On 10/05/2015 02:25 PM, Enzo Garofalo wrote:
Hello Sir Cimrman,
First, I want to thank you for responding so quickly. I read what you said
about the creation of new terms. Excellent tool and very good documentation.
Thanks!
I can see that numerical integration is used and I could infer, it is
integrated using Gauss quadrature, perhaps. I'm interested in implementing
an integration over the stiffness matrix of an customized element, not
numerical way, but semi-analytical.
Yes, it is integrated using the Gauss quadrature (the quadrature tables are in sfepy/discrete/quadratures.py - see also script/plot_quadratures.py).
As an example of what I want to do, in the following equation, which
corresponds to a stiffness sub-matrix of an axisymmetric element with
isoparametric formulation, I desire to introduce my own terms, not from the
numerical integration Smith-Griffiths, for example, but my own expressions.
<https://lh3.googleusercontent.com/-Uu2l84eJG4k/VhJnkvn-iwI/AAAAAAAABh8/nq0zp48VGag/s1600/Captura.PNG>
Would it be possible to create a customized finite element and continue
using all the advantages of SfePy?
A SfePy term has to be able to return the following: given the values of FE field variables, return the residual/stiffness matrix in all cells (elements) integrated over each element. The integration is done over a reference element, so a mapping to a physical element is needed, see Term.get_mapping() - this works with quadrature points.
So I would say that the answer is yes, provided you can do the integration/mapping yourself, given only the values of variables - those can be evaluated in any point inside the domain.
r.
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