[Insight-developers] Element3DC0LinearTetrahedronStrain stiffness Matrix calculation

[Fotis Drakopoulos]

Hi all,

In  Modules/Numerics/FEM/src/itkFEMElementBase.cxx   and in function
GetStiffnessMatrix()  the element stiffness matrix (Ke) is calculated.
I believe that when the Linear tetrahedron element is used (class
Element3DC0LinearTetrahedronStrain)  then stiffness matrix equals to :

Ke = *(1/6)* * detJ * w * B.transpose() * D * B
and not with
Ke = detJ * w * B.transpose() * D * B

In case of the  hexahedron element the infinitesimal volume dV that we want
to integrate the entries of the stiffness matrix equals to :
dV = dx*dy*dz = det(J) * dr*ds*dt

However in case of thetrahedron is:
dV = dx*dy*dz = (1/6) * det(J) * dr*ds*dt

where det(J) is the determinant of the Jacobian matrix.

Regards
Fotis Drakopoulos
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