%%% Element integration in 2D4N element

% EXAM January 2016 - PROBLEM 3 / 3.1
% xnod=[0;0;1;0;3;3;0;2];
% unod=[1;1;1;1]    function f=1
% integrate_2D4N(xnod,unod,npoints)

function integral=integrate_2D4N(xnod,unod,npoints)
% 1. Definition of Gauss Points
if npoints==1
	w(1)=2;
	ji(1)=0;
elseif npoints==2
	w(1)=1;
	w(2)=1;
	ji(1)=-0.577350269189626;
	ji(2)=-ji(1);
elseif npoints==3
	w(1)=0.888888888888889;
	w(2)=0.555555555555556;
	w(3)=w(2);
	ji(1)=0;
	ji(2)=-0.774596669241483;
	ji(3)=-ji(2);
end

integral=0.;
for i=1:npoints
	for j=1:npoints
		fun=shapefunction_2D4N([ji(i) ji(j)],unod);
        Jac=jacobian_2D4N([ji(i) ji(j)],xnod);
		detJac=det(Jac);
		integral=integral+fun*detJac*w(i)*w(j);
	end
end
return