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47 lines
1.1 KiB
47 lines
1.1 KiB
11 months ago
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function [Ke,Fe]=symbolicKF(num,D)
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h=1.0/num;
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syms x y z
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x0=0; y0=0; z0=0;
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N(1) = (h+x0-x) * (h+y0-y) * (h+z0-z) / (h^3);
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N(2) = (x-x0) * (h+y0-y) * (h+z0-z) / (h^3);
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N(3) = (h+x0-x) * (y-y0) * (h+z0-z) / (h^3);
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N(4) = (x-x0) * (y-y0) * (h+z0-z) / (h^3);
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N(5) = (h+x0-x) * (h+y0-y) * (z-z0) / (h^3);
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N(6) = (x-x0) * (h+y0-y) * (z-z0) / (h^3);
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N(7) = (h+x0-x) * (y-y0) * (z-z0) / (h^3);
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N(8) = (x-x0) * (y-y0) * (z-z0) / (h^3);
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for j=1:8
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for jj=1:3
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Dif(3*jj-2,j*3+jj-3) = diff(N(j),x);
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Dif(3*jj-1,j*3+jj-3) = diff(N(j),y);
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Dif(3*jj, j*3+jj-3) = diff(N(j),z);
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end
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end
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B9x24 = Dif;
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for j=1:24
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B(1,j) = B9x24(1,j);
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B(2,j) = B9x24(5,j);
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B(3,j) = B9x24(9,j);
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B(4,j) = B9x24(2,j) + B9x24(4,j);
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B(5,j) = B9x24(6,j) + B9x24(8,j);
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B(6,j) = B9x24(3,j) + B9x24(7,j);
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end
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K=B.'*D*B;
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Ke=zeros(24,24);
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for i=1:24
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for j=i:24
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Ke(i,j)=int(int(int(K(i,j),'x',0,h),'y',0,h),'z',0,h);
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end
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end
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Ke=Ke+Ke.'-diag(diag(Ke));
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F=B.'*D;
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Fe=zeros(24,6);
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for i=1:24
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for j=1:6
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Fe(i,j)=int(int(int(F(i,j),'x',0,h),'y',0,h),'z',0,h);
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end
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end
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end
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