Stochastic finite element method with decomposition and hermite polynomials approximation

To evaluate statistical moments of response, reliability and reliability sensitivity of stochastic structures, a new stochastic finite element method is presented on the basis of Hermite polynomials approximation. Decomposition is used to transform the multi-dimensional response function into one-dimensional function. And then the Hermite polynomials are employed to approximate the one-dimensional response function, and the coefficients of the Hermite polynomials can be determined by the Gauss-Hermite integration. The statistical moments, failure probability and reliability sensitivity of the approximately explicit response function are obtained by Monte-Carlo numerical simulation, where the computation of derivatives and design points becomes unnecessary. A few examples demonstrate the validity.