结构拓扑修改静态重分析自适应迭代方法  

AN ADAPTIVE ITERATION METHOD FOR STRUCTURAL STATIC REANALYSIS OF TOPOLOGICAL MODIFICATIONS

作　　者：杨志军[1] 陈新[1] 吴晓明[2] 陈塑寰[3] 

机构地区：[1]广东工业大学机电工程学院,广州510006 [2]厦门大学机电工程系,厦门361005 [3]吉林大学南岭校区力学系,长春130025

出　　处：《工程力学》2009年第11期36-40,67,共6页Engineering Mechanics

基　　金：国家自然科学基金项目(50905033);中国博士后科学基金项目(20070420761);广东省自然科学基金项目(8451009001001414);广州市科技计划项目(2006Z2-D9061);广东省科技计划项目(2009B010900032);粤港招标项目(20070103-1)

摘　　要：基于Guyan缩减和Epsilon算法,提出了结构拓扑修改静态重分析的自适应迭代方法。首先将新增加的自由度通过Guyan缩减方法凝聚到原结构自由度上,形成缩减方程。其次,根据刚度矩阵增量,利用Neumann级数建立基向量,采用向量Epsilon算法对基向量部分和系列进行迭代加速,并给出了控制迭代收敛精度的误差计算方法,可以根据结构改变的大小自适应选择迭代次数,从而快速求出原结构自由度的位移。新增加自由度的位移可从缩减方程恢复得到。给出了一个数值算例,将该方法与组合近似法(CA)进行比较。数值计算结果表明,该方法可以根据精度要求自动选择迭代次数,且计算效率比CA方法高。Based on the Guyan reduction and epsilon algorithm, an adaptive iteration method for structural static reanalysis of topological modification is presented. In this process, the equations of the newly added degree of freedoms （DOFS） （if any） are condensed to the original structure by means of Guyan reduction. And then, the basis vector is formed using Neumann serial according to the increment of the stiffness matrix, and the epsilon algorithm is used to accelerate the convergence of the partial sum of the basis vectors. An error evaluation method is introduced to control the accuracy of the iteration adaptively. A numerical example is given to compare the computational cost and approximation accuracy between the combined approximation and the presented method, the numerical results show that the present method is effective and easy to integrate into a general optimization approach.

关 键 词：静态重分析方法 结构拓扑修改 Epsilon算法 误差控制 自适应迭代 

分 类 号：O327[理学—一般力学与力学基础] TU311.4[理学—力学]