d2_cst.m

FEM tools for caculation of nonlinear problems

function [B,E,K,M] = D2_CST (x1, y1, x2, y2, x3, y3, Em, h, miu)

% returns a 2D linear constant strain triangle (CST) element K & M matrix
% in global coordinates

A = (0.5 * det([1 1 1; x1 x2 x3; y1 y2 y3]));

E = Em/(1-miu^2).*[ 1  miu  0; miu  1  0; 0  0  (1-miu)/2 ];

B = [  (y2-y3)   0      (y3-y1) 0       (y1-y2)  0;
       0        (x3-x2)  0      (x1-x3)  0       (x2-x1);
       (x3-x2)  (y2-y3) (x1-x3) (y3-y1) (x2-x1)  (y1-y2) ];
B = 1/(2*A).*B;
K = A*h.*B'*E*B ;

M = zeros(6,6);

M  = 1/12*h*A*[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 x2 y2 x3 y3]