?? lineartriangleelementstresses.m
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function y = LinearTriangleElementStresses(E,NU,t,xi,yi,xj,yj,xm,ym,p,u)
%LinearTriangleElementStresses This function returns the element
% stress vector for a linear
% triangular element with modulus of
% elasticity E, Poisson's ratio NU,
% thickness t, coordinates of the
% first node (xi,yi), coordinates of
% the second node (xj,yj),
% coordinates of the third node
% (xm,ym), and element displacement
% vector u. Use p = 1 for cases of
% plane stress, and p = 2 for cases
% of plane strain.
% The size of the element stress
% vector is 3 x 1.
A = (xi*(yj-ym) + xj*(ym-yi) + xm*(yi-yj))/2;
betai = yj-ym;
betaj = ym-yi;
betam = yi-yj;
gammai = xm-xj;
gammaj = xi-xm;
gammam = xj-xi;
B = [betai 0 betaj 0 betam 0 ;
0 gammai 0 gammaj 0 gammam ;
gammai betai gammaj betaj gammam betam]/(2*A);
if p == 1
D = (E/(1-NU*NU))*[1 NU 0 ; NU 1 0 ; 0 0 (1-NU)/2];
elseif p == 2
D = (E/(1+NU)/(1-2*NU))*[1-NU NU 0 ; NU 1-NU 0 ; 0 0 (1-2*NU)/2];
end
y = D*B*u;
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