FEATool Multiphysics
v1.17.2
Finite Element Analysis Toolbox
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SF_TRI_P5 Fifth order Lagrange shape functions for triangles (P5).
[ VBASE, NLDOF, XLDOF, SFUN ] = SF_TRI_P5( I_EVAL, N_SDIM, N_VERT, I_DOF, XI, AINVJAC, VBASE ) Evaluates conforming fifth order P5 Lagrange shape functions on 2D triangular elements with values defined in the nodes, edges, and center. XI are Barycentric coordinates.
Input Value/[Size] Description ----------------------------------------------------------------------------------- i_eval scalar: 1 Evaluate function values >1 Evaluate values of derivatives n_sdim scalar: 2 Number of space dimensions n_vert scalar: 3 Number of vertices per cell i_dof scalar: 1-21 Local basis function to evaluate xi array [3,1] Local coordinates of evaluation point aInvJac [n,6] Inverse of transformation Jacobian vBase [n] Preallocated output vector . Output Value/[Size] Description ----------------------------------------------------------------------------------- vBase [n] Evaluated function values nLDof [4] Number of local degrees of freedom on vertices, edges, faces, and cell interiors xLDof [3,n_ldof] Local coordinates of local dofs sfun string Function name of called shape function
nLDof = [3 12 0 6]; xLDof = [1 0 0 4/5 0 1/5 3/5 0 2/5 2/5 0 3/5 1/5 0 4/5 3/5 1/5 1/5 2/5 1/5 2/5; 0 1 0 1/5 4/5 0 2/5 3/5 0 3/5 2/5 0 4/5 1/5 0 1/5 3/5 1/5 2/5 2/5 1/5; 0 0 1 0 1/5 4/5 0 2/5 3/5 0 3/5 2/5 0 4/5 1/5 1/5 1/5 3/5 1/5 2/5 2/5]; sfun = 'sf_tri_P5'; switch i_eval case 1 switch i_dof case 1 vBase = (xi(1)*(5*xi(1) - 1)*(5*xi(1) - 2)*(5*xi(1) - 3)*(5*xi(1) - 4))/24; case 2 vBase = (xi(2)*(5*xi(2) - 1)*(5*xi(2) - 2)*(5*xi(2) - 3)*(5*xi(2) - 4))/24; case 3 vBase = (xi(3)*(5*xi(3) - 1)*(5*xi(3) - 2)*(5*xi(3) - 3)*(5*xi(3) - 4))/24; case 4 vBase = (25*xi(1)*xi(2)*(5*xi(1) - 1)*(5*xi(1) - 2)*(5*xi(1) - 3))/24; case 5 vBase = (25*xi(2)*xi(3)*(5*xi(2) - 1)*(5*xi(2) - 2)*(5*xi(2) - 3))/24; case 6 vBase = (25*xi(1)*xi(3)*(5*xi(3) - 1)*(5*xi(3) - 2)*(5*xi(3) - 3))/24; case 7 vBase = (25*xi(1)*xi(2)*(5*xi(1) - 1)*(5*xi(1) - 2)*(5*xi(2) - 1))/12; case 8 vBase = (25*xi(2)*xi(3)*(5*xi(2) - 1)*(5*xi(2) - 2)*(5*xi(3) - 1))/12; case 9 vBase = (25*xi(1)*xi(3)*(5*xi(1) - 1)*(5*xi(3) - 1)*(5*xi(3) - 2))/12; case 10 vBase = (25*xi(1)*xi(2)*(5*xi(1) - 1)*(5*xi(2) - 1)*(5*xi(2) - 2))/12; case 11 vBase = (25*xi(2)*xi(3)*(5*xi(2) - 1)*(5*xi(3) - 1)*(5*xi(3) - 2))/12; case 12 vBase = (25*xi(1)*xi(3)*(5*xi(1) - 1)*(5*xi(1) - 2)*(5*xi(3) - 1))/12; case 13 vBase = (25*xi(1)*xi(2)*(5*xi(2) - 1)*(5*xi(2) - 2)*(5*xi(2) - 3))/24; case 14 vBase = (25*xi(2)*xi(3)*(5*xi(3) - 1)*(5*xi(3) - 2)*(5*xi(3) - 3))/24; case 15 vBase = (25*xi(1)*xi(3)*(5*xi(1) - 1)*(5*xi(1) - 2)*(5*xi(1) - 3))/24; case 16 vBase = (125*xi(1)*xi(2)*xi(3)*(5*xi(1) - 1)*(5*xi(1) - 2))/6; case 17 vBase = (125*xi(1)*xi(2)*xi(3)*(5*xi(2) - 1)*(5*xi(2) - 2))/6; case 18 vBase = (125*xi(1)*xi(2)*xi(3)*(5*xi(3) - 1)*(5*xi(3) - 2))/6; case 19 vBase = (125*xi(1)*xi(2)*xi(3)*(5*xi(1) - 1)*(5*xi(2) - 1))/4; case 20 vBase = (125*xi(1)*xi(2)*xi(3)*(5*xi(2) - 1)*(5*xi(3) - 1))/4; case 21 vBase = (125*xi(1)*xi(2)*xi(3)*(5*xi(1) - 1)*(5*xi(3) - 1))/4; end case {2,3} switch i_dof case 1 dNdxi1 = (3125*xi(1)^4)/24 - (625*xi(1)^3)/3 + (875*xi(1)^2)/8 - (125*xi(1))/6 + 1; dNdxi2 = 0; dNdxi3 = 0; case 2 dNdxi1 = 0; dNdxi2 = (3125*xi(2)^4)/24 - (625*xi(2)^3)/3 + (875*xi(2)^2)/8 - (125*xi(2))/6 + 1; dNdxi3 = 0; case 3 dNdxi1 = 0; dNdxi2 = 0; dNdxi3 = (3125*xi(3)^4)/24 - (625*xi(3)^3)/3 + (875*xi(3)^2)/8 - (125*xi(3))/6 + 1; case 4 dNdxi1 = (25*xi(2)*(10*xi(1) - 3)*(25*xi(1)^2 - 15*xi(1) + 1))/12; dNdxi2 = (25*xi(1)*(5*xi(1) - 1)*(5*xi(1) - 2)*(5*xi(1) - 3))/24; dNdxi3 = 0; case 5 dNdxi1 = 0; dNdxi2 = (25*xi(3)*(10*xi(2) - 3)*(25*xi(2)^2 - 15*xi(2) + 1))/12; dNdxi3 = (25*xi(2)*(5*xi(2) - 1)*(5*xi(2) - 2)*(5*xi(2) - 3))/24; case 6 dNdxi1 = (25*xi(3)*(5*xi(3) - 1)*(5*xi(3) - 2)*(5*xi(3) - 3))/24; dNdxi2 = 0; dNdxi3 = (25*xi(1)*(10*xi(3) - 3)*(25*xi(3)^2 - 15*xi(3) + 1))/12; case 7 dNdxi1 = (25*xi(2)*(5*xi(2) - 1)*(75*xi(1)^2 - 30*xi(1) + 2))/12; dNdxi2 = (25*xi(1)*(5*xi(1) - 1)*(5*xi(1) - 2)*(10*xi(2) - 1))/12; dNdxi3 = 0; case 8 dNdxi1 = 0; dNdxi2 = (25*xi(3)*(5*xi(3) - 1)*(75*xi(2)^2 - 30*xi(2) + 2))/12; dNdxi3 = (25*xi(2)*(5*xi(2) - 1)*(5*xi(2) - 2)*(10*xi(3) - 1))/12; case 9 dNdxi1 = (25*xi(3)*(10*xi(1) - 1)*(5*xi(3) - 1)*(5*xi(3) - 2))/12; dNdxi2 = 0; dNdxi3 = (25*xi(1)*(5*xi(1) - 1)*(75*xi(3)^2 - 30*xi(3) + 2))/12; case 10 dNdxi1 = (25*xi(2)*(10*xi(1) - 1)*(5*xi(2) - 1)*(5*xi(2) - 2))/12; dNdxi2 = (25*xi(1)*(5*xi(1) - 1)*(75*xi(2)^2 - 30*xi(2) + 2))/12; dNdxi3 = 0; case 11 dNdxi1 = 0; dNdxi2 = (25*xi(3)*(10*xi(2) - 1)*(5*xi(3) - 1)*(5*xi(3) - 2))/12; dNdxi3 = (25*xi(2)*(5*xi(2) - 1)*(75*xi(3)^2 - 30*xi(3) + 2))/12; case 12 dNdxi1 = (25*xi(3)*(5*xi(3) - 1)*(75*xi(1)^2 - 30*xi(1) + 2))/12; dNdxi2 = 0; dNdxi3 = (25*xi(1)*(5*xi(1) - 1)*(5*xi(1) - 2)*(10*xi(3) - 1))/12; case 13 dNdxi1 = (25*xi(2)*(5*xi(2) - 1)*(5*xi(2) - 2)*(5*xi(2) - 3))/24; dNdxi2 = (25*xi(1)*(10*xi(2) - 3)*(25*xi(2)^2 - 15*xi(2) + 1))/12; dNdxi3 = 0; case 14 dNdxi1 = 0; dNdxi2 = (25*xi(3)*(5*xi(3) - 1)*(5*xi(3) - 2)*(5*xi(3) - 3))/24; dNdxi3 = (25*xi(2)*(10*xi(3) - 3)*(25*xi(3)^2 - 15*xi(3) + 1))/12; case 15 dNdxi1 = (25*xi(3)*(10*xi(1) - 3)*(25*xi(1)^2 - 15*xi(1) + 1))/12; dNdxi2 = 0; dNdxi3 = (25*xi(1)*(5*xi(1) - 1)*(5*xi(1) - 2)*(5*xi(1) - 3))/24; case 16 dNdxi1 = (125*xi(2)*xi(3)*(75*xi(1)^2 - 30*xi(1) + 2))/6; dNdxi2 = (125*xi(1)*xi(3)*(5*xi(1) - 1)*(5*xi(1) - 2))/6; dNdxi3 = (125*xi(1)*xi(2)*(5*xi(1) - 1)*(5*xi(1) - 2))/6; case 17 dNdxi1 = (125*xi(2)*xi(3)*(5*xi(2) - 1)*(5*xi(2) - 2))/6; dNdxi2 = (125*xi(1)*xi(3)*(75*xi(2)^2 - 30*xi(2) + 2))/6; dNdxi3 = (125*xi(1)*xi(2)*(5*xi(2) - 1)*(5*xi(2) - 2))/6; case 18 dNdxi1 = (125*xi(2)*xi(3)*(5*xi(3) - 1)*(5*xi(3) - 2))/6; dNdxi2 = (125*xi(1)*xi(3)*(5*xi(3) - 1)*(5*xi(3) - 2))/6; dNdxi3 = (125*xi(1)*xi(2)*(75*xi(3)^2 - 30*xi(3) + 2))/6; case 19 dNdxi1 = (125*xi(2)*xi(3)*(10*xi(1) - 1)*(5*xi(2) - 1))/4; dNdxi2 = (125*xi(1)*xi(3)*(5*xi(1) - 1)*(10*xi(2) - 1))/4; dNdxi3 = (125*xi(1)*xi(2)*(5*xi(1) - 1)*(5*xi(2) - 1))/4; case 20 dNdxi1 = (125*xi(2)*xi(3)*(5*xi(2) - 1)*(5*xi(3) - 1))/4; dNdxi2 = (125*xi(1)*xi(3)*(10*xi(2) - 1)*(5*xi(3) - 1))/4; dNdxi3 = (125*xi(1)*xi(2)*(5*xi(2) - 1)*(10*xi(3) - 1))/4; case 21 dNdxi1 = (125*xi(2)*xi(3)*(10*xi(1) - 1)*(5*xi(3) - 1))/4; dNdxi2 = (125*xi(1)*xi(3)*(5*xi(1) - 1)*(5*xi(3) - 1))/4; dNdxi3 = (125*xi(1)*xi(2)*(5*xi(1) - 1)*(10*xi(3) - 1))/4; end if( i_eval==2 ) vBase = aInvJac(:,1).*dNdxi1 + aInvJac(:,2).*dNdxi2 + aInvJac(:,3).*dNdxi3; else vBase = aInvJac(:,4).*dNdxi1 + aInvJac(:,5).*dNdxi2 + aInvJac(:,6).*dNdxi3; end case {22,23,32,33} % Evaluation of second derivatives. switch i_dof case 1 d2Ndxi1dxi1 = (125*(5*xi(1) - 2)*(10*xi(1)^2 - 8*xi(1) + 1))/12; d2Ndxi2dxi1 = 0; d2Ndxi3dxi1 = 0; d2Ndxi1dxi2 = 0; d2Ndxi2dxi2 = 0; d2Ndxi3dxi2 = 0; d2Ndxi1dxi3 = 0; d2Ndxi2dxi3 = 0; d2Ndxi3dxi3 = 0; case 2 d2Ndxi1dxi1 = 0; d2Ndxi2dxi1 = 0; d2Ndxi3dxi1 = 0; d2Ndxi1dxi2 = 0; d2Ndxi2dxi2 = (125*(5*xi(2) - 2)*(10*xi(2)^2 - 8*xi(2) + 1))/12; d2Ndxi3dxi2 = 0; d2Ndxi1dxi3 = 0; d2Ndxi2dxi3 = 0; d2Ndxi3dxi3 = 0; case 3 d2Ndxi1dxi1 = 0; d2Ndxi2dxi1 = 0; d2Ndxi3dxi1 = 0; d2Ndxi1dxi2 = 0; d2Ndxi2dxi2 = 0; d2Ndxi3dxi2 = 0; d2Ndxi1dxi3 = 0; d2Ndxi2dxi3 = 0; d2Ndxi3dxi3 = (125*(5*xi(3) - 2)*(10*xi(3)^2 - 8*xi(3) + 1))/12; case 4 d2Ndxi1dxi1 = (125*xi(2)*(150*xi(1)^2 - 90*xi(1) + 11))/12; d2Ndxi2dxi1 = (25*(10*xi(1) - 3)*(25*xi(1)^2 - 15*xi(1) + 1))/12; d2Ndxi3dxi1 = 0; d2Ndxi1dxi2 = (25*(10*xi(1) - 3)*(25*xi(1)^2 - 15*xi(1) + 1))/12; d2Ndxi2dxi2 = 0; d2Ndxi3dxi2 = 0; d2Ndxi1dxi3 = 0; d2Ndxi2dxi3 = 0; d2Ndxi3dxi3 = 0; case 5 d2Ndxi1dxi1 = 0; d2Ndxi2dxi1 = 0; d2Ndxi3dxi1 = 0; d2Ndxi1dxi2 = 0; d2Ndxi2dxi2 = (125*xi(3)*(150*xi(2)^2 - 90*xi(2) + 11))/12; d2Ndxi3dxi2 = (25*(10*xi(2) - 3)*(25*xi(2)^2 - 15*xi(2) + 1))/12; d2Ndxi1dxi3 = 0; d2Ndxi2dxi3 = (25*(10*xi(2) - 3)*(25*xi(2)^2 - 15*xi(2) + 1))/12; d2Ndxi3dxi3 = 0; case 6 d2Ndxi1dxi1 = 0; d2Ndxi2dxi1 = 0; d2Ndxi3dxi1 = (25*(10*xi(3) - 3)*(25*xi(3)^2 - 15*xi(3) + 1))/12; d2Ndxi1dxi2 = 0; d2Ndxi2dxi2 = 0; d2Ndxi3dxi2 = 0; d2Ndxi1dxi3 = (25*(10*xi(3) - 3)*(25*xi(3)^2 - 15*xi(3) + 1))/12; d2Ndxi2dxi3 = 0; d2Ndxi3dxi3 = (125*xi(1)*(150*xi(3)^2 - 90*xi(3) + 11))/12; case 7 d2Ndxi1dxi1 = (125*xi(2)*(5*xi(1) - 1)*(5*xi(2) - 1))/2; d2Ndxi2dxi1 = (25*(10*xi(2) - 1)*(75*xi(1)^2 - 30*xi(1) + 2))/12; d2Ndxi3dxi1 = 0; d2Ndxi1dxi2 = (25*(10*xi(2) - 1)*(75*xi(1)^2 - 30*xi(1) + 2))/12; d2Ndxi2dxi2 = (125*xi(1)*(5*xi(1) - 1)*(5*xi(1) - 2))/6; d2Ndxi3dxi2 = 0; d2Ndxi1dxi3 = 0; d2Ndxi2dxi3 = 0; d2Ndxi3dxi3 = 0; case 8 d2Ndxi1dxi1 = 0; d2Ndxi2dxi1 = 0; d2Ndxi3dxi1 = 0; d2Ndxi1dxi2 = 0; d2Ndxi2dxi2 = (125*xi(3)*(5*xi(2) - 1)*(5*xi(3) - 1))/2; d2Ndxi3dxi2 = (25*(10*xi(3) - 1)*(75*xi(2)^2 - 30*xi(2) + 2))/12; d2Ndxi1dxi3 = 0; d2Ndxi2dxi3 = (25*(10*xi(3) - 1)*(75*xi(2)^2 - 30*xi(2) + 2))/12; d2Ndxi3dxi3 = (125*xi(2)*(5*xi(2) - 1)*(5*xi(2) - 2))/6; case 9 d2Ndxi1dxi1 = (125*xi(3)*(5*xi(3) - 1)*(5*xi(3) - 2))/6; d2Ndxi2dxi1 = 0; d2Ndxi3dxi1 = (25*(10*xi(1) - 1)*(75*xi(3)^2 - 30*xi(3) + 2))/12; d2Ndxi1dxi2 = 0; d2Ndxi2dxi2 = 0; d2Ndxi3dxi2 = 0; d2Ndxi1dxi3 = (25*(10*xi(1) - 1)*(75*xi(3)^2 - 30*xi(3) + 2))/12; d2Ndxi2dxi3 = 0; d2Ndxi3dxi3 = (125*xi(1)*(5*xi(1) - 1)*(5*xi(3) - 1))/2; case 10 d2Ndxi1dxi1 = (125*xi(2)*(5*xi(2) - 1)*(5*xi(2) - 2))/6; d2Ndxi2dxi1 = (25*(10*xi(1) - 1)*(75*xi(2)^2 - 30*xi(2) + 2))/12; d2Ndxi3dxi1 = 0; d2Ndxi1dxi2 = (25*(10*xi(1) - 1)*(75*xi(2)^2 - 30*xi(2) + 2))/12; d2Ndxi2dxi2 = (125*xi(1)*(5*xi(1) - 1)*(5*xi(2) - 1))/2; d2Ndxi3dxi2 = 0; d2Ndxi1dxi3 = 0; d2Ndxi2dxi3 = 0; d2Ndxi3dxi3 = 0; case 11 d2Ndxi1dxi1 = 0; d2Ndxi2dxi1 = 0; d2Ndxi3dxi1 = 0; d2Ndxi1dxi2 = 0; d2Ndxi2dxi2 = (125*xi(3)*(5*xi(3) - 1)*(5*xi(3) - 2))/6; d2Ndxi3dxi2 = (25*(10*xi(2) - 1)*(75*xi(3)^2 - 30*xi(3) + 2))/12; d2Ndxi1dxi3 = 0; d2Ndxi2dxi3 = (25*(10*xi(2) - 1)*(75*xi(3)^2 - 30*xi(3) + 2))/12; d2Ndxi3dxi3 = (125*xi(2)*(5*xi(2) - 1)*(5*xi(3) - 1))/2; case 12 d2Ndxi1dxi1 = (125*xi(3)*(5*xi(1) - 1)*(5*xi(3) - 1))/2; d2Ndxi2dxi1 = 0; d2Ndxi3dxi1 = (25*(10*xi(3) - 1)*(75*xi(1)^2 - 30*xi(1) + 2))/12; d2Ndxi1dxi2 = 0; d2Ndxi2dxi2 = 0; d2Ndxi3dxi2 = 0; d2Ndxi1dxi3 = (25*(10*xi(3) - 1)*(75*xi(1)^2 - 30*xi(1) + 2))/12; d2Ndxi2dxi3 = 0; d2Ndxi3dxi3 = (125*xi(1)*(5*xi(1) - 1)*(5*xi(1) - 2))/6; case 13 d2Ndxi1dxi1 = 0; d2Ndxi2dxi1 = (25*(10*xi(2) - 3)*(25*xi(2)^2 - 15*xi(2) + 1))/12; d2Ndxi3dxi1 = 0; d2Ndxi1dxi2 = (25*(10*xi(2) - 3)*(25*xi(2)^2 - 15*xi(2) + 1))/12; d2Ndxi2dxi2 = (125*xi(1)*(150*xi(2)^2 - 90*xi(2) + 11))/12; d2Ndxi3dxi2 = 0; d2Ndxi1dxi3 = 0; d2Ndxi2dxi3 = 0; d2Ndxi3dxi3 = 0; case 14 d2Ndxi1dxi1 = 0; d2Ndxi2dxi1 = 0; d2Ndxi3dxi1 = 0; d2Ndxi1dxi2 = 0; d2Ndxi2dxi2 = 0; d2Ndxi3dxi2 = (25*(10*xi(3) - 3)*(25*xi(3)^2 - 15*xi(3) + 1))/12; d2Ndxi1dxi3 = 0; d2Ndxi2dxi3 = (25*(10*xi(3) - 3)*(25*xi(3)^2 - 15*xi(3) + 1))/12; d2Ndxi3dxi3 = (125*xi(2)*(150*xi(3)^2 - 90*xi(3) + 11))/12; case 15 d2Ndxi1dxi1 = (125*xi(3)*(150*xi(1)^2 - 90*xi(1) + 11))/12; d2Ndxi2dxi1 = 0; d2Ndxi3dxi1 = (25*(10*xi(1) - 3)*(25*xi(1)^2 - 15*xi(1) + 1))/12; d2Ndxi1dxi2 = 0; d2Ndxi2dxi2 = 0; d2Ndxi3dxi2 = 0; d2Ndxi1dxi3 = (25*(10*xi(1) - 3)*(25*xi(1)^2 - 15*xi(1) + 1))/12; d2Ndxi2dxi3 = 0; d2Ndxi3dxi3 = 0; case 16 d2Ndxi1dxi1 = 625*xi(2)*xi(3)*(5*xi(1) - 1); d2Ndxi2dxi1 = (125*xi(3)*(75*xi(1)^2 - 30*xi(1) + 2))/6; d2Ndxi3dxi1 = (125*xi(2)*(75*xi(1)^2 - 30*xi(1) + 2))/6; d2Ndxi1dxi2 = (125*xi(3)*(75*xi(1)^2 - 30*xi(1) + 2))/6; d2Ndxi2dxi2 = 0; d2Ndxi3dxi2 = (125*xi(1)*(5*xi(1) - 1)*(5*xi(1) - 2))/6; d2Ndxi1dxi3 = (125*xi(2)*(75*xi(1)^2 - 30*xi(1) + 2))/6; d2Ndxi2dxi3 = (125*xi(1)*(5*xi(1) - 1)*(5*xi(1) - 2))/6; d2Ndxi3dxi3 = 0; case 17 d2Ndxi1dxi1 = 0; d2Ndxi2dxi1 = (125*xi(3)*(75*xi(2)^2 - 30*xi(2) + 2))/6; d2Ndxi3dxi1 = (125*xi(2)*(5*xi(2) - 1)*(5*xi(2) - 2))/6; d2Ndxi1dxi2 = (125*xi(3)*(75*xi(2)^2 - 30*xi(2) + 2))/6; d2Ndxi2dxi2 = 625*xi(1)*xi(3)*(5*xi(2) - 1); d2Ndxi3dxi2 = (125*xi(1)*(75*xi(2)^2 - 30*xi(2) + 2))/6; d2Ndxi1dxi3 = (125*xi(2)*(5*xi(2) - 1)*(5*xi(2) - 2))/6; d2Ndxi2dxi3 = (125*xi(1)*(75*xi(2)^2 - 30*xi(2) + 2))/6; d2Ndxi3dxi3 = 0; case 18 d2Ndxi1dxi1 = 0; d2Ndxi2dxi1 = (125*xi(3)*(5*xi(3) - 1)*(5*xi(3) - 2))/6; d2Ndxi3dxi1 = (125*xi(2)*(75*xi(3)^2 - 30*xi(3) + 2))/6; d2Ndxi1dxi2 = (125*xi(3)*(5*xi(3) - 1)*(5*xi(3) - 2))/6; d2Ndxi2dxi2 = 0; d2Ndxi3dxi2 = (125*xi(1)*(75*xi(3)^2 - 30*xi(3) + 2))/6; d2Ndxi1dxi3 = (125*xi(2)*(75*xi(3)^2 - 30*xi(3) + 2))/6; d2Ndxi2dxi3 = (125*xi(1)*(75*xi(3)^2 - 30*xi(3) + 2))/6; d2Ndxi3dxi3 = 625*xi(1)*xi(2)*(5*xi(3) - 1); case 19 d2Ndxi1dxi1 = (625*xi(2)*xi(3)*(5*xi(2) - 1))/2; d2Ndxi2dxi1 = (125*xi(3)*(10*xi(1) - 1)*(10*xi(2) - 1))/4; d2Ndxi3dxi1 = (125*xi(2)*(10*xi(1) - 1)*(5*xi(2) - 1))/4; d2Ndxi1dxi2 = (125*xi(3)*(10*xi(1) - 1)*(10*xi(2) - 1))/4; d2Ndxi2dxi2 = (625*xi(1)*xi(3)*(5*xi(1) - 1))/2; d2Ndxi3dxi2 = (125*xi(1)*(5*xi(1) - 1)*(10*xi(2) - 1))/4; d2Ndxi1dxi3 = (125*xi(2)*(10*xi(1) - 1)*(5*xi(2) - 1))/4; d2Ndxi2dxi3 = (125*xi(1)*(5*xi(1) - 1)*(10*xi(2) - 1))/4; d2Ndxi3dxi3 = 0; case 20 d2Ndxi1dxi1 = 0; d2Ndxi2dxi1 = (125*xi(3)*(10*xi(2) - 1)*(5*xi(3) - 1))/4; d2Ndxi3dxi1 = (125*xi(2)*(5*xi(2) - 1)*(10*xi(3) - 1))/4; d2Ndxi1dxi2 = (125*xi(3)*(10*xi(2) - 1)*(5*xi(3) - 1))/4; d2Ndxi2dxi2 = (625*xi(1)*xi(3)*(5*xi(3) - 1))/2; d2Ndxi3dxi2 = (125*xi(1)*(10*xi(2) - 1)*(10*xi(3) - 1))/4; d2Ndxi1dxi3 = (125*xi(2)*(5*xi(2) - 1)*(10*xi(3) - 1))/4; d2Ndxi2dxi3 = (125*xi(1)*(10*xi(2) - 1)*(10*xi(3) - 1))/4; d2Ndxi3dxi3 = (625*xi(1)*xi(2)*(5*xi(2) - 1))/2; case 21 d2Ndxi1dxi1 = (625*xi(2)*xi(3)*(5*xi(3) - 1))/2; d2Ndxi2dxi1 = (125*xi(3)*(10*xi(1) - 1)*(5*xi(3) - 1))/4; d2Ndxi3dxi1 = (125*xi(2)*(10*xi(1) - 1)*(10*xi(3) - 1))/4; d2Ndxi1dxi2 = (125*xi(3)*(10*xi(1) - 1)*(5*xi(3) - 1))/4; d2Ndxi2dxi2 = 0; d2Ndxi3dxi2 = (125*xi(1)*(5*xi(1) - 1)*(10*xi(3) - 1))/4; d2Ndxi1dxi3 = (125*xi(2)*(10*xi(1) - 1)*(10*xi(3) - 1))/4; d2Ndxi2dxi3 = (125*xi(1)*(5*xi(1) - 1)*(10*xi(3) - 1))/4; d2Ndxi3dxi3 = (625*xi(1)*xi(2)*(5*xi(1) - 1))/2; end if( i_eval==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 ); elseif( i_eval==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 ); else 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 ); end otherwise vBase = 0; end