基于分裂法及Hermite多项式逼近的随机有限元

Stochastic Finite Element Method with Decomposition and Hermite Polynomials Approximation

针对随机结构响应的统计矩、可靠性、灵敏度分析问题,提出了一种新的基于Hermite多项式逼近的随机有限元方法。所提方法利用分裂法将多维响应函数问题转换成单维问题,并采用Hermite多项式逼近单随机变量的响应函数,Hermite多项式系数由Gauss-Hermite积分法求解,最后利用Monte-Carlo法求解显式化后的响应函数的统计矩、失效概率、灵敏度。本文方法简单实用,不用考虑计算导数和设计点问题,因此可十分方便的用于结构的概率分析。文中算例充分说明了所提方法的合理性与可行性。

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.