ホモロジー群による位相制約下における構造最適化 : 第3報, 任意の次元の複体に任意の位相制約を課す手法の定式化と適用例

概要

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When an element is removed from a ground structure or an initial shape by genetic algorithm, homogenization method and so forth in the process for optimizing topology of a structure, its topology is probably changed. In this paper, we propose a new method of inferring the change in topology of a structure before the elimination of each element. This method can show the relation between elements of a structure and invariant factors in homology groups representing topology of the structure. As a numerical example, the proposed method is utilized for imposing topological constraint conditions on a three-dimensional structure consisting of triangular elements. The number of elements and strain energy of the structure are minimized under the conditions. As a result, it was found that a topological constraint on a zero-dimensional homology group of which rank is equal to the number of connected components of the structure is the most important one to reduce the number of elements and strain energy.
一般社団法人日本機械学会の論文
2002-06-25