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SFE method using Hermite polynomials: An approach for solving nonlinear mechanical problems with uncertain parameters. (English) Zbl 1124.74044
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:
74S05Finite element methods in solid mechanics
74H50Random vibrations (dynamical problems in solid mechanics)
74H15Numerical approximation of solutions for dynamical problems in solid mechanics