Optimization of Frame Topology Using Boundary Cycle and Genetic Algorithm

Abstract

This paper deals with topological optimization of elastic frames by means of the boundary cycle used in the algebraic topology and genetic algorithm. The optimum frame is so defined in this study that the deformation of an interesting point of the frame is minimal for a given limit of weight, and that any members with a tip not connected to other members, except loading points, are eliminated. The optimum topology is searched efficiently through the boundary cycle which yields the one-dimensional simplicial complex without any tip, satisfying the topological condition of no idle tip present. The boundary cycle is derived from the chain and boundary homomorphism which plays an important role of decoding of the genotype into the phenotype in the genetic algorithm, and is included in the string used in the genetic algorithm for the representation of frame topology. The numerical examples are concerned with minimization of the deformation of two-dimensional frames subject to bending, and three-dimensional frames subject to torsion or expansion. © 1994, The Japan Society of Mechanical Engineers. All rights reserved.