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FEATool Multiphysics
v1.17.2
Finite Element Analysis Toolbox
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FEATool Multiphysics
v1.17.2
Finite Element Analysis Toolbox
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SF_HEX_Q2 Triquadratic conforming shape function for hexahedrons (Q2).
[ VBASE, NLDOF, XLDOF, SFUN ] = SF_HEX_Q2( I_EVAL, N_SDIM, N_VERT, I_DOF, XI, AINVJAC, VBASE ) Evaluates conforming triquadratic Q2 shape functions on hexahedrons with values defined in the nodes, edges, faces, and cell center. XI is [-1..1]^3 reference coordinates.
Input Value/[Size] Description
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i_eval scalar: 1 Evaluate function values
>1 Evaluate values of derivatives
n_sdim scalar: 3 Number of space dimensions
n_vert scalar: 8 Number of vertices per cell
i_dof scalar: 1-n_ldof Local basis function to evaluate
xi [n_sdim] Local coordinates of evaluation point
aInvJac [n,n_sdim*n_sdim] Inverse of transformation Jacobian
vBase [n] Preallocated output vector
.
Output Value/[Size] Description
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vBase [n] Evaluated function values
nLDof [4] Number of local degrees of freedom on
vertices, edges, faces, and cell interiors
xLDof [n_sdim,n_ldof] Local coordinates of local dofs
sfun string Function name of called shape function
nLDof = [8 12 6 1];
xLDof = [-1 1 1 -1 -1 1 1 -1 0 1 0 -1 -1 1 1 -1 0 1 0 -1 0 0 1 0 -1 0 0; ...
-1 -1 1 1 -1 -1 1 1 -1 0 1 0 -1 -1 1 1 -1 0 1 0 0 -1 0 1 0 0 0; ...
-1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 0 0 0 0 1 1 1 1 -1 0 0 0 0 1 0];
sfun = 'sf_hex_Q2';
switch i_eval % Evaluation type flag.
case 1 % Evaluation of function values.
switch i_dof % Basis function to evaluate.
case 1
vBase = -xi(1)*(1-xi(1))*xi(2)*(1-xi(2))*xi(3)*(1-xi(3))/8;
case 2
vBase = xi(1)*(1+xi(1))*xi(2)*(1-xi(2))*xi(3)*(1-xi(3))/8;
case 3
vBase = -xi(1)*(1+xi(1))*xi(2)*(1+xi(2))*xi(3)*(1-xi(3))/8;
case 4
vBase = xi(1)*(1-xi(1))*xi(2)*(1+xi(2))*xi(3)*(1-xi(3))/8;
case 5
vBase = xi(1)*(1-xi(1))*xi(2)*(1-xi(2))*xi(3)*(1+xi(3))/8;
case 6
vBase = -xi(1)*(1+xi(1))*xi(2)*(1-xi(2))*xi(3)*(1+xi(3))/8;
case 7
vBase = xi(1)*(1+xi(1))*xi(2)*(1+xi(2))*xi(3)*(1+xi(3))/8;
case 8
vBase = -xi(1)*(1-xi(1))*xi(2)*(1+xi(2))*xi(3)*(1+xi(3))/8;
case 9
vBase = (2-2*xi(1)^2)*xi(2)*(1-xi(2))*xi(3)*(1-xi(3))/8;
case 10
vBase = -xi(1)*(1+xi(1))*(2-2*xi(2)^2)*xi(3)*(1-xi(3))/8;
case 11
vBase = -(2-2*xi(1)^2)*xi(2)*(1+xi(2))*xi(3)*(1-xi(3))/8;
case 12
vBase = xi(1)*(1-xi(1))*(2-2*xi(2)^2)*xi(3)*(1-xi(3))/8;
case 13
vBase = xi(1)*(1-xi(1))*xi(2)*(1-xi(2))*(2-2*xi(3)^2)/8;
case 14
vBase = -xi(1)*(1+xi(1))*xi(2)*(1-xi(2))*(2-2*xi(3)^2)/8;
case 15
vBase = xi(1)*(1+xi(1))*xi(2)*(1+xi(2))*(2-2*xi(3)^2)/8;
case 16
vBase = -xi(1)*(1-xi(1))*xi(2)*(1+xi(2))*(2-2*xi(3)^2)/8;
case 17
vBase = -(2-2*xi(1)^2)*xi(2)*(1-xi(2))*xi(3)*(1+xi(3))/8;
case 18
vBase = xi(1)*(1+xi(1))*(2-2*xi(2)^2)*xi(3)*(1+xi(3))/8;
case 19
vBase = (2-2*xi(1)^2)*xi(2)*(1+xi(2))*xi(3)*(1+xi(3))/8;
case 20
vBase = -xi(1)*(1-xi(1))*(2-2*xi(2)^2)*xi(3)*(1+xi(3))/8;
case 21
vBase = -(2-2*xi(1)^2)*(2-2*xi(2)^2)*xi(3)*(1-xi(3))/8;
case 22
vBase = -(2-2*xi(1)^2)*xi(2)*(1-xi(2))*(2-2*xi(3)^2)/8;
case 23
vBase = xi(1)*(1+xi(1))*(2-2*xi(2)^2)*(2-2*xi(3)^2)/8;
case 24
vBase = (2-2*xi(1)^2)*xi(2)*(1+xi(2))*(2-2*xi(3)^2)/8;
case 25
vBase = -xi(1)*(1-xi(1))*(2-2*xi(2)^2)*(2-2*xi(3)^2)/8;
case 26
vBase = (2-2*xi(1)^2)*(2-2*xi(2)^2)*xi(3)*(1+xi(3))/8;
case 27
vBase = (2-2*xi(1)^2)*(2-2*xi(2)^2)*(2-2*xi(3)^2)/8;
end
case {2,3,4} % Evaluation of first order derivatives.
switch i_dof % Basis function to evaluate.
case 1
dNdxi1 = (xi(2)*xi(3)*(2*xi(1)-1)*(xi(2)-1)*(xi(3)-1))/8;
dNdxi2 = (xi(1)*xi(3)*(2*xi(2)-1)*(xi(1)-1)*(xi(3)-1))/8;
dNdxi3 = (xi(1)*xi(2)*(2*xi(3)-1)*(xi(1)-1)*(xi(2)-1))/8;
case 2
dNdxi1 = (xi(2)*xi(3)*(2*xi(1)+1)*(xi(2)-1)*(xi(3)-1))/8;
dNdxi2 = (xi(1)*xi(3)*(2*xi(2)-1)*(xi(1)+1)*(xi(3)-1))/8;
dNdxi3 = (xi(1)*xi(2)*(2*xi(3)-1)*(xi(1)+1)*(xi(2)-1))/8;
case 3
dNdxi1 = (xi(2)*xi(3)*(2*xi(1)+1)*(xi(2)+1)*(xi(3)-1))/8;
dNdxi2 = (xi(1)*xi(3)*(2*xi(2)+1)*(xi(1)+1)*(xi(3)-1))/8;
dNdxi3 = (xi(1)*xi(2)*(2*xi(3)-1)*(xi(1)+1)*(xi(2)+1))/8;
case 4
dNdxi1 = (xi(2)*xi(3)*(2*xi(1)-1)*(xi(2)+1)*(xi(3)-1))/8;
dNdxi2 = (xi(1)*xi(3)*(2*xi(2)+1)*(xi(1)-1)*(xi(3)-1))/8;
dNdxi3 = (xi(1)*xi(2)*(2*xi(3)-1)*(xi(1)-1)*(xi(2)+1))/8;
case 5
dNdxi1 = (xi(2)*xi(3)*(2*xi(1)-1)*(xi(2)-1)*(xi(3)+1))/8;
dNdxi2 = (xi(1)*xi(3)*(2*xi(2)-1)*(xi(1)-1)*(xi(3)+1))/8;
dNdxi3 = (xi(1)*xi(2)*(2*xi(3)+1)*(xi(1)-1)*(xi(2)-1))/8;
case 6
dNdxi1 = (xi(2)*xi(3)*(2*xi(1)+1)*(xi(2)-1)*(xi(3)+1))/8;
dNdxi2 = (xi(1)*xi(3)*(2*xi(2)-1)*(xi(1)+1)*(xi(3)+1))/8;
dNdxi3 = (xi(1)*xi(2)*(2*xi(3)+1)*(xi(1)+1)*(xi(2)-1))/8;
case 7
dNdxi1 = (xi(2)*xi(3)*(2*xi(1)+1)*(xi(2)+1)*(xi(3)+1))/8;
dNdxi2 = (xi(1)*xi(3)*(2*xi(2)+1)*(xi(1)+1)*(xi(3)+1))/8;
dNdxi3 = (xi(1)*xi(2)*(2*xi(3)+1)*(xi(1)+1)*(xi(2)+1))/8;
case 8
dNdxi1 = (xi(2)*xi(3)*(2*xi(1)-1)*(xi(2)+1)*(xi(3)+1))/8;
dNdxi2 = (xi(1)*xi(3)*(2*xi(2)+1)*(xi(1)-1)*(xi(3)+1))/8;
dNdxi3 = (xi(1)*xi(2)*(2*xi(3)+1)*(xi(1)-1)*(xi(2)+1))/8;
case 9
dNdxi1 = -(xi(1)*xi(2)*xi(3)*(xi(2)-1)*(xi(3)-1))/2;
dNdxi2 = -(xi(3)*(2*xi(2)-1)*(xi(1)^2-1)*(xi(3)-1))/4;
dNdxi3 = -(xi(2)*(2*xi(3)-1)*(xi(1)^2-1)*(xi(2)-1))/4;
case 10
dNdxi1 = -(xi(3)*(2*xi(1)+1)*(xi(2)^2-1)*(xi(3)-1))/4;
dNdxi2 = -(xi(1)*xi(2)*xi(3)*(xi(1)+1)*(xi(3)-1))/2;
dNdxi3 = -(xi(1)*(2*xi(3)-1)*(xi(2)^2-1)*(xi(1)+1))/4;
case 11
dNdxi1 = -(xi(1)*xi(2)*xi(3)*(xi(2)+1)*(xi(3)-1))/2;
dNdxi2 = -(xi(3)*(2*xi(2)+1)*(xi(1)^2-1)*(xi(3)-1))/4;
dNdxi3 = -(xi(2)*(2*xi(3)-1)*(xi(1)^2-1)*(xi(2)+1))/4;
case 12
dNdxi1 = -(xi(3)*(2*xi(1)-1)*(xi(2)^2-1)*(xi(3)-1))/4;
dNdxi2 = -(xi(1)*xi(2)*xi(3)*(xi(1)-1)*(xi(3)-1))/2;
dNdxi3 = -(xi(1)*(2*xi(3)-1)*(xi(2)^2-1)*(xi(1)-1))/4;
case 13
dNdxi1 = -(xi(2)*(2*xi(1)-1)*(xi(3)^2-1)*(xi(2)-1))/4;
dNdxi2 = -(xi(1)*(2*xi(2)-1)*(xi(3)^2-1)*(xi(1)-1))/4;
dNdxi3 = -(xi(1)*xi(2)*xi(3)*(xi(1)-1)*(xi(2)-1))/2;
case 14
dNdxi1 = -(xi(2)*(2*xi(1)+1)*(xi(3)^2-1)*(xi(2)-1))/4;
dNdxi2 = -(xi(1)*(2*xi(2)-1)*(xi(3)^2-1)*(xi(1)+1))/4;
dNdxi3 = -(xi(1)*xi(2)*xi(3)*(xi(1)+1)*(xi(2)-1))/2;
case 15
dNdxi1 = -(xi(2)*(2*xi(1)+1)*(xi(3)^2-1)*(xi(2)+1))/4;
dNdxi2 = -(xi(1)*(2*xi(2)+1)*(xi(3)^2-1)*(xi(1)+1))/4;
dNdxi3 = -(xi(1)*xi(2)*xi(3)*(xi(1)+1)*(xi(2)+1))/2;
case 16
dNdxi1 = -(xi(2)*(2*xi(1)-1)*(xi(3)^2-1)*(xi(2)+1))/4;
dNdxi2 = -(xi(1)*(2*xi(2)+1)*(xi(3)^2-1)*(xi(1)-1))/4;
dNdxi3 = -(xi(1)*xi(2)*xi(3)*(xi(1)-1)*(xi(2)+1))/2;
case 17
dNdxi1 = -(xi(1)*xi(2)*xi(3)*(xi(2)-1)*(xi(3)+1))/2;
dNdxi2 = -(xi(3)*(2*xi(2)-1)*(xi(1)^2-1)*(xi(3)+1))/4;
dNdxi3 = -(xi(2)*(2*xi(3)+1)*(xi(1)^2-1)*(xi(2)-1))/4;
case 18
dNdxi1 = -(xi(3)*(2*xi(1)+1)*(xi(2)^2-1)*(xi(3)+1))/4;
dNdxi2 = -(xi(1)*xi(2)*xi(3)*(xi(1)+1)*(xi(3)+1))/2;
dNdxi3 = -(xi(1)*(2*xi(3)+1)*(xi(2)^2-1)*(xi(1)+1))/4;
case 19
dNdxi1 = -(xi(1)*xi(2)*xi(3)*(xi(2)+1)*(xi(3)+1))/2;
dNdxi2 = -(xi(3)*(2*xi(2)+1)*(xi(1)^2-1)*(xi(3)+1))/4;
dNdxi3 = -(xi(2)*(2*xi(3)+1)*(xi(1)^2-1)*(xi(2)+1))/4;
case 20
dNdxi1 = -(xi(3)*(2*xi(1)-1)*(xi(2)^2-1)*(xi(3)+1))/4;
dNdxi2 = -(xi(1)*xi(2)*xi(3)*(xi(1)-1)*(xi(3)+1))/2;
dNdxi3 = -(xi(1)*(2*xi(3)+1)*(xi(2)^2-1)*(xi(1)-1))/4;
case 21
dNdxi1 = xi(1)*xi(3)*(xi(2)^2-1)*(xi(3)-1);
dNdxi2 = xi(2)*xi(3)*(xi(1)^2-1)*(xi(3)-1);
dNdxi3 = ((2*xi(3)-1)*(xi(1)^2-1)*(xi(2)^2-1))/2;
case 22
dNdxi1 = xi(1)*xi(2)*(xi(3)^2-1)*(xi(2)-1);
dNdxi2 = ((2*xi(2)-1)*(xi(1)^2-1)*(xi(3)^2-1))/2;
dNdxi3 = xi(2)*xi(3)*(xi(1)^2-1)*(xi(2)-1);
case 23
dNdxi1 = ((2*xi(1)+1)*(xi(2)^2-1)*(xi(3)^2-1))/2;
dNdxi2 = xi(1)*xi(2)*(xi(3)^2-1)*(xi(1)+1);
dNdxi3 = xi(1)*xi(3)*(xi(2)^2-1)*(xi(1)+1);
case 24
dNdxi1 = xi(1)*xi(2)*(xi(3)^2-1)*(xi(2)+1);
dNdxi2 = ((2*xi(2)+1)*(xi(1)^2-1)*(xi(3)^2-1))/2;
dNdxi3 = xi(2)*xi(3)*(xi(1)^2-1)*(xi(2)+1);
case 25
dNdxi1 = ((2*xi(1)-1)*(xi(2)^2-1)*(xi(3)^2-1))/2;
dNdxi2 = xi(1)*xi(2)*(xi(3)^2-1)*(xi(1)-1);
dNdxi3 = xi(1)*xi(3)*(xi(2)^2-1)*(xi(1)-1);
case 26
dNdxi1 = xi(1)*xi(3)*(xi(2)^2-1)*(xi(3)+1);
dNdxi2 = xi(2)*xi(3)*(xi(1)^2-1)*(xi(3)+1);
dNdxi3 = ((2*xi(3)+1)*(xi(1)^2-1)*(xi(2)^2-1))/2;
case 27
dNdxi1 = -2*xi(1)*(xi(2)^2-1)*(xi(3)^2-1);
dNdxi2 = -2*xi(2)*(xi(1)^2-1)*(xi(3)^2-1);
dNdxi3 = -2*xi(3)*(xi(1)^2-1)*(xi(2)^2-1);
end
if ( i_eval==2 ) % x-derivative.
vBase = aInvJac(:,1)*dNdxi1 + aInvJac(:,2)*dNdxi2 + aInvJac(:,3)*dNdxi3;
elseif ( i_eval==3 ) % y-derivative.
vBase = aInvJac(:,4)*dNdxi1 + aInvJac(:,5)*dNdxi2 + aInvJac(:,6)*dNdxi3;
elseif ( i_eval==4 ) % z-derivative.
vBase = aInvJac(:,7)*dNdxi1 + aInvJac(:,8)*dNdxi2 + aInvJac(:,9)*dNdxi3;
end
case {22,23,24,32,33,34,42,43,44} % Evaluation of second order derivatives.
if( any(any(abs([aInvJac(:,[2 3 4 6 7 8])])>eps*1e2)) )
warning('sf_hex_Q2: 2nd derivatives for non-rectangular cells shapes not supported.')
end
switch i_dof
case 1
d2Ndxi1dxi1 = (xi(2)*xi(3)*(xi(2) - 1)*(xi(3) - 1))/4;
d2Ndxi2dxi1 = (xi(3)*(2*xi(1) - 1)*(2*xi(2) - 1)*(xi(3) - 1))/8;
d2Ndxi3dxi1 = (xi(2)*(2*xi(1) - 1)*(2*xi(3) - 1)*(xi(2) - 1))/8;
d2Ndxi1dxi2 = (xi(3)*(2*xi(1) - 1)*(2*xi(2) - 1)*(xi(3) - 1))/8;
d2Ndxi2dxi2 = (xi(1)*xi(3)*(xi(1) - 1)*(xi(3) - 1))/4;
d2Ndxi3dxi2 = (xi(1)*(2*xi(2) - 1)*(2*xi(3) - 1)*(xi(1) - 1))/8;
d2Ndxi1dxi3 = (xi(2)*(2*xi(1) - 1)*(2*xi(3) - 1)*(xi(2) - 1))/8;
d2Ndxi2dxi3 = (xi(1)*(2*xi(2) - 1)*(2*xi(3) - 1)*(xi(1) - 1))/8;
d2Ndxi3dxi3 = (xi(1)*xi(2)*(xi(1) - 1)*(xi(2) - 1))/4;
case 2
d2Ndxi1dxi1 = (xi(2)*xi(3)*(xi(2) - 1)*(xi(3) - 1))/4;
d2Ndxi2dxi1 = (xi(3)*(2*xi(1) + 1)*(2*xi(2) - 1)*(xi(3) - 1))/8;
d2Ndxi3dxi1 = (xi(2)*(2*xi(1) + 1)*(2*xi(3) - 1)*(xi(2) - 1))/8;
d2Ndxi1dxi2 = (xi(3)*(2*xi(1) + 1)*(2*xi(2) - 1)*(xi(3) - 1))/8;
d2Ndxi2dxi2 = (xi(1)*xi(3)*(xi(1) + 1)*(xi(3) - 1))/4;
d2Ndxi3dxi2 = (xi(1)*(2*xi(2) - 1)*(2*xi(3) - 1)*(xi(1) + 1))/8;
d2Ndxi1dxi3 = (xi(2)*(2*xi(1) + 1)*(2*xi(3) - 1)*(xi(2) - 1))/8;
d2Ndxi2dxi3 = (xi(1)*(2*xi(2) - 1)*(2*xi(3) - 1)*(xi(1) + 1))/8;
d2Ndxi3dxi3 = (xi(1)*xi(2)*(xi(1) + 1)*(xi(2) - 1))/4;
case 3
d2Ndxi1dxi1 = (xi(2)*xi(3)*(xi(2) + 1)*(xi(3) - 1))/4;
d2Ndxi2dxi1 = (xi(3)*(2*xi(1) + 1)*(2*xi(2) + 1)*(xi(3) - 1))/8;
d2Ndxi3dxi1 = (xi(2)*(2*xi(1) + 1)*(2*xi(3) - 1)*(xi(2) + 1))/8;
d2Ndxi1dxi2 = (xi(3)*(2*xi(1) + 1)*(2*xi(2) + 1)*(xi(3) - 1))/8;
d2Ndxi2dxi2 = (xi(1)*xi(3)*(xi(1) + 1)*(xi(3) - 1))/4;
d2Ndxi3dxi2 = (xi(1)*(2*xi(2) + 1)*(2*xi(3) - 1)*(xi(1) + 1))/8;
d2Ndxi1dxi3 = (xi(2)*(2*xi(1) + 1)*(2*xi(3) - 1)*(xi(2) + 1))/8;
d2Ndxi2dxi3 = (xi(1)*(2*xi(2) + 1)*(2*xi(3) - 1)*(xi(1) + 1))/8;
d2Ndxi3dxi3 = (xi(1)*xi(2)*(xi(1) + 1)*(xi(2) + 1))/4;
case 4
d2Ndxi1dxi1 = (xi(2)*xi(3)*(xi(2) + 1)*(xi(3) - 1))/4;
d2Ndxi2dxi1 = (xi(3)*(2*xi(1) - 1)*(2*xi(2) + 1)*(xi(3) - 1))/8;
d2Ndxi3dxi1 = (xi(2)*(2*xi(1) - 1)*(2*xi(3) - 1)*(xi(2) + 1))/8;
d2Ndxi1dxi2 = (xi(3)*(2*xi(1) - 1)*(2*xi(2) + 1)*(xi(3) - 1))/8;
d2Ndxi2dxi2 = (xi(1)*xi(3)*(xi(1) - 1)*(xi(3) - 1))/4;
d2Ndxi3dxi2 = (xi(1)*(2*xi(2) + 1)*(2*xi(3) - 1)*(xi(1) - 1))/8;
d2Ndxi1dxi3 = (xi(2)*(2*xi(1) - 1)*(2*xi(3) - 1)*(xi(2) + 1))/8;
d2Ndxi2dxi3 = (xi(1)*(2*xi(2) + 1)*(2*xi(3) - 1)*(xi(1) - 1))/8;
d2Ndxi3dxi3 = (xi(1)*xi(2)*(xi(1) - 1)*(xi(2) + 1))/4;
case 5
d2Ndxi1dxi1 = (xi(2)*xi(3)*(xi(2) - 1)*(xi(3) + 1))/4;
d2Ndxi2dxi1 = (xi(3)*(2*xi(1) - 1)*(2*xi(2) - 1)*(xi(3) + 1))/8;
d2Ndxi3dxi1 = (xi(2)*(2*xi(1) - 1)*(2*xi(3) + 1)*(xi(2) - 1))/8;
d2Ndxi1dxi2 = (xi(3)*(2*xi(1) - 1)*(2*xi(2) - 1)*(xi(3) + 1))/8;
d2Ndxi2dxi2 = (xi(1)*xi(3)*(xi(1) - 1)*(xi(3) + 1))/4;
d2Ndxi3dxi2 = (xi(1)*(2*xi(2) - 1)*(2*xi(3) + 1)*(xi(1) - 1))/8;
d2Ndxi1dxi3 = (xi(2)*(2*xi(1) - 1)*(2*xi(3) + 1)*(xi(2) - 1))/8;
d2Ndxi2dxi3 = (xi(1)*(2*xi(2) - 1)*(2*xi(3) + 1)*(xi(1) - 1))/8;
d2Ndxi3dxi3 = (xi(1)*xi(2)*(xi(1) - 1)*(xi(2) - 1))/4;
case 6
d2Ndxi1dxi1 = (xi(2)*xi(3)*(xi(2) - 1)*(xi(3) + 1))/4;
d2Ndxi2dxi1 = (xi(3)*(2*xi(1) + 1)*(2*xi(2) - 1)*(xi(3) + 1))/8;
d2Ndxi3dxi1 = (xi(2)*(2*xi(1) + 1)*(2*xi(3) + 1)*(xi(2) - 1))/8;
d2Ndxi1dxi2 = (xi(3)*(2*xi(1) + 1)*(2*xi(2) - 1)*(xi(3) + 1))/8;
d2Ndxi2dxi2 = (xi(1)*xi(3)*(xi(1) + 1)*(xi(3) + 1))/4;
d2Ndxi3dxi2 = (xi(1)*(2*xi(2) - 1)*(2*xi(3) + 1)*(xi(1) + 1))/8;
d2Ndxi1dxi3 = (xi(2)*(2*xi(1) + 1)*(2*xi(3) + 1)*(xi(2) - 1))/8;
d2Ndxi2dxi3 = (xi(1)*(2*xi(2) - 1)*(2*xi(3) + 1)*(xi(1) + 1))/8;
d2Ndxi3dxi3 = (xi(1)*xi(2)*(xi(1) + 1)*(xi(2) - 1))/4;
case 7
d2Ndxi1dxi1 = (xi(2)*xi(3)*(xi(2) + 1)*(xi(3) + 1))/4;
d2Ndxi2dxi1 = (xi(3)*(2*xi(1) + 1)*(2*xi(2) + 1)*(xi(3) + 1))/8;
d2Ndxi3dxi1 = (xi(2)*(2*xi(1) + 1)*(2*xi(3) + 1)*(xi(2) + 1))/8;
d2Ndxi1dxi2 = (xi(3)*(2*xi(1) + 1)*(2*xi(2) + 1)*(xi(3) + 1))/8;
d2Ndxi2dxi2 = (xi(1)*xi(3)*(xi(1) + 1)*(xi(3) + 1))/4;
d2Ndxi3dxi2 = (xi(1)*(2*xi(2) + 1)*(2*xi(3) + 1)*(xi(1) + 1))/8;
d2Ndxi1dxi3 = (xi(2)*(2*xi(1) + 1)*(2*xi(3) + 1)*(xi(2) + 1))/8;
d2Ndxi2dxi3 = (xi(1)*(2*xi(2) + 1)*(2*xi(3) + 1)*(xi(1) + 1))/8;
d2Ndxi3dxi3 = (xi(1)*xi(2)*(xi(1) + 1)*(xi(2) + 1))/4;
case 8
d2Ndxi1dxi1 = (xi(2)*xi(3)*(xi(2) + 1)*(xi(3) + 1))/4;
d2Ndxi2dxi1 = (xi(3)*(2*xi(1) - 1)*(2*xi(2) + 1)*(xi(3) + 1))/8;
d2Ndxi3dxi1 = (xi(2)*(2*xi(1) - 1)*(2*xi(3) + 1)*(xi(2) + 1))/8;
d2Ndxi1dxi2 = (xi(3)*(2*xi(1) - 1)*(2*xi(2) + 1)*(xi(3) + 1))/8;
d2Ndxi2dxi2 = (xi(1)*xi(3)*(xi(1) - 1)*(xi(3) + 1))/4;
d2Ndxi3dxi2 = (xi(1)*(2*xi(2) + 1)*(2*xi(3) + 1)*(xi(1) - 1))/8;
d2Ndxi1dxi3 = (xi(2)*(2*xi(1) - 1)*(2*xi(3) + 1)*(xi(2) + 1))/8;
d2Ndxi2dxi3 = (xi(1)*(2*xi(2) + 1)*(2*xi(3) + 1)*(xi(1) - 1))/8;
d2Ndxi3dxi3 = (xi(1)*xi(2)*(xi(1) - 1)*(xi(2) + 1))/4;
case 9
d2Ndxi1dxi1 = -(xi(2)*xi(3)*(xi(2) - 1)*(xi(3) - 1))/2;
d2Ndxi2dxi1 = -(xi(1)*xi(3)*(2*xi(2) - 1)*(xi(3) - 1))/2;
d2Ndxi3dxi1 = -(xi(1)*xi(2)*(2*xi(3) - 1)*(xi(2) - 1))/2;
d2Ndxi1dxi2 = -(xi(1)*xi(3)*(2*xi(2) - 1)*(xi(3) - 1))/2;
d2Ndxi2dxi2 = -(xi(3)*(xi(1)^2 - 1)*(xi(3) - 1))/2;
d2Ndxi3dxi2 = -((2*xi(2) - 1)*(2*xi(3) - 1)*(xi(1)^2 - 1))/4;
d2Ndxi1dxi3 = -(xi(1)*xi(2)*(2*xi(3) - 1)*(xi(2) - 1))/2;
d2Ndxi2dxi3 = -((2*xi(2) - 1)*(2*xi(3) - 1)*(xi(1)^2 - 1))/4;
d2Ndxi3dxi3 = -(xi(2)*(xi(1)^2 - 1)*(xi(2) - 1))/2;
case 10
d2Ndxi1dxi1 = -(xi(3)*(xi(2)^2 - 1)*(xi(3) - 1))/2;
d2Ndxi2dxi1 = -(xi(2)*xi(3)*(2*xi(1) + 1)*(xi(3) - 1))/2;
d2Ndxi3dxi1 = -((2*xi(1) + 1)*(2*xi(3) - 1)*(xi(2)^2 - 1))/4;
d2Ndxi1dxi2 = -(xi(2)*xi(3)*(2*xi(1) + 1)*(xi(3) - 1))/2;
d2Ndxi2dxi2 = -(xi(1)*xi(3)*(xi(1) + 1)*(xi(3) - 1))/2;
d2Ndxi3dxi2 = -(xi(1)*xi(2)*(2*xi(3) - 1)*(xi(1) + 1))/2;
d2Ndxi1dxi3 = -((2*xi(1) + 1)*(2*xi(3) - 1)*(xi(2)^2 - 1))/4;
d2Ndxi2dxi3 = -(xi(1)*xi(2)*(2*xi(3) - 1)*(xi(1) + 1))/2;
d2Ndxi3dxi3 = -(xi(1)*(xi(2)^2 - 1)*(xi(1) + 1))/2;
case 11
d2Ndxi1dxi1 = -(xi(2)*xi(3)*(xi(2) + 1)*(xi(3) - 1))/2;
d2Ndxi2dxi1 = -(xi(1)*xi(3)*(2*xi(2) + 1)*(xi(3) - 1))/2;
d2Ndxi3dxi1 = -(xi(1)*xi(2)*(2*xi(3) - 1)*(xi(2) + 1))/2;
d2Ndxi1dxi2 = -(xi(1)*xi(3)*(2*xi(2) + 1)*(xi(3) - 1))/2;
d2Ndxi2dxi2 = -(xi(3)*(xi(1)^2 - 1)*(xi(3) - 1))/2;
d2Ndxi3dxi2 = -((2*xi(2) + 1)*(2*xi(3) - 1)*(xi(1)^2 - 1))/4;
d2Ndxi1dxi3 = -(xi(1)*xi(2)*(2*xi(3) - 1)*(xi(2) + 1))/2;
d2Ndxi2dxi3 = -((2*xi(2) + 1)*(2*xi(3) - 1)*(xi(1)^2 - 1))/4;
d2Ndxi3dxi3 = -(xi(2)*(xi(1)^2 - 1)*(xi(2) + 1))/2;
case 12
d2Ndxi1dxi1 = -(xi(3)*(xi(2)^2 - 1)*(xi(3) - 1))/2;
d2Ndxi2dxi1 = -(xi(2)*xi(3)*(2*xi(1) - 1)*(xi(3) - 1))/2;
d2Ndxi3dxi1 = -((2*xi(1) - 1)*(2*xi(3) - 1)*(xi(2)^2 - 1))/4;
d2Ndxi1dxi2 = -(xi(2)*xi(3)*(2*xi(1) - 1)*(xi(3) - 1))/2;
d2Ndxi2dxi2 = -(xi(1)*xi(3)*(xi(1) - 1)*(xi(3) - 1))/2;
d2Ndxi3dxi2 = -(xi(1)*xi(2)*(2*xi(3) - 1)*(xi(1) - 1))/2;
d2Ndxi1dxi3 = -((2*xi(1) - 1)*(2*xi(3) - 1)*(xi(2)^2 - 1))/4;
d2Ndxi2dxi3 = -(xi(1)*xi(2)*(2*xi(3) - 1)*(xi(1) - 1))/2;
d2Ndxi3dxi3 = -(xi(1)*(xi(2)^2 - 1)*(xi(1) - 1))/2;
case 13
d2Ndxi1dxi1 = -(xi(2)*(xi(3)^2 - 1)*(xi(2) - 1))/2;
d2Ndxi2dxi1 = -((2*xi(1) - 1)*(2*xi(2) - 1)*(xi(3)^2 - 1))/4;
d2Ndxi3dxi1 = -(xi(2)*xi(3)*(2*xi(1) - 1)*(xi(2) - 1))/2;
d2Ndxi1dxi2 = -((2*xi(1) - 1)*(2*xi(2) - 1)*(xi(3)^2 - 1))/4;
d2Ndxi2dxi2 = -(xi(1)*(xi(3)^2 - 1)*(xi(1) - 1))/2;
d2Ndxi3dxi2 = -(xi(1)*xi(3)*(2*xi(2) - 1)*(xi(1) - 1))/2;
d2Ndxi1dxi3 = -(xi(2)*xi(3)*(2*xi(1) - 1)*(xi(2) - 1))/2;
d2Ndxi2dxi3 = -(xi(1)*xi(3)*(2*xi(2) - 1)*(xi(1) - 1))/2;
d2Ndxi3dxi3 = -(xi(1)*xi(2)*(xi(1) - 1)*(xi(2) - 1))/2;
case 14
d2Ndxi1dxi1 = -(xi(2)*(xi(3)^2 - 1)*(xi(2) - 1))/2;
d2Ndxi2dxi1 = -((2*xi(1) + 1)*(2*xi(2) - 1)*(xi(3)^2 - 1))/4;
d2Ndxi3dxi1 = -(xi(2)*xi(3)*(2*xi(1) + 1)*(xi(2) - 1))/2;
d2Ndxi1dxi2 = -((2*xi(1) + 1)*(2*xi(2) - 1)*(xi(3)^2 - 1))/4;
d2Ndxi2dxi2 = -(xi(1)*(xi(3)^2 - 1)*(xi(1) + 1))/2;
d2Ndxi3dxi2 = -(xi(1)*xi(3)*(2*xi(2) - 1)*(xi(1) + 1))/2;
d2Ndxi1dxi3 = -(xi(2)*xi(3)*(2*xi(1) + 1)*(xi(2) - 1))/2;
d2Ndxi2dxi3 = -(xi(1)*xi(3)*(2*xi(2) - 1)*(xi(1) + 1))/2;
d2Ndxi3dxi3 = -(xi(1)*xi(2)*(xi(1) + 1)*(xi(2) - 1))/2;
case 15
d2Ndxi1dxi1 = -(xi(2)*(xi(3)^2 - 1)*(xi(2) + 1))/2;
d2Ndxi2dxi1 = -((2*xi(1) + 1)*(2*xi(2) + 1)*(xi(3)^2 - 1))/4;
d2Ndxi3dxi1 = -(xi(2)*xi(3)*(2*xi(1) + 1)*(xi(2) + 1))/2;
d2Ndxi1dxi2 = -((2*xi(1) + 1)*(2*xi(2) + 1)*(xi(3)^2 - 1))/4;
d2Ndxi2dxi2 = -(xi(1)*(xi(3)^2 - 1)*(xi(1) + 1))/2;
d2Ndxi3dxi2 = -(xi(1)*xi(3)*(2*xi(2) + 1)*(xi(1) + 1))/2;
d2Ndxi1dxi3 = -(xi(2)*xi(3)*(2*xi(1) + 1)*(xi(2) + 1))/2;
d2Ndxi2dxi3 = -(xi(1)*xi(3)*(2*xi(2) + 1)*(xi(1) + 1))/2;
d2Ndxi3dxi3 = -(xi(1)*xi(2)*(xi(1) + 1)*(xi(2) + 1))/2;
case 16
d2Ndxi1dxi1 = -(xi(2)*(xi(3)^2 - 1)*(xi(2) + 1))/2;
d2Ndxi2dxi1 = -((2*xi(1) - 1)*(2*xi(2) + 1)*(xi(3)^2 - 1))/4;
d2Ndxi3dxi1 = -(xi(2)*xi(3)*(2*xi(1) - 1)*(xi(2) + 1))/2;
d2Ndxi1dxi2 = -((2*xi(1) - 1)*(2*xi(2) + 1)*(xi(3)^2 - 1))/4;
d2Ndxi2dxi2 = -(xi(1)*(xi(3)^2 - 1)*(xi(1) - 1))/2;
d2Ndxi3dxi2 = -(xi(1)*xi(3)*(2*xi(2) + 1)*(xi(1) - 1))/2;
d2Ndxi1dxi3 = -(xi(2)*xi(3)*(2*xi(1) - 1)*(xi(2) + 1))/2;
d2Ndxi2dxi3 = -(xi(1)*xi(3)*(2*xi(2) + 1)*(xi(1) - 1))/2;
d2Ndxi3dxi3 = -(xi(1)*xi(2)*(xi(1) - 1)*(xi(2) + 1))/2;
case 17
d2Ndxi1dxi1 = -(xi(2)*xi(3)*(xi(2) - 1)*(xi(3) + 1))/2;
d2Ndxi2dxi1 = -(xi(1)*xi(3)*(2*xi(2) - 1)*(xi(3) + 1))/2;
d2Ndxi3dxi1 = -(xi(1)*xi(2)*(2*xi(3) + 1)*(xi(2) - 1))/2;
d2Ndxi1dxi2 = -(xi(1)*xi(3)*(2*xi(2) - 1)*(xi(3) + 1))/2;
d2Ndxi2dxi2 = -(xi(3)*(xi(1)^2 - 1)*(xi(3) + 1))/2;
d2Ndxi3dxi2 = -((2*xi(2) - 1)*(2*xi(3) + 1)*(xi(1)^2 - 1))/4;
d2Ndxi1dxi3 = -(xi(1)*xi(2)*(2*xi(3) + 1)*(xi(2) - 1))/2;
d2Ndxi2dxi3 = -((2*xi(2) - 1)*(2*xi(3) + 1)*(xi(1)^2 - 1))/4;
d2Ndxi3dxi3 = -(xi(2)*(xi(1)^2 - 1)*(xi(2) - 1))/2;
case 18
d2Ndxi1dxi1 = -(xi(3)*(xi(2)^2 - 1)*(xi(3) + 1))/2;
d2Ndxi2dxi1 = -(xi(2)*xi(3)*(2*xi(1) + 1)*(xi(3) + 1))/2;
d2Ndxi3dxi1 = -((2*xi(1) + 1)*(2*xi(3) + 1)*(xi(2)^2 - 1))/4;
d2Ndxi1dxi2 = -(xi(2)*xi(3)*(2*xi(1) + 1)*(xi(3) + 1))/2;
d2Ndxi2dxi2 = -(xi(1)*xi(3)*(xi(1) + 1)*(xi(3) + 1))/2;
d2Ndxi3dxi2 = -(xi(1)*xi(2)*(2*xi(3) + 1)*(xi(1) + 1))/2;
d2Ndxi1dxi3 = -((2*xi(1) + 1)*(2*xi(3) + 1)*(xi(2)^2 - 1))/4;
d2Ndxi2dxi3 = -(xi(1)*xi(2)*(2*xi(3) + 1)*(xi(1) + 1))/2;
d2Ndxi3dxi3 = -(xi(1)*(xi(2)^2 - 1)*(xi(1) + 1))/2;
case 19
d2Ndxi1dxi1 = -(xi(2)*xi(3)*(xi(2) + 1)*(xi(3) + 1))/2;
d2Ndxi2dxi1 = -(xi(1)*xi(3)*(2*xi(2) + 1)*(xi(3) + 1))/2;
d2Ndxi3dxi1 = -(xi(1)*xi(2)*(2*xi(3) + 1)*(xi(2) + 1))/2;
d2Ndxi1dxi2 = -(xi(1)*xi(3)*(2*xi(2) + 1)*(xi(3) + 1))/2;
d2Ndxi2dxi2 = -(xi(3)*(xi(1)^2 - 1)*(xi(3) + 1))/2;
d2Ndxi3dxi2 = -((2*xi(2) + 1)*(2*xi(3) + 1)*(xi(1)^2 - 1))/4;
d2Ndxi1dxi3 = -(xi(1)*xi(2)*(2*xi(3) + 1)*(xi(2) + 1))/2;
d2Ndxi2dxi3 = -((2*xi(2) + 1)*(2*xi(3) + 1)*(xi(1)^2 - 1))/4;
d2Ndxi3dxi3 = -(xi(2)*(xi(1)^2 - 1)*(xi(2) + 1))/2;
case 20
d2Ndxi1dxi1 = -(xi(3)*(xi(2)^2 - 1)*(xi(3) + 1))/2;
d2Ndxi2dxi1 = -(xi(2)*xi(3)*(2*xi(1) - 1)*(xi(3) + 1))/2;
d2Ndxi3dxi1 = -((2*xi(1) - 1)*(2*xi(3) + 1)*(xi(2)^2 - 1))/4;
d2Ndxi1dxi2 = -(xi(2)*xi(3)*(2*xi(1) - 1)*(xi(3) + 1))/2;
d2Ndxi2dxi2 = -(xi(1)*xi(3)*(xi(1) - 1)*(xi(3) + 1))/2;
d2Ndxi3dxi2 = -(xi(1)*xi(2)*(2*xi(3) + 1)*(xi(1) - 1))/2;
d2Ndxi1dxi3 = -((2*xi(1) - 1)*(2*xi(3) + 1)*(xi(2)^2 - 1))/4;
d2Ndxi2dxi3 = -(xi(1)*xi(2)*(2*xi(3) + 1)*(xi(1) - 1))/2;
d2Ndxi3dxi3 = -(xi(1)*(xi(2)^2 - 1)*(xi(1) - 1))/2;
case 21
d2Ndxi1dxi1 = xi(3)*(xi(2)^2 - 1)*(xi(3) - 1);
d2Ndxi2dxi1 = 2*xi(1)*xi(2)*xi(3)*(xi(3) - 1);
d2Ndxi3dxi1 = xi(1)*(2*xi(3) - 1)*(xi(2)^2 - 1);
d2Ndxi1dxi2 = 2*xi(1)*xi(2)*xi(3)*(xi(3) - 1);
d2Ndxi2dxi2 = xi(3)*(xi(1)^2 - 1)*(xi(3) - 1);
d2Ndxi3dxi2 = xi(2)*(2*xi(3) - 1)*(xi(1)^2 - 1);
d2Ndxi1dxi3 = xi(1)*(2*xi(3) - 1)*(xi(2)^2 - 1);
d2Ndxi2dxi3 = xi(2)*(2*xi(3) - 1)*(xi(1)^2 - 1);
d2Ndxi3dxi3 = (xi(1)^2 - 1)*(xi(2)^2 - 1);
case 22
d2Ndxi1dxi1 = xi(2)*(xi(3)^2 - 1)*(xi(2) - 1);
d2Ndxi2dxi1 = xi(1)*(2*xi(2) - 1)*(xi(3)^2 - 1);
d2Ndxi3dxi1 = 2*xi(1)*xi(2)*xi(3)*(xi(2) - 1);
d2Ndxi1dxi2 = xi(1)*(2*xi(2) - 1)*(xi(3)^2 - 1);
d2Ndxi2dxi2 = (xi(1)^2 - 1)*(xi(3)^2 - 1);
d2Ndxi3dxi2 = xi(3)*(2*xi(2) - 1)*(xi(1)^2 - 1);
d2Ndxi1dxi3 = 2*xi(1)*xi(2)*xi(3)*(xi(2) - 1);
d2Ndxi2dxi3 = xi(3)*(2*xi(2) - 1)*(xi(1)^2 - 1);
d2Ndxi3dxi3 = xi(2)*(xi(1)^2 - 1)*(xi(2) - 1);
case 23
d2Ndxi1dxi1 = (xi(2)^2 - 1)*(xi(3)^2 - 1);
d2Ndxi2dxi1 = xi(2)*(2*xi(1) + 1)*(xi(3)^2 - 1);
d2Ndxi3dxi1 = xi(3)*(2*xi(1) + 1)*(xi(2)^2 - 1);
d2Ndxi1dxi2 = xi(2)*(2*xi(1) + 1)*(xi(3)^2 - 1);
d2Ndxi2dxi2 = xi(1)*(xi(3)^2 - 1)*(xi(1) + 1);
d2Ndxi3dxi2 = 2*xi(1)*xi(2)*xi(3)*(xi(1) + 1);
d2Ndxi1dxi3 = xi(3)*(2*xi(1) + 1)*(xi(2)^2 - 1);
d2Ndxi2dxi3 = 2*xi(1)*xi(2)*xi(3)*(xi(1) + 1);
d2Ndxi3dxi3 = xi(1)*(xi(2)^2 - 1)*(xi(1) + 1);
case 24
d2Ndxi1dxi1 = xi(2)*(xi(3)^2 - 1)*(xi(2) + 1);
d2Ndxi2dxi1 = xi(1)*(2*xi(2) + 1)*(xi(3)^2 - 1);
d2Ndxi3dxi1 = 2*xi(1)*xi(2)*xi(3)*(xi(2) + 1);
d2Ndxi1dxi2 = xi(1)*(2*xi(2) + 1)*(xi(3)^2 - 1);
d2Ndxi2dxi2 = (xi(1)^2 - 1)*(xi(3)^2 - 1);
d2Ndxi3dxi2 = xi(3)*(2*xi(2) + 1)*(xi(1)^2 - 1);
d2Ndxi1dxi3 = 2*xi(1)*xi(2)*xi(3)*(xi(2) + 1);
d2Ndxi2dxi3 = xi(3)*(2*xi(2) + 1)*(xi(1)^2 - 1);
d2Ndxi3dxi3 = xi(2)*(xi(1)^2 - 1)*(xi(2) + 1);
case 25
d2Ndxi1dxi1 = (xi(2)^2 - 1)*(xi(3)^2 - 1);
d2Ndxi2dxi1 = xi(2)*(2*xi(1) - 1)*(xi(3)^2 - 1);
d2Ndxi3dxi1 = xi(3)*(2*xi(1) - 1)*(xi(2)^2 - 1);
d2Ndxi1dxi2 = xi(2)*(2*xi(1) - 1)*(xi(3)^2 - 1);
d2Ndxi2dxi2 = xi(1)*(xi(3)^2 - 1)*(xi(1) - 1);
d2Ndxi3dxi2 = 2*xi(1)*xi(2)*xi(3)*(xi(1) - 1);
d2Ndxi1dxi3 = xi(3)*(2*xi(1) - 1)*(xi(2)^2 - 1);
d2Ndxi2dxi3 = 2*xi(1)*xi(2)*xi(3)*(xi(1) - 1);
d2Ndxi3dxi3 = xi(1)*(xi(2)^2 - 1)*(xi(1) - 1);
case 26
d2Ndxi1dxi1 = xi(3)*(xi(2)^2 - 1)*(xi(3) + 1);
d2Ndxi2dxi1 = 2*xi(1)*xi(2)*xi(3)*(xi(3) + 1);
d2Ndxi3dxi1 = xi(1)*(2*xi(3) + 1)*(xi(2)^2 - 1);
d2Ndxi1dxi2 = 2*xi(1)*xi(2)*xi(3)*(xi(3) + 1);
d2Ndxi2dxi2 = xi(3)*(xi(1)^2 - 1)*(xi(3) + 1);
d2Ndxi3dxi2 = xi(2)*(2*xi(3) + 1)*(xi(1)^2 - 1);
d2Ndxi1dxi3 = xi(1)*(2*xi(3) + 1)*(xi(2)^2 - 1);
d2Ndxi2dxi3 = xi(2)*(2*xi(3) + 1)*(xi(1)^2 - 1);
d2Ndxi3dxi3 = (xi(1)^2 - 1)*(xi(2)^2 - 1);
case 27
d2Ndxi1dxi1 = -2*(xi(2)^2 - 1)*(xi(3)^2 - 1);
d2Ndxi2dxi1 = -4*xi(1)*xi(2)*(xi(3)^2 - 1);
d2Ndxi3dxi1 = -4*xi(1)*xi(3)*(xi(2)^2 - 1);
d2Ndxi1dxi2 = -4*xi(1)*xi(2)*(xi(3)^2 - 1);
d2Ndxi2dxi2 = -2*(xi(1)^2 - 1)*(xi(3)^2 - 1);
d2Ndxi3dxi2 = -4*xi(2)*xi(3)*(xi(1)^2 - 1);
d2Ndxi1dxi3 = -4*xi(1)*xi(3)*(xi(2)^2 - 1);
d2Ndxi2dxi3 = -4*xi(2)*xi(3)*(xi(1)^2 - 1);
d2Ndxi3dxi3 = -2*(xi(1)^2 - 1)*(xi(2)^2 - 1);
end
switch( i_eval )
case 22
vBase = aInvJac(:,1).*( aInvJac(:,1)*d2Ndxi1dxi1 + aInvJac(:,2)*d2Ndxi2dxi1 + aInvJac(:,3)*d2Ndxi3dxi1 ) + ...
aInvJac(:,2).*( aInvJac(:,1)*d2Ndxi1dxi2 + aInvJac(:,2)*d2Ndxi2dxi2 + aInvJac(:,3)*d2Ndxi3dxi2 ) + ...
aInvJac(:,3).*( aInvJac(:,1)*d2Ndxi1dxi3 + aInvJac(:,2)*d2Ndxi2dxi3 + aInvJac(:,3)*d2Ndxi3dxi3 );
case 33
vBase = aInvJac(:,4).*( aInvJac(:,4)*d2Ndxi1dxi1 + aInvJac(:,5)*d2Ndxi2dxi1 + aInvJac(:,6)*d2Ndxi3dxi1 ) + ...
aInvJac(:,5).*( aInvJac(:,4)*d2Ndxi1dxi2 + aInvJac(:,5)*d2Ndxi2dxi2 + aInvJac(:,6)*d2Ndxi3dxi2 ) + ...
aInvJac(:,6).*( aInvJac(:,4)*d2Ndxi1dxi3 + aInvJac(:,5)*d2Ndxi2dxi3 + aInvJac(:,6)*d2Ndxi3dxi3 );
case 44
vBase = aInvJac(:,7).*( aInvJac(:,7)*d2Ndxi1dxi1 + aInvJac(:,8)*d2Ndxi2dxi1 + aInvJac(:,9)*d2Ndxi3dxi1 ) + ...
aInvJac(:,8).*( aInvJac(:,7)*d2Ndxi1dxi2 + aInvJac(:,8)*d2Ndxi2dxi2 + aInvJac(:,9)*d2Ndxi3dxi2 ) + ...
aInvJac(:,9).*( aInvJac(:,7)*d2Ndxi1dxi3 + aInvJac(:,8)*d2Ndxi2dxi3 + aInvJac(:,9)*d2Ndxi3dxi3 );
case {23,32}
vBase = aInvJac(:,4).*( aInvJac(:,1)*d2Ndxi1dxi1 + aInvJac(:,2)*d2Ndxi2dxi1 + aInvJac(:,3)*d2Ndxi3dxi1 ) + ...
aInvJac(:,5).*( aInvJac(:,1)*d2Ndxi1dxi2 + aInvJac(:,2)*d2Ndxi2dxi2 + aInvJac(:,3)*d2Ndxi3dxi2 ) + ...
aInvJac(:,6).*( aInvJac(:,1)*d2Ndxi1dxi3 + aInvJac(:,2)*d2Ndxi2dxi3 + aInvJac(:,3)*d2Ndxi3dxi3 );
case {24,42}
vBase = aInvJac(:,7).*( aInvJac(:,1)*d2Ndxi1dxi1 + aInvJac(:,2)*d2Ndxi2dxi1 + aInvJac(:,3)*d2Ndxi3dxi1 ) + ...
aInvJac(:,8).*( aInvJac(:,1)*d2Ndxi1dxi2 + aInvJac(:,2)*d2Ndxi2dxi2 + aInvJac(:,3)*d2Ndxi3dxi2 ) + ...
aInvJac(:,9).*( aInvJac(:,1)*d2Ndxi1dxi3 + aInvJac(:,2)*d2Ndxi2dxi3 + aInvJac(:,3)*d2Ndxi3dxi3 );
case {34,43}
vBase = aInvJac(:,7).*( aInvJac(:,4)*d2Ndxi1dxi1 + aInvJac(:,5)*d2Ndxi2dxi1 + aInvJac(:,6)*d2Ndxi3dxi1 ) + ...
aInvJac(:,8).*( aInvJac(:,4)*d2Ndxi1dxi2 + aInvJac(:,5)*d2Ndxi2dxi2 + aInvJac(:,6)*d2Ndxi3dxi2 ) + ...
aInvJac(:,9).*( aInvJac(:,4)*d2Ndxi1dxi3 + aInvJac(:,5)*d2Ndxi2dxi3 + aInvJac(:,6)*d2Ndxi3dxi3 );
end
otherwise
vBase = 0;
end