B(K,J)=B(K,J)B(K,K) do I=1,N if(i.ne.k) then do J=1,N if(j.ne.k) then B(I,J)=B(I,J)-B(I,K)B(K,J) do I=1,N if(i.ne.k) then B(I,K)=-B(I,K)*B(K,K) do K

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1 module Lxz_Tools implicit none integer (kind(1)),parameter ::ikind=(kind(1)) integer (kind(1)),parameter ::rkind=(kind(0.d0)) real (rkind), parameter :: Zero=0.D0,One=1.D0,Two=2.D0,Three=3.D0, & & Four=4.D0,Five=5.D0,Six=6.D0,Seven=7.D0,Eight=8.D0,Nine=9.D0, & & Ten=10.D0 contains function matinv(a) result (B) real(rkind),intent (in)::a(:,:)!real(rkind), allocatable::b(:,:) real(rkind), pointer::b(:,:) integer(ikind):: N,I,J,K real(rkind)::d,t real(rkind), allocatable::is(:),js(:) N=size(A,dim=2) allocate(b(n,n)) allocate(is(n));allocate(js(n)) B=A do K=1,N D=0.0D0 do I=K,N do J=K,N if(abs(b(i,j))>d) then D=abs(B(I,J)) IS(K)=I JS(K)=J do J=1,N T=B(K,J) B(K,J)=B(IS(K),J) B(IS(K),J)=T do I=1,N T=B(I,K) B(I,K)=B(I,JS(K)) B(I,JS(K))=T B(K,K)=1/B(K,K) do J=1,N if(j.ne.k) then

2 B(K,J)=B(K,J)*B(K,K) do I=1,N if(i.ne.k) then do J=1,N if(j.ne.k) then B(I,J)=B(I,J)-B(I,K)*B(K,J) do I=1,N if(i.ne.k) then B(I,K)=-B(I,K)*B(K,K) do K=N,1,-1 do J=1,N T=B(K,J) B(K,J)=B(JS(K),J) B(JS(K),J)=T do I=1,N T=B(I,K) B(I,K)=B(I,IS(K)) B(I,IS(K))=T end function matinv subroutine IntSwap(a,b) integer(ikind),intent(in out)::a,b integer(ikind)::t t=a;a=b;b=t end subroutine IntSwap subroutine RealSwap(a,b) real(rkind),intent(in out)::a,b real(rkind)::t t=a;a=b;b=t end subroutine RealSwap

3 subroutine matprint(a,n) real(rkind),intent(in)::a(:,:) integer(ikind)::n integer(ikind)::n1,n2 integer(ikind)::i,j character(10)::c n1=size(a,dim=1) n2=size(a,dim=2) C='('//trim(itoc(n2))//'E'//trim(itoc(n))//& '.'//trim(itoc(n-7))//')' do I=1,n1 write(*,c)(a(i,j),j=1,n2) end subroutine matprint function matdet(b) result(det) real(rkind),intent(in)::b(:,:) real(rkind)::det integer(ikind)::n,i,j,k,is,js real(rkind),pointer::a(:,:) real(rkind)::f,d,q n=size(b,dim=1) allocate (A(n,n)) A=B f=1.0d0; det=1.0d0 do k=1,n-1 q=0.0d0 do i=k,n do j=k,n if(abs(a(i,j)).gt.q) then q=abs(a(i,j)) is=i js=j if(q+1.0d0.eq.1.0d0) then det=0.0d0 if(is.ne.k) then f=-f do j=k,n

4 d=a(k,j) a(k,j)=a(is,j) a(is,j)=d if(js.ne.k) then f=-f do i=k,n d=a(i,js) a(i,js)=a(i,k) a(i,k)=d det=det*a(k,k) do i=k+1,n d=a(i,k)/a(k,k) do j=k+1,n a(i,j)=a(i,j)-d*a(k,j) det=f*det*a(n,n) deallocate (a) end function matdet function itoc(i1) result (c) integer(ikind),intent(in)::i1 character(len=2)::c real(rkind)::x integer(ikind) ::n,b,i,j i=i1 x=i c(1:2)=' ' x=log10(x) n=int(x)+2 do j=n-2,0,-1 b=mod(i,10**j) b=(i-b)/(10**j) i=i-b*(10**j) c(n-j-1:n-j-1)=achar(iachar('0')+b) end function itoc

5 subroutine Gauss(GStif,GLoad,GDisp) real (rkind),intent (in) :: GStif(:,:),GLoad(:) real (rkind),intent (out) :: GDisp(:) integer (ikind) :: i,j,k integer (ikind) :: N real (rkind) :: P,I1,X,Y real (rkind),allocatable :: A(:,:) N=size(GDisp,dim=1) allocate (A(N,N+1)) A(1:N,1:N)=GStif(1:N,1:N) A(1:N,N+1)=GLoad(1:N) DO j=1,n P=0.0D0 DO k=j,n IF(ABS(A(k,j)).LE.P) cycle P=ABS(A(k,j)) I1=k IF(P.GE.1E-15)GO TO 230 WRITE(22,'(A)') 'NO UNIQUE SOLUTION' RETURN 230 IF(I1.EQ.j)GO TO 280 DO 270 K=J,N+1 X=A(J,K) A(J,K)=A(I1,K) 270 A(I1,K)=X 280 Y=1.D0/A(J,J) DO 310 K=J,N A(J,K)=Y*A(J,K) DO 380 I=1,N IF(I.EQ.J)GO TO 380 Y=-A(I,J) DO 370 K=J,N A(I,K)=A(I,K)+Y*A(J,K) 380 CONTINUE 390 GDisp=A(1:N,N+1) end subroutine Gauss end module Lxz_Tools module TypDef

6 use Lxz_Tools implicit none integer(ikind) :: NNode, NSolid, NShell! integer(ikind) :: NMaterial, NRealConstant!, integer(ikind) :: NGlbDOF! type Typ_Node! real(rkind) :: coord(3)! integer(ikind) :: EleTyp! 1 soild 2 shell integer(ikind) :: GDOF(6)! shell GDOF(4:6)=0 real(rkind) :: disp(6)! end type typ_node type Typ_Material! real(rkind) :: E! real(rkind) :: mu! end type Typ_Material type Typ_RealConstant! real(rkind) :: Thickness! end type Typ_RealConstant!============================================================================= type Typ_Plate!! real(rkind) :: NCoord(2,4)!! integer(ikind) :: NodeNo(4)! real(rkind) :: t!! real(rkind) :: E,MU!! real(rkind) :: D(5,5)![D]! real(rkind) :: B(5,12)![B]! real(rkind) :: EK(12,12)![EK]! real(rkind) :: S(5,12)![S]! real(rkind) :: GaussPoint(2,4)!! real(rkind) :: N(4,4)!,! real(rkind) :: dn(4,2,4)!,! real(rkind) :: d0(4,2,4)!,! real(rkind) :: Jacobi(2,2,4)!Jacobi,! real(rkind) :: InvJ(2,2,4)!Jacobi! real(rkind) :: SJ(4)! J Jacobi,!!!...! end type Typ_Plate!

7 !============================================================================= type Typ_Membrance! real(rkind) :: NCoord(2,4)!! integer(ikind) :: NodeNo(4)! real(rkind)::ek(8,8),b(3,8),d(3,3),j(2,2) real(rkind)::e,mu,t!... end type Typ_Membrance type Typ_Solid! integer(ikind) :: NodeNo(8)! integer(ikind) :: MatNo! real(rkind) :: E,MU real(rkind) :: EK(24,24)!... end type Typ_Solid type Typ_Shell! integer(ikind) :: NodeNo(4)! integer(ikind) :: MatNo! integer(ikind) :: RealNo! real(rkind) :: E,MU,t type(typ_plate) :: S_Plate(1)!Shell type(typ_membrance) :: S_Membrance(1)!shell real(rkind) :: TransMatrix(24,24)! real(rkind) :: EK(24,24)!!... real(rkind) :: NCoord(2,4)! end type Typ_Shell type Typ_Load integer(ikind) :: NodeNo integer(ikind) :: DOF real(rkind) :: Value end type Typ_Load type Typ_Support integer(ikind) :: NodeNo integer(ikind) :: DOF end type Typ_Support

8 contains subroutine TypDef_DOFCount(Node, Solid, Shell)! type(typ_node) :: Node(:) type(typ_solid) :: Solid(:) type(typ_shell) :: Shell(:) integer(ikind) :: i,j,k! integer(ikind) :: TempDOF! Node(:)%EleTyp=1! do i=1, NNode do j=1, NShell do k=1,4 if(shell(j)%nodeno(k)==i) then! j k i Node(i)%EleTyp=2;! i! for k!for j! for i! TempDOF=0! do i=1, NNode if(node(i)%eletyp==1) then! Node(i)%GDOF(1)=TempDOF+1; Node(i)%GDOF(2)=TempDOF+2; Node(i)%GDOF(3)=TempDOF+3; Node(i)%GDOF(4:6)=0; TempDOF=TempDOF+3;! 3 if(node(i)%eletyp==2) then! Node(i)%GDOF(1)=TempDOF+1; Node(i)%GDOF(2)=TempDOF+2; Node(i)%GDOF(3)=TempDOF+3; Node(i)%GDOF(4)=TempDOF+4; Node(i)%GDOF(5)=TempDOF+5; Node(i)%GDOF(6)=TempDOF+6; TempDOF=TempDOF+6;! 6!for i NGlbDOF=TempDOF end subroutine TypDef_DOFCount

9 end module TypDef module SolidDef use Lxz_Tools use TypDef contains!***************************************************! SUBROUTINE Solid_SHAP3(U,V,W,XQ,XJAC,XVJ,DETJ,SHP)!!***************************************************! ! COMPUTE SHAPE FUNCTION AND DERIVATIVES FOR 3D 8-NODE ELEMENT! IMPLICIT REAL*8(A-H,O-Z) DIMENSION SHP(3,8),XQ(3,8),XJAC(3,3),XVJ(3,3),& UI(8),VI(8),WI(8),IT2(3),IT3(3) DATA UI/-0.5D0,0.5D0,0.5D0,-0.5D0,-0.5D0,0.5D0,0.5D0,-0.5D0/ DATA VI/-0.5D0,-0.5D0,0.5D0,0.5D0,-0.5D0,-0.5D0,0.5D0,0.5D0/ DATA WI/-0.5D0,-0.5D0,-0.5D0,-0.5D0,0.5D0,0.5D0,0.5D0,0.5D0/ DATA IT2/2,3,1/, IT3/3,1,2/!! U,V,W! SHP(1:3,:) Ni U V, W X Y Z! SHP(4,:) Ni! XQ(:,8)! XJAC XVJ! Ni Ni U,V,W DO 10 I=1,8! SHP(4,I)=(0.5D0+UI(I)*U)*(0.5D0+VI(I)*V)*(0.5D0+WI(I)*W) SHP(1,I)=UI(I)*(0.5D0+VI(I)*V)*(0.5D0+WI(I)*W) SHP(2,I)=VI(I)*(0.5D0+UI(I)*U)*(0.5D0+WI(I)*W) SHP(3,I)=WI(I)*(0.5D0+UI(I)*U)*(0.5D0+VI(I)*V) 10 CONTINUE! DO 20 I=1,3 DO 20 J=1,3 XJAC(I,J)=0.0D0 DO 20 K=1,8 20 XJAC(I,J)=XJAC(I,J)+XQ(I,K)*SHP(J,K)! WJ1=XJAC(1,1)*XJAC(2,2)*XJAC(3,3)+XJAC(3,1)*XJAC(1,2)*&

10 XJAC(2,3)+XJAC(1,3)*XJAC(2,1)*XJAC(3,2) WJ2=XJAC(1,3)*XJAC(3,1)*XJAC(2,2)+XJAC(1,2)*XJAC(2,1)*& XJAC(3,3)+XJAC(2,3)*XJAC(3,2)*XJAC(1,1) DETJ=WJ1-WJ2! DO 25 I=1,3 DO 25 J=1,3 M2=IT2(I) M3=IT3(I) N2=IT2(J) N3=IT3(J) 25 XVJ(I,J)=(XJAC(M2,N2)*XJAC(M3,N3)-XJAC(M2,N3)& *XJAC(M3,N2))/DETJ! W1, W2, W3 Ni X Y Z DO 30 I=1,8 W1=0.0D0 W2=0.0D0 W3=0.0D0 DO 35 K=1,3 W1=W1+XVJ(1,K)*SHP(K,I) W2=W2+XVJ(2,K)*SHP(K,I) 35 W3=W3+XVJ(3,K)*SHP(K,I)! Ni X,Y,Z, SHP SHP(1,I)=W1 SHP(2,I)=W2 SHP(3,I)=W3 30 CONTINUE RETURN END subroutine! !! B(6,24) Subroutine Solid_GETB(B,SHP) implicit real*8(a-h,o-z) dimension B(6,24),SHP(3,8) integer i,j do 10 i=1,8 j=(i-1)*3+1 b(1,j)=shp(1,i) B(1,J+1)=0.0d0 B(1,J+2)=0.0D0 B(2,J)=0.0d0

11 B(2,J+1)=SHP(2,I) B(2,J+2)=0.0D0 B(3,J)=0.0d0 B(3,J+1)=0.0d0 B(3,J+2)=SHP(3,I) B(4,J)=SHP(2,I) B(4,J+1)=SHP(1,I) B(4,J+2)=0.0D0 B(5,J)=0.0d0 B(5,J+1)=SHP(3,I) B(5,J+2)=SHP(2,I) B(6,J)=SHP(3,I) B(6,J+1)=0.0d0 B(6,J+2)=SHP(1,I) 10 continue end subroutine!**********************************************************!********************************************************** subroutine Solid_MutBAB(M,N,A,B,C)!**********************************************************!**********************************************************!********************************************************** implicit real*8 (A-H,O-Z) Dimension A(N,N),C(M,M),B(N,M),AB(N,M)! do 12 I=1,N do 12 J=1,M W1=0.0d0 DO 14 K=1,N 14 W1=W1+A(I,K)*B(K,J) 12 AB(I,J)=W1 DO 16 I=1,M Do 16 J=1,M W2=0.0D0 Do 18 K=1,N 18 W2=W2+B(K,I)*AB(K,J) 16 C(I,J)=W2 end subroutine

12 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! subroutine Solid_GetDB(DB,D,B) implicit none real*8 DB(6,24),D(8,6,6),B(6,24) integer i,j,k,l do 5 i=1,6 do 5 j=1,24 5 DB(I,J)=0.0d0 Do 10 I=1,6 do 20 J=1,24 L=(J-1)/3+1 Do 30 K=1,6 DB(I,J)=DB(I,J)+D(L,I,K)*B(K,J) 30 continue 20 continue 10 continue end subroutine!******************************************************************** subroutine Solid_GetBDB(BDB,B,D) implicit none real*8 BDB(24,24),B(6,24),D(6,6) BDB=Matmul(matmul(transpose(B),D),B) end subroutine!******************************************************************** subroutine Solid_GetD(D,E,EMU) implicit real*8(a-h,o-z) Dimension D(6,6) integer I,J D=0.0d0 Temp=E*(1-EMU)/((1+EMU)*(1-2*EMU)) D(1,1)=1 D(2,2)=1 D(3,3)=1 D(1,2)=EMU/(1-EMU) D(2,1)=D(1,2) D(1,3)=EMU/(1-EMU) D(3,1)=D(1,3)

13 D(2,3)=EMU/(1-EMU) D(3,2)=D(2,3) D(4,4)=(1-2*EMU)/(2*(1-EMU)) D(5,5)=D(4,4) D(6,6)=D(4,4) D=temp*D end subroutine!********************************************************************** subroutine Solid_GetEK(EK,XQ,E0,EMU0) implicit none real*8 XQ(3,8),XJAC(3,3),XVJ(3,3),SHP(3,8) real*8 B(6,24),DB(6,24),BDB(24,24),D(6,6),DISP(24) real*8 E0,EMU0 real*8 EK(24,24),PLASTICD(8,6,6) real*8 U,V,W,H1,H2,H3,DETJ real*8 I,J,K,II,JJ,KK integer RETVAL DO 5 II=1,24 DO 5 JJ=1,24 5 EK(II,JJ)=0.0d0 DO 10 I=1,3 IF(I.EQ.1) U= d0 if(i.eq.1) H1= d0 if(i.eq.2) U=0.0d0 if(i.eq.2) H1= d0 if(i.eq.3) U= d0 if(i.eq.3) H1= d0 do 20 J=1,3 IF(J.EQ.1) V= d0 if(j.eq.1) H2= d0 if(j.eq.2) V=0.0d0 if(j.eq.2) H2= d0 if(j.eq.3) V= d0 if(j.eq.3) H2= d0 do 30 K=1,3 IF(K.EQ.1) W= d0 if(k.eq.1) H3= d0 if(k.eq.2) W=0.0d0

14 if(k.eq.2) H3= d0 if(k.eq.3) W= d0 if(k.eq.3) H3= d0 call Solid_SHAP3(U,V,W,XQ,XJAC,XVJ,DETJ,SHP) call Solid_GetB(B,SHP) call Solid_GetD(D,E0,EMU0) call Solid_GetBDB(BDB,B,D) do 100 II=1,24 do 100 JJ=1, EK(II,JJ)=EK(II,JJ)+H1*H2*H3*BDB(II,JJ)*DETJ 30 continue 20 continue 10 continue end subroutine subroutine Solid_EK(Solid,Node) type(typ_solid) :: Solid(:) type(typ_node) :: Node(:) integer(ikind) :: i,j,k real(rkind) :: XQ(3,8) do i=1,size(solid) do j=1,8 XQ(:,j)=Node(Solid(i)%NodeNo(J))%Coord!for j call Solid_GetEK(Solid(i)%EK,XQ,Solid(i)%E,Solid(i)%MU)!for i end subroutine end module program Main use lxz_tools use TypDef use SolidDef use IMSL implicit none type(typ_solid),pointer :: Solid(:) type(typ_node), pointer :: Node(:) real(rkind),pointer :: GK(:,:), GF(:), GD(:)

15 real(rkind) :: temp integer(ikind) :: NElem, NSupport, NLoad; integer(ikind) :: i,j,k,l,m open(55, file='datain.txt') read(55,*) read(55,*) NNode, NElem, NSupport, NLoad allocate(node(nnode)) allocate(solid(nelem)) allocate(gk(3*nnode,3*nnode)) allocate(gf(3*nnode)) allocate(gd(3*nnode)) read(55,*) do i=1,size(node) read(55,*) j, Node(i)%Coord(1:3) read(55,*) do i=1,size(solid) read(55,*) j, solid(i)%nodeno! do k=1,4! Plate(i)%NCoord(:,k)=Node(Plate(i)%NodeNo(k))%Coord(1:2)! solid(:)%e=210.0d9; solid(:)%mu=0.3d0; call Solid_EK(Solid,Node) GK=0.0d0; GF=0.0d0; GD=0.0d0 do i=1,size(solid) do j=1,8 do k=1,8 do l=1,3 do m=1,3 GK((Solid(i)%NodeNo(j)-1)*3+l,(Solid(i)%NodeNo(k)-1)*3+m)=& GK((Solid(i)%NodeNo(j)-1)*3+l,(Solid(i)%NodeNo(k)-1)*3+m)+& Solid(i)%Ek((j-1)*3+l,(k-1)*3+m)! for m! for l! for k! for j! for i GF(58)=1000;

16 temp=maxval(gk) GK(1,1)=GK(1,1)+1.0D5*temp; GK(2,2)=GK(2,2)+1.0D5*temp; GK(3,3)=GK(3,3)+1.0D5*temp; GK(4,4)=GK(4,4)+1.0D5*temp; GK(5,5)=GK(5,5)+1.0D5*temp; GK(6,6)=GK(6,6)+1.0D5*temp; GK(16,16)=GK(16,16)+1.0D5*temp; GK(17,17)=GK(17,17)+1.0D5*temp; GK(18,18)=GK(18,18)+1.0D5*temp; call DLSARG (size(gf), GK, size(gf), GF, 1, GD)! open (77,file='dataout1.txt')! write(77,*) i,shell(1)%ncoord! close(77) open (77,file='dataout.txt') do i=1,nnode!write(77,*) i write(77,'(i3,3e12.4)') i,gd((i-1)*3+1),gd((i-1)*3+2),gd((i-1)*3+3) close(77) stop stop end program

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