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Question about stochastic Finite Elements

tlaverne's picture

Hi to the community !

I would like to ask if anyone have some experience with stochastic finite elements in an industrial context ?

Would you know some software (free or commercial) package for stochastic finite elements ?

Why do I have the feeling that sfem methods which look to be very promising aren't used much in practice ? Am I wrong when I say that ?

Thank you very much for any help about that !

Thomas Laverne



M Huber's picture

Hi Thomas,

you'll find a short list on SFEM software in chapter 3.6 of the following paper:

There seems to be a probabilistic toolbox in the recent ANSYS release. Also COSSAN, NESSUS and FERUM are mentioned with references in this survey. From my point of view this paper summarizes nearly every method of SFEM except non-probabilistic ones. Therefore I'll include some papers in the following.

In general search for "Stochastic FEM" (SFEM), "Finite Element Method for Stochastic Problems" (FEMSP) and "Spectral Stochastic Finite Element Method" (SSFEM). I don't know, if this is interesting too: Fractal Finite Element Method (seems to be used mainly in fracture mechanics).

Probabilistic SFEM:

Isaac Elishakoff and Yongjian Ren. The bird’s eye view on finite element method for structures
with large stochastic variations. Computer Methods in Applied Mechanics and Engineering,
168(1-4):51 – 61, 1999. ISSN 0045-7825. doi: DOI:10.1016/S0045-7825(98)00133-9.

Isaac Elishakoff and Yongjian Ren. Finite Element Methods for Structures with Large Stochastic
Variations (Oxford Texts in Applied and Engineering Mathematics, 7). Oxford University Press,
USA, 9 2003. ISBN 9780198526315.

Seung-Kyum Choi, Ramana V. Grandhi, and Robert A. Canfield. Reliability-based Structural
Design. Springer, 1 edition, 10 2006. ISBN 9781846284441. URL .

Bruno Sudret and Armen Der Kiureghian. Stochastic finite element methods and reliability:
a state-of-the-art report. Technical report, Dept. of Civil and Environmental Engineering,
University of California, Berkeley, 2000. URL . UCB/SEMM-2000/08.


Also (some mybe quite old, so before 1990):


If you are interested in non-probabilistic FEM search for "David Moens and Dirk Vandepitte":

D. Moens and D. Vandepitte. Recent advances in non-probabilistic approaches for nondeterministic
dynamic finite element analysis. Archives of Computational Methods in
Engineering, 13(3):389–464, September 2006. ISSN 1134-3060 (Print) 1886-1784 (Online).
doi: 10.1007/BF02736398. URL .

David Moens and Dirk Vandepitte. A survey of non-probabilistic uncertainty treatment
in finite element analysis. Computer Methods in Applied Mechanics and Engineering,
194(12-16):1527–1555, 2005a. ISSN 0045-7825. doi: DOI:10.1016/j.cma.2004.03.019.
URL . Special Issue on Computational Methods
in Stochastic Mechanics and Reliability Analysis.

David Moens and Dirk Vandepitte. A fuzzy finite element procedure for the calculation
of uncertain frequency-response functions of damped structures: Part 1–
procedure. Journal of Sound and Vibration, 288(3):431–462, 2005b. ISSN 0022-460X. doi:
DOI:10.1016/j.jsv.2005.07.001. URL . Uncertainty
in structural dynamics.


You should definitely have a look at this journal:

Finite Elements in Analysis and Design


Maybe you'll find help also in this special issue of Computer Methods in Applied Mechanics and Engineering:

Hope I could help,




tlaverne's picture

Thank you very much Martin !

I knew that COSSAN was actively developped and that many consulting was done with it, even though no commercial release is available for now. I will check the probabilistic toolbox for ansys. Thank you for the references as well ! There are some of them that I was not aware of, so it should help !

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