基于观点法的谱随机有限元分析——随机响应面法

提出了一种基于配点法的谱随机有限元分析方法-随机响应面法(SRSM),这种方法与已有的谱随机有限元方法(SSFEM)类似,都用Karhunen-Loeve级数扩展式表示输入随机场而计算结果的输出用多项式混沌展式表达。然而这两种方法采用了不同的方法确定多项式混沌展式中的系数:SRSM利用概率最小二乘配点法而SSFEM利用概率Galerkin法。与解析的SSFEM相比,SRSM的优势在于有限元计算和随机分析计算不耦合,即可把通用有限元程序作为黑箱进行求解。与黑箱版的SSFEM相比,SRSM需要的样本计算更少。SRSM中的各配点来自高概率的区域并使均方差最小化,从而可用少量的样本计算获得较高的计算精度。算例突出了本文提出的方法的特点并显示此方法是有效的且有较高的计算精度。

A collocation-based spectral stochastic finite element analysis——stochastic response surface approach

A collocation-based stochastic finite element method(SRSM) has been developed,the formalism of the proposed method is similar to the spectral stochastic finite element method(SSFEM) in the sense that both of them utilize Karhunen-Loeve(K-L) expansion to represent the input,and polynomial chaos expansion to represent the output.However,the calculation of the coefficients in the polynomial chaos expansion is different: Analytical SSFEM uses a probabilistic Galerkin approach while SRSM uses a probabilistic collocation approach.Numerical example shows that compared to the Analytical SSFEM,the advantage of SRSM is that the finite element coee can be treated as a black box,as in the case of a commercial code.The proposed SRSM is also compared to a black box version SSFEM,and found to require less FEM evaluations for the same accuracy.The collocation points in the proposed method need to be selected for minimizing the mean square error,and from high probability regions,thus leading to fewer function evaluations for high accuracy.