%=========================================
%PARAMETRIC MODEL ANALYSIS RESULTS CONTROL
%=========================================
% _________________________________________________________________________
%|____10NODE_20DOF ISOPARAMETRIC TRIANGULAR PLANE STRESS FEM___[A.]_(C)(R)|
%| |
%| Shape function:Homogen |
%| Stifness :Topology+Accumulate method |
%|_______________________________Solve Equation:Cholesky-[L][D][u]_________|
%| Maxima 5.9.0.9beta2 http://maxima.sourceforge.net |
%| Using Lisp Kyoto Common Lisp GCL 2.6.3 (aka GCL) |
%| Distributed under the GNU Public License. See the file COPYING. |
%| Dedicated to the memory of William Schelter. |
%| This is a development version of Maxima. The function bug_report() |
%| provides bug reporting information. |
%| |
%|_____PARAMETRIC FEM ANALYSIS SUBPROGRMAM_______Maxima5.9.0.9beta2_[GPL]__|
%========================================This procedure runing MAXIMA
%PROCEDURE(1):Jacobian matrix
%PROCEDURE(2):Element Stiffness matrix depend the Jacobian transform
%_____________________________________[PROCEDURE(1)]
%N1(x,y):=1/2*e1*(3*e1-1)*(3*e1-2);
%N2(x,y):=1/2*e2*(3*e2-1)*(3*e2-2);
%N3(x,y):=1/2*e3*(3*e3-1)*(3*e3-2);
%N4(x,y):=9/2*e1*e2*(3*e1-1);
%N5(x,y):=9/2*e1*e2*(3*e2-1);
%N6(x,y):=9/2*e2*e3*(3*e2-1);
%N7(x,y):=9/2*e2*e3*(3*e3-1);
%N8(x,y):=9/2*e3*e1*(3*e3-1);
%N9(x,y):=9/2*e3*e1*(3*e1-1);
%N10(x,y):=27*e1*e2*e3;
%H1e(e,n):=diff(N1(e,n),e1)-diff(N1(e,n),e3);
%H2e(e,n):=diff(N2(e,n),e1)-diff(N2(e,n),e3);
%H3e(e,n):=diff(N3(e,n),e1)-diff(N3(e,n),e3);
%H4e(e,n):=diff(N4(e,n),e1)-diff(N4(e,n),e3);
%H5e(e,n):=diff(N5(e,n),e1)-diff(N5(e,n),e3);
%H6e(e,n):=diff(N6(e,n),e1)-diff(N6(e,n),e3);
%H7e(e,n):=diff(N7(e,n),e1)-diff(N7(e,n),e3);
%H8e(e,n):=diff(N8(e,n),e1)-diff(N8(e,n),e3);
%H9e(e,n):=diff(N9(e,n),e1)-diff(N9(e,n),e3);
%H10e(e,n):=diff(N10(e,n),e1)-diff(N10(e,n),e3);
%H1n(e,n):=diff(N1(e,n),e2)-diff(N1(e,n),e3);
%H2n(e,n):=diff(N2(e,n),e2)-diff(N2(e,n),e3);
%H3n(e,n):=diff(N3(e,n),e2)-diff(N3(e,n),e3);
%H4n(e,n):=diff(N4(e,n),e2)-diff(N4(e,n),e3);
%H5n(e,n):=diff(N5(e,n),e2)-diff(N5(e,n),e3);
%H6n(e,n):=diff(N6(e,n),e2)-diff(N6(e,n),e3);
%H7n(e,n):=diff(N7(e,n),e2)-diff(N7(e,n),e3);
%H8n(e,n):=diff(N8(e,n),e2)-diff(N8(e,n),e3);
%H9n(e,n):=diff(N9(e,n),e2)-diff(N9(e,n),e3);
%H10n(e,n):=diff(N10(e,n),e2)-diff(N10(e,n),e3);
%Pos(x,y):=matrix([x1,y1],[x2,y2],[x3,y3],[x4,y4],[x5,y5],[x6,y6],[x7,y7],[x8,y8],[x9,y9],[x10,y10]);
%N(e,n):=matrix([H1e(e,n),H2e(e,n),H3e(e,n),H4e(e,n),H5e(e,n),H6e(e,n),H7e(e,n),H8e(e,n),H9e(e,n),H10e(e,n)],
% [H1n(e,n),H2n(e,n),H3n(e,n),H4n(e,n),H5n(e,n),H6n(e,n),H7n(e,n),H8n(e,n),H9n(e,n),H10n(e,n)]);
%J(e,n):=N(e,n).Pos(x,y);
%J(e,n);
%Fortmx (J,J(e,n));
%_____________________________________[PROCEDURE(2)]
%Ju(e,n):=matrix([g11,g12],[g21,g22]);
%Ju(e,n);
%Nx(e,n):=Ju(e,n).N(e,n);
%Nx(e,n);
%fortmx(H,Nx(e,n));
%=====================================================[END MAXIMA]
% _________________________________________________________________________
%|_____10NODE_20DOF ISOPARAMETRIC TRIANGULAR PLANE STRESS FEM___[A.]_(C)(R)|
%| |
%| Shape function:Homogen |
%| Stifness :Topology+Accumulate method |
%|_______________________________Solve Equation:Cholesky-[L][D][u]_________|
%| |
%|_____PARAMETRIC FEM ANALYSIS SUBPROGRMAM_______Maxima5.9.0.9beta2_[GPL]__|
clc
clear
%===============================================INPUT DATA
%===============MATERIALS PROPERTIES
E=2E6; %Element elasticity constant;
v=0.3; %Element material poission ratio;
th=0.10; %Element thickness
%===============
%==================POSITION MATRIX
%Pos(Element No,:)=[Element Node Number]
Pos(1,:)= [1 4 22 2 3 10 16 15 8 9];
Pos(2,:)= [4 25 22 11 18 24 23 16 10 17];
Pos(3,:)= [4 28 25 12 20 27 26 18 11 19];
Pos(4,:)= [4 7 28 5 6 14 21 20 12 13];
Pos(5,:)= [22 25 43 23 24 31 37 36 29 30];
Pos(6,:)= [25 46 43 32 39 45 44 37 31 38];
Pos(7,:)= [25 49 46 33 41 48 47 39 32 40];
Pos(8,:)= [25 28 49 26 27 35 42 41 33 34];
Pos(9,:)= [43 46 64 44 45 52 58 57 50 51];
Pos(10,:)=[46 67 64 53 60 66 65 58 52 59];
Pos(11,:)=[46 70 67 54 62 69 68 60 53 61];
Pos(12,:)=[46 49 70 47 48 56 63 62 54 55];
%==================
Number=size(Pos);
No=Number(1);
%_____________Automatic coordinate function
%Cor=Element Node Castesian Coordinate for Global System Axis
% Cor=[ xi yi ]
Cor=[.99999 0
1.33332 0
1.66665 0
1.99998 0
2.33331 0
2.66664 0
2.99997 0
.9847979 .1736464
1.313064 .2315286
1.64133 .2894107
1.969596 .3472929
2.297862 .405175
2.626128 .4630572
2.954394 .5209394
.9396832 .3420167
1.252911 .4560223
1.566139 .5700279
1.879366 .6840335
2.192594 .798039
2.505822 .9120446
2.81905 1.02605
.8660167 .499995
1.154689 .66666
1.443361 .833325
1.732033 .99999
2.020706 1.166655
2.309378 1.33332
2.59805 1.499985
.7660368 .6427812
1.021382 .8570416
1.276728 1.071302
1.532074 1.285562
1.787419 1.499823
2.042765 1.714083
2.29811 1.928344
.6427812 .7660368
.8570416 1.021382
1.071302 1.276728
1.285562 1.532074
1.499823 1.787419
1.714083 2.042765
1.928344 2.29811
.499995 .8660167
.66666 1.154689
.833325 1.443361
.99999 1.732033
1.166655 2.020706
1.33332 2.309378
1.499985 2.59805
.3420167 .9396832
.4560223 1.252911
.5700279 1.566139
.6840335 1.879366
.798039 2.192594
.9120446 2.505822
1.02605 2.81905
.1736464 .9847979
.2315286 1.313064
.2894107 1.64133
.3472929 1.969596
.405175 2.297862
.4630572 2.626128
.5209394 2.954394
6.12297E-17 .99999
8.163961E-17 1.33332
1.020495E-16 1.66665
1.224594E-16 1.99998
1.428693E-16 2.33331
1.632792E-16 2.66664
1.836891E-16 2.99997];
Number=size(Cor);
Node=Number(1); %System Node Number
for i=1:Node;
Re(i,:)=[1 1];
end
%===============SYSTEM SUPPORT
%Re(Node number,:)=[ux vy]
Re(1,:) =[0 0];
Re(7,:) =[0 0];
Re(64,:) =[0 0];
Re(70,:) =[0 0];
%===============
Number=size(Re);
Nom=Number(2); %Plane Element node d.o.f Number
%_______________Topology and accumulate method
sayman=0;
for i=1:Node;
for j=1:Nom;
if Re(i,j)==1 ;
sayman = sayman +1;
Re(i,j) = sayman;
end
end
end
Item=sayman; %Plane system sum deplacement value
%_________________________________Modal deplacement parameter
for i=1:No;
for j=1:Nom;
R(i,j+0*Nom)= Re(Pos(i,1),j);
R(i,j+1*Nom)= Re(Pos(i,2),j);
R(i,j+2*Nom)= Re(Pos(i,3),j);
R(i,j+3*Nom)= Re(Pos(i,4),j);
R(i,j+4*Nom)= Re(Pos(i,5),j);
R(i,j+5*Nom)= Re(Pos(i,6),j);
R(i,j+6*Nom)= Re(Pos(i,7),j);
R(i,j+7*Nom)= Re(Pos(i,8),j);
R(i,j+8*Nom)= Re(Pos(i,9),j);
R(i,j+9*Nom)= Re(Pos(i,10),j);
end
end
%============SYSTEM LOAD
%Re(Node number, Freedoom number)[u v]
P(Item)=0;
P(Re(28,2)) =-5;
P(Re(49,2)) =-5;
%=============
%___________________________________________________END_INPUT_DATA
%===================================================SYSTEM_ANALYSIS
%open dimension local element stiffness matrix
K(20,20,No)=0;
for s=1:No;%Element number
X1=Cor(Pos(s,1),1); Y1=Cor(Pos(s,1),2);
X2=Cor(Pos(s,2),1); Y2=Cor(Pos(s,2),2);
X3=Cor(Pos(s,3),1); Y3=Cor(Pos(s,3),2);
X4=Cor(Pos(s,4),1); Y4=Cor(Pos(s,4),2);
X5=Cor(Pos(s,5),1); Y5=Cor(Pos(s,5),2);
X6=Cor(Pos(s,6),1); Y6=Cor(Pos(s,6),2);
X7=Cor(Pos(s,7),1); Y7=Cor(Pos(s,7),2);
X8=Cor(Pos(s,8),1); Y8=Cor(Pos(s,8),2);
X9=Cor(Pos(s,9),1); Y9=Cor(Pos(s,9),2);
X10=Cor(Pos(s,10),1); Y10=Cor(Pos(s,10),2);
Area=0.5*(-X1*(Y3-Y2)+X2*Y3-X3*Y2+(X3-X2)*Y1);
%12 Point Gauss_Legendre_Numerical_Integraton_Coefficients
%Multiply value
ha=0.050844906370207;hb=0.116786275726379;hc=0.082851075618374;
%Weight function value
wa=0.872831971016996;
wb=0.063089014491502;
wc=0.501426509659179;
wd=0.249286745170910;
we=0.636502499121399;
wf=0.310352451033785;
wg=0.053145049844816;
W=[wa wb wb; %ha
wb wa wb;
wb wb wa; %hb
wc wd wd;
wd wc wd;
wd wd wc; %hc
we wf wg;
we wg wf;
wf wg we;
wf we wg;
wg we wf;
wg wf we];
for j=1:12
if j==1 ;h=ha;end
if j==4 ;h=hb;end
if j==7 ;h=hc;end
e1=W(j,1);
e2=W(j,2);
e3=W(j,3);
%====================================[PROCEDURE(1)]Maxima
%Jacobian matrix terms
J11 = (9.0*(3*e1-1)*e3/2.0+27.0*e1*e3/2.0+(-9.0)*e1*(3*e1-1)/2.0)*X9+(9.0*e3*(3*e3-1)/2.0+(-9.0)*e1*(3*e3-1)/2.0+(-27.0)*e1*e3/2.0)*X8+((-9.0)*e2*(3*e3-1)/2.0+(-27.0)*e2*e3/2.0)*X7+(-9.0)*e2*(3*e2-1)*X6/2.0+9.0*e2*(3*e2-1)*X5/2.0+(9.0*(3*e1-1)*e2/2.0+27.0*e1*e2/2.0)*X4+(-(3*e3-2)*(3*e3-1)/2.0+(-3.0)*e3*(3*e3-1)/2.0+(-3.0)*e3*(3*e3-2)/2.0)*X3+(27*e2*e3-27*e1*e2)*X10+((3*e1-2)*(3*e1-1)/2.0+3.0*e1*(3*e1-1)/2.0+3.0*e1*(3*e1-2)/2.0)*X1;
J12 = (9.0*(3*e1-1)*e3/2.0+27.0*e1*e3/2.0+(-9.0)*e1*(3*e1-1)/2.0)*Y9+(9.0*e3*(3*e3-1)/2.0+(-9.0)*e1*(3*e3-1)/2.0+(-27.0)*e1*e3/2.0)*Y8+((-9.0)*e2*(3*e3-1)/2.0+(-27.0)*e2*e3/2.0)*Y7+(-9.0)*e2*(3*e2-1)*Y6/2.0+9.0*e2*(3*e2-1)*Y5/2.0+(9.0*(3*e1-1)*e2/2.0+27.0*e1*e2/2.0)*Y4+(-(3*e3-2)*(3*e3-1)/2.0+(-3.0)*e3*(3*e3-1)/2.0+(-3.0)*e3*(3*e3-2)/2.0)*Y3+(27*e2*e3-27*e1*e2)*Y10+((3*e1-2)*(3*e1-1)/2.0+3.0*e1*(3*e1-1)/2.0+3.0*e1*(3*e1-2)/2.0)*Y1;
J21 = (-9.0)*e1*(3*e1-1)*X9/2.0+((-9.0)*e1*(3*e3-1)/2.0+(-27.0)*e1*e3/2.0)*X8+(9.0*e3*(3*e3-1)/2.0+(-9.0)*e2*(3*e3-1)/2.0+(-27.0)*e2*e3/2.0)*X7+(9.0*(3*e2-1)*e3/2.0+27.0*e2*e3/2.0+(-9.0)*e2*(3*e2-1)/2.0)*X6+(9.0*e1*(3*e2-1)/2.0+27.0*e1*e2/2.0)*X5+9.0*e1*(3*e1-1)*X4/2.0+(-(3*e3-2)*(3*e3-1)/2.0+(-3.0)*e3*(3*e3-1)/2.0+(-3.0)*e3*(3*e3-2)/2.0)*X3+((3*e2-2)*(3*e2-1)/2.0+3.0*e2*(3*e2-1)/2.0+3.0*e2*(3*e2-2)/2.0)*X2+(27*e1*e3-27*e1*e2)*X10;
J22 = (-9.0)*e1*(3*e1-1)*Y9/2.0+((-9.0)*e1*(3*e3-1)/2.0+(-27.0)*e1*e3/2.0)*Y8+(9.0*e3*(3*e3-1)/2.0+(-9.0)*e2*(3*e3-1)/2.0+(-27.0)*e2*e3/2.0)*Y7+(9.0*(3*e2-1)*e3/2.0+27.0*e2*e3/2.0+(-9.0)*e2*(3*e2-1)/2.0)*Y6+(9.0*e1*(3*e2-1)/2.0+27.0*e1*e2/2.0)*Y5+9.0*e1*(3*e1-1)*Y4/2.0+(-(3*e3-2)*(3*e3-1)/2.0+(-3.0)*e3*(3*e3-1)/2.0+(-3.0)*e3*(3*e3-2)/2.0)*Y3+((3*e2-2)*(3*e2-1)/2.0+3.0*e2*(3*e2-1)/2.0+3.0*e2*(3*e2-2)/2.0)*Y2+(27*e1*e3-27*e1*e2)*Y10;
%Jacobian matrix
Jacobi=[J11 J12;
J21 J22];
%Invers to Jacobian matrix
InvJacobi=Jacobi^-1;
g11=InvJacobi(1,1); g12=InvJacobi(1,2);
g21=InvJacobi(2,1); g22=InvJacobi(2,2);
%====================================[PROCEDURE(2)]Maxima
Hx1 = ((3*e1-2)*(3*e1-1)/2.0+3.0*e1*(3*e1-1)/2.0+3.0*e1*(3*e1-2)/2.0)*g11;
Hx2 = ((3*e2-2)*(3*e2-1)/2.0+3.0*e2*(3*e2-1)/2.0+3.0*e2*(3*e2-2)/2.0)*g12;
Hx3 = (-(3*e3-2)*(3*e3-1)/2.0+(-3.0)*e3*(3*e3-1)/2.0+(-3.0)*e3*(3*e3-2)/2.0)*g12+(-(3*e3-2)*(3*e3-1)/2.0+(-3.0)*e3*(3*e3-1)/2.0+(-3.0)*e3*(3*e3-2)/2.0)*g11;
Hx4 = 9.0*e1*(3*e1-1)*g12/2.0+(9.0*(3*e1-1)*e2/2.0+27.0*e1*e2/2.0)*g11;
Hx5 = (9.0*e1*(3*e2-1)/2.0+27.0*e1*e2/2.0)*g12+9.0*e2*(3*e2-1)*g11/2.0;
Hx6 = (9.0*(3*e2-1)*e3/2.0+27.0*e2*e3/2.0+(-9.0)*e2*(3*e2-1)/2.0)*g12+(-9.0)*e2*(3*e2-1)*g11/2.0;
Hx7 = (9.0*e3*(3*e3-1)/2.0+(-9.0)*e2*(3*e3-1)/2.0+(-27.0)*e2*e3/2.0)*g12+((-9.0)*e2*(3*e3-1)/2.0+(-27.0)*e2*e3/2.0)*g11;
Hx8 = ((-9.0)*e1*(3*e3-1)/2.0+(-27.0)*e1*e3/2.0)*g12+(9.0*e3*(3*e3-1)/2.0+(-9.0)*e1*(3*e3-1)/2.0+(-27.0)*e1*e3/2.0)*g11;
Hx9 = (-9.0)*e1*(3*e1-1)*g12/2.0+(9.0*(3*e1-1)*e3/2.0+27.0*e1*e3/2.0+(-9.0)*e1*(3*e1-1)/2.0)*g11;
Hx10 = (27*e1*e3-27*e1*e2)*g12+(27*e2*e3-27*e1*e2)*g11;
Hy1 = ((3*e1-2)*(3*e1-1)/2.0+3.0*e1*(3*e1-1)/2.0+3.0*e1*(3*e1-2)/2.0)*g21;
Hy2 = ((3*e2-2)*(3*e2-1)/2.0+3.0*e2*(3*e2-1)/2.0+3.0*e2*(3*e2-2)/2.0)*g22;
Hy3 = (-(3*e3-2)*(3*e3-1)/2.0+(-3.0)*e3*(3*e3-1)/2.0+(-3.0)*e3*(3*e3-2)/2.0)*g22+(-(3*e3-2)*(3*e3-1)/2.0+(-3.0)*e3*(3*e3-1)/2.0+(-3.0)*e3*(3*e3-2)/2.0)*g21;
Hy4 = 9.0*e1*(3*e1-1)*g22/2.0+(9.0*(3*e1-1)*e2/2.0+27.0*e1*e2/2.0)*g21;
Hy5 = (9.0*e1*(3*e2-1)/2.0+27.0*e1*e2/2.0)*g22+9.0*e2*(3*e2-1)*g21/2.0;
Hy6 = (9.0*(3*e2-1)*e3/2.0+27.0*e2*e3/2.0+(-9.0)*e2*(3*e2-1)/2.0)*g22+(-9.0)*e2*(3*e2-1)*g21/2.0;
Hy7 = (9.0*e3*(3*e3-1)/2.0+(-9.0)*e2*(3*e3-1)/2.0+(-27.0)*e2*e3/2.0)*g22+((-9.0)*e2*(3*e3-1)/2.0+(-27.0)*e2*e3/2.0)*g21;
Hy8 = ((-9.0)*e1*(3*e3-1)/2.0+(-27.0)*e1*e3/2.0)*g22+(9.0*e3*(3*e3-1)/2.0+(-9.0)*e1*(3*e3-1)/2.0+(-27.0)*e1*e3/2.0)*g21;
Hy9 = (-9.0)*e1*(3*e1-1)*g22/2.0+(9.0*(3*e1-1)*e3/2.0+27.0*e1*e3/2.0+(-9.0)*e1*(3*e1-1)/2.0)*g21;
Hy10 = (27*e1*e3-27*e1*e2)*g22+(27*e2*e3-27*e1*e2)*g21;
%Connection Matrix
A(:,:,s)= [Hx1 0 Hx2 0 Hx3 0 Hx4 0 Hx5 0 Hx6 0 Hx7 0 Hx8 0 Hx9 0 Hx10 0 ;
0 Hy1 0 Hy2 0 Hy3 0 Hy4 0 Hy5 0 Hy6 0 Hy7 0 Hy8 0 Hy9 0 Hy10 ;
Hy1 Hx1 Hy2 Hx2 Hy3 Hx3 Hy4 Hx4 Hy5 Hx5 Hy6 Hx6 Hy7 Hx7 Hy8 Hx8 Hy9 Hx9 Hy10 Hx10 ];
%Elasticity Matrix
C=E/(1-v^2)*[1 v 0 ;
v 1 0 ;
0 0 0.5*(1-v)];
%Gauss-Legendre Numerical Integration
K(:,:,s)=K(:,:,s)+0.5*th*det(Jacobi)*h*A(:,:,s)'*C*A(:,:,s);
end
end
%open dimension system stiffness matrix dimension
Ksis(Item,Item)=0;
for n=1:No;
for sat=1:20;
for sut=1:20;
if (R(n,sat)~=0)
if (R(n,sut)~=0);
Ksis(R(n,sut),R(n,sat))=Ksis(R(n,sut),R(n,sat)) + K(sat,sut,n);
end
end
end
end
end
%System global stiffness matris singularity check
equation=size(Ksis);
if equation(1)~=rank(Ksis)
display('This system stiffness matrix is badly scaled')
R
error('Control system support boundary conditions')
else
Ku = inv(Ksis);
D = Ku *P';
end
clear equation
%Element per unit node topolog matrix
for v = 1 : No;
for m = 1 :20;
u = R(v, m);
if u ~=0
Hu(v, m) = D(u) ;
else
Hu(v,m)=0;
end
end
end
%Global system node displacement is moving local element nodes.
for s=1:No;
for i=1:10*Nom;
if R(s,i)~=0 ;
Dep(s,i)=D(R(s,i));
else
Dep(s,i)=0;
end
end
end
display('Global displacement [u(x) v(y)]T');
Dep'
for v=1 :No;
Pg(:,v) = K(:,:,v)*Hu(v,:)';
end
display('Global system node reactions');
Pg
contourf(Ksis)
title('Global system stiffness band matrix');
%=================================Node Patch Testing Code
for sutun=1:No;
for sat=1:10;
Pgx(sat,sutun)=Pg(2*sat-1,sutun);
Pgy(sat,sutun)=Pg(2*sat,sutun);
end
end
Pdx(Node)=0;
Pdy(Node)=0;
for Elemanno=1:No;
for sutun=1:10;
Pdx(Pos(Elemanno,sutun))=Pdx(Pos(Elemanno,sutun))+Pgx(sutun,Elemanno);
Pdy(Pos(Elemanno,sutun))=Pdy(Pos(Elemanno,sutun))+Pgy(sutun,Elemanno);
end
end
%Information:This Pdx,Pdy different the zero terms Support Reactions
('Manual Patch Test (node kin. eq. met. [Pgx Pgy])')
[Pdx' Pdy']
%================================================INFORMATION
%____________________PARAMETRIC Element stiffness matrix value (1)
%1.0e+006 *
%
% Columns 1 through 9
%
% 0.0409 0 0 -0.0067 -0.0084 0.0067 0.0036 -0.0548 0.0036
% 0 0.1168 -0.0058 0 0.0058 -0.0240 -0.0470 0.0103 0.0198
% 0 -0.0058 0.0747 0 -0.0154 0.0058 0.0066 0.0198 0.0066
% -0.0067 0 0 0.0262 0.0067 -0.0054 0.0231 0.0023 -0.0548
% -0.0084 0.0058 -0.0154 0.0067 0.1156 -0.0607 -0.0102 0.0054 -0.0102
% 0.0067 -0.0240 0.0058 -0.0054 -0.0607 0.1429 0.0054 -0.0126 0.0054
% 0.0036 -0.0470 0.0066 0.0231 -0.0102 0.0054 0.4590 -0.1205 -0.0918
% -0.0548 0.0103 0.0198 0.0023 0.0054 -0.0126 -0.1205 0.5674 -0.0427
% 0.0036 0.0198 0.0066 -0.0548 -0.0102 0.0054 -0.0918 -0.0427 0.4590
% 0.0231 0.0103 -0.0470 0.0023 0.0054 -0.0126 -0.0538 -0.1135 -0.1205
% -0.0036 0 -0.1187 0.0548 0.0629 -0.0251 0.0325 -0.0241 -0.1623
% 0 -0.0103 0.0470 -0.0415 -0.0284 0.0311 -0.0241 0.0927 0.1205
% -0.0036 0 0.0593 -0.0231 -0.1151 0.0416 0.0325 -0.0241 0.0325
% 0 -0.0103 -0.0198 0.0208 0.0495 -0.0312 -0.0241 0.0927 -0.0241
% 0.0325 -0.0198 -0.0066 0 -0.0583 0.0495 0.0593 -0.0241 0.0593
% -0.0231 0.0927 0 -0.0023 0.0416 -0.1831 -0.0241 0.0208 -0.0241
% -0.0649 0.0470 -0.0066 0 0.0390 -0.0284 -0.2967 0.1205 0.0593
% 0.0548 -0.1854 0 -0.0023 -0.0251 0.0950 0.1205 -0.1038 -0.0241
% 0 0 0 0 0 0 -0.1947 0.1446 -0.3560
% 0 0 0 0 0 0 0.1446 -0.5563 0.1446
% Columns 10 through 18
% 0.0231 -0.0036 0 -0.0036 0 0.0325 -0.0231 -0.0649 0.0548
% 0.0103 0 -0.0103 0 -0.0103 -0.0198 0.0927 0.0470 -0.1854
% -0.0470 -0.1187 0.0470 0.0593 -0.0198 -0.0066 0 -0.0066 0
% 0.0023 0.0548 -0.0415 -0.0231 0.0208 0 -0.0023 0 -0.0023
% 0.0054 0.0629 -0.0284 -0.1151 0.0495 -0.0583 0.0416 0.0390 -0.0251
% -0.0126 -0.0251 0.0311 0.0416 -0.0312 0.0495 -0.1831 -0.0284 0.0950
% -0.0538 0.0325 -0.0241 0.0325 -0.0241 0.0593 -0.0241 -0.2967 0.1205
% -0.1135 -0.0241 0.0927 -0.0241 0.0927 -0.0241 0.0208 0.1205 -0.1038
% -0.1205 -0.1623 0.1205 0.0325 -0.0241 0.0593 -0.0241 0.0593 -0.0241
% 0.5674 0.1205 -0.4636 -0.0241 0.0927 -0.0241 0.0208 -0.0241 0.0208
% 0.1205 0.4590 -0.1205 -0.2698 0.0909 0 0.0241 0 0.0241
% -0.4636 -0.1205 0.5674 0.1020 -0.1758 0.0241 0 0.0241 0
% -0.0241 -0.2698 0.1020 0.4590 -0.1205 0 -0.1205 0 0.0241
% 0.0927 0.0909 -0.1758 -0.1205 0.5674 -0.1205 0 0.0241 0
% -0.0241 0 0.0241 0 -0.1205 0.4590 -0.1205 -0.1891 0.0909
% 0.0208 0.0241 0 -0.1205 0 -0.1205 0.5674 0.1020 -0.3916
% -0.0241 0 0.0241 0 0.0241 -0.1891 0.1020 0.4590 -0.1205
% 0.0208 0.0241 0 0.0241 0 0.0909 -0.3916 -0.1205 0.5674
% 0.1446 0 -0.1446 -0.1947 0.1446 -0.3560 0.1446 0 -0.1446
% -0.1246 -0.1446 0 0.1446 -0.5563 0.1446 -0.1246 -0.1446 0
% Columns 19 through 20
% 0 0
% 0 0
% 0 0
% 0 0
% 0 0
% 0 0
% -0.1947 0.1446
% 0.1446 -0.5563
% -0.3560 0.1446
% 0.1446 -0.1246
% 0 -0.1446
% -0.1446 0
% -0.1947 0.1446
% 0.1446 -0.5563
% -0.3560 0.1446
% 0.1446 -0.1246
% 0 -0.1446
% -0.1446 0
% 1.1015 -0.2893
% -0.2893 1.3619
%__________________________ISOPARAMETRIC element stiffness matrix value(1)
%K(:,:,1) =
%
% 1.0e+006 *
%
% Columns 1 through 9
%
% 0.0406 0.0000 -0.0000 -0.0067 -0.0084 0.0067 0.0036 -0.0545 0.0036
% 0.0000 0.1161 -0.0057 -0.0000 0.0057 -0.0239 -0.0467 0.0101 0.0197
% -0.0000 -0.0057 0.0743 0.0000 -0.0153 0.0057 0.0066 0.0197 0.0065
% -0.0067 -0.0000 0.0000 0.0260 0.0067 -0.0054 0.0230 0.0023 -0.0545
% -0.0084 0.0057 -0.0153 0.0067 0.1149 -0.0604 -0.0102 0.0054 -0.0102
% 0.0067 -0.0239 0.0057 -0.0054 -0.0604 0.1421 0.0054 -0.0126 0.0054
% 0.0036 -0.0467 0.0066 0.0230 -0.0102 0.0054 0.4578 -0.1204 -0.0913
% -0.0545 0.0101 0.0197 0.0023 0.0054 -0.0126 -0.1204 0.5669 -0.0427
% 0.0036 0.0197 0.0065 -0.0545 -0.0102 0.0054 -0.0913 -0.0427 0.4583
% 0.0230 0.0103 -0.0467 0.0023 0.0054 -0.0126 -0.0538 -0.1129 -0.1204
% -0.0036 -0.0000 -0.1181 0.0545 0.0627 -0.0250 0.0323 -0.0240 -0.1615
% -0.0000 -0.0103 0.0467 -0.0413 -0.0283 0.0310 -0.0240 0.0923 0.1201
% -0.0036 0.0000 0.0591 -0.0230 -0.1145 0.0414 0.0325 -0.0241 0.0323
% 0.0000 -0.0103 -0.0197 0.0207 0.0492 -0.0312 -0.0241 0.0928 -0.0240
% 0.0323 -0.0197 -0.0066 0.0000 -0.0581 0.0492 0.0590 -0.0240 0.0594
% -0.0230 0.0924 0.0000 -0.0023 0.0414 -0.1822 -0.0240 0.0206 -0.0241
% -0.0646 0.0467 -0.0066 -0.0000 0.0389 -0.0283 -0.2956 0.1201 0.0590
% 0.0545 -0.1845 -0.0000 -0.0023 -0.0250 0.0947 0.1201 -0.1033 -0.0240
% 0.0001 -0.0000 0.0001 0.0000 0.0002 -0.0001 -0.1947 0.1446 -0.3560
% -0.0000 0.0002 0.0000 0.0000 -0.0001 0.0002 0.1446 -0.5563 0.1446
% Columns 10 through 18
% 0.0230 -0.0036 -0.0000 -0.0036 0.0000 0.0323 -0.0230 -0.0646 0.0545
% 0.0103 -0.0000 -0.0103 0.0000 -0.0103 -0.0197 0.0924 0.0467 -0.1845
% -0.0467 -0.1181 0.0467 0.0591 -0.0197 -0.0066 0.0000 -0.0066 -0.0000
% 0.0023 0.0545 -0.0413 -0.0230 0.0207 0.0000 -0.0023 -0.0000 -0.0023
% 0.0054 0.0627 -0.0283 -0.1145 0.0492 -0.0581 0.0414 0.0389 -0.0250
% -0.0126 -0.0250 0.0310 0.0414 -0.0312 0.0492 -0.1822 -0.0283 0.0947
% -0.0538 0.0323 -0.0240 0.0325 -0.0241 0.0590 -0.0240 -0.2956 0.1201
% -0.1129 -0.0240 0.0923 -0.0241 0.0928 -0.0240 0.0206 0.1201 -0.1033
% -0.1204 -0.1615 0.1201 0.0323 -0.0240 0.0594 -0.0241 0.0590 -0.0240
% 0.5657 0.1201 -0.4619 -0.0240 0.0923 -0.0241 0.0208 -0.0240 0.0206
% 0.1201 0.4575 -0.1198 -0.2692 0.0907 -0.0000 0.0240 0.0000 0.0241
% -0.4619 -0.1198 0.5655 0.1018 -0.1752 0.0240 -0.0000 0.0241 0.0000
% -0.0240 -0.2692 0.1018 0.4581 -0.1206 0.0002 -0.1202 -0.0000 0.0240
% 0.0923 0.0907 -0.1752 -0.1206 0.5670 -0.1202 0.0002 0.0240 -0.0000
% -0.0241 -0.0000 0.0240 0.0002 -0.1202 0.4584 -0.1206 -0.1886 0.0907
% 0.0208 0.0240 -0.0000 -0.1202 0.0002 -0.1206 0.5661 0.1018 -0.3908
% -0.0240 0.0000 0.0241 -0.0000 0.0240 -0.1886 0.1018 0.4574 -0.1198
% 0.0206 0.0241 0.0000 0.0240 -0.0000 0.0907 -0.3908 -0.1198 0.5657
% 0.1446 -0.0001 -0.1446 -0.1948 0.1447 -0.3561 0.1447 -0.0001 -0.1446
% -0.1246 -0.1446 -0.0000 0.1447 -0.5563 0.1447 -0.1248 -0.1446 -0.0002
% Columns 19 through 20
% 0.0001 -0.0000
% -0.0000 0.0002
% 0.0001 0.0000
% 0.0000 0.0000
% 0.0002 -0.0001
% -0.0001 0.0002
% -0.1947 0.1446
% 0.1446 -0.5563
% -0.3560 0.1446
% 0.1446 -0.1246
% -0.0001 -0.1446
% -0.1446 -0.0000
% -0.1948 0.1447
% 0.1447 -0.5563
% -0.3561 0.1447
% 0.1447 -0.1248
% -0.0001 -0.1446
% -0.1446 -0.0002
% 1.1014 -0.2893
% -0.2893 1.3618
