o- 7-Q:-
6-0-
'Tx s ' / 10
■♦x -Q-'Z
-6.- 'rs! -a,-- 4/|N
S' / -Or:
15
21 s I / -/Ps"
9^-
z i
^ v «_- _rf L-
19-N6- 18 -O-
Figure 77. Nuclear Burst Orientations, Horizontal Aircrafi: Axis System
-258-
■MMto il^M,^^.^^.—,J..,, ^,J,„ ,..._„—,_ ..L..^.^....-^.. ....„,, ^
KHnB^BHilUaiiaUHHBRBHHaMaMKUBWUE-3|F
both the leading and trailing edges of the wing and horizontal tail
should be on the aircraft centerline, and the last point should be at
the tip. For the vertical tail leading edge, the first point should be
at the intersection of the leading edge with the fuselage surface and
the last point should be at the tip. The first point for the trailing
edge of the vertical tail should have a z coordinate less than or equal
to the z coordinate of the first point for the leading edge, and the
last point should be at the tip.
Groups 21 through 24 define the fuselage geometry. As a
minimum, fuselage sections should be iocated.,ias?£ollows:
1. At the center of each panel, stringer or longeron
being analyzed
2. At each frame or bulkhead being analyzed
3. At any radome section which is being analyzed
Regardless of the number of fuselage structural elements being analyzed,
a sufficient number of fuselage stations must be selected to define the
fuselage outline reasonably well. The radius for each equivalent fuse-
lage section is determined by considering a circular cross section o;:
equal area to the actual cross section at that station. These, data are
not particularly critical; therefore, sections may be located near,
rather than exactly at, the above positions, and the i^dii may be found
approximately.
Group 28 locate" the center of the structural element (panel,
stringer, or longeron) on the circumference of the equivalent, circular
section for the fuselage. This is the point at which the pressures are
applied (see fig. 19).
The NOVA input data are defined by the following groups:
-259-
— ■■i.. . „Ma^jiiM—il—lii^M,«^-
mmf-mmm-mmm —^P^BPIW——Pi
Group 1: (40A2) Title
Description of aircraft, date, etc, left blank. (TITLE)
Free field. Can be
Group 2: (2112) INOUT, NDBUG
Program output option code (INOUT): 0, do not print out description of input data 1, print out description of input data.
Debugging option code (NDBUG): 0, no additional debugging information printed out
normal option. 1, most additional information printed out 2, all additional information printed out - can
be voluminous.
Group 3: (4F12.1) ALT, VEL, WKT, HG
Aircraft altitude (ALT), ft Aircraft velocity (VEL), ft/sec Weapon yield (WKT) , KT Height of ground above sea level (HG), ft
Group 4: (4F12.1) ALFAA, HTINC, BAF, XBF
Aircraft angle of attack (ALFAA), rad Horizontal tail incidence angle (HTINC), rad Bend angle (S) of the fuselage (fig. 26) (BAF), rad X coordinate (Aircraft Axis System) of fuselage station at which bend angle (3) occurs (fig. 26) (XBF), in
Groups 5-7 provide data for the desired nuclear burst orientations, and are repeated until data for all desired orientations have been provided. The last value of NORMAX in Group 5 must be the largest value. Refer to table 22 for the direction cosines which define the orientations (fig.77 provided in the program.
Group 5: (2112) NOR, NORMAX
First orientation to be considered (NOR) Last orientation to be considered (NORMAX)
Note: Program considers all intermediate orientations. For KALT=1, (Group 10), orientation numbers 3 and 9 are not permitted for iteration runs (KDAM=0,1).
-260-
MMfltaM
If NORMAX < 22. skip to Group 7.
Group 6 provides the capability for reading in direction cosines (EFAS) for orientations other than the 21 provided in the program. Repeat Group 6 for N » Nl, NORMAX, where Nl is the larger of NOR and 22.
Group 6: (3F12.1) (XOSRO(N), YOSRO(N), ZOSRO(N)), N«N1, NORMAX
X direction cosine (XOSRO(N)) Y direction cosine (YOSRO(N)) Z direction cosine (ZOSRO(N))
Group 7: (6F12.1) (REST(N), N-NOR, NORMAX)
Range at which response is desired or estimated range at which desired response occurs (RESTCN)), ft
Group 8;
Blank card.
Group 9: (2112) KB, KGRD
Control constant for ground reflection model (KB) 1, REFRA tape, based on REFLECT code. 2, Analytical model
Control constant for ground reflection (KGRD) 0, no ground reflection in model 1, ground reflection included in model
Note: For KGRD«G, it makes no difference whether KB»1 or 2.
Group 10: (2112) KDAM, KALT
Range iteration/damage code (KDAM) 0, iterate to determine range at which permanent
damage first occurs 1, iterate to determine range at which catastrophic
damage occurs 2, determine response only at specified range
Constant altitude code (KALT) 0, no restriction on iteration. 1, iteration is restricted to constant altitude.
Note: KALT is not necessary for KDAM=2. Otherwise KALT must be 1 if KB is 1 and KGRD is also 1.
If KDAM = 2, skip to Group 12.
-:6i-
———>'--—- ■ - -—-
1 I I« 1^ I > 11 «I
Group 11: (1F12.1) PDAM
Probability of exceeding specified damage level, m, expressed as a fraction (0<m<l) (PDAM), dlmenslonless (Use 0.5 to neutralize probability of damage calculation)
Group 12: (2112) NLEW, NTEW
Number of points used to define the leading edge of the wing (NLEW) (Set - 0 if no model on wing)
Number of points used to define the trailing edge of the wing (NTEW) (Set « 0 if no model on wing)
If NLEW = 0, skip to Group 15.
Group 13: (2FI2.1) (XLEW(N), YLEW(N)), N-l, NLEW
X coordinate (AAS) of point used to define wing leading edge (XLEW(N)), In
Y coordinate (AAS) of point used to define wing leading edge (YLEW(N)), in
Group 14: (2F12.1) (XTEW(N), YTEW(N)) N»l, NTEW
X coordinate (AAS) of point used to define wing trailing edge (XTEW(N)), in
Y coordinate (AAS) of point used to define wing trailing edge (YTEW(N)), in
Group 15: (2112) NLEHT, NTEHT
Number of points used to define the leading edge of the horizontal tail (NLEHT) (Set ■ 0 if model is not on horizontal tail)
Number of points used to define the trailing edge of Che horizontal tail (NTEHT) CSet - 0 if model is not on horizontal tail)
If NLEHT = 0, skip to Group 18.
:62-
MMMMMaBsai
Group 16: (2F12.1) (XLEHT(N), YLEHT(N)), N-l, NLEHT
X coordinate (AAS) of point used to define horizontal tail leading edge (XLEHT(N)), in
Y coordinate (AAS) of point used to define horizontal tail leading edge (YLEHT(N)), in
Group 17: (2F12.1) (XTEHT(N), YTEHT(N)), N-l, NTEHT
X coordinate (AAS) of point used to define horizontal tail trailing e^ge (XTEHT(N)), in
Y coordinate (AAS) of point used to define horizontal tail trailing edge (YTEHT(N)), in
Group 18: (2112) NLEVT, NTEVT
Number of points used to define the leading edge of the vertical tail (NLEVT) (Set - 0 if model is not on verti- cal tail
Number of points used to define the trailing edge of the vertical tail (NTEVT) (Set - 0 if model is not on vertical tail)
If NLEVT - 0. skip to Group 21.
Group 19: (2F12.1) (XLEVT(N), ZLEVT(N)), N-l, NLEVT
X coordinate (AAS) of point used to define vertical tail leading edge (XLEVT(N)), in
Z coordinate (AAS) of point used to define vertical tail leading edge (ZLEVT(N)), in
Group 20: (2F12.1) (XTEVT(N) , ZTEVT(N)), N-I, NTEVT
X coordinate (AAS) of point used to define vertical tail trailing edge (XTEVT(N)), in
Z coordinate ("AAS) o point used to define vertical tail trailing edge (ZTEVT(N)), in
Group 21: (1112) (NFS)
Number of fuselage sections used to describe fuselage geometrv (NFS)(Set = 0 if model is not on fuselage)
If NFS ; 0, skip to ^roup 25.
-263-
MHMtt^ i
Group 22: (2F12.1) XNOSE, XTAIL
X coordinate (AAS) of nose of fuselage (XNOSE), in
X coordinate (AAS) of tail of fuselage (XTAIL), in
Group 23: (2F12.1) YF, ZF
Y coordinate (AAS) of center of fuselage (will ordi- narily be 0.0; it is included to accommodate external stores or nacelles) (YF), in
Z coordinate (AAS) of fuselage axis (ZF), in
Group 24: (2F12.1) (XB(N), RF(N)), N=l, NFS
X coordinate (AAS) of fuselage section (XB(N)), in
Radius of equivalent fuselage (RF(N)), in
Groups 25-31 provide data for a structural element and are repeated until all structural element data have been provided.
Group 25: (3X12) ICOMP, KTYPE, IUL
Code designating aircraft component on which the struc- tural element is located (ICOMP)
1, Wing 2, Fuselage 3, Horizontal tail 4, Vertical tail
Code designating structural type (KTYPE) 1, Single-layer metal panel 2, Single-layer plastic panel 3, Honeycomb metal panel 4, Honeycomb plastic panel 5, Multilayer plastic panel 6, Metal stringer or longeron 7, Metal frame 8, Free metal ring 9, Free plastic ring, e.g., a radome
10, Metal rib
Code designating side of lifting surface being considered (IUL)
1, Upper surface, or right side of vertical tail 2, Lower surface, or left side of vertical tail
Note: Omit IUL when structural element is located on fuselage (ICOMP = 2) or for rib elements (KTYPE=I0).
I: IC0MP=2, skip to Grouo 27. ■ ■ -_n'-»-
— —■■—
—^p-1 W' i ~.^.»- i an——a B^a
Group 26: (3F12.1) XP, YP, ZP
X coordinate (AAS) of point at which pressure is desired (middle of panel, stringer, longeron; rib station) (XP), in
Y coordinate (AAS) of point at which pressure is desired (middle of panel, stringer, longeron; rib station), (YP), in
Z coordinate (AAS) of point at which pressure is desired (middle of panel, stringer, longeron; rib station) (Z?), in
For KTYPE« :10, skip to Group 30.
For KTYPE-10. skip to Group 31.
Group 27: (1112) NFP
y The number of the fuselage section at which pres- sures are desired (that is, the section at which the structural element is located) (NFP)
If the structural element is a metal frame or a ring (KTYPE > 6), skip to Group 29.
Group 28: (1F12.1) THETAR
Angular location of the center of the structural element (panel, stringer, or longeron) on the circumference of the equivalent, circular section for the fuselage (see fig. 19). This is the point at which the pressures are applied (-iT<8<7r) (THETAR), rad
Group 29: (1F12.1) DRDX
Rate of change of radius of equivalent body cross section with respect Co x (Aircraft Axis System) at ehe fuselage station where the pressures are desired (DRDX) , dimensionless
Group 30: (1F12.1) PINT
Internal pressurizacion. Difference between the internal pressure and external ambient pressure (p.-p ) (PINT), lbs/in-.
-:65-
-M^—~J-^- .^»i^-^. . , |—M—M|-
t^^^^^^^&^^r ^RMHNwv*"
1 ■ " '■ ■^iWTPWW^»* I
Group 31:
Group 32:
Group 31 consists of the DEPROB (KTYPE > 5) and the DEPROP (KTYPE < 6) data sets for the structural elements being analyzed.
A blank card is placed after the last data set in Group 31 to end program execution.
6.3.2 DEPROB Input Data Set
The DEPROB routine calculates the response of a beam to pre-
blast and blast-induced pressures. The beam can be of arbitrary cross
section and shape, both of which can vary spanwise along the beam. Any
combination of clamped, simply supported or free boundary conditions is
possible. Also treated are complete (free) rings, either circular or
not, and end loaded beams (ribs) characterized by a sliding clamp con-
dition. Panels exhibiting large aspect ratio can also ofcen be analyzed
by only considering a strip in the short direction; however, it is up to
the analyst to verify the validity of such an approximation.
In general, the analyst must model the structural element by
selecting a bar-mass representation, as indicated in figure 28, and
dividing the cross section into regular layers as indicated in figures
29 and 78.
The paragraphs which follow amplify the specific input instruc-
tions put forth later in this section. The theoretical discussion in
section 4.1 should also be consulted, and certain input parameters
should be compared with the maximum allowable dimensions as delineated
in table 18.
Group 1 describes the beam in general terms. If Che struc-
tural element is circular in shape (KEYRG-1), the program will auto-
matically evenly space the masses. The end constraints are specified by
KZYB1 and KEYB2, Any combination is theoretically possible; but because
preblast loading necessitates a complicated static solution, only the
following seven combinations are permissible for elements experiencing
preload :
-266-
mtmmmmtmmammmm^mt\ linn ■ M—
«»•^PBPpWiBPP
ay- +
^^@
Tq-© .»■ J»
SECTION A-A
-♦ X
Z u
INNER SURFACE
,'0 c e s :
EDGE l
OUTER SURFACE
a) (Ljindicates layer nvimber 1, etc. b) 1 indicates mass number 1, e^c. c) inner and outer surfaces are Jefined :or KIS=L,
Figure 78. Bar-Mass and Rectangular Layer Model of Beam Element
26;
t^mmmm
1st End
1) Clamped
2) Clamped
3) Clamped
A) Clamped
5) Simply Support2d (3)
6) Simply Supported (3)
7) Free Ring (1)
(KEYB1)
(2)
(2)
(2)
(2)
2nd End (KEYB2)
Clamped (2)
Free (4)
Symmetric (5)
Simply Supported (3)
Simply Supported (3)
Symmetric (5)
Free Ring (1)
The symmetric option, where only half of the structure is treated, is
appropriate for structures exhibiting both geometrical and loading
(preblast and postblast) symmetry. Special caution should be exercised
in modeling frames since the burst orientation will not, in general, be
in a position to induce a symmetrical load. Radomes (free rings) do not
attempt to take advantage of symmetry for this reason, although it
should be noted that the bar-mass representation selected by the analyst
must be symmecrically spaced about the z-axis. (fig. 34(e)).
It should be noted that the boundary code 2 (KEYB1,KEYB2=2)
actually represents a clamped-sliding boundary for rib elements (KTYPE=10)
In all other cases it represents an ideal clamp.
The parameter KIS removes all ambiguity associated with which
surface of the beam element is loaded. Such ambiguities arise when the
spanwise shape exhibits curve reversal. It is assumed that the outer
surface always receives the blast loading and hence, KIS=1 represents
normal loading (see fig. 78). Care should always be taken, however, to
assign the correct loading code, KIS, to curved elements and those with
nonsymmetrical nonuniform cross section. The exception to this involves
rings and ribs (KTYPE=8,9 and 10) where the parameter KIS is not needed.
The boundary fixity, or support code, of the outstanding leg
of an element must also be specified in the Group 1 input data. In
figure 78, the outstanding leg is segment 5, and the appropriate support
code is 2, because segment 5 is supported on both ends by the two parts
of segment 4. If the right hand oortion of segment 4 were absent, Che
support code would be 1. In practice, if there is a bulb present, the
•268-
l IjtlMlüMl
Support code should be 2. In addition, a small bulb can be accounted
for in the layer modeling by combining its area with that of an adjoin-
ing layer.
Group 2 assigns the number of masses, layers and flanges ro
the model of the structural element. The model consists of discrete
masses interconnected by weightless bars, with cross sections which may
consist of several layers. The DEPROB routine represents each layer by
several flanges. The modeling accuracy increases when the number of
masses, layers, or flanges is increased. For a straight beam element,
about 14 masses (7 for a symmetrical case) are usually required to
adequately represent the beam; a curved beanrfeqrÄres up to 20 for a 180
degree arc; a complete ring requires approximately 40 (the maximum
number the program is dimensioned for). Oie maximum number of flanges
allowed in any layer (NX) must be an even number and six is recommended,
except for a cross section wr.th more than three layers when 4 is sug-
gested. The total number in the cross section must not exceed 20. As
explained in section 4.1.4, fewer flanges are assigned tr some layers.
Groups 5-7 locate the element in the local coordinate system
(LAS) described in table 21. The location and orientation of the y-z
coordinate frame is unimportant— only relative positions are relevant,
except in the case of frames and radomes, as noted. In general, even
spacing of masses is recommended except at the ends where the spacings
indicated in figure 34 a "e suggested.
Groups 8-11 provide for external elastic supporting elements,
fixed to the frame (or whatever element is being analyzed by DEPROB) at
one or more mass point locations.
The parameter, WT, specified in Group 14, represents an effec-
tive width over which the pressure acts. This adjustment takes into
account the skin area subjected to loading but not included in the cross
section model (see discussion of Group 16). For a stringer or longeron,
WT should be the stringer or longeron spacing; for a frame, the frame
spacing is appropriate; for a radome ring, the width should be the same
as the width of the structural ring used, presumably 1 inch. For rib
-269-
■aMMMMM^^i
elements, WT should represent the aveiage spacing, d, between webs, as
indicated in figure 79. It is assumed in this case that a strip of unit
width situated between lightening holes and running the depth of the web
is being analyzed, where the external pressure load is equally dis-
tributed on either end of the column.
BEAM SEGMENT ANALYZED
—4 \*—w
Figure 79. Rib Element Loading Definition
Groups 15 and 16 describe,the cross section geometry at each
mass point unless the beam is uniform, in which case only one descrip-
tion is required. The analyst divides the arbitrary cross section into
rectangular segments or layers as indicated in figure 78. The effective
skin (layer 1 in fig. 78), acting with the stringer or longeron, must
also be determined. There are many approaches available in the liter-
ature for determining the amount of effective skin. A simple approach
is suggested below; however, the user is free to exercise his own
preference in the determination of effective skin. The suggested
approach is as follows:
-270-
ii m
■ »
1.70 t { (148)
where
w - effective skin width, in.
t - skin thickness, in.
E - Young's Modulus for tne skin material, lbs/in'' 2 f - yield stress for the skin material, lbs/in
The appropriate width for layer 4 in figure 78 is the combined width of
the two segments labeled "4".
Each layer or segment of the original cross section can have a
different stress-strain curve, which may be different In tension than in
compression. This capability allows the analyst to consider nonh« 3-
geneous cross sections. The analyst must define the stress-strain curve
for the material in each layer by a series of straight lines (figs. 30
and 31). The points at which these straight lines join are referred to
as break points, and the appropriate data are provided by Groups 17-20.
As noted, the elastic slope must be the same in tension and compression,
and the total number of distinct stress-strain slopes (excluding zero
slope) must not exceed five. The first break point is taken to repre-
sent yielding for metals (ultimate for plastic) and the last break point
represents rupture conditions.
Group 21 provides the initial imperfection necessary to
initiate rib buckling, unless already incorporated into the spanwise
shape in Group 6. Without an imperfection, the end loaded element
cannot displace laterally. The parameter AMP represents the ampli'.ude 5
of an initial 1 - cosine deflection shape imposed on an otherwise
straight beam element:
-271-
MMM^MMH - - i
mumKyzi'jaiidW' «•*iÄÄtwiwW;..<Xi'. ■■■rftiiit y ■m.t_\:....
Aw cos (27Ty)
(149)
Finally, Group 22 provides the integration time increnent, the
response time and the printout interval. If a zero time increment is
specified, the program computes the largest it which in most cases will
give a stable solution. One exception may be initially curved elements
experiencing "snap-through" or rib buckling where a smaller M and a
larger response time may be required.
Although the stop time can vary a great deal, the total number
of integration steps to capture peak response will roughly be between
400-1000. Buckling situations (curved beams, ribs, etc.) may require
considerably more. A printout frequency of once every 20 steps is
usually adequate for monitoring the response time history; a frequency
of 100 is probably more appropriate for the buckling situations.
The DEPROB input data are defined by the following groups.
Group 1: (6112) KEYRG, KEYB1, KEYB2, KUNF, KIS, KSUP
Structural shape code (KEYRG) 1, structure is circular in shape,' but not necessarily
an entire ring. Polar coordinates are used to define ends of beam, if necessary. Program evenly spaces mass points.
2, rectilinear coordinates ars used to specify the center of the cross section for each mass point.
Boundary condition code, first end of beam (KEYB1)
I, complete ring, no supports at either end (KTYPE=8 or 9). KEYB2 must also be 1 for this case.
1, clamped (clamped-sliiing for KTYPE=10) J, simply supported 4, free (as in a cantilevered or tree-free situation)
ms&mif^'?$mmmHmammmamBiSK&tsm*
Boundary condition code, second end of beam (KEYB2)
1, complete ring, no sunports at either end (KTYPF-S or 9).
2, clamped (clamped-sliding for KTYPE=10) 3, simplv supported 4, free (is in a cantilevered or free-free situation) 5, symmetry is assumed, second end of beam is specified
as point of symme'.ry
Cross section uniformity coo5» (KUNF)
0, cross section is not uniform spanwise along the structure
1, cross section is uniform spanwise along t^-c structure
Outer surface definition code (KISTf* ^^
1, outer surface of cross section is defined as being on the right when proceeding spanwise from the first end to the second end. See fig. 78.
2, outer surface is defined just opposite to that above, i.e., oute • surface is on left.
Note: Net positive pressure loading is always applied to "outer" surface. KIS is not needed for KTYPE-8, 9 or 10
Support code for outstanding (inne: ) leg (KSUP) 0, no outstanding leg 1, outstanding leg supported at one end 2, outstanding leg supported at both ends
Nute: KSUP is not needed if KDAM>0 or if KTYPE>7)
Group 2: (3112) N, NL, NX
Number of masses in Che model. (For symmetric cases, onlv half of the structure is modeled.) Must be an even number for complete rings (KTYPE=8 or 9). (N)
Number of layers in the cross section of the structural element. (NL)
Maximum number of flanges allowed in a layer. Must be an even number. (NX)
If K£YRG"2 and KTYPE^o,: or 10. skip to Grour 5.
If KgYRG-2 and KTYPE-8 or 9, skip to Group 6.
-273-
MMMM
Group 3: (112.1) BIGR3
Radius to the center of the ring cross section . in. (BIGR3)
If KTYPE=8 or 9, a.-ip to Group 8.
Group 4: (2F12.1) THETA1, THETA2
Angular position of first end of beam, rad. (THETA1) Angular position of second end of beam (or point of synmetry) rad. (TKETA2)
Note: The angular position is specified with respect to the local axis system (LAS) as follows:
0.0 -z direction TT/2 +y direction
IT +z direction
Skip to Group 8.
Note: The y and z coordinates (LAS) in Groups 5, 6, and 7 are to be specified et the center of the cross section.
Group 5: (2F12.1) VI, Wl
Y coordinate (LAS) of first end of beam, in. (VI)
Z coordinate (LAS) of first end of beam, in. (Wl)
Group 6: (2F12.1) (V(I), W(I), 1=1,N)
Y coordinate (LAS) of mass point, in. (V(I))
Z coordinate (LAS) of mass point, in. (W(I))
If KTYPE=6 or 9, skip Group 7.
Group 7: (2F12.1) V2, W2
Y coordinate (LAS) of second end of beam (or point of symme- try), in. (V2)
Z coordinate (LAS) of second end of beam (or point of symme- try), in. (W2)
Group 8: (112) NSEL
Number of supporting elastic elements. (0<_N'SEL^_M) (NSEL)
If NSEL=0, skip to Group 12.
^tt^tttm^mi^mmimmm '--■- • ■ -~A
m**' ■'■vnmmmmmimm^^m^mm&ii&B***''
Group 9- (6112) (NAY(I),1-1,NSEL)
Mass point number corresponding to elastic supporting element, May be listed in any order.
Group 10: (6F12.1) (EI(I), I»1,NSEL)
Elastic stiffness. El, equal to the product of the modulus of elasticity and the moment of inertia, corresponding to each supporting element, and ordered as in Group 9, Ib-in .
Group 11: (F12.1) ELL
Length of the sup .cc '., element (SK i^. CEach is assumed to be the same leng'.."1)
Group 12-. (6112) (iPT.;Jl'(L), L-l, NL)
Material code for layer (IPRGP(L)) 0, stress-strai'. curve is the same in tension as in
compression 1, different stress-strain curves will be specified for
comprespj-on and tension
Group 13: (6F12.1) (RHO(L), L-1,NL)
2 4 Mass density of material, lb-sec /in .
Group 1^: (F12.1) WT
Width over which pressure acts, in.
Groups 15-20 specify data for each layer and are to be repeated for L'l.NL " " ' " ^ """
Note: The thickness and width of each layer can vary along the beam for KUNF=0. In this case data must be provided for each end of the beam (unless it is a ring) as well as for each mass point, and the data are entered in the following order: first end, N mass points, second end (or point of symmetry). The parameter N2 is defined as follows:
N2 = 1, uniform beam (KUNF=1) N, nonuniform beam, complete ring
(KUNF=0 and KTYPE=8 or 9) ^2, uonuniform beam, not a ring
(KUNF=0 and KTYPE^S or ^9)
-275-
tmmm
Group 15: (6F12.1) (H(L,I),1-1,N2)
Thickness of the layer at each station, in,
Group 16: (6F12.1) (WR(L,I),1-1 ,N2)
Width of the layer at each station, in.
Group 17: (112) NSSC(L)
Number of straight-line segments specified in the representa- tion of the stress-strain curve for compression CNSSC(L))
Group 18: (2Fi2.1) (STRM(L, II) , STRSO(L, II)) 11=1, NSSC(L)
Strain at break, point on the stress-strain curve for compres- sion, in/in (STRNA(L,II)}
Absolute value of stress at break point on the stress-strain curve for compression, lbs/in^ (S7RS0(L,II))
Note: For KDAM-1, the last break, points on the stress-strain curves must correspond to ultimate strain. The program assumes con- stant stress (zero slope) curve beyond the last break point.
If the tensile and compressive stress-strair. curves are the same (IPROP(L) = 0), skip Groups 19 and 20.
Group 19: (112) (NSSCT(L))
Number of straight-line segment ; specified in the representa- tion of the stress-strain curve for tension (NSSCT(L))
Group 20: (2F12.1) (STRNAT(L,II) , STRS0T(L,II)), II-l, NSSCT(L)
Strain at break point on the stress-strain curve for tension, in/in (STRNAT (L.II))
Stress at break point on the stress-strain curve for tension, lbs/in2 (STRS0T(L,II)
Note: The slope of the first segment must be the same in both tension and compression)
If KTYPE<10, skip Group 21,
-276-
i. „^utmiamm
Group 21: (F12.1) AMP
Amplitude of the initial imperfection introduced into the rib element, in. If imperfection is already specified through V and W (Group 6), set equal to 0.0. (AMP)
Group 22: (3F12.1) DELTIM, TSTOP, PRINT
Integration time increment, sec. If DELTIM^O.O, the program determines the time increment required for stability. (DELTIM)
Integration stop time, sec. (TSTOP)
Print frequency (integration steps per printout). If PRINT-O.O, printout of intermediate data wilL^-oppressed. (PRINT)
6.3.3 DEPRÜP Input Data Set
The DEPRÜP program calculates ehe elastic or elastic-plastic
response of cylindrical o fiat panels to preblast and blast-induced
pressures aniformly distributed ove" the surface. The panel can be
single or multilayered, have orthotropic or Isotropie material prop-
erties, and can have any combination of clamped or simply supported edge
conditions. The following paragraphs are intended to amplify the
specific input data instructions for using the DEPROP code. All input
parameters, where appropriate, should be compared with the maximum
dimensions provided for in the program, as delineated in table 19.
Group 1 contains the number of modes to be used in the solu-
tion, and the number of integration points to be used. The accuracy of
the solution is based on the degree of convergence of stress and strain
quantities. These quantities converge less rapidly than the radial
displacement. Also, cases involving a clamped edge condition will
converge less rapidly than simply supported cases. Since both computer
time and accuracy increase with more modes and points, a trade-off
usually becomes necessary.
In general, a minimum of nine modes should be used for panel
solutions and it is recommended that the maximum of 25 modes be used for
clamped panels where edge stresses and strains are impcrtant. The
program uses modes 1 through MB in the 2 or ^-direction ai.d 1 through MG
in the < or x-direction. Fuc maximum value that the modJ numbers MG and
-277-
i—MMMMMM aättui 11
MB can assume in the program is seven. Spatially, the desired number of
integration points (MBAR and NEAR) for a full panel should be approxi-
mately four times the maximum mode number used in that direction, plus
one. However, when MB or MG is large, this condition may not be satis-
fied for nonsymmetrical panels, since MBAR and NBAR are dimensioned at
19 in the program (see cable 19.) For symmetric solutions (whenever the
same edge condition is specified for opposite sides), MBAR (or NBAR)
need only be approximately half the value for a full panel since only
one half (or one quarter) of the panel is actually analyzed in the
solution. For a nonsymmetric condition, MBAR (or NBAR) must be an odd
number. For an elastic-plastic solution, a minimum of four integration
points through the thickness is recommended, and a maximum of six is
provided in the program.
In Group 2, the user is given the option of a purely elastic
solution, or an elastic-plastic solution. The elastic-plastic option
will tend to be slower and require more computer memory. The second
option (elastic-plastic) must be used for metal panel solutions which
iterate to a catastrophic damage level.
Groups 3 and 4 provide a mechanism for selecting a maximum of
25 modal combinations from a 7 by 7 combination array (MG=MB"7). Thus,
the more significant modal combinations for an optimal solution with
respect to accuracy and computer time can be selected and the other
combinations eliminated. A general rule of thumb is to eliminate the
higher frequency modes which are usually associated with modal combina-
tions having the larger MG+MB values. An example of this would be the
selection of MG=MB*7, but eliminating the following 24 combinations:
3,4 4,3 5,3 ^,3 7,3
3,5 4,4 5,4 >,4 ',4
3,6 4,5 5,5 ",5 7,5
3,7 4,6 5,6 (,6 7,6
4,7 5,7 o,7 7,7
-278-
'„I t, widHu. ttt^M^ammtmt^HmttttmtKä
mmmm—mmmmmmmmmmmmmmmmm—mmmmmmmm—mm^mmmimmmmiimmimmammmmm
The relative importance of each modal combination can be evaluated by
examining the response output and comparing the magnitudes of the dis-
placement coefficients.
Group 10 provides the data required for computing allowable
stresses for honeycomb panels. The core cell size (DC) is defined as
the distance befween opposite flat sides of the honeycomb cell.
Group 13 contains the modal components, 6 , for the initial on
radial imperfections. The analyst must compute the 6 's from measured — mn
data using the integration technique applied to Fourier series coeffi-
cients. Generally, such data will not be available, and :ero values
should be specified for the 6 's. The capabilitv of considering ini- mn
Bilfty
tial imperfections also enables the analyst to determine the sensitivity
of panel response to initial imperfections.
Group 14 provides the integration time increment, the response
stop time, and printout interval. If the user specifies a zero time
increment, the program computes an appropriate Jit which in ^ost cases
will give a stable solution. Because it is approximate, the analyst may
want to make comparable runs using different It's. In general, an
elastic solution which is numerically stable will be accurate. Hence,
the optimum it is the largest which remains stable. For an elastic-
plastic solution, however, the accuracy of the solution may deteriorate
slightly as the point at which the solution diverges is approached.
Once a time increment is selected, it should be valid for other orienta-
tious and moderate changes in response level.
Although the stop time can vary a great deal, the total number
of integration steps required to capture peak response will be roughly
between 500 and 1500. One exception to this may be a curved panel exper-
iencing "snap-through" buckling, in which case considerably larger
response times may be required. A printout frequency of once every 20
steps is usually adequate for monitoring the response time history. The
program checks response values every ten time steps.
-279-
am ^^m^gmgn ,,,
«Piiuaji
Group 1: (5112) MG, MB, MBAK, NBAR, LBAR
Maximum gamma mode number to be used. (MG)
Maximum beta mode number to be used. (MB)
Number of gamma integration points actually used over the portion of the panel analyzed. Must be an odd number for full panel. (MBAR)
Number of beta integration points actually used over the portion of the panel analyzed. Must be an odd number for full panel. (NBAR)
Number of z integration points used through the thick- ness. (LBAR) (Not needed for NDERV=-1 (See Group 2))
Group 2: (3112) NPLT, MW, NDERV
Panel type (NPLT): 0, flat panel 1, cylindrical panel
Boundary condition code (NBND)
i-direction 1, clamped-clamped; 2, simple-simple; 3, clamped-clamped; 4, simple-simple; 5, clamped-simple; 6, clamped-clamred; 7, clamped-simple; 8, simple-pimple; 9, clamped-simple;
S-direction clamped-clamped simple-simple simplr imple clamped-clamped clamped-clamped clamped-simple simple-simple clamped-simple clamped-simple
Note: Whenever a clamped-clamped or a simple-simple condition is selected, only hall of the panel is analyzed in that direction, and MBAR and NBAR should reflect this.
Response option (NDERV):
1, elastic only 2, elastic-plastic
(NDERV must be 2 for KTYP^l or 3, whenever KDAM=1)
-280-
Mta. MaaMMMUiUa
Group 3: (112) NNOUT
Number of modal combinacions to be eliminated from solution (NNOUT). (0 < NNOUT < MG*MB)
If NNOUT^O, skip to Group 5
Group 4: (2112) MOUT(I), NOUT(I)
Gamma mode. (MOUT(I)) Beta mode. (NOUT(I))
Repeat Group 4 for 1-1, NNOUT. The cards in Group 4 may be arranged in any order.
Group 5: (112) NL
Number of layers. (NL) (NL must be 1 for KTYPE-l or 1. and 3 for KTYPE=»3 or ■* i
Group 6: (3F12.1) XLP, THETAO, A
Full length of panel, ^, in. (XL?)
Full width of flat panel, b (sho in. (NPLT-0)
rt direction), \
or / (THETAO"I
Full subtended angle of cylindrical panel. - , deg. ^NPLT»1)
Radius of cylindrical panel, in. (A) (Not needed for NTLT=0)
If NDERV'Z, skip to Group 11.
Group 7: (2F12.1) HM(I), RHOM(I)
Distance (h) from the inner panel surface to the outer surface of layer I, in. (HM(I))
Mass density of layer I, lb-sec"/in . (RHöM(I))
■281-
r—-^-- -.-.^^^MMMM—^
■
Group 3: (5F12.1) EX(I), ET(I), XXNU(I), THNU(I), GXT(I)
Modulus of elasticity in the x-direction, psi. (EX(I))
Modulus of elasticity in the r.heta-direction, psi. (ET(I))
Poisson's ratio in the x-direction. (XXNU(I))
Poiison's ratio in the theta-direction. (THNU(I))
Shear modulus, psi. (GXT(I})
Group 9: (2F12.1) SAT(I), SAC(I)
Tensile yield stress for metal panels; tensile ultimate stress for plastic panels, psi. (SAT(I))
absolute value of compressive yield stress for metal panels; absolute value of compressive ultimate stress for plastic panels, psi. (SAC(I))
Repeat Groups 7-9 for NT.
to core depth,
If KTYPE'1,2, or 5, skip to Gcoup 13.
If KDAM=1 or _, skip tc Group 13.
Group 10: (3F12.1) EC.GC.DC
Core modulus of elasticity parallel psi. 'EC)
shear modulus of core, psi. (GC)
Core cell size, in. (DC)
Skip to Group 13.
Group 11: (JFIC.I) HMU), RHCM(I), EM(I)
Distance (h) from inner shell surface in the outer surface of layer I, in. (HM(I))
Mass density of layer I, lb-sec~/in . (RHOM(I))
Modulus of elasticity, psi. (EM(I))
Repeat Group 11 for 1=1, NL.
-?H?-
■ - u.
^p» -i-»»» 1
Group 12: (4F12.1) TNU, SIGO, EP, EPSIF
Poisson's ratio. (TNU)
Yield stress for a metal panel, psi. (SIGO)
Strain hardening modulus (E ), psi. <E?)
Ultimate strain, in/in. (EPSIF) (Not necessary for KDAM-2)
Group 13: (6F12.1) ((FG(N,M), N-l.MB). M-1,MG)
Modal displacement coefficients for initial radial imperfections, in. (FG(N',M))
Group 14: (3F12.1) DELTIM, TSTOP. PRINT
Integration time increment, sec. If DELTIM-0.0, the program Jeternines the time increment required for stability. (DELTIM)
Integration stop time, sec. (TSTOP^
Print frequencv (integration steps per printout ' . If PRINT-0.0, printout of intermediate data will be sup- pressed. (PRINT)
b.4 PRÜGRAM OPERATION AND OUTPUT
The NOVA program is written in FORTRAN-IV ana consists of 103 user-
suppiied routines and approximately 12,000 caras. Die program is orga-
nized so as to take full advantage of overlaying techniques without
sacrificing computer time. This is accomplished by identifying the
routines in main execution loops and keeping those routines all in jore
at the same time.
The code was developed on the Control Data Corporation (CDC) 6600
computer under the SCOPE 3.4.3 operating system. The segmentation
loader is utilized due ;n its flexibility. The overlaying directives
are contained within the job control sequence; hence, routines can be
reassigned or eliminated from the deck at load time without necessi-
tating changes in the FORTRAN program. The default loader can even be
used without any overlaying, but the user must: 1) selectively load
-283-
mmmm — - ■ — *— ■■•
only the routines required and 2) avoid loading DEPROB and DEPROP simul-
taneously. The program will require approximately 100,000 (octal)
additional cells of central memory.
The recommended segmentation layout is presented in figure 80 and
tables 23-24. Note that subroutine SIGMA and the associated common
block CBLANK are required only for the elastic-plastic option of DEPROP.
This option corresponds to selecting NDERV-2 in Group 2, section b.3.3.
This distinction is made because this subroutine and common block
require approximately 74,400 cells of memory. Of that amount, only o
21000 can be overlayed against other routines. ö
The FTN compiler has been used to compile the code, using options
0PT-1 and R»2. Compilation requires 60,000 cells and 121.4 seconds
(using fast compile mode (0PT»1 I and 147 seconds using fast execution
mode (0PT-2).
Without SIGMA and CBLANK, 137,3002 cells are required to load and
execute; adding them necessitates a total of 213,000 cells. Once the
program is executed, an absolute file is created by the segmentation
loader which, if saved, will eliminate the need to load the program
again, unless changes are sade in eitrier the segmentation directives or
the program. An example of the required job control sequence is pre-
sented in table 25. It is not necessary to preset core to zero 'rior to
execution.
It should be noted that the additional core required for SIGMA ar"i
CBLANK is almost entirely due to the length of the common block CBLANK.
Additional core can be easily obtained on a CDC 7600 by simply assigning
CBLANK to large core memory (LCM) by inserting a LEVEL 2 statement in the
program.
When tne REFRA near-ground reflection 'blasti model is selected ind
ground reflection is to be included in the analysis (vflB=l, KGRD=1 ' , the
REFRA data must be available on logical file TAPE10. This data is
unformatted (binary) with record type S and block type C. This record
type-blocking combination is compatible with SCOPE 3.3 and possesses the
important feature that the system copy utility C0PYBF can be used with
-284-
M^MMM
u o. z < i z a- c 5 < r^ l
■Si >—» < : > w ^ ^ a a c^ a; <: a.
x 3. CNI r^ Q ■o -J-. > ä X. T. Z
JC 2- ^ — H ?: < 3 S 3
^ _: ai ai , r- r- a - > s- — — ^« UJ Ua U« i O w 3 3 3 3
> * z ^ < 2 ^ ^ a: '^ ä
^. OM U. -i- ~ i^ > ^J i -S 3 y: i —
v,! ^ ■r. — 'J£ 2 X
1 "^ —
r 1
t > —«
&^ Al 2 10 . "^ u
CM
1X1 > LU
< -^ — Z a: s
H !/5 M H H — IJJ^XUS^AI^X V3a;<t/;vjcv!33ea
1 -r -r: x x at at J- u.
I? at <
> '--: -r. _; _■
>
a.
u ^
^_i
a. a w z ^M e- il E- '-0 O ^J r- UJ cc o _: a
LU > LU
to a
i^ vO m %T m
I 2 2 2 2 2
^i — c ? ? - ^ r- t- 3 3 "^ UJ x •-/; H u p- at C O ü- ac 2 a. a. a. IO a. - 3
< >
a. u CO : r io w ' 2 P ? \ — a, a. A ~ a. u. , \
I]' r J
at =3 _; x W O vi -yj LJ H H > 3 Z C
at a: 5 Z z S
CD
LU > LU
-2S5-
■AMMMMi MMM I I --
I TABLE 23. LIST OF COMMON BLOCKS WHICH MUST BE DESIGNATED
GLOBAL AND SAVE IN SEGMENTATION
Common block owner sh ip for segme ntat ion
Routine Comnon Blocks
NOVA CNCVA DNOVA CTLX
HYDRA CONSTC SCALLC
VHTRES
REFRA
DEPROB
DEPROF
PW1
S-K- BLNJ
BL.<D
:3LK1 :3LK7 CBLK: CBLNS
CBLN3 :BLK9 CBLK-. JBLKIO CBLfO C3LK11 CBLK6 CBLKlJ
RELAX? CBLK12
13b-
'■--"^^—■ ■■-■ -■ ■
TABLE 24. SEGMENTATION DIRECTIVES
■JOVA
DTMT, IDDUM.SFC
MN.N^^^L'^OV^LiMtPITC'WITra
OPBROP
OF:r,-)0M,rR,FRCTL»POIMTl,^Li'<,:"»STPM?
woprc;
yMTSLo«DOE«»SrTW.30STWl,Po<;T,i;tD0ST^l»Pn<;T*^,P0STW5iP
TQCF
NOVA INCLUDP
LFVFL TOEE
•^I.OCK IMCLUOP TPEF Torp
rtpopoq iNCL'jnc
TBEF foPES I'MCL'jnF
TPTF *POES INCLUOP
.OSTW^.OO«;T^7
L^VFL TOFF Topp
ricFT? IMCLU'TF TOFF
DSE^ I^JCLUDF
TDFE TDFF
MIy I^CLUHF TC3FF
COMOi INCLUDE
TPEF
TPEE iNCt'ioc- TaFr
i- O M <; F ▼ I M C L U - r
TPEF
L r V F L TPEE
C ;rT: o iMCLUn6"
TPEE j w r c; c; [ V C L i J H F
:PFF
-'^nc.\ IMCL'JP57
^-"O ''■ICL'JOF
,K -p , ,:• P, -^Fv/Ot 4 I 3
■^r-/ a r,|_'>P4[ CNOV.i.lNOVi.CTLX-^AVE
-,vnps ^| ^a^L '■nSjS"rr«e;C-\LrC <PPF- r,| -JPJL PWl-^4Vr
3="»P4 Rl. C9AL PF^PfiC-^AVF TFPPnc GLOOM ^»L1*^ VBL« B.^LK^-C; . >;c
-Fppoo ■?)_ P q a L C ^ L K 1 .CaL,<2tC^LK'3«CaLK'*traLK'^«C;:tL<*)«CaLK7,rHL'<^«C^L,'9
.<!CaL<1 ^ »CBL^l 1 «CRL<r3-<;:iVE
PFLA^O GLOBAL C^L*1! ^-^AVF F^lO NOVA
cv r L e'
nsFT]
nsFTP
L^GF^n^nr^TEP nsETi PQLT PEL A XD
HTM- (LI5;T1 .Ll^T? ) ncpyp
COMOJ CQMDp.SL AY.STPM .VCS
nplip,F-5i,i:L<iP='c:FT,Fc;^L.Pc:<:;^«=E<;lfrTt;;,Li<-l»>T-,ES'<.ST^,rT
CVCL«7
► UlTL3» ^TPESS.FI\4L
PFAoi .Tc;Ti!;p aLa^T-(,<c*LiST-(IkJ'r?.TPr\T;.P~crPA-(^3Tl.CPT?,oaTln
! V * 1 S ^ L V E p -_ F ' ": ' NTP
M v ^ p 4 - <; - n C •<
•-iP'-i,:ripT?,jr«pTl,i'rMOS.^4'«»'?
(,F,,'OMT,i<FPt<nr).«»FPxV»i«Fop,-FPPMTtwc-v^MT,wFi_i,wF'>. 2C,*rp
Note: To include subroucine SIi,:M\, add the following card: LIST2 INCLUDE SIOA.
-237-
UIMiili^BMMMKM«Bnite.^MMa»AMIMaaH
IM tmmm
TABLE 25. JOB CONTROL SEQUENCE
Job Control Sequence Comments
MAP,ON.
REWIND(BIN)
ATTACH (TAPE10, )
FILE,TAPE10,RT-S, BT=C.
ID SET, FILES=TAPE10.
LDSET.OMIT-SIGMA.
SEGLOAD(B-ABS)
LOAD(BIN)
EXECUTE (NOVA)
REWIND(ABS)
CATALOG (ABS )
EXIT.
7/8/9
(Object code on file BIN)
(REFRA data on file TAPE10)
(Exclude SIGMA from load)
(Save absolute file for future jobs)
Segmentation directives
7/8/9
Data
6/7/8/9
-288-
'■""'"■*■■*"'■—"'"---" - - ■ i .i.r ■ ■ - - ■■ ■■ —
BP^iw*'""'-" im ^BH '■'i!.1 ^"I' i " "•" ' "/"""i ''".'■■'-"J|"I.^ '.^rw.iwi.ww»»*™
SCOPE 3.4 to transfer the data to disk, tape, etc. When used with the
NOVA program under SCOPE 3.4, however, a FILE card Is required prior to
loading to specify the record type and block type. The REFRA routine
will usually operate more efficiently when the Information Is on disk,
so a transfer to disk Is recommended whenever possible.
Input and output are equated with logical files TAPE5 and TAPE6,
respectively.
Computation times will vary considerably depending on the struc-
ture, the complexity of the model, the response time required, and the
number of Iterations required to determine the critical range. In
general, DEPROP, a three-dimensional code, will require more computer
time than DEPROB, a two-dimensional code. Computer times for two sample
problems are given In section 6.5.
Although program output is largely self-explanatory, the normal
output is described in detail in tables 26-29. When possible, the
corresponding program variable is given parenthetically.
If the INOÜT option is specified in the NOVA input data set, the
input data are included as part of the printed output thus recording the
aircraft altitude and airspeed, the nuclear weapon yield and orientation
at burst, and the data used to model the structural element.
Selection of additional debugging output (NDBUG-1,2) will yield
additional Information which can be useful to the analyst only when it
is accompanied by careful examination of the program.
Certain errors in the input data, particularly those which cause
calculated array sizes to exceed the allotted dimensions, and certain
other errors detected by the program, are identified by error messages
in the program output. The subroutines which originate these messages
are given in table 30 along with an explanation of each message and the
manner in which the error affects the program. It is the user's respon-
sibility to check that the array sizes which he specifies in the input
data do not exceed the limits given in tables 17, 18 and 19. For example,
the number of masses (NMASS or N) in the NOVA and DEPROB cannot exceed
-289-
'^a^—^- -—-TIT mir
m"i i» JMP" i f ■!' iw "■ nwmim* ■
40 in this version of NOVA. If the user specifies 50 masses, no error
message is given and the solution is erroneous. In most cases, the
program, after identifying an error or a potential error, will auto-
matically cycle to the next burst orientation or structural element so
that the entire run is not necessarily wasted.
-0 90-
«MflHBBi Mfaiiilm ■.- i 1 -^ :tt.. ■ -J—,..■•» M-t-.m^.. JUi
• .UM mmpmrnm ^•~mmmm^^^*mm ^^ F m <*mmmm^m*~*mm^
TABLE 26. NOVA HEADING OUTPUT
Aircraft altitude, ft (ALT;
Aircraft velocity, ft/sec (VEL)
Height of ground, ft (KG)
Weapon yield, KT(WKT)
Aircraft angle of attack, rad (ALFAA)
Horizontal tail incidence, rad (HTINC)
Blast model used and if ground reflection included (KB,KURD)
Damage level code (KDAM)
Message indicating Iteration restricted to constant altitude (omitted for KALT-0)
Probability of exceeding specified damage level (PDAM) (omitted if KDAM-2)
Structural element number (NEL)
Struci ural element identification (KTYPE)
Structural element location (ICOMP.IUL)
2 Internal pressurization, lb/in (PINT)
For each new trial or orientation, the following information is printed out:
Orientation number (NOR)
Direction cosines corresponding to above orientation (XOSRO(NOR), YOSRO(NOR), ZOSRO(NOR))
Range, ft (RTRIAL(l))
Number of the present trial in iteration for critical range (NTRIAL) (omitted if KDAM-2)
Message indicating whether aircraft is intercepted by the free-air or Mach shock.
-291-
mm tmm^mmm
fPIBWW ^WWWWCTI .^"FIB^^■■T1WV|'■^'■
TABLE 27. DEPROB STRUCTURAL RESPONSE OUTPUT
Heading Output
Integration interval, sec (DELTIM)
2 Mass of the structure, lb-sec /in (SMASSF)
Stop time, sec (TSTOP)
Message indicating whether the structure is circular or not.
Edge condition and coordinates of the two ends of the structure, relative to the center of gravity of the structure, in. (VI, Wl, V2, W2) (omitted if KTYPE - 8 or 9)
Amplitude of initial imperfection (only for KTYPE=10)
Radius to the center of the ring, in (BIGR3) (omitted if KF/RG-2)
Table of material properties:
Number of flanges assigned to layer (FNFL)
Density of layer for the equivalent cross section, lb-sec2/in4 (RHO)
Geometrical description of each layer of cross section:
Layer number (L)
Thickness of layer at each station along beam, in (H)
Width of layer at each station along beam, in (H)
Width over which pressure is assumed to act, in (WT)
Area ratios associated with mechanical sublayer stress-strain model for each layer:
Layer number (L)
Area ratio for each sublayer (ARSL)
Position of each flange in cross-section for each station along beam:
Flange number
Position in cross-section, in (ZETA)
-29:
-—— MM«
ii M IIMII .iii.ipfwwiiiw^iil^^^'^ww» , i. » 7^*r*m^immmim^mm^^^^*^m*^^^*^mfip ^^mm^m*^m
TABLE 27 (Continued)
I
Table of stress-strain information for compression:
2 Break point stresses for material in layer, lb/\n (STRSO)
Break point strains for material in layer, in/in (STRNA)
2 Stress-strain slope, lb/in (SSS)
Table of stress-strain information for tension:
Seme as the table for compression, with variables STRSOT, STRNAT, and SSST
Stiffness of each supporting longeron (omitted if NS'EL-O), lb/in (E_)
Time-History Output
Integration step number (JTIM)
Time, sec (TIME)
End axial load (only for KTYPE-10), lb (PPP)
Edge strain information (clamped or clamped-sliding boundary condition only)
Edge strain at inner surface, in/in (EDGI)
Number of trials in iterative edge solution (NTI)
Table of response information:
y coordinate of mass point, in (VM)
z coordinate of mass point, in (WM)
Resultant internal force in bar preceding mass point, lb (BIGN)
Resultant internal moment, Ib-in (BIGM)
Strain at inner surface, in/in (EPSILL)
Strain at outer surface, in/in (EPSILU)
Flag ("*") indicating if strain in any flange has exceeded the strain at the first break point in either tension or compression
-293-
mtmu ^-J:.^._ i.. ■■ -*'--M|1h|TT*l^Ltf|iUMMLiü
WH"'?»"" '■ ^n, I-^TW^>T ■^wn'rj.Tirr-'—
-.■•/»Mr^MTOWBRww.-,,-... * ■
TABLE 27. (Concluded)
Acceleration of mass point in the y direction, in/sec (ACCNV)
Acceleration of mass point in the z direction, in/sec" (ACCNW)
2 External (lateral) pressure, lb/in (PB)
Absolute value of net total displacement, in (DIS)
Summary Output (range iteration only)
Critical flange for damage criteria:
Bar in which flange is located (LSTMXI, LSTMXO, LSCMXI or LSCMXO)
Layer in which flange is located (LMAX)
Flange (KMAX)
Time at which maximum ratio of stress/strain to allowable stress/strain occurred, sec (TSTMXI, TSTMXO, TSCMXL or TSCMXO)
Critical strain, in/in (ETKXI, ETMXÜ, ECMXI or ECMXO)
2 Corresponding stress, lb/in , STMXI or STMXO (omitted for KDAM-1)
Maximum ratio of stress/strain to allowable stress/ strain (CRIT(l))
Message indicating whether structural element yielded (that is, whether strain in any flange has exceeded the strain of the first break point in either tension or compression ).
Net CP time for response, sec.
-294-
III« INI "■■-—-'■-iiirr riiriiii^iMUIIf'"" A ,. i.i; >r- •'■ -.-. ■■'- .^-
iiiffiii.«|ftlii,Liiiii,|iiipi»i.i.... iijii.ii.1 ),i.ji»iJ!ii,Hij,w..i.i,ii.iiuii.>iitpyiwili'!W!l ' n "Im mwwMMn ■■"■"ll111 n'1 I "*• n i i ii *^^*m^m*wm
TABLE 28. DEPROP STRUCTURAL RESPONSE OUTPUT
Time-History Output
Time from shock arrival, sec (TIME)
2 External Pressure, lb/in (PPP)
Normalized axial, tangential, and radial displacement modal coefficients for all modes, with the beta mode index varying most rapidly ((UU(I.J), W(I,J), WW(I,J), J»1,MB), I-1,MG)
Table of stress-strain information (every third spatial point, inner and outer surfaces):
X coordinate, in (XG) Beta position, in or deg (XB) Depthwise position, in Axial strain, dimenslonless Circumferential strain, dimenslonless Shearing strain, dimenslonless Axial stress, Ib/in^ Circumferential stress, lb/in Shearing stress, lb/in^ Flag ("*") indicating equivalent strain has exceeded yield strain (elastic runs only) Counter Indicating number of unloading and revieldings (KY) (elastic-plastic runs only)
Displacement information (every third spatial point):
X-coordinate, in (XG) Beta-position, in or de^ (XB) Axial displacement, in (ÜF) Tangential displacement, in (VF) Radial displacement, in (WF)
Summary Output (range iteration only)
Message indicating whether run was terminated normally or abnormally
Time at which computations stopped, sec (TIME)
Iterative trial number (NTRIAL)
Case number (NCASE)
Range, ft (RTRIAL(l))
Maximum ratio of stress (strain) to allowable stress (strain) (CRIT(l))
-295-
mimai II I ' lltNllfWr-:"■:a'"^■'^^ ' ' '
um in- UPmwWBBWpp^wmi^^^» m^^^^
TABLE 28. (Concluded)
Time corresponding to maximum ratio, sec (TMAX)
Message indicating whether maximum ratio occurred in tension or compression.
Net CP time for response, sec
Number of integration points which yielded, if any. (Elastic-plastic response only)
-296-
^^^—iMMMMM^MIhi .i n -
(•«-'irir'-.u'iw^rr '."■ ■""—•■■-^r^' Tr^mwrfuifir**
TABLE 29, NOVA TERMINAL OUTPUT
For each element for each orientation for each trial, the following information is printed out:
Structural element number (NEu)
Orientation number (NOR)
Direction cosines corresponding to above orientation (XOSRO(NOR), YOSRO(NOR), ZOSRO(NOR))
Range, ft (RTRIAL(l))
Number of the present trial in iteration for critical range (NTRIAL) (omitted if KDAM-2)
Message indicating whether aircraft was intercepted by th«i, free-air or Mach shock.
Components of vector from aircraft to burst point at. shock arrival time, ft
Components of vector from aircraft to burst point at burst time, ft
Shock arrival time, sec
2 Shock overpressure, lb/in
When all structural elements have been considered, the following suranary of results is printed out (omitted for KDAM-2):
Table containing the following information for each orientation and structural element considered:
Original orientation number (the direction cosines associated with this orientation number may have changed for a constant altitude iteration)
Structural element number
Components of critical range vector from aircraft to burst at shock arrival time
Components of critical range vector from aircraft to burst at burst time
Critical range, ft (RCRIT)
2 Shock overpressure, lb/in
-297-
MlMMiHIIIIMHiM : t-nrirwinmieU^-*1****"**^""^ '
mmm iWWWiRiiHPIMipiran
TABLE 29. (Concluded)
Shock arrival time, sec.
Table indicating the critical element corresponding to each orientation considered:
Original orientation number
Structural element number
-298-
■*—-""• — ■ - -
ftifnynii M,mti.\w.M}m'i;. '"ly^tF, m*^" T '»flii" 7t;*!»>-: HHWI1-1
TABLE 30. ERROR MESSAGES
AIRCRAFT FLYING OUT OF BLAST REGION.
At the time at which the shock front and the aircraft center of gravity coincide for the given range and orientation, the aircraft is emerging from the shock region rather than being overtaken by the shock. Program sets critical range for given element and orientation equal to zero and continues to next case. (FPRES and WPRES)
ALTITUDE MUST BE GREATER THAN ZERO IN S/R REFRA.
The altitude of the burst must be above sea level. Program stops, (REFRA)
AMACH-XXX. GMACH-XXX. PROGRAM IS TEEMINATED IN S/R SETW DUE TO THE ABOVE VALUES.
The aircraft and gust Mach numbers cannot be -1.0 or 1.0. Pro- gram stops. (SETW)
AMBIENT CONDITIONS RETURNED BEHIND SHOCK IN FPRES, T-XXX.
Program expects nonambient conditions just behind shock but gets ambient conditions from BLAST. May need to increase time bias in BLAST. Program aborts this case and continues to next case. (FPRES)
A SMALLER RANGE IS NOT POSSIBLE FOR THIS ALTITUDE AND HOB. PLETED-XXX. RANGE, GRIT XXX, XXX.
TRIALS COM-
The minimum range possible has been found to be too large for an iteration constrained to constant altitude. Program aborts this case, and continues to next case. (RITC)
CAN NOT TOTALLY CORRECT FOR OVERSHOOT. XXX.
An iterative process to correct for overshoot associated with yielding has not converged in five trials. This probably means a numerical instability is creeping into the solution. Program continues until such errors occur 100 times. (See section 4.2.6, (SIGMA)
-299-
JSSSSaBSBSSSäSmkmm iHmmigi MMÜMMMMIMMMM. -B5HB
—' m
TABLE 30. (Continued)
CRITERIA VS RANGE SLOPE REVERSAL IN RITER. NTRIAL=XXX. RANGE, CRIT, XXX,XXX.
The criterion, CRIT, has decreased v/ith decreasing trial r^nge or increased with increasing trial range, which violates the as&uiro- tion of the range iteration program that the criterion increases monotonically as the trial range decreases. Program sets critical range for given element and orientation equal to zero and continues with next case. (RITER)
DATA OUT OF RANGE IN S/R BISH. T = XXX. TIM (LLL) » XXX. TIM(LLU) = XXX.
This indicates an error in the program. Program stops. (BISH)
DC IS OUT OF RANGE lil S/R 0PT2.
d, , which is described on page 59, ref. 7, is not within the range
pe. P:
to the calling program. (0PT2)
of d 's on the data tape. Program flags the error and returns ma^
DEPROB IS ABORTED AT T, SEC = XXX.
DEPROB returns control of program to NOVA due to error. This case is aborted. (DEPROB)
DEPROP IS ABORTED AT T, SEC = XXX.
DEPROP returns control of program to NOVA due to error. This case is aborted. (DEPROP)
DIMENSIONS ABOVE ARE NOT LARGE ENOUGH FOR REFRA TAPE.
The dimensions of the variables in REFRA need to be increased. Program stops. (REFRA)
ELC IS OUT OF RANGE IN S/R 0PT2
2 whicb is described on page 54, ref. 7, is not within the range
of 2, ' s on the data tape. Program flags the error and returns
to the calling program. (0PT2)
-300-
HMBM ■■MM
• '«
TABLE 30. (Continued)
END OF DATA REACHED ON TAPE XXX IN S/R ADVANC.
This indicates an error exists in the program or in the way the data tape was prepared. Program stops. (ADVANC)
END OF DATA REACHED ON TAPE XXX IN S/R READ.
This indicates an error exists in the program or in the way the data tape was prepared. Program stops. (READ)
END OF DATA REACHED ON TAPE XXX IN S/R SKIP.
This indicates an error exists in the program or in the way the data tape was prepared. Program stops. (SKIP)
EPP IS OUT OF RANGE
Numerical instability detected. A smaller At may be required. This case is aborted. (SIGMA)
FIRST ARGUMENT IS OUTSIDE TABLE, X = XXX. XT = XXX...XXX.
Tabulated data provided does not bracket first argument. Program stops. (INT2)
IMMEDIATE RELOADING, XXX.
Probable numerical instability creeping into solution. Program continues until such errors occur 100 times. (See section 4.2.6.) (SIGMA)
INSUFFICIENT DATA AVAILABLE IN FPRES XXX.
A REFRA tape with data at later times is required. Program aborts this case. (FPRES)
INSUFFICIENT DATA AVAILABLE IN WPRES XXX.
A REFRA tape with data at later times is required. Program aborts this case. (WPRES)
-301-
MaMMttOHM ■ i
mmmmjm*™ ■Ml
TABLE 30. (Continued)
INTERPOLATION ERROR IN INTP, X-VALUE XXX OUTSIDE TABLE. Y-VALUE RETURNED - XXX. X-TABLE - XXX.
Linear interpolation of pressure vs time has a time which is out- side table. Indicates probable error in FPRES, WPRES or PINIT. Program continues. (INTP)
J OR JP IS OUT OF RANGE IN 0PT2.
j, as calculated in equations 86 or 97, ref. 7, is too large. Program flags the error and returns to the calling program. (0PT2)
MORE THAN XXX LAYERS ARE REQUIRED IN DEPROB.
Available storage for variables dimensioned at NL has been exceeded. Case is aborted. (C0MP1)
MORE THAN XXX SUBFLANGES REQUIRED IN LAYER XXX IN DEPROB.
available storage for variables dimensioned at MAXSF has been exceeded due to an excessive number of stress-strain segments. Case is aborted. (C0MP1)
MORE THAN XXX TOTAL FLANGES REQUIRED IN DEPROB XXX.
Available storage for variables dimensioned at NLK has been exceeded. Case is aborted. (C0MP1)
NAMELIST NI0PT3
Possible error in I0PT3, Program may stop. (I0PT3)
NO ITERATIVE SOLUTION FOR THIS AZIMUTH.
A range iteration constrained to constant altitude cannot begin with the burst directly above or below aircraft. Program aborts this case. (RITC)
NUMBER OF CASES EXCEEDS STORAGE IN MOVA XXX.
The total combination of orientations and structural elements exceeds the maximum dimensions. Program prints summary and stops. (NOVA)
-302-
mmm MMM ^M^H^M
»'"Mi i " iWMP
TABLE 30. (Continued)
NUMBER OF TRIALS COMPLETED - XXX. PROBLEM REQUIRED TOO MANY ITERATIONS OF RLAXB.
Too many Iterations (20) were required to find static equilibrium. The final conditions are printed out. Program may need more trials and/or adjustment of the variable CON in RLAXB. This case is
. aborted. (DEFORM)
NUMBER OF TRIALS COMPLETED - XXX. SOLUTION DIVERGING IN S/R RLAXB, PROGRAM ABORTED IN S/R DEFORM.
Iterative process to find static equilibrium has failed. The final conditions are printed out. This case is aborted. (DEFORM)
PS I IS OUT OF RANGE IN S/R OPT2.
ii , which is described on page 58, ref. 7, is not within the range
of ^_ 's on the data tape. Program flags the error and returns to
the calling program. (0PT2)
RANGE ITERATION HAS NOT CONVERGED IN RITER. NTRIAL = XXX. RANGE, CRIT, XXX, XXX.
To avoid a possible iteration loop in searching for the critical range, the number of trials allowed is restricted. Iteration can be continued on a subsequent run by specifying appropriate directions cosines and range. Program aborts this case. (RITER)
SCALED GROUND RANGE OUTSIDE MACH SHOCK DATA TABLE IN XBLAST. I0PT, SH, SRMS, SRMT(l), SRMT(15). XXX XXX
Thi'. scaled ground range SRMS is either too small or too large. A new range should be estimated for subsequent runs. Program aborts this case. (XBLAST)
SECOND ARGUMENT IS OUTSIDE TABLE, Y = XXX. YT = XXX...XXX.
Tabulated data provided does not bracket second argument. Prop.äin stops. (INT2)
SINGULARITY NEAR LEADING EDGE, TIME = XXX. X/C XXX. CP = XXX.
Point on lifting surface is too near leading edge to obtain a meaningful pressure. Program continues. (POSTW1, P0STW4)
-303-
tMMflM MiU
■fii i n"!'-"'! ' . >■ 'n mu wwwwwwpi mm '
TABLE 30. (Continued)
SINGULAR MATRIX IN RLAXF. XXX.
The quasi-static edge solution cannot be found. Case is aborted except for rib elements. (RLAXF)
SINGULAR MATRIX IN S/R SOLVE.
The relaxation process has generated a singular matrix in deter- mining static equilibrium. Program aborts this case. (SOLVE)
SOLUTION DIVERGING AT TIME, SEC «= XXX.
v'ory large accelerations have been computed in CYCLE, indicating a numerical instability. A smaller At may be required. This case i=, aborted. (CYCLE)
SOLUTION DIVERGING IN DEPROP.
Very large accelerations have been computed in DERV2, indicating a numerical instability, A smaller At may be required. This case is aborted. (DERV2;
SOLUTION DIVERGING IN RELAXP.
The iterative process to find static equilibrium has failed. Program aborts this case. (RELAXP)
SOLUTION DIVERGING IN RLAXF. TIME, SEC = XXX.
The quasi-static edge solution cannot be found. A smaller At may be required. For a structure which can buckle, this may also indicate dynamic buckling. Case is aborted except for rib elements. (FB)
SOLUTION IS UNSTABLE.
Numerical instability has been detected in elastic-plastic solution. A smaller At is required. This case is aborted. (SIGMA)
STATIC SOLUTION ABORTED, NTR - XXX.
Static equilibrium cannot be found. Program continues. (DEFORM)
-304-
'mmmwimmmmi^iiiiim "" '"
TABLE 30. (Continued)
STORAGE REQUIRED FOR WING PRESSURES EXCEEDS AVAILABLE STORAGE.
Allowable storage for variables dimensioned at NTP1+1 has been exceeded in the calculation of pressure on a lifting surface. Program aborts this case. (WPRES)
TAPE XXX IS IN POSITION JUST PRIOR TO TRANSITION IN S/R ADVANC. NT - XXX.
This indicates an error exists in the program or in Lht way the data tape was prepared. Program stops. (ADVANC)
TAPE XXX IS IN POSITION JUST PRIOR TO TRANSITION IN S/R SKIP.
This indicates an error exists in the program or in the way the data tape was prepared. Program stops. (SKIP)
TAUB IS OUT OF RANGE IN S/R OPT2
T , which is described on page 54, ref. 7, is not within the range B
of TT 's on the data tape. Program flag's the error and returns K
to calling program. (OPT2)
THE NUMBER OF MASS POINTS MUST BE EVEN IN DEPROB. N = XXX.
For KTYPE ■ 8 or 9, an even number of masses must be used. This case is aborted. (READ1)
THE VALUE OF LBAR IS INVALID. LBAR = XXX.
An incorrect value of LBAR has been specified. This case is aborted. (LEGEND)
THE X COORDINATE IS GREATER THAN THAT OF THE TRAILING EDGE.
The chordwise position at which pressure is desired is aft of the trailing tdge. Program stops. (PREW)
THE X COORDINATE IS LESS THAN THAT OF THE LEADING EDGE.
The chordwise position at which pressure is desired is in front jf the leading edge. Program stops. (PREW)
-305-
*"—--■--■ -■
m^^^tjmtmmmm
■i» »m.» ■" 'u' BI .HI 1 JlillJI ll.|"l ■ ^in |i mmw mimrn* i. pr>V ... . >!■_
TABLE 30. (Continued)
THE Y COORDINATE IS LAP.^ER THAN THE EFFECTIVE SPAN.
The spanwise coordinate of the point at which pressure is desired is greater than the span as defined by the points which specify the leading and trailing edges. Program stops. (PREW)
THE Y COORDINATE IS LESS THAN ZERO.
The spanwise coordinate of the point at which pressure is desired is smaller than the first point defining the leading edge. Pro- gram stops. (PREW)
TIME REQUESTED EXCEEDS LAST REFRA TIME XXX, XXX.
A REFRA tape with data at later times is required. Program aborts this case. (BLAST)
TOO FEW TIMES ON DATA TAPE XXX IN S/R CPT1.
Data is needed for a time for which there is no data on the tape. Three times are printed out in seconds: the time requested, the first time on the tape and the last time on the tape. Program
' stops. (0PT1)
TOO FEW TIMES ON REFRA TAPE FOR MACH SHOCK IN S/R 0PT2.
The searching process described on page 59, ref. 7, failed to find a time on the data tape. Program flags the error and returns to the calling program. (0PT2)
TOO FEW TIMES ON REFRA TAPE FOR REF SHOCK IN S/R 0PT2.
The data tape does not extend far enough in time for Option 2, Program flags the error and returns to the calling program. (0PT2)
TOO LITTLE STORAGE FOR FN ARRAY, XXX.
The dimensions for FN, or the variables representing Che dimensions, MAXSF, MAXLK and N, are not sufficiently large for the problem. This case is aborted. (C0MP1)
TOO MANY ITERATIONS IN WFPKOD. XXX.
Convergence has not been obtained in function WFPKOD. Program continues. (WFPKOD)
-306-
MM mam ■MM
■itipmuwi. winwW!)''-,'!-!"1."" „,( .^.„Mfimiii ay..^.»umu-..ul|if .w iiiiiimmumi ill"nff I ,' - - ^T^rrrlTrv,wl,,Wfmi,my" ~~*m>m*m**m .■.--.,.~l
TABLE 30. (Continued)
TOO MAI^Y TRIALS IN FB XXX. TIME, SEC - XXX.
The quasi-static edge solution cannc«: be found. A smaller At may be required. For a structure which can buckle, this may also indicate dynamic buckling. Case is aborted except for rib ele- ments. (FB)
TOO MANY TRIALS IN STATIC SOLUTION. MTR - XXX.
To avoid looping indefinitely in attempting a solution representing static equilibrium, an upper limit of 10 is placed on the number of trials. Program may need more trials and adjustment of the variable CON in RELAX?. (DEPROP)
VALUE OF NU WON'T CONVERGE XXX XXX, TIME, SEC - XXX.
Numerical instability detected. This case is aborted. (SIGMA)
WARNING - HONEYCOMB PANE! , PROGRAM ASSUMES FACE SHEETS ARE LAYERS 1 AND 3, BUT PANEL HAS XX LAYERS.
The code KTYPE is equal to 3 or 4, indicating a honeycomb panel, which the program assumes to have three layers, two face sheets and a core. The panel does not have three layers, however. Program continues (CSETUP)
WARNING - ONE OF THESE FOUR PARAMETERS HAS EXCEEDED THE LIMITS OF ITS CURVE FIT IN S/R PREW.*** ETA - XXX, SWPM - XXX, TRATIO - XXX, ASPRM • XXX.
A quadratic curve fit of aerodynamic data may be invalid. The four parameters and their domains are:
0.0 <_ ETA < 0.924 0.0 <_ SWPM _< 1.0472
0.0 £ TRAT0 <_ 1.0 1.5 < ASPRM < 8.0
Percent of semispan Modified Sweep Parameter, Ag, (see table 2) Taper ratio , \. Modified aspect ranio, B^» (see table 2)
Program applies quadratic fit and continues. (PREW)
-307-
r-'" ■■'— 1M^^ ■fl-rT '- -:-■■■■ •i-"^--
"" i ll,l mW '■■■"'"'' '" ww'~mm»ni ■! ■■■ ii
TABLE 30. (Continued)
WARNING - ORIENTATION OF BLAST IS INCORRECT FOR SYMMETRIC RESPONSE XXX.
A frame element modeled so as only half of element is analyzed must receive blast loading so as to preserve symmetry. Program continues. (PINIT)
X - VALUE XXX, OUTSIDE TABLE. Y-VALUE RETURNED - XXX. X-TABLE = XXX.
Tabulated data do not bracket X-value given. Nearest value is returned. Program continues. (INT1)
X-VALUE XXX OUTSIDE TABLE. Y-VALUE RETURNED = XXX. X-TABLE - XXX...XXX. Y-TABLE - XXX...: XX. ADDRESS OF X - XXX. ADDRESS OF NX = XXX. ADDRESS OF XT - XXX. ADDtESS OF YT - XXX. ADDRESS OF R * XXX.
Tabulated data provided do not bracket X-Value jjiven. . Tables and addresses are printed out to help user to identify problem. Pro- gram stops. (INTSLO)
ZETA NOT IN RANGE
Zeta (as found from equation 58, page 45, ref. 7) is not between 0 and 1. ZETA is set equal to 1 and the program continues. (0PT1)
ZETA1 NOT IN RANGE
Zeta (as found from equation 58, page 45, ref. 7) is not between 0 and 1. ZETA1 is set equal to 1 and the program continues. (0PT1)
**** WARNING **** - ELASTIC CURVES IN TENSION AND COMPRESSION DIFFER SIGNIFICANTLY IN LAYER XXX.
The stress-strain curves in tension and compression must have the same modulus of elasticity. Here they differ by more than 10%, Program continues. (C0MP1)
**** WARNING **** - STATIC PRELOAD CANNOT BE FOUND FOR THESE CONDITIONS. KEYB1 = XXX. KEYB2 = XXX.
Only selected combinations of boundary conditions can be treated stat- ically. Program continues without preblast load. (DEFORM)
-308-
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TABLE 30. (Concluded)
**** WARNING **** YIELD STRAIN HAS BEEN EXCEEDED DURING STATIC LOADING. ONLY ELASTIC SOLUTIONS ARE ALLOWED.
Static equilibrium has been reached, but yield strain has been exceeded. Solution is constrained to be elastic, so inconsis- tencies may arise during dynamic response. The preload :'.s probably too large. Program continues. (DEF0ÄM)
•309-
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6.5 EXAMPLE PROBLEMS
Presented In this section are the results of three example problems
intended to demonstrate the use of the DEPROB and DEPROP options of NOVA
and the REPRA ground-reflected blast model. These examples are also
intended to serve as check cases for running the code. The structural
elements consist of a curved metal panel and a stringer. Data for the
components are taken from reference 51. Certain data have been modified
to better demonstrate the code. Also, relatively few modes are used in
the DEPROP model to minimize the computer time needed to exercise the
examples.
The first element considered is a titanium alloy panel situated
between frames on an aft fuselage section; it is assumed to be clamped
on all edges. A threshold of permanent damage criteria is selected, and
the aircraft altitude and burst orientation specified so that the air-
craft is intercepted by a Mach shock. This and the other two examples
involve a scaled burst height of 525 feet. In this case, the analytical
curve-fit ground reflection model is used (KB«2).
Figure 81 presents the input data used: first a listing of the data
cards, then the interpretation by the program. It shows that DEPROP
computes a time increment of 3.36 ysec. As will be seen, less than 1
millisecond of response is required to capture peak response. There-
fore, only 298 integration steps are required.
From the program output, most of which ig presented in figure 82,
an initial range estimate of 2600 feet turns out to be a very propitious
choice; the critical response compared to the appropriate allowable is
0.968, very near the desired ratio of 1.0. In this case the critical
stress occurred at 0.739 millisecond. The output shows that the panel
defJected outward 0.00032 inch (at the center) due to the net preblast
load on it. At 0.538 millisecond into the response (corrasponding to
the printout included in fig. 82) the panel has deflected 0.270 inch
inward. From the radial displacement coefficients (WRS) at that time,
it can be seen that the dominant modes involve the first gamma mode; if
more accuracy were required one would probably begin by adding modes
-310-
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1,4; 1,5; etc. Based on the response, the program predicts a critical
range of 2535 feet and terminates after only the one Iteration. The
computer time required Is only 57 seconds.
After computing a new range vector, shock overpressure, and shock
arrival time, the results are summarized as final outpuc. If more than
one structural element had been considered, or If additional orienta-
tions had been considered, the summary would select the element most
susceptible to nhat damage level for each orientation.
The second exaaple p. cblem Involves an aluminum skin-stringer
combination on the horizontal tail. Again, clamped edges are assumed,
.id due to symmetry only one half of the element is modeled. A thresh-
old of permanent damage criteria is selected. In this case, the REFRA
ground reflection blast model is used to provide the dynamic loading
(KB-1).
The actual input data are presented in figure 83. A listing of the
data cards is followed by the interpretation by the program. Including
some additional parameters computed by the program. The appropriate
integration time increment of 4.46 usec is calculated.
This problem requires two iterations before selecting a final
estimated range. Selected portions of the output are contained in
figure 84. For example, the response output is shown at t*0, t»0.214
msec, (the time approxinritely corresponding to peak response), and at
t=0.3 msec corresponding tu >he final output. The printout at t=»0.214
msec indicates a center deflection of about 0.050 inch and the maximum
strain (-0.005299), which is slightly less than the yield strain, occurs
in the segment nearest the wall. The element is -lot allowed to yield,
however, because of the threshold damage criteria selected.
The output indicating range and "CRIT" (ratio of maximum response
to critical value) are presented for each of the two trial ranges. In
general, if the logarithm of."CRIl" is plotted versus range, the points
will quickly indicate the critical range where, by definition, CRIT=1.
The program estimates a final range of 27J9 feet and summarizes the
results. The entire run consumed 95 CP seconds of computer time.
-311-
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The third example problem Is identical to the second, except the
analytical blast model (KB^Z) Is used for comparison. In both cases
the aircraft is intercepted by the Mach shock. Here the final estimated
range is 2924.1 feet with a corresponding shock overpressure of 10.594
psi (figure 85). When compared with the REFRA results, this indicates
the analytical model predicts a critical range 7.6 percent larger than
REFRA due to a predicted shock overpressure which is 24.7 percent higher.
■312-
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NOVa-2 SAMPLE PP08LEM - CURVEO PANEL ON FUSELAGt 1 0
5000. Q3S. 10, 4C)50. 0.1 -.1 0.0 0.0
2? 2? 0.0 -0.80638 -0.44329 2600.0
(BLANK CARD) 2 1 0 1
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0. 0. 0. 0. 0. 0. 0. 0.0 0.001 10,
0.6?E7
0.
(PLANK C4PD)
Figure 81. Example Input Data for Curved Panel on Fuselage
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REFERENCES
1. Kaman AviDyne, NOVA - A Digital Computer Program for Calcu- lating the Response of Aircraft co the Overpressure from a Nuclear Explosion, Volume 1, Technical Report No. AFWL-TR-72- 115, Volume I, Air Force Weapons Laboratory, Air Force Sys- tems Command, Kirtland Air Force Base, New Mexico, July 1973.
2. Needham, Charles E., et al. Nuclear Blast Standard (1KT), Technical Report No. AFWL-TR-73-55, April 1973.
3. Needham, Charlss E., et al, Nuclear Blast Standard (1KT), Technical Report No. AFWI-TR-73-55 (Rev) dated 1 April 1975.
4. "Progress Report on the 1-KT Standard Data Analysis", Private Communication from Cordell Smith of the Air Force Weapons Laboratory to SPLN, Defense Nuclear Agency, dated 29 October 1971.
5. Broyles, CD., IBM Problem M Curves, SCTM 268-56-51, Los Alamos Scientific Laboratory, December 1956.
6. Hobbs, N.P., Zartariau, C, and Walsh, J.P., A Digital Com- puter Program for Calculating the Blast Response of Aircraft to Nuclear Explosions, Volume I: Program Description, AFVL- TR-70-14G Volume I, Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico, April 19 71.
7. Zartarian, G., and Lee, W. , Program REFRA - Blast Routine Based on REFLECT Code, Defense Nuclear Agency Report No. DNA 3596F, May 2, 1975.
5. Ruetenik, J.R., et al. Computer Code f-r Ground-Reflected Blast Waves, Volume I, Kaman AviDyne Technical Report No. TR-Q6, August 1973.
9. DeYoung, J., and Harper, C.W., Theoretical Symmetric Span Loading at Subsonic Speeds for Wings Having Arbitrary Plan- form, NACA TR No. 921, 1948.
10. Nielsen, J.N., Missile Aerodynamics, Chapter 2, McGraw-Hill Book Co. , Inc. , 1960.
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REFERENCES (Continued)
11. Donovan, A.F., and Lawrence, H.R., Editors, Aerodynamic Components of Aircraft at High Speeds, Vol. VII of the High Speed Aerodynamics and Jet Propulsion Series, Chapter 3, Princeton University Press, 1957.
12.
13.
Ruetenik, J.R., and Witmer, E.A., Two-Dimensional Airfoils, Part 2,
Transient Aerodynamics of Interferometric Measure-
ments of Airflow Development about an NAGA 65-010 Airfoil in Shock-Initiated Subsonic Flow, Including Transient Stalling Effects, WADC TR 5A-368, Part 2, (AD 151018), Wright Air Development Center, WPAFB, Ohio, March 1958.
Andrews, P.T., and Ruetenik, J.R., Transient Aerodynamics of Two-Dimensional Airfoils, Part 3. Interferometric Measure- ments of Airfoil Development about an NACA 65-010 Airfoil in Shock-Initiated Transonic Flow, WADC TR 54-368, Part 3, (AD 209497), Wright Air Development Center, WPAFB, Ohio, January 1959.
14. Ruetenik, J.R., Evaluation of Traveling-Gust Method for Airfoils in Strcn? Plast Waves by Shock-Tube Tests, WADD TR 60-279, Wright Mr Development Division, WPAFB, Ohio May 1960.
15. Ruetenik, J.R., "Traveling-Gust Method for Airfoils in Strong Blast Waves", Journal of Aeronautical Sciences, Volume 27, No. 10, October 1960. "" "" ' "*
IJ. Ruetenik, J.R., Herrmann, W., and Witmer, E.A., "Shock-Tube Studies of Blast-Loading on Airfoils", ALA Symposium, Struc- tural Dynamics of High Speeds Flight, Los Angeles, CA, ONR, ACR-62, Volume 1, April 25, 1961.
17 Ruetenik, J.R., and Hermanu W. Shock-Tube Measurements of Step-Blast Loads on a NASA faAAQlO Airfoil, ASD-TR-61-219, Aeronautical Systems Division, WPAFB, Ohio, February 1962.
18. Lemcke, B., and Ruetenik, J.R., Methods for Calculating the Transient Airloads on a Supersonic Delta Wing with Subsonic Leading Edges Using Aerodynamic Influence Coefficients, AfFDL-TR-65-168, Mr Force Flight Dynamics Laboratory, WPAFB, Ohio, March 1966
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r REFERENCES (Continued)
19. Smiley, R.T., and Krasnoff, E.L., Unsteady Aerodynamic Forces on Subsonic Aircraft Exposed to Blast Gusts of Arbitrary Orientation. WADC TR 57-594, (AD 142336), Wright Air Develop- ment Center, WPAFB, Ohio, June 1958.
20. Drischl^r, J.A., and Diederich, F.W., Lift and Moment Responses to Penetration of Sharp-Edged Traveling Gusts, with Application to Penetration of Weak Blast Waves, NACA TN 3956, May 1957,
21. Lotnax, H., Heaslet, M.A., Fuller, F.B., and Sluder, L. , Two- and Three-Dimensional Unsteady Lift Problems in High-Speed Flight, NACA Report No. 1077, 1952.
22. Morris, C.H., Hansen, R.J., et. al.,. Structural Design for Dynamic Loads, McGraw-Hill Civil Engineering Series, McGraw- Hill Book Company, Inc., New York, 1959.
23. Kaiman, J.P., Rodden, W.P., and Geising, J.P., "Application of the Doublet-Lattice Method to Nonplanar Configuration in Subsonic Flow", Journal of Aircraft, Volume 8, No. 6, June 1971.
24. Woodward, F.A., "Analysis and Design of Wing-Body Combinations at Subsonic and Supersonic Speeds", Journal of Aircraft, Volume 5, No. 6, Nov-Dec 1968.
25. Liepmann, H.W., and Roshko, A., Elements of Gasdynamics, Galcit Aeronautical Series, John Wiley & Sons, Inc., New York, 1957.
26. Allen, J.H., and Perkins, E.W., A Study of Effects of Vis- cosity on Flow Over Slender Inclined Bodies of Revolution, NACA TR-1048, 1951.
Zartarian, G., Correlation of the Loading and Response Data from the Nike-Hercules Nose Cone/DASACON Shock Tube Tests, Part I: Aerodynamic Loading Correlation and Development of Pressure Model. BRL CR-66, Kaman AviDyne TR-77, Ballistic Research Laboratories, APG, Maryland, August 1971.
Airloads Blast-Intercept Model for the AIRS I Vehicle, Internal Kaman AviDyne Memorandum, February 1, 1967.
23.
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REFERENCES (Continued)
29. Witmer, E.A., Balmer, H.A., Theoretical-Experimental Corre- lation of Large Dynamic and Permanent Deformations of Impul- sively-Loaded Simple Structures, Technical Documentary Report No. FDL-TDR-64-108, Air Force Flight Dynamics Labora- tory Research and Technology Division, Air Force Systems Command, Wright-Patterson Air Force Base, Ohio, July 1964.
30. Witmer, E.A., Balmer, H.A., Leech, J.W., and Plan, T.H.H., "Large Dynamic Deformations of Beams, Rings, Plates, and Shells", AIAA Journal, Volume I, No. 8, August 1963.
31. Wu, Richard W-H, Witmer, Emmet A., Finite-Element Predictions of Transient Elastic-Plastic Large Deflections of Stiffened and/or Unstiffened Rings and Cylindrical Shells, Report No. AMMRC CTR 74-31, Army Material and Mechanic Research Center, Watertown, Mass, April 1974.
32. Mente, L.J., The Dynamic, Elastic-Plastic, Large Displacement Response of Buckling Sensitive Cylindrical Shells to Blast- Type Loadings, -- Part I Analytical Formulation, AMC-2-68-(T), Kaman AviDyne TR-53, Kaman Sciences Corporation, August 1968.
33. Mente, L.J., and Manzelli, J.C., The Dynamic Elastic-Plastic, Large Displacement Response of Buckling Sensitive Cylindrical Shells to Blast-Type Loadings — Part II: Applications and DEPICS User's Manual, AMC-11-71-(T), Kaman AviDyne TR-74, Kaman Sciences Corporation, April 1971.
34. Mente, L.J., "Dynamic Nonlinear Response of Cylindrical Shells to Asymmetric Pressure Loading", AIAA Journal, Vol. 11, No. 6, June 1973, pp. 793-800. ~ ~
35. Washizu, K. , Variational Methods in Elasticity and Plasticity, Pergamon Press, New York, N.Y., 1968.
36. Novozhilov, V.V., Foundations or t.ie Nonlinear Theory of Elasticity, Graylock Press, Rochester, N.Y., 1953.
37. Donnell, L.H., "A New Theory for the Buckling of Thin Cylin- drical Shells Under Axial Compression and Bending", ASME Transactions, Vol. 56, 1934.
38. Hill, R., The Mathematical Theory of Plasticity, The Oxford Engineering Science Series, Clarendon Press, Oxford, England, 1956.
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REFERENCES (Concluded)
39. Annan, H., Jr., Levine, H.S., and Pifko, A.B., "Plasticity- Theory and Finite Element Applications", Advances in Compu- tational Methods in Structural Mechanics and Design, UAH Press, Huntsville, Alabama, 1972.
40. Ambartsumayan, S.A., Theory of Anisotropie Shells, NASA TT F-118, May 1964.
41. Hildebrand, F.B., Introduction to Numerical Analysis, McGraw- Hill, New York, 1956.
42. Leissa, A.W. , Vibration of Plates, NASA SP-160, 1969.
43. Leissa, A.W., Vibration of Shells. NASA SP-288, 1973.
44. Atluri, S., Witmer, E.A., Leech, J.W., and Morino, L., PETROS 3: A Finite-Difference Method and Program for the Calculation of Large Elastic-Plastic Dynamically-Induced Deformations of Multilayer, Variable-Thickness Shells, BRL CR 60 (MIT-ASRL TR 152-2), November 1971.
45. Strickland, W.S., and Ross, C.A., The Plastic Response of Rectangular Membrane Plates to Mild Explosive Loading Functions, Air Force Armament Laboratory, Eglin AFB, AFATL-TR-74-181, November 1974.
46. Pirotin, S.D., Berg, B.A., and Witmer, E.A., PETROS 3.5: New Developments and Program Manual for the Finite-Difference Calculation of Large Elastic-Plastic Transient Deformacions of Multilayer Variable-Thickness Shells. MIT, BRL CR 211, February 1975.
47. Goode, H.H., and Machol, R.E., System Engineering, McGraw-Hill Series in Control Systems Engineering, McGraw-Hill Book. Co. , Inc. , New York, 1957.
48. Plantema, F.J., Sandwich Construction—The Bending and Buckling of Sandwich Beams, Plates and Shells, John Wiley and Sons, Inc., New York, 1966.
49. Kaman AviDyne, Handbook for Analysis of Nuclear Weapon Effects on Aircraft. DNA 2048. KA TR-114. January, 1975 (to be published) .
50. Kaman AviDyne. NOVA — A Digital Computer Program for Calcula- ting the Response of Aircraft to the Overpressure from a Nuclear Weapon. Vol. II. KA TR-87-2, August, 1972.
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