SFDerivatives.m

function [dndx,dndy,dndz,detj,elvolume] = SFDerivatives(iele,nnpe,nqptv,wtqp,np,x,y,z,dndxi,dndet,dndze)
% compute shape function derivatives in global coordinates

detj = zeros(1,nqptv);
dndx = zeros(nnpe,nqptv);
dndy = zeros(nnpe,nqptv);
dndz = zeros(nnpe,nqptv);
elvolume=0.;

for i=1:1:nqptv  
    
    tjac=zeros(3,3);
         
  for j=1:1:nnpe  
	
      j1=np(iele,j) ;  
	  
      tjac(1,1)=tjac(1,1)+dndxi(j,i)*x(j1);                           
      tjac(1,2)=tjac(1,2)+dndet(j,i)*x(j1);	  
      tjac(1,3)=tjac(1,3)+dndze(j,i)*x(j1);                          
      tjac(2,1)=tjac(2,1)+dndxi(j,i)*y(j1);                          
      tjac(2,2)=tjac(2,2)+dndet(j,i)*y(j1);                         
      tjac(2,3)=tjac(2,3)+dndze(j,i)*y(j1); 	  
      tjac(3,1)=tjac(3,1)+dndxi(j,i)*z(j1);                           
      tjac(3,2)=tjac(3,2)+dndet(j,i)*z(j1);                          
      tjac(3,3)=tjac(3,3)+dndze(j,i)*z(j1);  
	  
  end                                                         
                                                                    
      detj(i)=det(tjac);
      
      elvolume = elvolume + detj(i)*wtqp(i);
	  
      tjaci = inv(tjac);                                      
                                                                     
  for  j=1:1:nnpe
	
      dndx(j,i)=tjaci(1,1)*dndxi(j,i)+tjaci(2,1)*dndet(j,i)+tjaci(3,1)*dndze(j,i);            
      dndy(j,i)=tjaci(1,2)*dndxi(j,i)+tjaci(2,2)*dndet(j,i)+tjaci(3,2)*dndze(j,i);       
      dndz(j,i)=tjaci(1,3)*dndxi(j,i)+tjaci(2,3)*dndet(j,i)+tjaci(3,3)*dndze(j,i);
  end      
  

end