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Zbl 1124.74044
Baroth, J.; Bodé, L.; Bressolette, Ph.; Fogli, M.
SFE method using Hermite polynomials: An approach for solving nonlinear mechanical problems with uncertain parameters. (English)
[J] Comput. Methods Appl. Mech. Eng. 195, No. 44-47, 6479-6501 (2006). ISSN 0045-7825

Summary: We propose a stochastic finite element (SFE) method for nonlinear mechanical systems whose uncertain parameters can be modeled as random variables. This method is based on a Gaussian standardization of the problem and on an Hilbertian approximation of nonlinear mechanical function using Hermite polynomials. The coefficients of the approximation are obtained using cubic B-spline interpolation of the response function. The approximation provides simple expressions for response moments. Some of its possibilities are illustrated through four numerical examples concerning one linear problem and three nonlinear problems (elasto-plastic behaviors and contact problem) in which random parameters are modeled as correlated lognormal random variables. The numerical results attest the relevance of this approach.

MSC 2000:: *74S05 Finite element methods
74H50 Random vibrations
74H15 Numerical approximation of solutions

Keywords: Hilbertian approximation; B-spline interpolation; lognormal random variable

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Zentralblatt MATH Berlin [Germany]