SFE method using Hermite polynomials: An approach for solving nonlinear mechanical problems with uncertain parameters

We propose a stochastic finite element 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 the nonlinear mechanical function using Hermite polynomials. The coefficients of the approximation are obtained using a cubic B-spline interpolation of the response function. It provides simple expressions of the 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 the random parameters are modeled as correlated lognormal random variables. The numerical results obtained attest the relevance of this approach.