随机结构有限元分析的递推求解方法

提出了一种新的谱随机有限元分析方法——递推求解方法。该方法将随机结构的随机响应表示成非正交多项式展式，建立了和摄动法类似的一系列确定的递推方程，并通过确定性有限元方法对这些递推方程进行静力问题求解。算例表明，当随机量出现较大涨落时，计算结果相对于传统摄动法有不小的改进。

Recursive stochastic finite element method

A new spectral stochastic finite element method for the solution of static problems involving material variability is proposed.The method is called as recursive random finite element method in this paper.The random material properties such as modulus of elasticity are represented using Karhunun-Loeve expansion or other transformation.Random structural response is expressed as non-orthogonal polynomials chaos expansion.So the control equation of random static problem can be formed using FEM,which is a matrix equation containing many uncorrelated random variables.Then a series of deterministic recursive equations are set up through non-orthogonal polynomials of the same order.Such method is similar in form to perturbation method,but it can solve static problem including random variables at large fluctuation levels.A static response problem of random cantilever beam under centralized load is investigated.Compared with traditional perturbation stochastic FEM,the results obtained using the new method are more close to that of Monte-Carlo simulation when fluctuation of random variables becomes large.