Application of homology theory to topology optimization of three-dimensional structures using genetic algorithm

In the process of topology optimization of structures using genetic algorithms (GA), many structures, which cannot be analyzed by the finite element method (FEM) often appear and deteriorate the performance of GA. In this paper, a new method that gives such unanalyzable structures fitness values based on their topology represented by homology groups (Abelian groups) is proposed. As numerical examples, strain energy of three-dimensional structures consisting of triangular shell elements is minimized using GA. In some cases, the average fitness value of structures obtained by the proposed method is more than 10 times higher than that of an existing method. (C) 2001 Elsevier Science B.V. All rights reserved.