Stochastic finite element: a non intrusive approach by regression
Keywords:
stochastic finite element, non intrusive method, polynomial chaos, stochastic response surface methodAbstract
The stochastic finite element method allows to solve stochastic boundary value problems where material properties and loads are random. The method is based on the expansion of the mechanical response onto the so-called polynomial chaos. In this paper, a non intrusive method based on a least-squares minimization procedure is presented. This method is illustrated by the study of the settlement of a foundation. Different analysis are proposed: the computation of the statistical moments of the response, a reliability analysis and a parametric sensitivity analysis.
Downloads
References
Berveiller M., Eléments finis stochastiques : approches intrusive et non intrusive pour des analyses
de fiabilité, PhD thesis, Université Blaise Pascal - Clermont Ferrand, 2005.
Berveiller M., Sudret B., Lemaire M., « Presentation of two methods for computing the response
coefficients in stochastic finite element analysis », Proc. 9th ASCE specialty Conference on
Probabilistic Mechanics and Structural Reliability, Albuquerque, USA, 2004.
Berveiller M., Sudret B., Lemaire M., « Non linear non intrusive stochastic finite element
method - Application to a fracture mechanics problem », Proc. 9th Int. Conf. Struct. Safety
and Reliability (ICOSSAR’2005), Rome, Italie, 2005.
Ditlevsen O., Madsen H., Structural reliability methods, J. Wiley and Sons, Chichester, 1996.
Ghanem R.-G., Spanos P.-D., Stochastic finite elements - A spectral approach, Springer Verlag,
Isukapalli S. S., Uncertainty Analysis of Transport-Transformation Models, PhD thesis, The
State University of New Jersey, 1999.
Mahadevan S., Huang S., Rebba R., « A stochastic response surface method for random field
problems », Proc. ICASP9 "Applications of Statistics and Probability to Civil Engineering
Reliability and Risk Analysis", vol. 1, p. 177-184, 2003.
Saporta G., Probabilités, analyse des données et statistique, Editions Technip, 1990.
Sudret B., Berveiller M., Lemaire M., « Eléments finis stochastiques en élasticité linéaire », C.
R. Mécanique, vol. 332, p. 531-537, 2004.
Sudret B., Berveiller M., Lemaire M., « A stochastic finite element procedure for moment and
reliability analysis », Rev. Eur. El. Finis, 2005. soumis pour publication.
Webster M., Tatang M., McRae G., Application of the Probabilistic Collocation Method for an
Uncertainty Analysis of a Simple Ocean Model, Technical report, MIT Joint Program on
the Science and Policy of Global Change Reports Series No. 4, Massachusetts Institute of
Technology, 1996.
