[ITK-users] ITK:FEM : FEM SOLVERS

[Jliang]

There maybe an error in itkfem codes. The tetra element 

stffness matrix should be corrected by factor of 1/6. 
If you do not change the code, you need 
multiply the displacement by 6 to get the correct solution. 
After such correction, the results from 
tetra2 test example will match with the results from ABaqus.

Suggestion to change: in tetra specific class, 
find function of getting one-point weight, change 
the weight from 1 to 1/6

Why codes are wrong:
They use R,s,t and (1-r-s-t) as shape function, 
the integration is executed in R,s,t=0-1. That is 
wrong.
  think about 2d problem (triangle):
Int[f(x,y) dx dy] =int[ f(s,t) |J| ds dt]=f |J|  int [ds dt]

In itk code ( 4.8.0?)', int [ds dt]=1. Wrong!
Actually, int [dt ds]=1/2. In 3d, int [ dr ds dt] 
=1/6