Upload
vuquynh
View
225
Download
5
Embed Size (px)
Citation preview
Institute of Structural Mechanics 1
Virtual Testing of Aircraft Structures, considering Postcritical & Thermal Behavior
J. Teßmer, R. Degenhardt, A. Kling, R. Rolfes, T. Spröwitz, S. Waitz (DLR – Institute of Structural Mechanics, Braunschweig, Germany),
COMPOSIT Thematic Network,Workshop on Modeling and Prediction of Composite Transport Structures
in Zaragoza, Spain, 30.06.2003
Institute of Structural Mechanics 2
Validation / Verification
RealityExperiment
ComputerModel
ModelValidation
ModelQualification
ModelVerification
ComputerSimulation
Analysis
Programming
ConceptualModel
Model Verification:„Solve the equations right“
Model Validation:„Solve the right equations“
Institute of Structural Mechanics 3
Postcritical behavior of stiffened panels
Deformation pattern (ARAMIS)Panel in Buckling Test Facility
Top plate
Clamping box
Specimen
Clamping Box
Displacementpickup
Load distributor
Load cells
Drive plate
Institute of Structural Mechanics 4
Non linear FEM using ABAQUS/Standard
roughestimate
FE-Model
Linear Eigenvalue Analysis
Buckling Load
Nonlinear AnalysisNewton-Raphson-Method + automatic / adaptive
damping to stabilize the analysis (*STATIC, STABILIZE)
scaled imperfektions
Postprocessing(Load-Shortening-Curve, deformation of the structure, ...)
Buckling Modes
Real StructureCFRP-Panel
MeasuredImperfections
roughestimate
FE-Model
Linear Eigenvalue Analysis
Buckling Load
Nonlinear AnalysisNewton-Raphson-Method + automatic / adaptive
damping to stabilize the analysis (*STATIC, STABILIZE)
scaled imperfektions
Postprocessing(Load-Shortening-Curve, deformation of the structure, ...)
Buckling Modes
Real StructureCFRP-Panel
MeasuredImperfections
Institute of Structural Mechanics 5
Numerical Pre-Test Analysis
„Experimental Validatition of computational Analysis is expensive & time consuming“
„Pre-Test Analysis and Pre-Test Planing“
„Validation Experiments“ versus „Phenomenological Experiments“
Goal: Load – Deformation curve showing:- characterristic skin buckling, coupeled with axial stiffness reduction- large load bearing capacity during postbuckling without structural failure
FEA investigation w.r.t.: panel geometriediscretisationexperimental boundary conditionsinitial imperfections...
Institute of Structural Mechanics 6
Pre-Test Analysis 1. Influence of different STABILIZE parameters 2. Investigation of different failure criteria
0
10
20
30
40
50
60
70
80
0 0.5 1 1.5 2 2.5 3 3.5 4
Shortening [mm]
Loa
d [k
N]
STABILIZE = 2e-4
STABILIZE = 2e-5
STABILIZE = 2e-6
STABILIZE = 2e-7
Nominal dataABAQUS/StandardMesh I (3024 elements)
Tsai HillAzzi Tsai Hill Maximum Stress
Tsai Wu
Institute of Structural Mechanics 7
Pre-Test AnalysisConvergence study
0
10
20
30
40
50
60
0 0.5 1 1.5 2 2.5 3 3.5 4Shortening [mm]
Loa
d [k
N]
Mesh I: 3024 elementsMesh II: 2*3024 elementsMesh III: 16*3024 elements
Nominal dataABAQUS/StandardSTABILIZE = 2.e-6
Institute of Structural Mechanics 8
Pre-Test AnalysisInfluence of lateral boundary conditions
0
10
20
30
40
50
60
70
80
90
100
0 0.5 1 1.5 2 2.5 3 3.5 4
Shortening [mm]
Loa
d [k
N]
Covered width = 25.0 mm Covered width = 12.5 mm Only lateral nodes fixed
Nominal dataABAQUS/StandardSTABILIZE = 2.e-6Mesh I (3024 elements)
Edge support
Filler
Gliding plane
Test panel
Detail
Institute of Structural Mechanics 9
Pre-Test AnalysisInfluence of imperfections
0
10
20
30
40
50
60
0 0.5 1 1.5 2 2.5 3 3.5 4
Shortening [mm]
Loa
d [k
N]
No imperfectionsMode 1, 2% skin thicknessMode 1, 10% skin thicknessMode 1, 100% skin thickness
Nominal dataSTABILIZE = 2.e-6Mesh I (3024 elements)
Institute of Structural Mechanics 10
Pre-Test AnalysisABAQUS/Standard vs. ABAQUS/Explicit
0
10
20
30
40
50
60
0 0.5 1 1.5 2 2.5 3 3.5 4
Shortening [mm]
Loa
d [k
N]
ABAQUS/Standard, STABILIZE = 2e-6
ABAQUS/Explicit, v=10mm/s, no damping
ABAQUS/Explicit, v=10mm/s, with damping
Nominal dataMesh I (3024 elements)
Institute of Structural Mechanics 11
Measurement of geometrical Imperfections (1)Optical 3D - digitalization
ATOS – Sensor strip sequenz
4 Measurment of real radius vs. nominal radius (ca. 6% deviation)
4 Measurement of initial imperfection
Institute of Structural Mechanics 12
Measurement of geometrical Imperfections
Data points (ASCII-Format):
1093.6441 211.5491 1.6805
1093.1718 211.1541 1.6764
1093.8102 210.6003 1.6764
1093.0879 210.3660 1.6910
…
Modification of „perfect“ FE – geometry
Application of initial imperfection
Fringe – plot w.r.t.perfect shell
Institute of Structural Mechanics 13
Results of FEA using ABAQUS/Standard
0
0,5
1
1,5
2
2,5
0 0,5 1 1,5 2 2,5 3 3,5 4
Skalierte Verschiebung
Ska
lierte
Las
t
ABAQUS/Standard ohne Imperfektionen
ABAQUS/Standard mit Imperfektionen
Lokal skin buckling
Global „unsymmetric“ Buckle
Global „symmetric“Buckle
Institute of Structural Mechanics 14
Validation of FEA (Animation)
Institute of Structural Mechanics 15
Validation of computational results
„Globale“ Ebene
0
0,5
1
1,5
2
2,5
0 0,5 1 1,5 2 2,5 3 3,5 4Skalierte Verschiebung
Skal
ierte
Las
t
Experiment (1)Experiment (2)ABAQUS/Standard mit Imperfektionen
Institute of Structural Mechanics 16
Validation of computational results
-10
-5
0
5
10
15
20
25
0 0,5 1 1,5 2 2,5 3
Skalierte Verschiebung
Rad
ialv
ersc
hieb
ung
[mm
]
Wegaufnehmer W88
Knoten 40696; entspricht W88 Position
Wegaufnehmer W89
Knoten 46666; entspricht W89 Position
Wegaufnehmer W90
Knoten 52636; entspricht W90 Position
Wegaufnehmer W91
Knoten 58606; entspricht W91 Position
„Lokale“ Ebene
W88W89W90
W91
Institute of Structural Mechanics 17
direct Sun Radiation
thermal Radiation
Reflected Sun Radiation
Cross SectionFuselage
InsideOutside
Time
Tem
pera
ture
Taxiing Stop Take Off
Thermal ProblemFML’s in future aircraft structures
Institute of Structural Mechanics 18
Modeling (on panel level)
Institute of Structural Mechanics 19
Model Verification4 Convergence study with 6 different
discretisations (1 to 36 elements in thickness direction)
4 Homogenisation of smeared layers with:
_ ,
_ ,
/ ( / ) ,
( ) / .out plane i i i normali i
in plane i plane i ii i
k t t k
k k t t
=
= ⋅
∑ ∑∑ ∑
345
350
355
360
365
370
375
380
-2,70
Thickness-Coordinate of skin (mm)
Tem
pera
tur
(K)
layered skin
smeared homogenous skin
Institute of Structural Mechanics 20
Experimental Test in THERMEX – B test site
Infrared Radiator
Isolation (optional)
Skin
Water
Frame
Stringer
Institute of Structural Mechanics 21
Validation
20
30
40
50
60
70
0 2000 4000 6000 8000 10000
Zeit (sec)
Tem
pera
tur (
°C) MP43/TE43
MP43_RF1MP34/TE04MP34_RF1MP24/TE09MP24_RF1
Experiment vs. Computation
Institute of Structural Mechanics 22
Modeling of large fuselage structure
Institute of Structural Mechanics 23
2D Finite Elements for Thermal Analysis of FML‘s
Motivation
4 Reduction of modeling effort by using 2D geometrical models
4 Reduction of CPU-time
4 Compatible temperature field for thermo-mechanical calculations
Scientific Challenge
4 3D temperature field description based on 2D geometry
4 Shape functions in z-direction
4 2D-3D-Coupling (Connection to local 3D meshes)
Institute of Structural Mechanics 24
Layerwise Thermal Lamination Theories
Composite structures
3D temperature distribution by 2D finite elements
• Idealisation as layered structure
• Homogenisation of layers including heat conduction, radiation, convection
zt
t
z +d-z
z
N
z=0
11
k
k kk
b
1
k2
•Linear Layered Theory (LLT)
• Quadratic Layered Theory (QLT)
T
T
T
0
0,z
(k)
(k)
(z)Hybrid composite structures
Aluminum sheet
Fiber/resin
Sandwich structuresFace sheet
Honeycombcore
Institute of Structural Mechanics 25
Assumptions and Prerequisites
convection
conduction
radiation
radiation
equivalent thermal conductivity
conductionconvection
homogenisation
N
12k
b
t1
tk
z
z = 0
z1
zk +dk -zk
approximation by layered construction4 perfect thermal contact at interfaces
4 monolithic conduction within layers
4 no internal heat sources
4 temperature independent material properties
Institute of Structural Mechanics 26
FE-Formulation(Weak form for heat conduction)
( ) 0ddd =Ω+Γ+Ω ∫∫∫ΩΓΩ
vTvnqTKv ρcgradgrad TT
Boundary conditions
- Convection (Robin)
- Heat flux density (Neumann)
q
q T Tc c= - •a Wandb g
q nT cq q= +
FE-FormulationWeak form for heat conduction
Institute of Structural Mechanics 27
FE-Formulation(Weak form for heat conduction)
h r a h r h r
a h
T T
zAc
T T T T
zA
cT T
z A c z A
T q
S KS R R R R
R
d d d d d
d
zz z zz
z
+ +
= -•
G
G
G
G
b g
K S KS
S K S
=
=
zz +
=
T
z
k T k k
z
z
k
N
z
zk
k
d
db g b g b ge j1
1
Composite-heat-conduction-matrix Composite-heat-capacity-matrix
( )
C R R
R R
=
=
zz +
=
c z
c z
T
z
k kk T k
z
z
k
N
k
k
d
dr c h b g1
1
FE-FormulationWeak form for heat conduction
Institute of Structural Mechanics 28
Example: 3D vs. 2D FEA
Number of 3D-elements: 2
Number of 3D-elements: 36
Number of 2D-elements: 1
GLARE skin with 3D finite elements (Nastran)
345
350
355
360
365
370
375
380
-2,70
Thickness-Coordinate of skin (mm)
Tem
pera
tur
(K)
layered skin
smeared homogenous skin
Thermal Lamination Theory (QLT)
Institute of Structural Mechanics 29
Summary4 Experimental data basis for validation of non linear FEA w.r.t. postbuckling of
stiffened shells under axial loading
4 Investigation of sensitivity w.r.t. to different modeling parameters
4 Excellent agreement between experimental and computational results deep into elastic postcritical regime (global & local)
4 Reliable thermal analysis of FML structures by verification of discretisation through fine 3D model on panel level
4 Validation of thermal panel model by experiments in THERMEX – B test site
4 Application of thermal model to large fuselage structures
4 Description of fast 2D Finite-Element-Formulation
4 Question: How many experiments are needed for validation of a specified parameter space?