ホモロジー郡による位相の表現とその構造最適化への応用 : 第1報, 抽象的な図形問題を例題としたホモロジー理論応用の可能性に関する検証

概要

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In this paper, application of the homology theory, which is a field of mathematics concerned with topology, to structural optimization is attempted. A homology group, which is one of the Abelian groups, can represent the topology of a structure in a standardized way ; that is, the canonical direct sum decomposition. Therefore, topological information of a structure can be described in the formulation using homology groups. An abstract combination problem of triangular elements is chosen as a numerical example to verify the generality of this method using the homology theory. Several of the triangular elements are combined into a structure. Under the topological constraint condition represented by homology groups, a structure which has the minimum sum of numbers of triangular elements, its sides, and its vertices, is found by genetic algorithm. Furthermore, homology groups are utilized to describe the fitness function in the genetic algorithm as another example.
一般社団法人日本機械学会の論文
1997-08-25