%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2020-10-29 15:04:15
 % @LastEditTime: 2020-11-18 13:47:03
%--------------------------
% int in [-a,a], [-b,b]
function gaussB = shapeDerivatives(a, b, optKE)
%     jac = lx*ly/4;
    GaussNodes = [-1/sqrt(3); 1/sqrt(3)]; GaussWeigh = [1 1]; 
    if optKE==1
        L = [1 0 0 0; 0 0 0 1; 0 1/2 1/2 0]; 
    else
        L = [1 0 0 0; 0 0 0 1; 0 1 1 0]; 
    end

    gaussB = cell(4,1);
    
    for i = 1:2
        for j = 1:2
            GN_x = GaussNodes(i); 
            GN_y = GaussNodes(j);              
                        
            dN_x = 1/4*[-(1-GN_y)  (1-GN_y) (1+GN_y) -(1+GN_y)];
            dN_y = 1/4*[-(1-GN_x) -(1+GN_x) (1+GN_x)  (1-GN_x)];   
            
            J = [dN_x; dN_y]*[ -a  a  a  -a;  
                                -b  -b  b  b]';            
            G = [inv(J) zeros(size(J)); 
                zeros(size(J)) inv(J)]; 

            dN(1,1:2:8) = dN_x; dN(2,1:2:8) = dN_y;            
            dN(3,2:2:8) = dN_x; dN(4,2:2:8) = dN_y;   

            Be = L*G*dN;  
            gaussB{2*(i-1)+j} = GaussWeigh(i)*GaussWeigh(j)*Be;
        end
    end
end