复合材料层合板的谱随机无网格伽辽金法  

SPECTRAL STOCHASTIC ELEMENT-FREE GALERKIN METHOD FOR LAMINATED COMPOSITE PLATES

作　　者：周立明[1] 孟广伟[1] 李峰[1] 温泳[2] 周振平[1] 

机构地区：[1]吉林大学机械科学与工程学院 [2]长春工程学院土木工程学院

出　　处：《固体力学学报》2014年第1期71-76,共6页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(51305157);吉林省科技厅基金项目(201215048;201205011;20130305006GX)资助

摘　　要：针对基于摄动理论的计算方法不适用于分析随机结构参数大变异问题,提出谱随机无网格伽辽金法,该方法基于随机场正交分解理论,将随机场采用Karhunen-Loève级数展开为一系列不相关随机变量,再引入结构位移随机响应的混沌多项式分解,结合无网格伽辽金法,从而导出含随机变量的复合材料层合板的谱随机无网格伽辽金法,给出结构响应的统计特征值的计算公式,该方法既适用于随机参数大变异情况,又具有无网格法的优势;数值算例结果表明该方法是正确有效的.A spectral stochastic element-free Galerkin method was proposed to solve the stochastic structural problems with parameters having big changes,which can not be solved by the methods based on the perturbation theory.Based on the orthogonal decomposition theory of random fields,this method applied the Karhunen-Loève series to expand a random field into a series of uncorrelated random variables.A spectral expansion with use of polynomial chaos was employed to represent the stochastic nodal displacements in terms of standard normal random variables.The spectral stochastic element-free Galerkin method of the composite laminated plates with random variables was derived,with the computational formulas of the statistical characteristics of structural responses being given.This method not only is suitable for the cases with large random coefficient variation but also has an advantage of the element-free Galerkin method.And numerical results show that the method is correct and effective.

关 键 词：谱随机无网格伽辽金法 复合材料层合板 Karhunen Loeve展开 混沌多项式 

分 类 号：TB33[一般工业技术—材料科学与工程]