Quad8 Shape Functions

Quad8.m

N = [  0.25* (1+s) * (1+r) * (r+s-1),...
	0.25* (1+s) * (r-1) * (r+1-s),...
	-0.25* (s-1) * (r-1) * (r+s+1),...
	-0.25* (s-1) * (1+r) * (r-1-s),...
	-0.5 * (1+r) * (r-1) * (1+s)  ,...
	0.5 * (r-1) * (1+s) * (s-1)  ,...
	0.5 * (1+r) * (r-1) * (s-1)  ,...
	-0.5 * (1+r) * (1+s) * (s-1) ]';
dN = [   0.25*  (1+s) * (s+2*r) ,...
	0.25*  (1+s) * (-s+2*r),...
	-0.25*  (s-1) * (s+2*r) ,...
	-0.25*  (s-1) * (-s+2*r),...
	-r *  (1+s)           ,...
	0.5 *  (1+s) * (s-1)   ,...
	r *  (s-1)           ,...
	-0.5 *  (1+s) * (s-1)   ;...
	0.25*  (1+r) * (r+2*s) ,...
	0.25* (-1+r) * (r-2*s) ,...
	-0.25* (-1+r) * (r+2*s) ,...
	-0.25*  (1+r) * (r-2*s) ,...
	-0.5 *  (1+r) * (-1+r)  ,...
	s * (-1+r)           ,...
	0.5 *  (1+r) * (-1+r)  ,...
	-s *  (1+r)          ]';