70 lines
2.0 KiB
Mathematica
70 lines
2.0 KiB
Mathematica
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function [Ke]=platre(ex,ey,ep,D)
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% Ke=platre(ex,ey,ep,D)
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% [Ke]=platre(ex,ey,ep,D)
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%-------------------------------------------------------------
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% PURPOSE
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% Calculate the stiffness matrix for a rectangular plate element.
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% NOTE! Element sides must be parallel to the coordinate axis.
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%
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% INPUT: ex = [x1 x2 x3 x4] element coordinates
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% ey = [y1 y2 y3 y4]
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%
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% ep=[t] thicknes
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%
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%
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% D constitutive matrix for
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% plane stress
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%
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%
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% OUTPUT: Ke : element stiffness matrix (12 x 12)
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%------------------------------------------------------------
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Lx=ex(3)-ex(1); Ly=ey(3)-ey(1); t=ep(1,1);
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D=t^3/12*D;
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A1=Ly/(Lx^3); A2=Lx/(Ly^3); A3=1/Lx/Ly; A4=Ly/(Lx^2); A5=Lx/(Ly^2); A6=1/Lx;
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A7=1/Ly; A8=Ly/Lx; A9=Lx/Ly;
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C1= 4*A1*D(1,1)+4*A2*D(2,2)+2*A3*D(1,2)+5.6*A3*D(3,3);
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C2=-4*A1*D(1,1)+2*A2*D(2,2)-2*A3*D(1,2)-5.6*A3*D(3,3);
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C3= 2*A1*D(1,1)-4*A2*D(2,2)-2*A3*D(1,2)-5.6*A3*D(3,3);
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C4=-2*A1*D(1,1)-2*A2*D(2,2)+2*A3*D(1,2)+5.6*A3*D(3,3);
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C5=2*A5*D(2,2)+A6*D(1,2)+0.4*A6*D(3,3);
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C6=2*A4*D(1,1)+A7*D(1,2)+0.4*A7*D(3,3);
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C7=2*A5*D(2,2)+0.4*A6*D(3,3);
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C8=2*A4*D(1,1)+0.4*A7*D(3,3);
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C9= A5*D(2,2)-A6*D(1,2)-0.4*A6*D(3,3);
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C10=A4*D(1,1)-A7*D(1,2)-0.4*A7*D(3,3);
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C11=A5*D(2,2)-0.4*A6*D(3,3);
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C12=A4*D(1,1)-0.4*A7*D(3,3);
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C13=4/3*A9*D(2,2)+8/15*A8*D(3,3);
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C14=4/3*A8*D(1,1)+8/15*A9*D(3,3);
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C15=2/3*A9*D(2,2)-8/15*A8*D(3,3);
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C16=2/3*A8*D(1,1)-8/15*A9*D(3,3);
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C17=2/3*A9*D(2,2)-2/15*A8*D(3,3);
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C18=2/3*A8*D(1,1)-2/15*A9*D(3,3);
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C19=1/3*A9*D(2,2)+2/15*A8*D(3,3);
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C20=1/3*A8*D(1,1)+2/15*A9*D(3,3);
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C21=D(1,2);
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Keq=zeros(12,12);
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Keq(1,1:12)=[C1 C5 -C6 C2 C9 -C8 C4 C11 -C12 C3 C7 -C10];
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Keq(2,2:12)=[C13 -C21 C9 C15 0 -C11 C19 0 -C7 C17 0];
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Keq(3,3:12)=[C14 C8 0 C18 C12 0 C20 -C10 0 C16];
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Keq(4,4:12)=[C1 C5 C6 C3 C7 C10 C4 C11 C12];
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Keq(5,5:12)=[C13 C21 -C7 C17 0 -C11 C19 0];
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Keq(6,6:12)=[C14 C10 0 C16 -C12 0 C20];
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Keq(7,7:12)=[C1 -C5 C6 C2 -C9 C8];
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Keq(8,8:12)=[C13 -C21 -C9 C15 0];
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Keq(9,9:12)=[C14 -C8 0 C18];
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Keq(10,10:12)=[C1 -C5 -C6];
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Keq(11,11:12)=[C13 C21];
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Keq(12,12)=[C14];
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Keq=Keq'+Keq-diag(diag(Keq));
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Ke=Keq;
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%--------------------------end--------------------------------
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