?? d3_tetrah.m
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function [K,M,B,E] = D3_TETRAH (x1, y1, z1, x2, y2, z2, x3, y3, z3, x4, y4, z4, Em, miu)
% returns a 3D tetrahedron (CST) element K & M matrix
% in global coordinates
J = [1 1 1 1; x1 x2 x3 x4; y1 y2 y3 y4; z1 z2 z3 z4];
detJ = det(J);
V = 1/6 * detJ;
Q = inv(J)*detJ;
a1 = Q(1,2); b1 = Q(1,3); c1 = Q(1,4);
a2 = Q(2,2); b2 = Q(2,3); c2 = Q(2,4);
a3 = Q(3,2); b3 = Q(3,3); c3 = Q(3,4);
a4 = Q(4,2); b4 = Q(4,3); c4 = Q(4,4);
s=(1-miu);
E = Em*(1-miu)/((1+miu)*(1-2*miu)).*...
[ 1 miu/s miu/s 0 0 0;
miu/s 1 miu/s 0 0 0;
miu/s miu/s 1 0 0 0;
0 0 0 (1-2*miu)/(2*s) 0 0;
0 0 0 0 (1-2*miu)/(2*s) 0;
0 0 0 0 0 (1-2*miu)/(2*s)];
B = 1/(6*V)*[ a1 0 0 a2 0 0 a3 0 0 a4 0 0;
0 b1 0 0 b2 0 0 b3 0 0 b4 0;
0 0 c1 0 0 c2 0 0 c3 0 0 c4;
0 c1 b1 0 c2 b2 0 c3 b3 0 c4 b4;
c1 0 a1 c2 0 a2 c3 0 a3 c4 0 a4;
b1 a1 0 b2 a2 0 b3 a3 0 b4 a4 0];
K = V.*B'*E*B ;
M = zeros(12,12); % memory allocation
M = 1/12*abs(V)*diag([1 1 1 1 1 1 1 1 1 1 1 1]);
M__ = 1/12*V*[2 0 1 0 1 0;
0 2 0 1 0 1;
1 0 2 0 1 0;
0 1 0 2 0 1;
1 0 1 0 2 0;
0 1 0 1 0 2];
% displacement vector: [x1 y1 z1 x2 y2 z2 x3 y3 z3 x4 y4 z4]
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