[vtk-developers] Pentagonal prism bug resolved!

[Bill Lorensen]

Brings back memories of my finite element days, 1968-1978, at
Watervliet Arsenal. At that time we worked with NASTRAN and we added a
few elements for crack tip analysis....


Pu, S. L., M. A. Hussain, and W. E. Lorensen, The Collapsed Cubic
Isoparametric Element as a Singular Element for Crack Problems,
International Journal for Numerical Methods in Engineering, vol. 12,
no. 11, pp. 1727-1742, 1978.

Hussain, M. A. and W. E. Lorensen, Isoparametric Elements as Singular
Elements for Crack Problems, AR-LCB-TR-77041, Benet Weapons
Laboratory, Watervliet, NY, November 1977.

Hussain, M. A.; Pu, S. L.; Lorensen, W. E., Singular Plastic Element:
NASTRAN Implementation and Application, Sixth NASTRAN Users' Colloq.,
pp. 257-274, October, 1977, (NASA CP-2018).

Pu, S. L., M. A. Hussain, and W. E. Lorensen, Collapsed 12-Node
Triangular Elements as Crack Tip Elements for Elastic Fracture,
ARLCB-TR-77047, Watervliet Arsenal, Watervliet, NY, December 1977.

Lorensen, W. E. and M. A. Hussain, "The Stability of Isoparametric
Elements as a Singular Element for Crack Problems," in Developments in
Mechanics, ed. T. C. T. Ting, 1977.

Pu, S. L., M. A. Hussain, and W. E. Lorensen, The Collapsed Cubic
Isoparametric Element as a Singular Element for Crack Problems,
AR-LCB-TR77047, Watervliet Arsenal, 1977.

Hussain, M. A., W. E. Lorensen, and G. Pflegl, The Quarter-Point
Quadratic Isoparametric Element as A Singular Element for Crack
Problems, TM-X-3428, p. 419, NASA, 1976.


On Mon, Jun 15, 2015 at 2:17 PM, Berk Geveci <berk.geveci at kitware.com> wrote:
> You rock Bill.
>
> On Mon, Jun 15, 2015 at 1:31 PM, Bill Lorensen <bill.lorensen at gmail.com>
> wrote:
>>
>> Folks,
>>
>> I reported recently of issues with the shape functions and derivatives
>> for the pentagonal prism. Since I could not find any references for
>> the current implementation I used the formulation in this paper:
>> http://dilbert.engr.ucdavis.edu/~suku/nem/papers/polyelas.pdf
>> Since this paper did not have the shape function derivatives, I used
>> SymPy ( http://www.sympy.org/en/index.html ) to compute the
>> derivatives.
>>
>> I'm happy to report that the new formulation does a great job and
>> passes the new unit test I created for cells.
>>
>> I have not submitted a patch yet since I want the code to document the
>> process. I wrote c++ code and SymPy code to generate the statements
>> for the new formulation.
>>
>> I wanted to give a heads up in case someone else is looking into this.
>>
>> Bill
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