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KR0000263 KAERI/TR-1584/2000 m<n\ me Assessment for Hydrodynamic Masses of HANARO Flow Tubes Korea Atomic Energy Research Institute

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KR0000263

KAERI/TR-1584/2000

m<n\ m eAssessment for Hydrodynamic Masses of HANARO

Flow Tubes

Korea Atomic Energy Research Institute

Please be aware that all of the Missing Pages in this document wereoriginally blank pages

(Assessment for Hydrodynamic Masses of HANARO Flow Tubes)

2000^ 6-H 20

(Post-Doc.)

(KALIMER

- 1 -

consistent

(lumped) ^

- 11 -

Abstract

The effect of hydrodynamic masses is investigated in dynamic characteristics

and seismic response analyses of the submerged HANARO hexagonal flow tubes.

Consistent hydrodynamic masses of the surrounding water are evaluated by the

prepared program using the finite element method, in which arbitrary

cross-sections of submerged structures and boundary conditions of the surrounding

fluid can be considered. Also lumped hydrodynamic masses are calculated using

simple formula applied to hexagonal flow tubes in the infinite fluid.

Modal analyses and seismic response spectrum analyses were performed

using hydrodynamic masses obtained by the finite element method and the simple

formula. The results of modal analysis were verified by comparing the results

measured from modal tests. And the displacement results of the seismic response

spectrum analysis were assessed by comparing the consistent and the lumped

hydrodynamic masses obtained by various methods. Finally practical criteria based

on parametric studies are proposed as the lumped hydrodynamic masses for

HANARO flow tubes.

iL < £- ii

Abstract iii

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^r^ II. User's Manual t Hydrodynamic_Mass 46

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- 22 -

[I] ^-3*r, "HANARO $!&& ^ - # # ^ S^f* « g <*/#", KAERVTR-595/95,fb^€*r3<?!^, 1995.5.

[2] S.S. Chen and H. Chung, "Design Guide for Calculating Hydrodynamic Mass;Part I: Circular Cylindrical Structures", ANL-CT-76-45, Argonne NationalLaboratory, Argonne, IL, 1976.

[3] H. Chung and S.S. Chen, "Design Guide for Calculating Hydrodynamic Mass;Part II: Non-Circular Cylindrical Structures", ANL-CT-78-49, ArgonneNational Laboratory, Argonne, IL, 1978.

[4] R.D. Blevins, Formulas for Natural Frequency and Mode Shape, Van NostrandReinhold Company, New York, NY, 1979.

[5] J.F. Loeber, "Consistent Hydrodynamic Mass for Parallel Prismatic Beams ina Fluid-Filled Container", KAPL-4170, Knolls Atomic Power Laboratory,Schenectady, NY, 1983.

[6] ^ S l , 3*H^, ^ 8 * r , °*W£. «?£.S#SMM/ XJ-&&? # # " ,KAER1/RR-1810/97, t H ^ ^ H W ^ , 1998.1.

[7] S.S. Chen, M.W. Wambsganss, and J.A. Jendrzejczyk, "Added Mass andDamping of a Vibrating Rod in Confined Viscous Fluids", Trans. ASME 98;J. Appl. Mech. 43, 325-329, 1976.

[8] G.G. Stokes, "On Some Cases of Fluid Motion", Proceedings of the CambridgePhilosophical Society, Vol. 8, pp.105-137, 1843.

[9] RJ. Fritz, "The Effect of Liquids on the Dynamic Motions of ImmersedSolids", Journal of Engineering for Industry, Vol. 94, 167-173, 1972.

[10] S.S. Chen, "Vibrations of a Row of Circular Cylinders in a Liquid", Journal ofEngineering for Industry, Vol. 97, 1212-1218, 1975.

[II] S. Levy and J.PO.D. Wilkinson, "Calculation of Added Water Mass Effects forReactor System Components", Transactions of the 3rd International Conferenceon Structural Mechanics in Reactor Technology, Paper F2/5, 1975.

[12]J.K. Biswas, A.S. Banwatt, and S.A. Usmanl, "Stress Analysis Interface Datafor the Korea Multipurpose Research Reactor", ACEL 37-31000-200-900,Rev.l, 1993.

- 23 -

I. Program - Hydrodynamic_Mass

- 24 -

main.for

c

cc This program calculates hydrodynamic masses ofc multiple two dimensional structures coupled byc inviscid and incompressible fluid.ccc [ original ]c H. Chung & S.S. Chen (1978)c Design Guide for Calculating Hydrodynamic Massc Part II: Non-Circular Cylindrical Structurescc [ modified ]c - dynamic array allocationc - 4 node rectangular elementsc - general input formatcc Modified by Kim, Doo-Kie & Ryu, Jeong-Sooc November 1999, KAERIcc

program Hydrodynamic_Massc

implicit integer*4 (i-n)implicit real*8 (a-h,o-z)

cc., . dynamic array Ic

parameter (mbyte=15*1000*1000,mtot=mbyte/4)common maxm,np,ma(mtot)common /dbsys/ numa,next,idir, ip(4)

ccharacter title»80

common /sys/ ior,iowcc... dynamic array IIc

maxm = mtotnuma = 0next = 1idir = mtot

call izero (ma,mtot)cc... i/o filesc

ior = 7iow = 6call openfile (l,ior)call openfile (2,iow)

cc... control datacc nbodyc nnodec nelemc rhoc

read(ior,'(a,/)') title

# of structures# of nodes# of FE's for fluidfluid density

- 25 -

read(ior,*) neltype,nbody,nnode,nelem,nbound, rho

write(iow, '(a,/)') title

cc.c

cc.c

cc.cc

cc.cc

cc.c

cc.c.c.c

write(iow, *)write(iow,*)write(iow,*)write(iow,*)write(iow, *)write(iow,*)write(iow, *)

-> INPUT <-# of element type ='# of bodies'# of nodes'# of elements ='# of boundaries ='Fluid density

,neltype,nbody,nnode,nelem,nbound

= ',rho

assign array

call defini Cnnbccall defini Ckodecall defini Cibound—call defini ('iconn—call defini ('inumtype

,innbc, nbody,1),ikode, nnode, 1),iibound,nbody,nnode*2),iiconn,nelem,neltype),inumtype,nelem,neltype)

callcallcallcallcallcallcallcall

read data

define ('area—define Cppdefine ('xxdefine (':define C x k K —define Cxkdefine ('coord-define ('addms-

,iarea,nelem,1),ipp,nbody*2,nnode),ixx,nbody*2,nnode),ix,nnode,1),ixkk,nnode,nnode),ixk,nnode,nnode),icoord, nnode,2),iaddms, nbody*2,nbody*2)

call rdata ( neltype, nbody,nnode,nelem, nbound,& ma(innbc),ma(dkode),ma(icoord),ma(iiconn),

& ma(inumtype),ma(iarea),ma(iibound) )

band widthiband : bandwidth of stiffness matrix [xk]

call bandw (iband, neltype,nelem,nnode, ma(iiconn))

stiffness matrix, [xfc][xkk]

— > idx(nnode,iband)— > idx(nnode,iband)

if(neltype.eq.3) thencall stiff3 (neltype,nelem,iband, nnode, rho,

& ma(ixKK),ma(ixK),ma(iarea),& ma(icoord),ma(iiconn))elseif(neltype.eq.4) then

call stiff4 (neltype,nelem,iband,nnode,rho,& ma(ixkk),ma(ixk),

& ma(iccord),ma(iiconn),ma(inumtype))endif

force, {x}

call force ( nbody,nnode,& ma(ix),ma(innbc),ma(iibound),& ma(icoord), ma(ipp))

1) apply BC's2) call system solver3) return x -> xx

call execute ( nbody,nnode,iband.

— > idx(nnode)

- 26 -

& ma(innbc),ma(ipp),ma(ixx),nia(ix),& ma(ixkK),ma(ixlO,ma(:iKode) )

cc... hydrodynamic mass matrix, addms(,)c

call hmass ( nbody,nnode,& ma(ipp),ma(ixx),ma(iaddms) )

cclose(ior)close(iow)

stopend

filcforccc subroutine openfile (ioption,iorw)cc

subroutine openfile (ioption,iorw)c

implicit integer*4 (i-n)logical ef ile, input,outputcharacter infile*12,outfile*12, sign*l, inlst*8,outlst*8

ccc... name = ' input'c = 'output'c

input = ioption .eq. 1output = ioption .eq. 2

cc

if(input) thencc

10 write(*,2000) ' data filename ? : 'infile = 'read'(a)', infileif( infile .eq. ' ' ) goto 10inquire( file=infile, exist=efile )if( efile ) then

open(unit=iorw,file=infile,status='old')else

write(*,9000) ' *** error : cannot find ', infilegoto 10

end ifcall fstname (infile,inlst,*10)

elseif(output) thencc100 write(*,2000) ' output filename ? :

outfile =read'(a)', outfileif( outfile .eq. ' ' ) goto 100inquire( file=outfile, exist=efile)if( infile .eq. outfile ) then

write(*,9000)

— 97 —

& '** error : output filename coincides with input filename.'goto 100

else if( efile ) thenwrite(«,9001) '*** output file exist, overwrite (y/n) ? 'read'(a)', signif( sign.eq.'Y' .or. sign.eq. 'y' ) then

open (unit=iorw,file=outf ile, status='unknown')else

goto 100end if

elseopen(unit=iorw,file=outfile,status='new')

end ifcall fstname (outfile,outlst,*100)

cc

end ifcc

returnc1000 format(tl0,lx,'[l;33m',a,'[l;32m',$)2000 format(tl0,lx,a,$)9000 formatdx,'[l;31m',2a,/)9001 formatdx,' [l;31m', a,' [l;32m' ,$)

endcC***********ss*****ss***sss****ss«****»»**»»»*********«**»*********»*»**

csubroutine fstname (tot_filename,chrlst,*)

cc. find first name from full filename.c. the length of the first name is 8 characters,c

character tot_filename(12)*l, chrlst(8)*lc

do i=l,8chrlst(i) = ' '

end doc

do i=l,12if( tot_filename(i) .eq. '.' ) goto 101

end doc101 if( i .eq. 1 ) return 1

cid = 8jl = i-1do j=jl,l,-l

chrlst(id) = tot_filename(j)id = id-1

end do

returnend

subs.forcc... subroutinescc subroutine rdata

c subroutine bandwc subroutine forcec subroutine hmasscc

subroutine rdata ( neltype, nbody,nnode,nelem,nbound,& nnbc, kode, coord, iconn, numtype, area, abound )

cc... read inputsc

implicit integer*4 (i-n)implicit real*8 (a-h,o-z)

character macro*15dimension nnbc(nbody),xx(neltype),yy(neltype),& Kode(nnode),coord(nnode,2),& iconn(nelem,neltype),area(nelem),& ibound(nbody,nnode,2),numtype(nelem)common /sys/ ior,iow

cc.c.c. read analysis datac.cc. macro cardc

1 continueread(ior,'(al5,5i5)') macro

cc. control cardsc

if( macro .eq. '*node ' ) thendo K=l,nnode

read(ior,«) i,coord(i,l),coord(i,2)end dogoto 1

else if( macro .eq. '*felem ' ) thendo k=l,nelem

read(ior,») i,nuratype(i),(iconn(i, j),j=l,numtype(i))end dogoto 1

else if( macro .eq. '*fe-boundary ' ) thendo k=l,nbound

read(ior,») i,Kode(i)end dogoto 1

else if( macro .eq. '*fe-force ' ) thengoto 100

end ifcccccccccc

todeO :

s

coord(,):

iconn(,)

nnbcO :

BC'sl(Dirichlet)O(Neuman)coordinates

: connectivity

# of Neuman BC's

—> idx(nnode)

—> idx(nnode, 2)

—> idx(nelem,neltype)

—> idx(nbody)

100 continueread(ior,«) (nnbc(j),j=l,nbody)

c

- 29 -

cc...cc

cc

area & centroidarea() : area of a element — > idx(nelem)iconn(f) : connectivity — > idx(nelem,3)

do i=l,nelem

&

&&&

do j=l,neltypeix=iconn(i,j)xx(j)=coord(ix,l)yy(j)=coord(ix,2)

end doif(neltype.eq.3) then

area(i) = ( (xx(2)-xx(l))»(yy(3)-yy(D)-(xx(3)-xx(l))*(yy(2)-yy(D) ) /2.0d0

elseif(neltype.eq.4) thenarea(i) = ( (xx(2)-xx(l))*(yy(4)-yy(i))

-(xx(4)-xx(l))*(yy(2)-yy(l)) ) /2.0d0+ ( (xx(2)-xx(4))*(yy(3)-yy(4))

-(xx(3)-xx(4))»(yy(2)-yy(4)) ) /2.0d0end if

end do

do ibody=l,nbodynbc=nnbc(ibody)do n=l,nbc

readdor,*) i,ibounddbody,i, 1),abound(ibody,i,2)end do

end do

returnend

c

Csidjroutine bandw (iband, neltype,nelem,nnode,iconn)

cc . . . band widthc

implicit integer*4 (i-n)implicit real*8 (a-h,o-z)dimension iconn(nelem,neltype)common /sys/ ior,iow

ciband = 0do i=l,nelemdo j=l,neltype

ix=iconn(i,j)if(ix.le.nnode .and. ix.ne.O) then ! 4 + 3 nodes

do jj=l,neltypeixx=iconn(i,jj)if(ixx.lt.ix .and. ixx.ne.0) then ! 4 + 3 nodes

iband = maxO(iband, ix-ixx)end if

end doend if

end doend doiband = iband + 1write(iow,«) '# of band width = '.iband

creturnend

- 30 -

ccc

subroutine force ( nbody,nnode,& x,nnbc,ibound, coord, pp)

cc... force, {x} — > idx(nnode)c

implicit integer»4 (i-n)implicit real*8 (a-h,o-z)dimension x(nnode),nnbc(nbody),coord(nnode,2),& ibound(nbody,nnode,2), pp(nbody*2,nnode)common /sys/ ior,iow

cdo ibody=l,nbody

nbc=nnbc(ibody)c

do ixy=l,2 ! x,y directionsir=(ibody-1)*2+ixy

cdo inode=l,nnode

x(inode)=0.0d0end do

cdo inbc=l,nbc

inode=ibound(ibody,inbc,1)jnode=ibound(ibody,inbc,2)xi =coord(inode, 1)yi =coord(inode,2)xj =coord(jnode, 1)yj =coord(jnode,2)

cxleng=sqrt( (xj-xi)*»2 + (yj-yi)**2 )

cc... unit accelerationc

if(ixy.eq.1) thenacc= (yj-yi)Zxleng

elseacc=-(xj-xi)/xleng

end ifx(inode) = x(inode) + 0.5*acc*xlengx(jnode) = x(jnode) + 0.5*acc*xleng

end doc

do inbc=l,nbcinode=ibound(ibody,inbc, 1)jncde=ibound(ibody,inbc,2)pp(ir,inode)=x(inode)pp(ir,jnode)=x(jnode)

end doend do

end doc

returnend

ccc

subroutine hmass ( nbody,nnode, pp,xx,addms )cc... hydrodynamic mass matrix, addms(,)c 1. consistent, 2. lumped

- 31 -

implicit integer*4 (i-n)implicit real*8 (a-h,o-z)dimension pp(nbody*2,nnode)>xx(nbody*2,nnode),& addms(nbody«2,nbody*2)common /sys/ ior,iow

cdo i=l,nbody»2

do j=l,nbody*2sum = 0.OdO

do k=l,nnodesum = sum + xx(i,k)*pp(j,k)

end do ! pressure*forceaddms(i,j)=sum

end doend do

cc... check

ibody = 1nbc=24

do inbc=l,nbcinode=ibound(ibody,inbc, 1)write(iow,'(4(e20.7,5x))')

& (pp(ir,inode),ir=l,l),(xx(ir,inode),ir=l,l)end do

write(iow,'(///,a)') ' > OUTPUT (I) <-write(iow,*) 'hydrodynamic mass matrix : consistent 'writeUow,' (5x, 100(lx, i8,a))') (i, V , i, 'y',i=l,nbody)

cdo j=l,nbody

write(iow,'(i4,a,100(fl0.2))') j,'x',& (addms(i,2*j-l),i=l,nbody*2)

write(iow,'U4.a,100(fl0.2))') j,'y\& (addms(i,2*j),i=l,nbody*2)

end doc

writeUow.'(///.a)') ' > OUTPUT (II) < 'write (iow,*) 'hydrodynamic mass matrix : lumped 'writeUow,' (5x,100(lx,i8,a))') (i, 'x' ,i, 'y' ,i=l,nbody)

cc... diagonalizedc

do j=l,nbodysum_x = O.OdOsum_y = O.OdO

do i=l,nbody«2sum_x = sum_x + addms(i,2*j-l)sum_y = sum_y + addms(i,2»j)addms(i,2*j-l) = O.OdOaddms(i,2*j) = O.OdO

end doc

do i=l,nbody*2if( (2»j-l).eq.i ) addms(i,2«j-l) = sum_xif( (2*j) .eq.i ) addms(i,2*j) = sum_y

end doc

writeUow,' (i4,a,100(fl0.2))') j , ' x ' ,& (addms(i,2*j-l),i=l,nbody*2)

write(iow,'(i4,a,100(f!0.2))') j , ' y \

- 32 -

& (addms(i,2*j),i=l,nbody*2)end do

creturnend

execute, for

c

csubroutine execute ( nbody,nnode,iband,

& nnbc,pp,xx,x,xkk,xk,kode )cc... {pp} = [xkk] {xx}c {x} = [xk] {x}cc... 1) apply BC'sc... 2) call system solverc... 3) return x -> xxc

implicit integer*4 (i-n)implicit real*8 (a-h,o-z)dimension nnbc(nbody),pp(nbody*2,nnode),& xx(nbody*2,nnode),x(nnode),& xldc(nnode, nnode), xk(nnode, nnode), kode(nnode)common /sys/ ior,iow

cc

do ibodv=l,nbodynbc=nnbc(ibody)

cdo ixy=l,2

ir=(ibody-l)*2+ixyc

do i=l,nnodex(i)=pp(ir,i)

end doc

do i=l,nnodedo j=l,iband

xk(i,j)=xkk(i,j)end doend do

cc. ., apply BC'sc

call appbc ( nnode, iband, Rode, xk, x )cc... call system solverc returned 'x' is approximate solution for pressure at nodal pointc

call symsoKxk, x, nnode, iband)cc... return x -> xxc

do ix=l,nnodexx(ir,ix)=x(ix)

end doend do

cc... screen check

- 33 -

cif(ibody.eq.l) thenwrite(*,95) ' computing # of nbody = '. ibody,'/', nbody

95 format(2(a,i3))else

vn-ite(«,100) ' computing # of nbody = '.ibody,'/'.nbody100 format(r+',2(a,i3))

endifc

end doc

returnend

c

csubroutine appbc ( nnode,iband, kode,xk,x )

cc... apply BC'sc

implicit integer*4 (i-n)implicit real*8 (a-h,o-z)dimension kode(nnode),xk(nnode,nnode),x(nnode)common /sys/ ior.iow

cdo inode=l,nnode

if(kode(inode).ne. 0) thendo m=2, iband

k=inode-m+lif(k.gt.O) then

xk(k,m)=0.0end ifk=inode+m-lif(k.le.nnode) then

xk(inode,m)=0.0end if

end doxk(inode,l)=1.0x(inode)=0.0

end ifend do

creturnend

subroutine symsol (a,b,nn,mm)cc... band solver by Gaussian eleminationc

implicit integer*4 (i-n)implicit real*8 (a-h,o-z)dimension a(nn,mm),b(nn)dimension c(nn)

cc

do n=l,nnc... devide right side by diagonal element

b(n)=b(n)/a(n,l)c... devide n-th equation by diagonal element

do k=2,mmc(k)=a(n,k)

- 34 -

a(n,k)=a(n,k)/a(n,l)end do

c... reduce remaining equationdo 1=2,mminllif((nn-i).ge.0) thenj=odo k=l,mm

3=3+1a(i,j)=a(i,j)-c(l)*a(n,k)

end dob(i)=b(i)-c(l)*b(n)

end ifend do

end docc... back substitution300 do nl=n-l,0,-l

c. .. calculate unknown b(n)do k=2,mm

l=nl+k-lif((nn-l).ge.0) then

b(nl)=b(nl)-a(nl,k)*b(l)end if

end doend do

returnend

stiff3.forc

csubroutine stiff3 (neltype,nelem,iband,nnode,rho,

& xkk, xk, area, coord, iconn)cc 3-node triangler elementc... stiffness matrix, [xk] — > idx(nnode, iband)c [xkk] — > idx(nnode,iband)c

implicit integer*4 (i-n)implicit real*8 (a-h,o-z)dimension xkk(nnode,nnode),xk(nnode,nnode),& area(nelem),coord(nnode,2),iconn(nelem, neltype)common /sys/ ior,iow

cc

call rzero2 (xkk,nnode,iband)call rzero2 (xk,nnode,iband)

cdo iel=l,nelem

a=area(iel)/rho ! /rhodo i=l,neltype

ir=iconn(iel, i)Bix=Bmtx(iel, i, 1, neltype, nnode, nelem, coord, iconn) !BixBiy=Bmtx(iel, i,2, neltype, nnode, nelem, coord, iconn) !Biydo j=l,neltype

jc=iconn(iel, j)jd=jc-(ir-l)if(jd.ge.l) then

- 35 -

Bjx=Bmtx(iel,j,l, neltype,nnode,nelem,coord,iconn) !BjxBjy=Bmtx(iel,j,2, neltype,nnode,nelem,coord,iconn) !Bjy

c... assemblagexfc(ir,jd) =xk(ir,jd) + (Bix«Bjx+Biy*Bjy)«axkk(ir,jd) = xk(ir,jd)

end ifend do

end doend do

cc

returnend

function BmtxUel, jnode.ixy, neltype,nnode,nelem,coord,iconn)cc... derivatives of interpolating functionc at i-th element in j-th nodec

implicit integer*4 (i-n)implicit real*8 (a-h,o-z)dimension ccord(nnode,2),iconn(nelem,neltype)

cc

12 = mod(jnode,neltype) + 113 = mod(jnode+l,neltype) + 1

c11 = iconn(iel,jnode)12 = iconn(iel,i2)13 = iconn(iel,i3)

cc

xl = coord(il,l)yl = coord(il,2)x2 = coord(i2,l)y2 = coord(i2,2)x3 = coord(i3,l)y3 = coord(i3,2)

cif(neltype.eq.4) then

i4 = mod(jnode+2,neltype) + 1i4 = iconn(iel,i4)x4 = coord(i4,l)y4 = coord(i4,2)

end ifcc

if(neltype.eq.3) thendlt=( (x2-xl)*(y3-yl) - (x3-xl)*(y2-yl) )/2.0D0if(ixy.eq.l) then

Bmtx =-(y3-y2)/(dlt*2.0D0)return

elseBmtx = (x3-x2)/(dlt*2.0D0)return

end ifelseif(neltype.eq.4) thendlt=( (x2-xl)»(y3-yl) - (x3-xl)«(y2-yl) )/2.0D0if(ixy. eq.l) then

Bmtx =-(y3-y2)/(dlt*2.0D0)return

- 36 -

elseBmtx = (x3-x2)/(dlt*2.0DO)return

end ifend if

cc

end

stiff4.forccc

subroutine stiff4 (neltype,nelem,iband,nnode,rho,& xkk, xk,coord, iconn, numtype)

cc 4-node rectangular elementc... stiffness matrix, [xk] — > idx(nnode,iband)c [xkk] — > idx(nnode, iband)c

implicit integer*4 (i-n)implicit real*8 (a-h,o-z)dimension xkK(nnode,nnode),xk(nnode,nnode),& coord(nnode,2),iconn(nelem, neltype),numtype(nelem)common /sys/ ior,iow

c... temporarydimension elc(neltype, neltype), ecoord(neltype, 2),& xi(neltype,2),w(neltype)

cc

call rzero2 (xkk,nnode,iband)call rzero2 (xk,nnode,iband)

ccall setint (neltype,xi,w)

cdo iel=l,nelem

call rzero2 (ecoord,neltype,2) ! coordinatescall rzero2 (ek,neltype,neltype) ! ele stiffness mtx

cif(numtype(iel).eq.4) then ! 4-node

cc

do i=l,neltypeinode=iconn(iel, i)ecoord(i,l)=coord(inode, 1)ecoord(i,2)=coord(inode, 2)

end docall elem4 (ek, iel,neltype, ecoord,xi,w,rho)

cc... assemblagec

do i=l,neltypeir=iconn(iel,i)do j=l,neltype

jc=iconn(iel,j)jd=jc-(ir-l)if(jd. ge. 1) then

xk(ir,jd) = xk(ir,jd)xkk(ir,jd) = xk(ir, jd)

end ifend do

— T7 _Of

end docc

elseif(numtype(iel).eq.3) then ! 3-nodecc

do i=i,3inode=iconn(iel,i)ecoord(i,1)=coord(anode,1)ecoordU, 2)=coord(inode, 2)

end doc

area3 = ( (ecoord(2,l)-ecoord(l,l))*(ecoord(3,2)-ecoord(l,2))& -(ecoord(3,l)-ecoord(l,i))»(ecx)ord(2,2)-ecoord(l,2)))& / 2.OdO / rho

cc... assemblagec

do i=l,3ir=iconn(iel,i)Bix=Bmtx(iel,i,l, 3,nnode,nelein,coord, iconn) !BixBiy=Bmtx(iel,i,2, 3,nnode,nelem,coord, iconn) !Biydo j=l,3

jcFiconn(iel,j)()jj

if(jd.ge. 1) thenBjx=Bmtx(iel,j,l, 3,nnode,nelem,coord,iconn) !BjxBjy=Bmtx(iel,j,2, 3,nnode,nelem,coord,iconn) !Bjyxk(ir,jd) = xk(ir,jd) + (Bix«Bjx+Biy*Bjy)»area3xkk(ir,jd) = xk(ir,jd)

end ifend do

end do

cc

c

cc—c

c

c

c

end ifend do

returnend

subroutine s

implicitimplicit

setint (ngpnt,xi,w)

integer*4 (i-n)real*8 (a-h,o-z)

dimension xi(ngpnt,2),w(ngpnt)

xi(l,l)xi(2,l)xi(3,l)xi(4,l)xi(l,2)xi(2,2)xi(3,2)xi(4,2)

w(i)w(2)w(3)w(4)

=-1.= 1.= 1.=-1.=-1.=-1.= 1.= 1.

= 1,= 1.= 1,

/sqrt(3.)/sqrt(3.)Vsqrt(3.),/sqrt(3.),/sqrt(3.),/sqrt(3.),/sqrt(3.),/sqrt(3.)

- 3 8 -

returnend

c

csubroutine elem4 (eK, iel,neltype,ecoord,xi,w,rho)

cimplicit integer*4 (i-n)implicit real»8 (a-h,o-z)

cdimension ek(neltype,neltype),ecoord(neltype, 2),& xi(neltype,2),w(neltype)dimension Zmtx(2,2),Gmtx(2,2), Bmtx4(2,neltype)dimension psi(neltype),Dpsi(2,neltype)

cc... for each Gauss pointc

do igpnt=l,neltypecall shape(neltype, xi,igpnt, psi.Dpsi) ! Cook [6.3.13]do i=l,2do j=l,2

Zmtx(i,j) =0.0do k=l,neltype

Zmtx(i,j) = Zmtx(i.j) + Dpsi(i,k)«ecoord(k,j) ! Cook [6.3.12]enddo

enddoenddo

cc

detJ = Zmtx(l,l)*Zmtx(2,2) - Zmtx(l,2)*Zmtx(2,l) ! Cook [6.3.15]if(detJ.le.O.) then

write(iow,») 'Negative Jacobian, element § = ',ielstop

end if

c ! Cook [6.3.14]c

Gmtx(l,l) = Zmtx(2,2)/deUGmtx(l,2) = -Zmtx(l,2)/detJGmtx(2,2) = Zmtx(l,i)/detJGmtx(2,l) = -Zmtx(2,l)/detJ

cc... d(psi)/dx ! Cook [6.3.8]c

do i=l,2do j=l,neltypeBmtx4(i,j) = O.dO

do k=l,2Bmtx4(i,j) = Bmtx4(i,j) + Gmtx(i,k)*Dpsi(k, j)

end doend doend do

cc... integration ! Cook [6.3.5]c

fac = deU*w(igpnt)/rhodo i=l,neltypedo j=l,neltype

do k=l,2ek(i,j) = ek(i,j) + fac*Bmtx4(k,i)*Bmtx4(k, j)

end doend do

end do

- 39 -

end doc

returnend

cc

subroutine shape(neltype, xi,igpnt,psi,Dpsi)implicit integer*4 (i-n)implicit real*8 (a-h,o-z)dimension psi(neltype),Dpsi(2,neltype),xi(neltype,2)

cc four node LINEAR shape function ! Cook [6.3.2]c

psi(l)= .25*(l.-xi(igpnt,l))*(l.-xi(igpnt,2))psi(2)= .25*(l.+xi(igpnt,l))*(l.-xi(igpnt,2))psi(3)= .25*(i.+xi(igpnt,l))*(l.+xi(igpnt,2))psi(4)= .25*(l.-xi(igpnt,l))*(l.+xi(igpnt,2))

cc.... derivatives of shape function ! Cook [6.3.6]

_. J = -.25*(l-xi(igpnt,2))Dpsi(l,2) = .25*(l-xi(igpnt,2))Dpsi(l,3) = .25*(l+xi(igpnt,2))Dpsi(l,4) = -.25»(l+xi(igpnt,2))Dpsi(2,l) = -.25*(l-xi(igpnt,D)Dpsi(2,2) = -.25*(l+xi(igpnt,D)Dpsi(2,3) = .25*(l+xi(igpnt,l))Dpsi(2,4) = .25*(l-xi(igpnt,l))

returnend

arr-iy forccaaaa*a*aa*a*aat***taa*aaaasaaaataa**aaaaaa*aaaataa***aa******xasaaa****C

subroutine defin (name,na,nr,nc)c.

c.c. defin

c.c. purpose : define and reserve storage for array.c.c. arguments :c.c. name = name of array ( 8 character maximum ).c. na = location of array in blank common.c. nr = number of rows.c. nc = number of columns.c.c. variables :c.c. mtot = end of directory.c. numa = number of arrays in data base.c. next = next available storage location.c. idir = start of directory in blank common.c. ip() = (number of bytes)/4 contained in data type.c ip(l) = 1

- 40 -

c. ip(2) = 1c. ip(3) = 2c. ip(4) = 4c.c. lenr = number of logicals in physical record.c. np = type of datac. = 1 integer datac. = 2 single real datac. = 3 integer real or single complex datac. = 4 integercomplex datac.c. : directory definition for core.c.c. idir(l,n) = name of array - iname (8 char.)c. idir(9,n) = number of rows - nrc. idir(10,n) = number of columns - ncc. idir(ll,n) = type of data - npc. idir(12,n) = incore address - nac. idir(13,n) = size of array (nsize)c. idir(14,n) = 0 if in core storagec.c.c.

implicit integer*4 (i-n)character name(8)*lcommon mtot, np, ia (1)common /dbsys / numa,next,idir,ip(4)

cc if first, initialize parametersc

if( numa .eq. 0 ) thennext = 1idir = mtotip(l) = 1ip(2) = 2ip(3) = 2ip(4) = 4

endifcc.... evaluate storage requirementsc

nsize = (nr*nc) * ip(np)na = nextnext = next + nsize

cc set up new directoryc

numa = numa + 1idir = idir - 14

cc.... check storage limitsc

if( idir .It. next ) thenid = next - idir + mtot - 1write («,2000) id,mtotstop

end ifc

call icon (name,ia(idir))c

ia(idir+8) = nria(idir+9) = ncia(idir+10) = np

- 41 -

ia(idir+ll) = naia(idir+12) = nsizeia(idir+13) = 0

creturn

cc.... format.c2000 format(/lx,

& '*** error (defin) : insufficient in core memory.',&//,' storage required (integer type) =',i8,& /,' storage available (integer type) =',i8)end

cc***********************************************************************c

subroutine defini (name,na,nr,nc)c.c... integer type (4 bytes),c.

implicit integer»4 (i-n)character name(8)*lcommon mtot.np, ia(l)

cnp = 1call defin (name,na,nr,nc)returnend

cc*************************************************s********s************c

subroutine define (name,na/nr,nc)c.c... double precision real type (8 bytes),c.

implicit integer *4 (i-n)character name(8)*lcommon mtot, np, ia (1)

cnp = 2call defin (name,na,nr,nc)returnend

cc»*is*******************************************************************c

subroutine define (name,na,nr,nc)c.c... double precision complex type (16 bytes),c.

implicit integer*4 (i-n)character name(8)*1common mtot,np, ia(1)

cnp = 4call defin (name,na,nr,nc)returnend

cexxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxc

subroutine delete (name)c.

- 42 -

c... delete array from storage,c.

implicit integer*4 (i-n)character name(8)*ldimension iname(8)common mtot, np, ia(l)common /dbsys / numa,next,idir,ip(4)

cc100 call icon (name.iname)

id = ifind(iname, 0)if( id .eg. 0 ) return

cc.... check on storage location,c

nsize = ia(id+12)cc.... set size of array,c

next = next - nsizenuma = numa - 1na = ia(id+ll)

cc.... check wether the deleyed array is the latest or not.c

if( na .eg. next ) thenidir = idir+14return

end ifcc.... compact storage,c

ii = na + nsizennxt = next - 1do 200 j=na,nnxtia(j) = ia(ii)ii = ii + 1

200 continuecc.... compact and update directory.c

nupp = id - idiridir = idir + 14

cnupp = nupp/14do 300 k=l,nupp

ii = id + 13do 250 j=l,14

ia(ii) = ia(ii-14)ii - ii - 1

250 continueif( ia(id+ll) .le. 0 ) go to 300if( ia(id+13) .eg. 0 ) ia(id+ll) = ia(id+ll) - nsize

300 id = id - 14c

return1000 format(/,' name ',4al,' is being used for an',

* ' out of core file',/)end

cC*******************************************************************S*S*c

subroutine icon (name,iname)

-43 -

c.c. icon : convert characters to integer data.c.

implicit integer»4 (i-n)character name(8)*ldimension iname(8)

cdo i = 1,8

iname(i) = ichar( name(i) )end do

creturnend

c

cinteger*4 function ifind (iname,lun)

c.c... find array location.c.

implicit integer*4 (i-n)logical outofcore, thisarraydimension iname(8)common mtot, np, ia(1)common /dbsys / numa,next,idir,ip(4)

c.c. id = starting pointer of the current array.c.

id = idirdo 100 n=l,numa

outofcore = lun .ne. ia(id+13)if( outofcore ) go to 100do 50 j=l,8

thisarray = iname(j) .eq. ia(id+j-l)if( .not. thisarray ) then

id = id + 14go to 100

end if50 continue

ifind = idreturn

100 continuec

ifind = 0c

returnend

matrix.forcc subroutine izero (ia,n)c subroutine rzero (a,n)c subroutine rzero2 (a,na,nb)c subroutine wunit2 (a,na,nb, iorw)c

csubroutine izero (ia,n)

cc. initialize integer vectorc

- 44 -

implicit double precision (a-h,o-z)implicit integer*4 (i-n)dimension ia(n)

do i=l,nia(i) = 0

end doreturnend

c

csubroutine rzero (a,n)

cc. initialize double precision vectorc

implicit double precision (a-h,o-z)implicit integer«4 (i-n)dimension a(n)

do i=l,na(i) = O.OdO

end doreturnend

cc — — — — • — ~ —

csubroutine rzero2 (a,na,nb)

cc. initialize double precision matrixc

implicit double precision (a-h,o-z)implicit integer*4 (i-n)dimension a(na,nb)

do i=l,nado j=l,nb

a(i,j) = O.OdOend doend do

returnend

cC — — — — — — — — — • '

csubroutine wunit2 (a,na,nb,iorw)

cc. write double precision matrix in Ciorw]c

implicit double precision (a-h,o-z)implicit integer*4 (i-n)dimension a(na,nb)

do i=l,nawriteUorw,'(50(5x,fl5.7))') ( a(i,j), j=l,nb

end doreturnend

- 45 -

II. User's Manual 'Hydrodynamic_Mass

- 46 -

IIydrodynamIc_Mass

HydroJMassThis program calculates hydrodynamic masses ofmultiple two dimensional structures coupled byinviscid and incompressible fluid

Data

# : Title (A80)

# ^ f e 4 ^ - 4 £°1 "Control Card" ^ § °J^2r, "Data Set Associated withControl Card" <% ^ £ ) f e DataoJ^-i- ^>4*4 .

[Control Card #1][Data Set Associated with Control Card #1]

[Control Card #2][Data Set Associated with Control Card #2]

[Control Card #??][Data Set Associated with Control Card #??]

SUMMARY of Control Card & Control Paramctcr(s)

Control cards and associated parametersAll data is free-format type.

*system • system parameters*node ' nodal coordinates (x,y)*felem ' element connectivity*fe-boundary - boundary conditions*fe~force - boundary forces

- 47 -

* systemWiLypi1] lubodjj [imuiH [IILILIU] Inbound] [rlio]

neltype : number of element type- 3 = 3-node triangular element- 4 = 4-node rectangular element

nbody : number of bodiesnnode : number of nodesnelem •' number of elementsnbound : number of boundary conditionsrho : fluid density

*npdcWilltaonXi,l)l UoardGJDJ jft Lnnodc]"! line £ J fl-'!

- coord(i,) : i

•felem . . .fil fnumtypeCOJ ficonn(i,)1".'. •':

- i- numtype(i) '• element type

- 3 = 3-node triangular element- 4 = 4-node rectangular element

- iconn(i,) : i^ i^ ^ - i ^ | connectivity

- 48 -

*fc-boundarytil Ik,hlt(i)J A Inbound] rl lint' \'1T.1 SI

- i :- kode(i,) = 1 : fixed

= 0 : free

fc-forcecdhody)] X [iibody] tf J- l7fl

til lwound(ihnly,i,l)] Iihound(ibody,i,?)I

nnbc(ibody) : i b o d y 1 ^ body^l

i : ibody^l^l n 1 ^ ^ ^ i«*||

ibound(ibody,i,l) : vtibound(ibody,i,2) : nfl

- 49 -

m.

- 50 -

### ^r*!5! ?if> 0|7| : 4-node rectangular elements ###'system

4 2 72 48 1 1.0*node

1 0 -6.9282 -1.5 -6.0623 1.5 -6.0624 0 -5.7735 -3 -5.1966 3 -5.1967 -1.25 -5.0528 1.25 -5.0529 0 -4.619

10 -4.5 -4.3311 -2.5 -4.3312 2.5 -4.3313 4.5 -4.3314 -1 -4.04115 1 - 4 . 0 4 116 -3.75 -3.60817 3.75 -3.60818 -6 -3.46419 -2 -3.46420 2 -3.46421 6 -3.46422 -5 -2.88723 -3 -2.88724 3 -2.88725 5 -2.88726 -4 -2.30927 4 -2.30928 -6 -1.73229 6 -1.73230 -5 -1.44331 5 -1.43432 -4 -1.15533 4 -1.13734 -6 035 -5 036 -4 037 4 038 5 039 6 040 -4 1.15541 4 1.15542 -5 1.44343 5 1.44344 -6 1.73245 6 1.73246 -4 2.30947 4 2.30948 -5 2.88749 -3 2.88750 3 2.88751 5 2.88752 -6 3.46453 -2 3.46454 2 3.46455 6 3.464

51 -

5657585960616263646566676869707172

*felen123456789101112131415161718192021222324252627282930313233343536373839404142434445

-3.753.75-11

-4.5-2.52.54.50

-1.25

444444444444444444444444444444444444444444444

1.25-330

-1.51.50

3.3.4.4.AAAA4.5.5.5.5.5.6.6.6.

11234456781011121316171821222528293031343537384041424346474849505153545657585961

608608041041r.33r.33.33r.33619052052196196773062062928

347689111314121619172123252229263130393238353638394643484549515653575558626163646665

8711121514161719202223242526273031323335383637424043454851525556576061626365666768696970

425897101211151816201722242825302734313533444241434247445148505256545761596062656467

- 52 -

464748

444

*fe-boundary37 1

*fe-force24123456789101112131415161718192021222324123456789101112131415161718192021222324

24374147505459645853494640363226231914915202427333929211363125101828344452606770727168635545

414750545964585349464036322623191491520242733372921136312510182834445260677072716863554539

626566

686971

717272

667069

- 53 -

IV.

- 54 -

### ^r^m S f | Ofi^: 4-node rectangular elements ###

—####

— > INPUT <of

of

of

of

of

element type

bodies

nodes

elements

boundariesFluid density

# of

Iroc

lx

ly2x

2y

band width

=

=

==

=

==

lynamic mass matrix :

lx149.40

.00

-204. 82

ly.00

149.40

.00

.00 -204.82

4

2

72

48

1

1.000000000000000

13

consistent

-204.

329.

2x

82

00

52

00

2y.00

-204.82

.00

329.52

- 55 -

V.

- 56 -

!!n

•a ©

& 8ID

. * CNCN (NCNCNCN • vH«f *

VV'i< ' iHTT'i lVtt ' i l ' i (" i ( f ' i< t t TlT'*i<'T'VT''Tl7''7'V"r'V'7<T'T'WVV W'T"r'T''r*i<W'TT'TWT'Y'rYV V

3 oNN«ptoo^wcTtc^cocoococ^o3cou5U3c^Ncscsinincjic\copooio^c^ro^^io^tt*H^^*Hiou30cocoinin*H^H^T*in^o inm<oi2ScococPio\>H>H inm-3-*?3<smmcsci3?5m^i.-tSo t^c-c3ioicooo-5"3 • - O O O O H H oocominmco-H^oococoSSinin -H—• • —n.-<ininn> coco • >*-iv-i • o>O) coco t^c^ cs*0*-<in m -Hvocs • *ioiota . . N M 00 03 T* •«* Ol O\ COCO • -CM 03 00 00 00 05^*"* CO CO CO CO • ««H«-!C^t~CQCQCsN<NN*#*#t~r~ . «H«-tr*-C^lOU?COCOaiCTiQQOpCN*H*H t ^H*HCNU5(Qix oo < O I D H 1 H S I M N N N cocoipioiiiHiiSrtSNN-*'"*?}?} inin^^Hw^f-3 i cocoiniSo)M inm^i^i-(TH?5KNc;4ininSco-«:5 i i i ?3?3

8384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175

29.4-49.9949.99-25.225.2-38.438.4

-74.8974.8955.15-55.15-32.6732.67-42.4342.43-2828

-80.1480.14-60.6360.63-46.6146.61-63.5663.56-3636

-84.8984.89-30.830.8

-69.0269.02-50.9250.92-39.4139.41-89.1789.17-74.1774.17-33.633.6

-55.3555.35-42.8942.89-93.0293.02-79.0379.03-58.0358.03-63.7363.73-83.6283.62-36.436.4

-96.4896.48-46.4546.45-69.1669.16-87.9787.97-74.3374.33-99.699.692.1-92.1-79.2779.27-39.239.2

-50.0850.08-8484

-52.552.5

-102.4102.496.01-96.01-58.1358.13-88.5388.53-63.6463.64

-114.6-114.5-114.5-114.1-114.1-113.7-113.7-112.3-112.3-111.5-111.5-110.7-110.7-110.3-110.3-109.2-109.2-108.6-108.6-108.4-108.4-106.8-106.8-106.7-106.7-106.6-106.6-105-105

-104.3-104.3-103.5-103.5-103-103

-102.5-102.5-101.4-101.4-100.5-100.5-99.5-99.5-98.96-98.96-98.25-98.25-97.84-97.84-97.72-97.72-97.42-97.42-95.59-95.59-95.05-95.05-94.65-94.65-94.42-94.42-93.94-93.94-93.74-93.74-92.53-92.53-91.91-91.91-91.14-91.14-90.13-90.13-90.1-90.1-89.8-89.8-89.53-89.53-88.34-88.34-88.13-88.13-87.98-87.98-87.86-87.86-87.19-87.19-86.64-86.64-86.27-86.27

- 58 -

176 -99.74 -85.7177 99.74 -85.7178 -69.04 -85.37179 69.04 -85.37180 -92.88 -84.99181 92.88 -84.99182 -42 -84.95183 42 -84.95184 -74.33 -84.49185 74.33 -84.49186 -79.51 -83.62187 79.51 -83.62188 -97.08 -83.41189 97.08 -83.41190 -106.3 -83.19191 106.3 -83.19192 -84.58 -82.78193 84.58 -82.78194 -89.55 -81.95195 89.55 -81.95196 -94.43 -81.13197 94.43 -81.13198 -103.1 -80.7199 103.1 -80.7200 -44.8 -80.1201 44.8 -80.1202 -91.77 -78.85203 -86.17 -78.85204 -80.57 -78.85205 -74.97 -78.85206 -69.37 -78.85207 -63.77 -78.85208 -58.17 -78.85209 -52.57 -78.85210 -46.97 -78.85211 46.97 -78.85212 52.57 -78.85213 58.17 -78.85214 63.77 -78.85215 69.37 -78.85216 74.97 -78.85217 80.57 -78.85218 86.17 -78.85219 91.77 -78.85220 -100.4 -78.6221 100.4 -78.6222 -110.1 -78.17223 110.1 -78.17224 -97.42 -76.23225 97.42 -76.23226 -106.5 -75.66227 106.5 -75.66228 -42 -75.25229 42 -75.25230 -94.57 -74231 -44.17 -74232 44.17 -74233 94.57 -74234 -103.7 -73.66235 103.7 -73.66236 -113.6 -72.93237 113.6 -72.93238 -100.4 -71.32239 100.4 -71.32240 -110 -70.59241 110 -70.59242 -39.2 -70.4243 39.2 -70.4244 -97.37 -69.15245 -41.37 -69.15246 41.37 -69.15247 97.37 -69.15248 -106.9 -68.61249 106.9 -68.61250 -116.9 -67.5251 116.9 -67.5252 -103.4 -66.4253 103.4 -66.4254 -36.4 -65.55255 36.4 -65.55256 -113.4 -65.49257 113.4 -65.49258 -100.2 -64.3259 -38.57 -64.3260 38.57 -64.3261 100.2 -64.3262 -109.9 -63.47263 109.9 -63.47264 -120 -61.92265 120 -61.92266 -106.5 -61.46267 106.5 -61.46268 -33.6 -60.7

- 59 -

t^l> CO CO 00 U>U>NC40QOQ{SC9*Or- t - t O ^ ^ C O C O t ^ I ^ N M ^ ^*O\O\ • • • • . rH* -4CNCN • • >«H «H . » • . . * . * . •CO

83sss'ii*<' ss8ef o8^^ss33!?as^.H ^H^H^HCO CO ^H *H W I H «H «-t «H I *-4O4

^ *H *H *7* T ^ 7 *"*

• 'COCO •COCO • • • •

a a t < a i a a 8

nNNnNNNNN(silsiNnniN(Nnis(s(sn^nnnn(N(s W ft co co co K co W Co co coco coco coco coco coco KM MM coMW

361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453

25.2-119.3119.3-114114

-131.2131.2-108.6-30.1730.17108.6-124.1124.1-2828

-118.5118.5-112.2112.2-132.4132.4-105.8-32.9732.97105.8-124.1124.1-30.830.8

-117.7117.7-110.3110.3-133.4133.4-103

-35.7735.77103

-124.1124.1-33.633.6

-116.8116.8108.5

-108.5-100.2-38.5738.57100.2-134.2134.2-36.436.4124.2

-124.2-115.8115.8106.5

-106.5-97.37-41.3741.3797.37-39.239.2

-134.7134.7-124.2124.2-114.6114.6-104.6104.6-94.57-44.17a. 1794.57-4242

-135135

-124.2124.2-113.4113.4-102.6102.6

-91.77-86.17-80.57-74.97

-33.95-33.35-33.35-31.86-31.86-31.64-31.64-30.35-30.35-30.35-30.35-29.92-29.92-29.1-29.1-28.57-28.57-27.04-27.04-26.54-26.54-25.5-25.5-25.5-25.5-24.89-24.89-24.25-24.25-23.6-23.6-22.13-22.13-21.03-21.03-20.65-20.65-20.65-20.65-19.58-19.58-19.4-19.4-18.42-18.42-17.11-17.11-15.8-15.8-15.8-15.8-15.09-15.09-14.55-14.55-13.96-13.96-13.02-13.02-11.98-11.98-10.95-10.95-10.95-10.95-9.7-9.7-8.69-8.69-8.009-8.009-7.395-7.392-6.745-6.745-6.1-6.1-6.1-6.1-4.85-4.85-1.839-1.839-1.692-1.692-1.544-1.544-1.397-1.397-1.25-1.25-1.25-1.25

- 61 -

454 -69.37 -1.25455 -63.77 -1.25456 -58.17 -1.25457 -52.57 -1.25458 -46.97 -1.25459 46.97 -1.25460 52.57 -1.25461 58.17 -1.25462 63.77 -1.25463 69.37 -1.25464 74.97 -1.25465 80.57 -1.25466 86.17 -1.25467 91.77 -1.25468 -44.8 0469 44.8 0470 -91.77 1.25471 -86.17 1.25472 -80.57 1.25473 -74.97 1.25474 -69.37 1.25475 -63.77 1.25476 -58.17 1.25477 -52.57 1.25478 -46.97 1.25479 46.97 1.25480 52.57 1.25481 58.17 1.25482 63.77 1.25483 69.37 1.25484 74.97 1.25485 80.57 1.25486 86.17 1.25487 91.77 1.25488 -102.6 1.397489 102.6 1.397490 -113.4 1.544491 113.4 1.544492 -124.2 1.692493 124.2 1.692494 -135 1.839495 135 1.839496 -42 4.85497 42 4.85498 -94.57 6.1499 -44.17 6.1500 44.17 6.1501 94.57 6.1502 -104.6 6.745503 104.6 6.745504 114.6 7.392505 -114.6 7.395506 -124.2 8.009507 124.2 8.009508 -134.7 8.69509 134.7 8.69510 -39.2 9.7511 39.2 9.7512 -97.37 10.95513 -41.37 10.95514 41.37 10.95515 97.37 10.95516 106.5 11.98517 -106.5 11.98518 -115.8 13.02519 115.8 13.02520 124.2 13.96521 -124.2 13.96522 -36.4 14.55523 36.4 14.55524 -134.2 15.09525 134.2 15.09526 -100.2 15.8527 -38.57 15.8528 38.57 15.8529 100.2 15.8530 -106.5 17.11531 108.5 17.11532 -116.8 18.42533 116.8 18.42534 -33.6 19.4535 33.6 19.4536 -124.1 19.58537 124.1 19.58538 -103 20.65539 -35.77 20.65540 35.77 20.65541 103 20.65542 -133.4 21.03543 133.4 21.03544 -110.3 22.13545 110.3 22.13546 -117.7 23.6

- 62 -

547 117.7 23.6548 -30.8 24.25549 30.8 24.25550 -124.1 24.89551 124.1 24.89552 -105.8 25.5553 -32.97 25.5554 32.97 25.5555 105.8 25.5556 -132.4 26.54557 132.4 26.54558 -112.2 27.04559 112.2 27.04560 -118.5 28.57561 118.5 28.57562 -28 29.1563 28 29.1564 -124.1 29.92565 124.1 29.92566 -108.6 30.35567 -30.17 30.35568 30.17 30.35569 108.6 30.35570 -131.2 31.64571 131.2 31.64572 -114 31.86573 114 31.86574 -119.3 33.35575 119.3 33.35576 -25.2 33.95577 25.2 33.95578 -124.1 34.69579 124.1 34.69580 -111.4 35.2581 -27.37 35.2582 27.37 35.2583 111.4 35.2584 -130 36.34585 130 36.34586 -115.7 36.58587 115.7 36.58588 -120 37.94589 120 37.94590 -22.4 38.8591 -16.8 38.8592 -11.2 38.8593 -5.6 38.8594 0 38.8595 5.6 38.8596 11.2 38.8597 16.8 38.8598 22.4 38.8599 -124.1 39.22600 124.1 39.22601 -114.2 40.05602 -24.57 40.05603 24.57 40.05604 114.2 40.05605 -128.7 40.68606 128.7 40.68607 -117.5 41.21608 117.5 41.21609 -22.4 41.3610 -16.8 41.3611 -11.2 41.3612 -5.6 41.3613 0 41.3614 5.6 41.3615 11.2 41.3616 16.8 41.3617 22.4 41.3618 -120.8 42.37619 120.8 42.37620 -124.1 43.53621 124.1 43.53622 -127.4 44.69623 127.4 44.69624 -111.4 44.9625 -27.37 44.9626 27.37 44.9627 111.4 44.9628 -25.2 46.15629 25.2 46.15630 -114.7 46.25631 114.7 46.25632 -118.3 47.69633 118.3 47.69634 -121.4 48.96635 121.4 48.96636 -106.6 49.75637 -30.17 49.75638 30.17 49.75639 108.6 49.75

- 63 -

640 -125.2 50.48641 125.2 50.48642 -28 51643 28 51644 -112 51.31645 112 51.31646 115.6 52.99647 -115.6 52.99648 -118.8 54.43649 118.8 54.43650 -105.8 54.6651 -32.97 54.6652 32.97 54.6653 105.8 54.6654 -30.8 55.85655 30.8 55.85656 -122.7 56.24657 122.7 56.24658 -109.2 56.38659 109.2 56.38660 -112.9 58.26661 112.9 58.26662 -103 59.45663 -35.77 59.45664 35.77 59.45665 103 59.45666 -116.1 59.94667 116.1 59.94668 -33.6 60.7669 33.6 60.7670 -106.5 61.46671 106.5 61.46672 -120 61.92673 120 61.92674 -109.9 63.47675 109.9 63.47676 -100.2 64.3677 -38.57 64.3678 38.57 64.3679 100.2 64.3680 -113.4 65.49681 113.4 65.49682 -36.4 65.55683 36.4 65.55684 -103.4 66.4685 103.4 66.4686 -116.9 67.5687 116.9 67.5688 -106.9 63.61689 106.9 68.61690 -97.37 69.15691 -41.37 69.15692 41.37 69.15693 97.37 69.15694 -39.2 70.4695 39.2 70.4696 -110 70.59697 110 70.59698 -100.4 71.32699 100.4 71.32700 -113.6 72.93701 113.6 72.93702 -103.7 73.66703 103.7 73.66704 -94.57 74705 -44.17 74706 44.17 74707 94.57 74708 -42 75.25709 42 75.25710 -106.5 75.66711 106.5 75.66712 -97.42 76.23713 97.42 76.23714 -110.1 78.17715 110.1 78.17716 -100.4 78.6717 100.4 78.6718 -91.77 78.85719 -86.17 78.85720 -80.57 78.85721 -74.97 78.85722 -69.37 78.85723 -63.77 78.85724 -58.17 78.85725 -52.57 78.85726 -46.97 78.85727 46.97 78.85728 52.57 78.85729 58.17 78.85730 63.77 78.85731 69.37 78.85732 74.97 78.85

- 64 -

733734735736737738739740741742743744745746747748749750751752753754755756757758759760761762763764765766767768769770771772773774775776777778779780781782783784785786787788789790791792793794795796797798799800801802803804805806807808809810811812813814815816817818819820821822823824825

80.5786.1791.77-44.844.8

-103.1103.1

-94.4394.43-89.5589.55-84.5884.58-106.3106.3

-97.0897.08

-79.5179.51

-74.3374.33-4242

-92.8892.8869.04-69.04-99.7499.74-63.6463.64-88.5388.5358.13-58.13-96.0196.01-102.4102.4-52.552.5-8484

-50.0850.08-39.239.2

-79.2779.27-92.192.1-99.699.6

-74.3374.33-87.9787.97-69.1669.16-46.4546.45-96.4896.48-36.436.4

-83.6283.62-63.7363.73-58.0358.03-79.0379.03-93.0293.02-42.8942.89-55.3555.35-33.633.6

-74.1774.17-89.1789.17-39.4139.41-50.9250.92-69.0269.02-30.830.8

78.8578.8578.8580.180.180.780.781.1381.1381.9581.9582.7882.7883.1983.1983.4183.4183.6283.6284.4984.4984.9584.9584.9984.9985.3785.3785.785.786.2786.2786.6486.6487.1987.1987.8687.8687.9887.9888.1388.1388.3488.3489.5389.5389.889.890.190.190.1390.1391.1491.1491.9191.9192.5392.5393.7493.7493.9493.9494.4294.4294.6594.6595.0595.0595.5995.5997.4297.4297.7297.7297.8497.8498.2598.2598.9698.9699.599.5100.5100.5101.4101.4102.5102.5103103

103.5103.5104.3104.3

- 65 -

826 -84.89 105827 84.89 105828 -36 106.6829 36 106.6830 -63.56 106.7831 63.56 106.7832 -46.61 106.8833 46.61 106.8834 -60.63 108.4835 60.63 108.4836 -80.14 108.6837 80.14 108.6838 -28 109.2839 28 109.2840 -42.43 110.3841 42.43 110.3842 32.67 110.7843 -32.67 110.7844 -55.15 111.5845 55.15 111.5846 -74.89 112.3847 74.89 112.3848 -38.4 113.7849 38.4 113.7850 -25.2 114.1851 25.2 114.1852 -49.99 114.5853 49.99 114.5854 -29.4 114.6855 29.4 114.6856 -69.09 116857 69.09 116858 -34.51 116.9859 34.51 116.9860 -45.11 117.3861 45.11 117.3862 -65.9 117.8863 65.9 117.8864 -26.19 118.5865 26.19 118.5866 -22.4 118.9867 -16.8 118.9868 -11.2 118.9869 -5.6 118.9870 0 118.9871 5.6 118.9872 11.2 118.9873 16.8 118.9874 22.4 118.9875 40.51 119.9876 -40.51 119.9877 -30.77 120878 30.77 120879 -59.83 121880 59.83 121881 -23.05 122.3882 23.05 122.3883 36.14 122.4884 -36.14 122.4885 -17.31 122.5886 17.31 122.5887 -11.55 122.6888 11.55 122.6889 -5.783 122.8890 5.783 122.8891 0 122.9892 -27.16 122.9893 27.16 122.9894 -54.01 123.7895 54.01 123.7896 -32.01 124.8897 32.01 124.8898 -23.7 125.8899 23.7 125.8900 -48.46 126901 48.46 126902 -17.84 126.3903 17.84 126.3904 -11.93 126.7905 11.93 126.7906 -5.976 126.9907 5.976 126.9908 0 126.9909 -28.08 127.1910 28.08 127.1911 -43.19 127.9912 43.19 127.9913 -24.35 129.2914 24.35 129.2915 -38.22 129.5916 38.22 129.5917 -18.32 129.7918 18.32 129.7

- 6 6 -

919 -12.26920 12.26921 -6.148922 6.148923 -33.53924925

33.530

926 -29.13927 29.13928 -24.99929 24.99930 -18.89931 18.89932 -12.66933 12.66934 -6.352935936

»felen

6.3520

1 4 12 <1 13 4 24 4 35 4 46 4 57 4 68 4 79 4 810 4 911 4 1012 iI 1113 4 1214 4 1215 4 1316 '17 '

1 14I 15

18 4 1619 4 1720 4 1821 4 1922 4 2023 4 2124 4 2225 4 2326 4 2427 <I 2528 4 2629 4 2730 i31 i32 '

1 28, 291 29

33 4 3034 4 3135 4 3236 4 3337 4 3438 iI 3539 4 3640 4 3741 <42 t43 '

1 38I 391 40

44 4 4145 <46 -47 '48 '

I 42i 43i 441 45

49 4 4650 4 4651 4 4752 4 4853 4 4954 4 5055 4 5156 4 5257 4 5358 4 5459 4 5560 4 5661 4 5762 4 5863 4 5964 t65 <66 <67 <68 i69 <7071 <72 i

1 60, 61, 62, 72, 73, 74, 75, 76I 77

73 4 7874 4 79

130.1130.1130.5130.5130.8130.8131

131.8131.8132.7132.7133.7133.7134.4134.4134.9134.9

3121551771992311271416294022301832203424532638286137444131464733493551397643554559548458726048676650655264567862637393758279887786831028196859489

135

161517181920232427284041313053543233343538396162444576775960484749505152555684857273787993928283686665696470637188898687102103949596979899106107104105108109

1224166188201024132829152141173119332335255427393662404546303248345038524277445653605785597367474968516955706179727174927883768982878010384978895

- 67 -

75767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167

444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444

80818283848588899091929394959697100101102103104105106107108109110111114115116117118119120121122123126127128129130131132133134135136137138139142143144145146147148149150151152153154155156157160161162163164165166167168169170171172173174175176177178179180181184185186

1069198951049210897114101103116112109118105122111126107128117134115124119132121136123144127140129138131146133160135158145148143150139164137170147156149155153182161174151162154178157169167168172184163200165186173210171176191177180209175192181208179188199207185194189206187205

1141151121131161171181191221231271261241251281291321331341351+4145136137140141138139146147160161158159148149150151164165182183155154156157170171174175162163169168200201178179172173184185176177181180186187210211192193209212198199189188208213194195207214220221206215196197205216204

9010794999310596109100115117102108113104119110123106127116129114135118125120133122137126145128141130139132147134161144159142149138151136165146171148157152154160183150175155163156179166168173169162185164201172187170211190177181176174212180193178213198189184214188195186215192

- 68 -

168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260

444444444444444444444444444444444444444444444444444444444444444444444444444444444444444434444

187188189190191192193194195196197198199200201220221222223224225226227228229234235236237238239240241242243248249250251252253254255256257262263264265266267268269270271276277278279280281282283288289290291292293294295296297302303304305306307308309314315316317318319320320321322323324

193196221198223204195203197202225220227228211224235226237230239234241242232238249240251244253248257254246252263256265258267268260262271266277270281272279282274276289278290284293288297294286291303305292298307308300302315304317306319310330320312316332318338329349321339322323324325

217224225226227203218202219230233234235231232238239240241244247248249245246252253256257258261262263259260266267270271272275273274276277278279288289284287285286291290292293298301302303299300304305307306310313311312316317318319329330333336334335337338348349350351340334341342343344

216220197222199194217196218224219226221210229234225236227238233240235231243248239250241252247256249245255262253264257266261259269270263276267280271278275273283288277291279292287296289285295302290293304306301299309314303316305318307329313311328331317337319348330339

340341342343

261 4262 <263 i264 !265 <266 i267 <268 i269 '270 i271 <272 <273 -1274 tZ7S '276 *

•zn '278 '279 t280 '281282 '283284285 i286287288 i

325326327328329330

, 331, 332334

, 335L 337I 338k 348349350351352

I 353I 355356358359362363

. 364365

. 366L 367

289 4 369290 4 370291 4 372292 4 373293 4 376294 4 377295 4 378296 4 379297 4 380298 4 381299 4 383300 4 384301 4 386302 4 387303 <304 <305 <306 i307 <308 '309 i310 '311 <312 <313 '314 '315 '316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353

I 390i 391\ 392\ 393I 394\ 395I 397I 398I 400\ 401I 404I 405I 406I 407I 409i 410I 412i 413I 416I 417I 418I 419L 420I 421I 423I 424L 428I 429k 430L 4311- 432I 433I 434L 435I 437L 438L 442I 443L 444I 445I 446I 447I 448I 449I 450I 4511 452I 4531 454I 455i 456

326327328335333351337353339356348359350363354365358367360370362373364377368379372381374384376387378391382393386395388398390401392405396406400413402410404416407419420408414424417429431418421433435422426438430443432445434447436449440459444495446493448491450489451452453454455456457

345346347347354357358359360361362363364365368371372373374375376377378379382385386387388389390391392393396399400401402403404405407406408411417416414415418419421420425422426427430431433432434435439436440441444445446447448449450467468469492493490491488489470487471472473474475476477

344345346

350336352338355347358349362351364357366359369361372363376365378371380373383375386377390379392385394387397389400391404393407399412401409403417405418406411421423415428416419430432420425434437427442431444433446435448439458441494445492447490449488467470471472473474475476

- 70 -

4»«»<*^^«t^fr^l^»4fc»4fc4k4*4*4**»^^<^^'*^»»»»fc4*4^

OHMpQMHto J

447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477478479480481482483484485486487488489490491492493494495496497498499500501502503504505506507508509510511512513514515516517518519520521522523524525526527528529530531532533534535536537538539

444443444444444444444444444444444444444444444444444444444444444444444444444444444444444444444

593594595596597598599600601602603604607608618619620621624625626627630631632633634635636637638639644645646647648649650651652653658659660661662663664665666667670671674675676677678679680681684685688689690691692693696697698699702703704705706707710711712713716717718719720721722723724

594595596597598603620606624609626608630619632621634623636628638631644633647635648641650642652645658646649660666657662654664659670661674667676668678671680673684675688681690682692685696687698689702697704694706699710701712703716711718708727713738715740717748739719720721722723724725

613614615616617617622623630628629631632633634635640641644642643645647646648649656657658654655659660661667666672673670668669671674675680681684682683685686687688689696697698694695699700701702703710711712708709713714715716717738739740736737741746747748749760761742744750752759762767

612613614615616

605621607625617627618631620633622635630637629639632645634646640649644651643653647659661648656667658663655665660671666675670677669679672681674685680689684691683693686697688699696703698705695707700711702713710717712726709735714739716741738749740742744750752759762

- 72 -

540541542543544545546547548549550551552553554555556557558559560561562563564565566567568569570571572573574575576577578579580581582583584585586587588589590591592593594595596597598599600601602603604605606607608609610611612613614615616617618619620621622623624625626627628629630631632

4 7254 7264 7274 7274 7284 7294 7304 7314 7324 7334 7344 7364 7374 7384 7394 7404 7414 7424 7434 7444 7454 7484 7494 7504 7514 7524 7534 7544 7554 7564 7574 7584 7594 7604 7614 7624 7634 7644 7654 7664 7674 7684 7694 7724 7734 7744 7754 7764 7774 7784 7794 7804 7814 7824 7834 7864 7874 7884 7894 7904 7914 7924 7934 7964 7974 7984 7994 8004 8014 8024 8034 8044 8054 8084 8094 8104 8114 8124 8134 8144 8154 8184 8194 8204 8214 8224 8234 8244 8254 8284 8294 8304 831

726736728773729730731732733734735754777760747742749744757750765756761752775759781778793764769787762768771767791774783801772782785776803780789792811796809786799788795790805798807800815808821812819804817802823810831814827818833820835824829822837828841832845830847838842843849834857

772776766777763758753751745743741792793770771756757764765774775768769780781786787808809782783791790784785800801788789803802794795810811798799820821818819804805806807814815816817822823832833828829826827830831834835836837840841844845843842846847848849852853856857854855858859862863

767772773737766763758753751745743776755746761748743756745764751760757774753780758792779768765763786770769790766782775773800784783802777788781810793808797798787794789804791806799814801820809818813816805822803830811826815832819834821828825836823840829844833846831843839848842856835

- 73 -

4 8324 8334 8344 835

838839840841842843844845

4 8484 849

850851852853

44

4 ___4 8544 855

858859860861

. 8644 8654 866

444

4

633634635636637638639640641642643644645646647648649650651652653654655656657658659660661662663664665666667668669670671672673674675676677678679680681682683684685686687688689690691692693694695696697698699700701702

»fe-boundary443 1

11111111111111111

867868869870871872873875876877878881882883884885886887888889890892893896897898899902903904905

4 9064 9074 9094 9104 9134 9144 9174 9184 9194 920A 921

922

840 860 852853 861 841844 879 862863 880 845850 864 854855 865 851848 876 860861 875 849859 878 855854 877 858852 894 879880 895 853858 884 876875 883 859866 881 864865 882 874860 900 894895 901 861864 892 877878 893 865877 896 884833 897 878876 911 900901 912 875881 898 892893 899 882867 885 881868 887 885869 889 887870 891 889871 890 891872 888 890873 886 888874 882 886912 916 883884 915 911892 909 896897 910 893885 902 898899 903 886916 924 897896 923 915887 904 902903 905 888889 906 904905 907 890891 908 906907 908 891898 913 909910 914 899909 926 923924 927 910902 917 913914 918 903904 919 917918 920 905906 921 919920 922 907908 925 921922 925 908913 928 926927 929 914917 930 928929 931 918919 932 930931 933 920921 934 932933 935 922925 936 934935 936 925

429413395381367353332315297281265251237223191167153143 1131121111 1

- 74 -

1019181755843372622141197

3

246810132125364257748090100110120130142152166190222236250264280296314331352366380394421428442494508524542

1

11111111

11111111

111111111111

1111

11

11111111

111

11

556 1570584605622640 1656 1672 1686 1700 1714 1746 1770784794806816826836846862879894900911915923 1926928930932934936935933931

- 75 -

929 1927 1924 1916 1912 1901 1895 1880 1863 1857 1847 1837 1827 1817 1807 1795 1785 1771 1747 1715 1701 1687 1673 1657 1641 1623 1606 1585 1571 1557 1543 1525 1509 1495 1*fe-force48 48 48 48 48

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748123456789

469497511523535549563577598597596595594593592591590576562548534522510496468440426414402388374360339340341342343344345346347361375389403415427441604627639653665679693707735

497 ! 1511523535549563577598597596595594593592591590576562548534522510496468440426414402388374360339340341342343344345346347361375389403415427441469

627639653665679693707735734

48 48 149

! 2

- 76 -

101112131415161718192021222324252627282930313233343536373839404142434445464748123456789101112131415161718192021222324252627282930313233343536373839404142434445464748123456

734733732731730729728727706692678664652638626603582568554540528514500479480481482483484485486487501515529541555569583737755779797813825839841874873872871870869868867866850838824812796778754736708694682668654642628609610611612613614615616617629643655669683695709602625637651663677

733732731730729728727706692678664652638626603582568554540528514500479480481482483484485486487501515529541555569583604

755779797813825839841874873872871870869868867866850838824812796778754736708694682668654642628609610611612613614615616617629643655669683695709737625637651663677691

! 3

! 4

- 77 -

789101112131415161718192021222324252627282930313233343536373839404142434445464748123456789101112131415161718192021222324252627282930313233343536373839404142434445464748123

691705726725724723722721720719718704690676662650636624601580566552538526512498470471472473474475476477478499513527539553567581334355369383397409423437458457456455454453452451450436422408396382368354333310298284272258244230202203204205206207208209210231245259273285299311201229243

705726725724723722721720719718704690676662650636624601580566552538526512498470471472473474475476477478499513527539553567581602355369383397409423437458457456455454453452451450436422408396382368354333310298284272258244230202203204205206207208209210231245259273285299311334229243255

! 5

- 78 -

456789101112131415161718192021222324252627282930313233343536373839404142434445464748123456789101112131415161718192021222324252627282930313233343536373839404142434445464748

25526928329530932832732632532432332232132030829428226825424222820018215814012411298866364656667686970718799113125141159183336357371385399411425439467466465464463462461460459438424410398384370356335312300286274260246232211212213214215216217218219233247261275287301313

26928329530932832732632532432332232132030829428226825424222820018215814012411298866364656667686970718799113125141159183201357371385399411425439467466465464463462461460459438424410398384370356335312300286274260246232211212213214215216217218219233247261275287301313336

! 7

- 79 -

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293

4434294133953813673533323152972812652512372231911671531431311211111019181755843372622141197531246810132125364257748090100110120130142152166190222236250264280296314331352366380394421428442494508524542556570584605622640656672686700714746770784

4294133953813673533323152972812652512372231911671531431311211111019181755843372622141197531246810132125364257748090100110120130142152166190222236250264280296314331352366380394421428442494508524542556570584605622640655672686700714746770784794

! 8

949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149

794806816826836846862879894900911915923926928930932934936935933931929927924916912901895880863857847837827817807795785771747715701687673657641623606585571557543525509495

806816826836846862879894900911915923926928930932934936935933931929927924916912901895880863857847837827817807795785771747715701687673657641623606585571557543525509495443

- 81 -

VI.

#### 7 hexagonal tubes with a gap, multiple structures ###

> INPUT <# of element type =

# of bodies =

# of nodes =

# of elements =

# of boundaries =Fluid density =

# of band width

48

936

702

149

1.00

57

> OUTPUT <

hydrodynamic mass matrix (kg/mm): consistent

ly2y

3y

4y5y

6y

7y

ly51522.25

-166.80-24348.95

-164.83-166.38

-24336.15-166.55

2y-166.80

18060.10

4389.77

1123.08

-1111.17-5837.49

-14611.57

3y-24348.95

4389.77

33118.62

4320.65

-5733.02-5892.64

-5842.10

4y-164.83

1123.08

4320.65

17575.51

-14021.83

-5748.95-1114.64

5y-166.38

-1111.17-5733.02

-14021.83

17350.86

4301.96

1119.58

6y-24336.15

-5837.49

-5892.64

-5748.95

4301.96

32998.84

4408.57

7y-166.55

-14611.57-5842.10

-1114.64

1119.58

4408.5718060.10

vn.

modalrsa.m

- 84 -

Matlab M

modalrsa.m

felem.m

nodal.dat

elstif.dat, elmass.dat

rsa.i

emass. m

estif.m

locmtx.m

frs.m

rsa.dat

- 85

modalrsa.m

x This program calculates natutal frequency and mode shapex (3-D beam anlaysis, only one direction exciation)x and then response spectrum analysis are performed.

x Prepared by Kim, Doo-Kie & Ryu, Jeong-Soo

xclearxxXfelemxxxxAdd_B

ele. stif. & mass matrices

distributed (consistent) masses only for translational dof's (kg/mm3)==> Y-translational direction

=[ 51522.25-166.80

-24348.95-164.83-166.38

-24336.15-166.55

-166.8018060.104389.771123.08

-1111.17-5837.49-14611.57

-24348.954389.77

33118.624320.65

-5733.02-5892.64-5842.10

-164.831123.084320.6517575.51

-14021.83-5748.95-1114.64

-166.38-1111.17-5733.02-14021.8317350.864301.961119.58

-24336.15-5837.49-5892.64-5748.954301.9632998.844408.57

-166.55-14611.57-5842.10-1114.641119.584408.57

18060.10 ] ;

x following chen's practical suggestionsx

x if ij==lx EEig=eig(Add_m);x Md_ml=diag(EEig);x Add_m=Md_ml;x endx

Add_m = Add_m*le-6xxxTM = zeros(ndofsys,ndofsys);nn = 6;nnl=nn+l;TM( l: 1+nn. 1: 1+nn) = TH( 1:

8: 8+nn) » TO( 8:15: 15+nn) - TH( 15:22: 22+nn) » TH( 22:29: 29+nn) » TH( 29:36: 36+nn) » TH( 36:43: 43+nn) = TH( 43:50: 50+nn) » TH( 50:57: 57+nn) - TH( 57:64: 64+nn) - TH( 64:

71+nn. 71: 71+nn) = TH( 71:78: 78+nn) - TM( 78:85: 85+nn) - TH( 85:92: 92+nn) - TH( 92:99: 99+nn) - TM( 99:

TH(106:

x scale Rg/mm2/m ==> Kg/mm3

l:TH( 8: 8+nnTH( 15: 15+nnTM( 22: 22+nnTH( 29: 29+nnTH( 36: 36+nnTH( 43:TH( 50:TH( 57: 57+nnTH( 64: 64+nnTH( 71:TH( 78: 78+nn,TH( 85: 85+nn,TH( 92:TH( 99:

43+nn,50+nn,

92+nn,99+nn,

TH(106:106+nn,106:106+nn)

1+nn,8+nn,15+nn,22+nn,29+nn,36+nn,43+nn,50+nn,57+nn,64+nn,71+nn,78+nn,85+nn,92+nn,99+nn,106+nn,

l: 1+nn)8: 8+nn)15: 15+nn)22: 22+nn)29: 29+nn)36: 36+nn)43: 43+nn)50: 50+nn)57: 57+nn)64: 64+nn)71: 71+nn)78: 78+nn)85: 85+nn)92: 92+nn)99: 99+nn)106:106+nn)

Add_n*(Add_a«(Add_a*(Add_a«(

AdcU»«(Add_n*(Add_m*(

Md_n*(Md_a*(Add_n*(Add_n*(Add_B»{

Add_a«(

Ln( 1)+Ln( 1+nnl) )/2Ln( 8)+Ln( 8+nnl) )/2Ln( 15)+Ln( 15+nnl) )/2Ln( 22)+Ln( 22+nnl) )/2Ln( 29)+Ln( 29+nnl) )/2Ln( 36)+Ln( 36+nnl) )/2Ln( 43)+Ln( 43+nnl) )/2Ln( 50)+Ln( 50+nnl) )/2Ln( 57)+Ln( 57+nnl) )/2Ln( 64)+Ln( 64+nnl) )/2Ln( 71)+Ln( 71+nnl) )/2Ln( 78)+Ln( 78+nnl) )/2Ln( 85)+Ln( 85+nnl) )/2Ln( 92)+Ln( 92+nnl) )/2Ln( 99)+Ln( 99+nnl) )/2Ln(106)+Ln(106+nnl) )/2

TM(113:113+tm.ll3:ll3+nn) - 18(113:ll3+nn, 113:113+tm)TM(i20:120+nn,120:120+nn) - TM(120:120+nn,120:12CHnn)TM(127:l27+m»,127:127+nn) - TM(127:127+nn,127:l27+nn)xxx TH = zeros(ndofsys,ndofsys); x checkxx inner waterxfor i=l:133

if i<127

Mdj»(Add_a»( Ln(120)+Ln(12O+nnl)Addji»( Ln(127)

elseif i>=127

x global stiffness matrix

x assembling of Ke => TKx assembling of Me => TM

.,i:i) + 4.794e-3*Ln(l);

.,i:i) + 4.794e-3*Ln(127)/2;end

endxx assembling of TK, TMxTK= zeros(ndofsys,ndofsys);for e=l:nmem

eval(['Ke=Ke' int2str(e)eval(C'Me=Me' int2str(e)TK = TK + Ke;TM = TM + Me;

endxx running checkxsize(TK);size(TM);TM1=TM(1=266,1:266);TK1=TK(1=266,1:266);xx mode shape & nat. freq.x[psi,wnsq]= eig(TKl,TMl);diag(wnsq)xx sorting in ascending & real partsx only for the 1st halfxfor jm=nmem+l:ndofsys

jmode=ndofsys+1-jm;naf(jmode) = sqrt(real(wnsq(jm,jm)))/2/pi;mode(:,jmode)= real(psi(:,jm)) ;

endxx normalized mode by generalized mass(gm)xfor jmode=l:nmem

gm = mode(:,jmode)' * TM » mode(:,jmode);modeO, jmode) = mode(:, jmode) / sqrt(gm);

endxx save as filesxsave modal.dat naf mode /ascii /doubleclear psi wnsqxx response spectra analysisxrsax

x (in Sec)

- 87 -

felcmun

x% calculate element stiffness matrices% & element mass matricesx

xxndofmem = 4 ; x 2-Dimensional beamnmem = 19*7; % 19 members * 7 tubes = 133 membersndofsys = nmem*2;xxEt= 9.5143e7 ; % Young's modulus of a tube 1 (kg/mm/sec*2)E=[ Et*ones(nmem,1) ]; x Young's modulus vector%xIxx=[ 2.3019e+5*ones(nmem,1)]; % moment of inertia (mm"4)Den=[ 6.5550e-6*ones(nmem,1)]; % mass density (kg/mnf3)Area=[ 421.2348*ones(nmem,1)]; x cross sectional area (mm"2)Ln= [ 50*ones((nmem-7),l) x length of the elements (mm)

25*ones(l*7,l)];xx connectivityx dof of elements; 1st half(trans), 2nd half(rotation)xcode=[ 0 0 1 134 % 1st floor (l-7ele)

0 0 2 1350 0 3 1360 0 4 1370 0 5 1380 0 6 1390 0 7 1401 134 8 141 x 2nd floor (8-14ele)2 135 9 1423 136 10 1434 137 11 1445 138 12 1456 139 13 1457 140 14 1478 141 15 148 % 3rd floor (15-21ele)9 142 16 149

10 143 17 15011 144 18 15112 145 19 15213 146 20 15314 147 21 15415 148 22 155 x 4th floor (22-28ele)16 149 23 15617 150 24 15718 151 25 15819 152 26 15920 153 27 16021 154 28 16122 155 29 162 % 5th floor (29-35ele)23 156 30 16324 157 31 16425 158 32 16526 159 33 16627 160 34 16728 161 35 16829 162 36 169 % 6th floor (36-42ele)30 163 37 17031 164 38 17132 165 39 17233 166 40 17334 167 41 174

3536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110

168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243

42434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117

175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204206206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250

x 7th floor (43-49ele)

x 8th floor (50-56ele)

x 9th floor (50-56ele)

x 10th floor (50-56ele)

x 11th floor (50-56ele)

x 12th floor (50-56ele)

x 13th floor (50-56ele)

x 14th floor <50-56ele)

x 15th floor (50-56ele)

x 16th floor (50-56ele)

x 17th floor (50-56ele)

x 18th floor (50-56ele)

% 19th floor (57-63ele)

111 244 118 251112 245 119 252113 246 120 253114 247 121 254115 248 122 255116 249 123 256117 250 124 257118 251 125 258119 252 126 259120 253 127 260121 254 128 261122 255 129 262123 256 130 263124 257 131 264125 258 132 265126 259 133 266

x callate element stiffness matricesx element mass matricesxke4save=[];me4save=[];for e=l:nmem

ke= zeros(4,4);me= zeros(4,4);ke= estif(E(e),Ixx(e),Ln(e));me= emass(Den(e),Area(e),Ln(e),l);L = locmtx(code(e,:),ndofmem,ndofsys);Ke= L'«ke*L;Me= L'»me*L;eval(['Ke' int2str(e) '=Ke;'3);eval(['Me' int2str(e) '=Me;']);ke4save=Cke4save; ke; zeros(1,4)] ;me4save=[me4save; me; zeros(l,4)] ;

endxxXsave elstif.dat ke4save /ascii /doublesave elmass.dat me4save /ascii /doubleclear ke4saveclear me4save

% consistant(0),lumped(l)x for each elementx global mapping

va.functionxXXXXXXXXXXXXX

me=emass(d,A,L,opt)

This function is to calculate element mass matrixof a plane frame member

me = emass(d,L,opt)

d = mass densityA = cross sectional areaL = length of elementopt= kind of mass matrix

consistent-mass matrixlumped-mass matrixhigher order mass matrix (average of 0 and 1)

cem(l,l)= 156;cem(2,l)= 22*L;cem(3,l)= 54;cem(4,l)= -13*L;

cem(l,2)= 22*L;cem(2,2)= 4*L*2;cem(3,2)= 13*L;cem(4,2)= -3*L;

cem(l,3)= 54;cem(2,3)= 13*L;cem(3,3)= 156;cem(4,3)= -22*L;

cem(l,4)cem(2,4)cem(3,4)= -22«L;cem(4,4)

90 -

cem= d*A*L/420 * cem;

lem=zeros(4,4);lem(l,l)=l; lem(3,3)=l;lem = d*A*L/2 * lem;

xif ( opt==0 )

roe = cem;elseif ( opt==l )

roe = lem;elseif ( opt==2 )

me = ( cem+lem ) /2;end

cslif.for

function ke=estif(E,I,L)

x This function is to calculate element stiffness matrixx of a plane frame memberx% Re = estif(E,I,L)%x E = Young's modulusx I = flexural rigidity% L = length of elementxke(l,l)= 12; lce(l,2)= 6*L; Ke(l,3)= -12; ke(l,4)= 6*L;ke(2,l)= 6«L; ke(2,2)= 4*1/2; Ke(2,3)= -6*L; ke(2,4)= 2«L*ke(3,l)= -12; ke(3,2)= -6»L; ke(3,3)= 12; ke(3,4)= -6»L;ke(4,l)= 6*L; ke(4,2)= 2*1/2; ke(4,3)= -6*L; ke(4,4)= "ke= E*I/(LA3) * ke;

rsa.m

Xx response spectra analysisx

%xx influence vector in the horizontal directionxIL=[ ones(nmem,1)

zeros(nmem,1) ];x% response from floor response spectra(frs)xopt = 2 ; x X-direction(2), Y-direction(3)scale = 1.00e3; x ( Acc(m/sec*2) => mm/sec*2 )for jmode=l:nmein

read_a = frs(naf(jmode),opt)*scale;read_d = read_a/((naf(jmode)*2*pi)*2);

- 91 -

Xgamma = mode(:, jmode)' * TM « IL;resp_d(:,jmode) = gamma*mode(:,jmode)*read_d;

endxx square root of sum of squres(SRSS)xmax_naf = lelO;for idof=l:ndofsys

resp_sum(idof) = 0;for jmode=i:nmem

if(naf(jmode) <= max_naf)resp_sum(idof) = resp_sum(idof) + resp_d(idof,jmode)

endendendresp_sum = sqrt(resp_sum);resp_sum = resp_sum';xx plotxchK_mode=l;r_mode=zeros(9,1);r_mode( l)=niode( l,chK_mode);r_mode( 2)=mode( 8,chkjnode);r_mode( 3)=mode( 15, chk_jnode) ;r_xoode( 4)=mode( 22,chk_mode);r_mode( 5)=mode( 29,chk_mode);r_mode( 6)=mode( 36,chk_mode);r_mode( 7)=mode( 43,chK_mode);r_mode( 8)=mode( 50,chk_mode);r_mode( 9)=mode( 57,chk_mode);r_mode(10)=mode( 64,chk_mode);r_mode(ll)=mode( 71,chk_mode);r_mode(12)=mode( 78,chK_mode);r_mode(13)=mode( 85,chk_mode);r_mode(14)=mode( 92,chk_mode);r_mode(15)=mode( 99, cWunode);r_mode (16) =mode (106, chk_oode);r_niode(17)=n>ode(113, chkjnode);r_mode (18) =mode (120, chlunode);r_mode(19)=mode(127, chtcjnode);plot(r_mode(l:19));pauser_max=zeros(19,7);for j=l:7

r_max( l , j ) = resp_sum( 1 + j - l )»r_max( 2 , j ) = resp_sum( 8 + j -1 ) ;r_max( 3 , j ) = resp_sum( 15 + j -1 ) ;r_max( 4 , j ) = resp_sum( 22 + j -1 ) ;r_max( 5 , j ) = resp_sum( 29 + j - 1 ) ;r_max( 6,j) = resp_sum( 36 + j - 1 ) ;r_max( 7,j) = resp_sum( 43 + j - 1 ) ;r_max( 8, j) = resp_sutn( 50 + j - 1 ) ;r_max( 9 , j ) = resp_sum( 57 + j - 1 ) ;r_max(10,j) = resp_sum( 64 + j -1 ) ;r_max(ll,j) = resp_sum( 71 + j -1 ) ;r_max(12,j) = resp_sum( 78 + j - 1 ) ;r_max(13,j) = resp_sum( 85 + j -1 ) ;r_max(14,j) = resp_sum( 92 + j -1 ) ;r_max(15,j) = resp_sum( 99 + j - 1 ) ;r_max(16,j) = resp_sum(106 + j - 1 ) ;r_max(17,j) = resp_sua(113 + j - 1 ) ;

- 92 -

r_max(18,j) = resp_sum(120 + j-i);r_max(19,j) = resp_sum(127 + j-1);

endplot(r_max(l:19,l));save rsa.dat r_max /ascii /double

locn lx.ro

function L = locmtx (code,ndofmem,ndofsys)

code= code(:);L= zeros(ndofmemfor

end

\

i=l:ndofmemif coded) >

,ndofsys);

0L(i,code(i))= 1

end

function resp=frs(naf

XXX

X

XXXXXX

XX

This function is

^••-.•>' f r s , m •'•

.opt)

to calculate[ floor response spectra ]at 'naf' in

resp =

the opt' direction

frs(naf.opt)

resp = response at nafnaf = natural frequency(Hz)opt = kinds of directions

2 :3 :

Hzdata=C 1.00

XX

1.502.002.703.504.355.356.507.4014.5015.0016.0017.50100.00

location ofXndata=size(data)for

columncolumn

ACC.X

6.558.009.009.0014.5014.5017.5017.5014.5014.5013.0010.008.002.50

naf.

idata=l:ndata(l)-l

of data ( X-direction )of data ( Z-direction )

(m/sec*2)Z

4.56.58.010.011.511.511.511.59.59.58.56.05.52.0 ];

id_data

- 93 -

compl=data(idata, 1);comp2=data(idata+1, 1);if ((naf <= compl) & (idata ==1))

id_data=O;elseif ((naf > compl) & (naf <= comp2))

id_data=idata;elseif ((naf > comp2) & (idata = (ndata(l)-l)))

id_data=idata+l;end

endxx linear interpolationxif (id_data == 0)

resp = data(l,opt);elseif ((id_data >= 1) & (id_data < ndata(l)))

xl = data(id_data,l);x2 = data(id_data+l,l);yl = data(id_data,opt);y2 = data(id_data+l,opt);m = (y2-yl)/(x2-xl);b = (x2*yl-xl»y2)/(x2-xl);resp = m*naf+b;

elseif (id_data == ndata(D)resp = data(id_data,opt);

endxxx

- 94 -

IMS

KAERI/TR-1584/2000

(TR, AR<2 / smssss a•?• •¥• . a¥?l (Pst -Doc) ,

^5JS(KAUMER ^I

(SfUSSSS)

2000. 6. 20.

94 p. EL 7} 29 Cm.

V ),

consistent

4 s Xlfe^^(lumped)

BIBLIOGRAPHIC INFORMATION SHEET

Performing Qrg.Report No.

Sponsoring Qrg.Report No.

StamdardReport No.

INIS Subject Code

KAERI/TR-1584/2000

Title/Subtitle Assessment for Hydrodynamic Masses of HANARO Flow Tubes

Project Managerand Department(or Main author)

Jeong-Soo Ryu / HANARO Operation Team

Researcher andDepartment

Yeong-Garp Cho, Doo-Kie Kim, Jong-Sup Woo,(HANARO Operation Team)Jin-Ho Park (KALIMER Technology Development Team)

PublicationPlace

Taejon Publisher KAERI PublicationDate

2000. 6. 20.

Page 94 p. Fig. & Tab. Yes( V ), No ( ) Size 29 Cm.

Note

Classified Open( V ), RestrictedC ),Class Document Report Type Technical Report

Sponsoring Org. Contract No.

Abstract(15-20 Lines)

The effect of hydrodynamic masses is investigated in dynamic characteristics

and seismic response analyses of the submerged HANARO hexagonal flow tubes.

Consistent hydrodynamic masses of the surrounding water are evaluated by the

prepared program using the finite element method, in which arbitrary cross-sections

of submerged structures and boundary conditions of the surrounding fluid can be

considered. Also lumped hydrodynamic masses are calculated using simple formula

applied to hexagonal flow tubes in the infinite fluid.

Modal analyses and seismic response spectrum analyses were performed using

hydrodynamic masses obtained by the finite element method and the simple

formula. The results of modal analysis were verified by comparing the results

measured from modal tests. And the displacement results of the seismic response

spectrum analysis were assessed by comparing the consistent and the lumped

hydrodynamic masses obtained by various methods. Finally practical criteria based

on parametric studies are proposed as the lumped hydrodynamic masses for

HANARO flow tubes.

Subject Keywords(About 10 words)

HANARO, Flow Tubes, Hydrodynamic Mass,

Finite Element Method, Modal Analysis,

Seismic Response Spectrum Analysis