结构边界约束修改后的重分析方法

在结构设计优化中经常将结构边界约束作为设计优化对象,结构边界约束的修改通常导致系统的求解规模发生改变,使得快速准确分析修改后结构的响应成为一个挑战。本文发展了逐次矩阵逆(SMI)方法,提出了一种适合各种结构边界约束(包括初始结构中的约束)修改的快速重分析算法。该方法利用边界约束修改后对应刚度矩阵的对称性,有效缩减了计算量。数值算例表明,本文方法能够快速给出精确的重分析结果。

Reanalysis of structures with modification of boundary constraints

The optimal layout of boundary constraints is one of the key factors that dominate static performances of the structure.The repeated analyses required in design and optimization of the location of boundary constraints are difficult because the imposition or release of boundary constraints change the number of degrees of freedom of structures.This paper deals with reanalysis of structures with modification of boundary constraints.A successive matrix inversion (SMI) method is developed and an efficient reanalysis algorithm is presented for such a problem.The symmetry of modified structural stiffness matrix is sufficiently utilized in the algorithm.Exact solution can be achieved by the proposed method.Numerical examples are given to demonstrate the efficiency of the proposed algorithm.