基于响应面法的几何非线性结构概率响应分析  

Probabilistic Response Analysis of Geometrically Nonlinear Structures Based on Systematic Response Surface Method

作　　者：程进[1] 

机构地区：[1]同济大学桥梁工程系,上海200092

出　　处：《同济大学学报（自然科学版）》2006年第9期1147-1151,共5页Journal of Tongji University:Natural Science

基　　金：国家自然科学基金资助项目(50408037)

摘　　要：将响应面法、有限元法和蒙特卡罗法各自的优点相结合,提出一种新的结构概率响应分析方法———集成化响应面法.通过对几何非线性桁架结构的概率性响应分析,验证了该方法的有效性和准确性.选取五种响应面分析模型,比较它们的计算结果,得出一些有益的结论.A stochastic finite-element-based algorithm for the probabilistic response analysis of geometrically nonlinear structures is proposed in this paper by combining the advantages of the response surface method, finite element method and Monte Carlo simulation. The accuracy and efficiency of the method are demonstrated through a numerical example of geometrically nonlinear truss structure with system parametric uncertainties. The choice of response surface models is a key element for the proposed method. Particular attention is given to investigate effects of response surface models on statistics of the response of both linear and geometrically nonlinear structures under certainties. To this aim five response surface models are considered, namely, star experiment design based on a quadratic polynomial without cross terms, hyper-cube experiment design by using a quadratic polynomial without cross terms, complete factorial experiment design based on a quadratic polynomial with cross terms, minimum experiment design based on a quadratic polynomial with cross terms and composite experiment design by using a quadratic polynomial with cross terms. Results obtained by the proposed method based on the five response surface models are compared and appropriate conclusions are drawn.

关 键 词：几何非线性结构 响应分析 概率 不确定参数 响应面 

分 类 号：U448.22[建筑科学—桥梁与隧道工程]