结合拓扑分析进行平面连续体拓扑优化

避免目前平面连续体结构拓扑化过程中经常出现的单元铰接以及“棋盘格”等现象，研究了边疆体结构拓扑优化过程的拓扑分析方法，以及在计算机上实现的简便算法，根据代数拓扑理论，单元及连续体的边 作为1－复形进行运算，利用图论中的邻接向量概念，在计算机上实现了结构的拓扑描述及在扑运算，得到了结构在拓扑演化过程吵的拓扑特性，方法简单，可靠，在一定的拓扑约束下，根据应力分析结果，采用删除单元，单元退化，移动节点等方法，可以用较少单元得到更为满意的结果，提高计算效率，为演示方法的有效性，给出几个包括常见经典问题的解答。

TOPOLOGY OPTIMIZATION OF PLANE CONTINUUM WITH TOPOLOGY ANALYSIS

To completely avoid producing elements jointed at their corner nodes and checkerboard patterns,which frequently occur when the topology optimization of plane continuum is studied,the theory of topology analysis of plane continuum in topology optimization process and the simple algorithm for programming are studied.According to algebraic topology theory,the boundary of elements and plane continuum are operated as a one dimensional complex.By use of the adjacency vector in graph theory,the structural topology is described and the topological operation is achieved on a computer.By above,the structural topological feature in the evolutionary process is gained.These methods are effcient and reliable.Under topology constraints,according to the results of stress analysis,by deleting elements and moving nodes at the boundary,more satisfactory results can be gained by using a few numbers of elements and iterations.To demonstrate the efficiency of these methods,solutions including some well known classical problems are presented.