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clear nel=16;nnel=4;ndof=6;nnode=25;sdof=nnode*ndof;edof=nnel*ndof;emodule=3e6;poisson=0.0;t=3;nglxb=2; nglyb=2;nglb=nglxb*nglyb;nglxs=1; nglys=1;ngls=nglxs*nglys;gcoord=[0.0 0.0 0.0; 0.0 6.25 0.0; 0.0 12.5 0.0; 0.0 18.75 0.0;0.0 25.0 0.0; 4.34 0.0 -0.38;4.34 6.25 -0.38;4.34 12.5 -0.38;4.34 18.75 -0.38;4.34 25.0 -0.38;

8.55 0.0 -1.51;8.55 6.25 -1.51;8.55 12.5 -1.51;8.55 18.75 -1.51;8.55 25.0 -1.51;12.5 0.0 -3.35;12.5 6.25 -3.35;12.5 12.5 -3.35;12.5 18.75 -3.35;12.5 25.0 -3.35; 16.1 0.0 -5.85;16.1 6.25 -5.85;16.1 12.5 -5.85;16.1 18.75 -5.85;16.1 25.0 -5.85];gcoord=12.0*gcoord;

nodes={{6,7,2,1},{7,8,3,2},{8,9,4,3},{9,10,5,4},{11,12,7,6},{12,13,8,7},{13,14,9,8},{14,15,10,9},{16,17,12,11},{17,18,13,12},{18,19,14,13},{19,20,15,14},{21,22,17,16},{22,23,18 17},{23,24,19,18},{24,25,20,19];bcdof={1 3 5 6 7 11 12 13 17 18 19 23 24 25 26 28 29 30 31 33 56 58 60 61 63 8688 90 91 93 116 118 120 121 122 123 146 148 150};

bcval=Table[0,{1},{bcdof}];ff=Table[0,{sdof},{1}];kk=Table[0,{sdof},{sdof}];disp=Table[0,{sdof},{1}];index=Table[0,{edof},{1}];kinmtsb=Table[0,{3},{edof}];

matmtsb=Table[0,{3},{3}];kinmtsm=Table[0,{3},{edof}];matmtsm=Table[0,{3},{3}];kinmtss=Table[0,{2},{edof}];matmtss=Table[0,{2},{2}];tr3d=Table[0,{edof},{edof}];

ff[3,1]=-613.6;ff[9,1]=-1227.2;ff[15,1]=-1227.2;ff[21,1]=-1227.2;

ff[27,1]=-613.6;ff[33,1]=-1227.2;ff[39,1]=-2454.4;ff[45,1]=-2454.4;ff[51,1]=-2454.4;ff[57,1]=-1227.2;ff[63,1]=-1227.2;ff[69,1]=-2454.4;ff[75,1]=-2454.4;ff[81,1]=-2454.4;

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 ff[87,1]=-1227.2;ff[93,1]=-1227.2;ff[99,1]=-2454.4;ff[105,1]=-2454.4;ff[111,1]=-2454.4;ff[117,1]=-1227.2;ff[123,1]=-613.6;ff[129,1]=-1227.2;ff[135,1]=-1227.2;ff[141,1]=-1227.2;ff[147,1]=-613.6;

if iopt==1matmtrx= elastic/(1-poisson*poisson)* ...[1 poisson 0; ...poisson 1 0; ...0 0 (1-poisson)/2];

elseif iopt==2matmtrx= elastic/((1+poisson)*(1-2*poisson))* ...[(1-poisson) poisson 0;poisson (1-poisson) 0;0 0 (1-2*poisson)/2];

elseif iopt==3matmtrx= elastic/((1+poisson)*(1-2*poisson))* ...[(1-poisson) poisson poisson 0;poisson (1-poisson) poisson 0;poisson poisson (1-poisson) 0;0 0 0 (1-2*poisson)/2];

elsematmtrx= elastic/((1+poisson)*(1-2*poisson))* ...[(1-poisson) poisson poisson 0 0 0;poisson (1-poisson) poisson 0 0 0;poisson poisson (1-poisson) 0 0 0;

0 0 0 (1-2*poisson)/2 0 0;0 0 0 0 (1-2*poisson)/2 0;0 0 0 0 0 (1-2*poisson)/2];

end

shearm=0.5*emodule/(1.0+poisson);shcof=5/6;matmtss=shearm*shcof*t*{{1 0}, {0 1}};

/*****************************************/

feglqd1[ngl_] := [ngll = ngl; point1 = Table[0, {ngll}];  weight1 = Table[0, {ngll}];  If[ngll == 1, point1[[1]] = 0.0; weight1[[1]] = 2.0;,

If[ngll == 2, point1[[1]] = -0.577350269189626;  point1[[2]] = -point1[[1]];  weight1[[1]] = 1.0;  weight1[[2]] = weight1[[1]];,

If[ngll == 3, point1[[1]] = -0.774596669241483;  point1[[2]] = 0.0;  point1[[3]] = -point1[[1]];

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  weight1[[1]] = 0.555555555555556;  weight1[[2]] = 0.888888888888889;  weight1[[3]] = weight1[[1]];,

If[ngll == 4, point1[[1]] = -0.861136311594053;  point1[[2]] = -0.339981043584856;  point1[[3]] = -point1[[2]];  point1[[4]] = -point1[[1]];  weight1[[1]] = 0.347854845137454;  weight1[[2]] = 0.652145154862546;  weight1[[3]] = weight1[[2]];  weight1[[4]] = weight1[[1]];, point1[[1]] = -0.906179845938664;  point1[[2]] = -0.538469310105683;  point1[[3]] = 0.0;  point1[[4]] = -point1[[2]];  point1[[5]] = -point1[[1]];  weight1[[1]] = 0.236926885056189;  weight1[[2]] = 0.478628670499366;  weight1[[3]] = 0.568888888888889;  weight1[[4]] = weight1[[2]];  weight1[[5]] = weight1[[1]];]]]] Return[{weight1, point1}]];

/&**********************************************************&/

function [tr3d,xprime,yprime]=fetransh(xcoord,ycoord,zcoord,n)

%--------------------------------------------------------------% Purpose:% Compute direction cosines between three-dimensional% local and global coordinate axes%% Synopsis:% [tr3d,xprime,yprime]=fetransh(xcoord,ycoord,zcoord,n)%% Variable Description:

% xcoord - nodal x coordinates (4x1)% ycoord - nodal y coordinates (4X1)% zcoord - nodal z coordinates (4X1)% n - number of nodes per element% tr3d - 3d transformation matrix from local to global axes% xprime - coordinate in terms of the local axes (4x1)% yprime - coordinate in terms of the global axes (4X1)%% Note:% The local x-axis is defined in the direction from the first node% to the second node. Nodes 1, 2 and 4 define the local xy-plane.% The local z-axis is defined normal to the local xy-plane.% The local y-axis is defined normal to the x and z axes.

%--------------------------------------------------------------------------

%% compute direction cosines% v12x=xcoord(2)-xcoord(1);v12y=ycoord(2)-ycoord(1);v12z=zcoord(2)-zcoord(1);l12=sqrt(v12x^2+v12y^2+v12z^2);

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v23x=xcoord(3)-xcoord(2);v23y=ycoord(3)-ycoord(2);v23z=zcoord(3)-zcoord(2);l23=sqrt(v23x^2+v23y^2+v23z^2);v34x=xcoord(4)-xcoord(3);v34y=ycoord(4)-ycoord(3);v34z=zcoord(4)-zcoord(3);l34=sqrt(v34x^2+v34y^2+v34z^2);v14x=xcoord(4)-xcoord(1);v14y=ycoord(4)-ycoord(1);v14z=zcoord(4)-zcoord(1);l14=sqrt(v14x^2+v14y^2+v14z^2);v13x=xcoord(3)-xcoord(1);v13y=ycoord(3)-ycoord(1);v13z=zcoord(3)-zcoord(1);l13=sqrt(v13x^2+v13y^2+v13z^2);v1tx=v12y*v14z-v12z*v14y;v1ty=v12z*v14x-v12x*v14z;v1tz=v12x*v14y-v12y*v14x;v1yx=v1ty*v12z-v1tz*v12y;v1yy=v1tz*v12x-v1tx*v12z;v1yz=v1tx*v12y-v1ty*v12x;vxx=v12x/l12;vxy=v12y/l12;

vxz=v12z/l12;vyx=v1yx/sqrt(v1yx^2+v1yy^2+v1yz^2);vyy=v1yy/sqrt(v1yx^2+v1yy^2+v1yz^2);vyz=v1yz/sqrt(v1yx^2+v1yy^2+v1yz^2);vzx=v1tx/sqrt(v1tx^2+v1ty^2+v1tz^2);vzy=v1ty/sqrt(v1tx^2+v1ty^2+v1tz^2);vzz=v1tz/sqrt(v1tx^2+v1ty^2+v1tz^2);

%% transformation matrix%for i=1:2*ni1=(i-1)*3+1;

i2=i1+1;i3=i2+1;tr3d(i1,i1)=vxx;tr3d(i1,i2)=vxy;tr3d(i1,i3)=vxz;tr3d(i2,i1)=vyx;tr3d(i2,i2)=vyy;tr3d(i2,i3)=vyz;tr3d(i3,i1)=vzx;tr3d(i3,i2)=vzy;tr3d(i3,i3)=vzz;end

%% compute nodal values in terms of local axes%alpa213=acos((l12^2+l13^2-l23^2)/(2*l12*l13));alpa314=acos((l13^2+l14^2-l34^2)/(2*l13*l14));alpa41y=2*atan(1)-alpa213-alpa314;xprime(1)=0; yprime(1)=0;xprime(2)=l12; yprime(2)=0;xprime(3)=l13*cos(alpa213); yprime(3)=l13*sin(alpa213);xprime(4)=l14*sin(alpa41y); yprime(4)=l14*cos(alpa41y);

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