不确定结构时域响应分析的多项式维数分解法  

A polynomial dimensional decomposition method for analyzing response of uncertain structures in time domain

作　　者：赵岩[1] 刘凡 孙晓旭 ZHAO Yan;LIU Fan;SUN Xiao-xu(State Key Laboratory of Structural Analysis for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室工程力学系,大连116024

出　　处：《计算力学学报》2021年第6期722-728,共7页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(11772084,U1906233);国家重点研发计划(2017YFC0307203);山东省重点研发计划(2019JZZY010801)资助项目.

摘　　要：针对具有不确定参数结构,提出时域不确定性传播和量化的多项式维数分解法,确定了结构响应统计量的演变过程。首先,采用参数概率模型来描述结构参数的不确定性,建立结构动力学方程,将结构响应表达为不确定参数的函数;进一步,将所关心的结构响应采用成员函数进行维数分解,并利用正交多项式基底对成员函数进行Fourier展开;最后,应用降维积分方法进行展开系数的求解,给出了响应均值和标准差的计算表达式。在数值算例中,将本文方法与蒙特卡洛方法进行对比,结果表明所建立方法具有较高的求解效率和计算精度。A polynomial dimensional decomposition method for uncertainty propagation and quantification in time domain is proposed for structures with uncertain parameters,and the evolution processes of statistical moments of structural responses are determined.Firstly,the uncertainties of structural parameters are described by the parametric probabilistic model to establish the dynamic equation of the structure,and the structural response is expressed as a function of uncertain parameters.Furthermore,a dimensional decomposition of the structural response is performed using component functions,and the Fourier expansion of the component function is carried out using orthonormal polynomial basis.Finally,the dimension-reduction integration method is used to calculate the expansion coefficients,and the calculation expressions of the mean value and standard deviation of the response are given.The proposed method is compared with the Monte Carlo method using numerical examples,and the results show that the proposed method has good accuracy and efficiency.

关 键 词：不确定性量化 多项式维数分解 正交多项式 降维积分 

分 类 号：O321[理学—一般力学与力学基础]