轴对称结构拓扑变化重分析的新方法

提出了轴对称结构的两种基本拓扑变化,并应用Moore-Penrose逆理论及单元刚度矩阵的一种分解,给出了轴对称结构拓扑变化公式。利用该公式提出了一种轴对称结构拓扑修改的重分析新方法。该方法在计算静力响应时,不需反复组装、求解线性方程组,一切只需经过结构拓扑变化来实现,节省了大量的计算时间。因此该方法是一种精确的方法,并且由于公式简单,容易上机,适于拓扑优化设计(特别是局部优化设计)的重分析。最后给出的算例证明了该方法的有效性。

New reanalysis method for topology changes of axial symmetric structures

Two elementary topological changes for axial symmetric structures were presented and a set of explicit formulae of elementary topology changes of axial symmetric structures were given by using Moore-Penrose inverse theory and a factorization of stiffness matrix. Utilizing these formulae, a new reanalysis method for topological modifications of static structures were presented. This method has advantages of that the repeated assembling and solving of a set of linear equations is not needed, and all the reanalysis can be obtained by the formulae of topological changes. This method is an exact method and has little computational effort. It is suitable for the reanalysis of topological optimization designs especially the local optimal designs because the formulae are easy to realize on the computer. An example was given to illustrate the valid of this method.