抄録
We report topological optimization of elastic frames by means of the boundary cycle used in algebraic topology and a genetic algorithm. In this study the optimum frame is defined as that in which the deformation at a point is minimal for a given weight limit. Members that have a tip which is not connected to other members, and increase the weight without making any mechanical contribution are neglected. The optimum topology is identified efficiently using a boundary cycle which yields a one-dimensional simplicial complex with no tips, satisfying the topological condition of no idle tip. The boundary cycle is derived from a chain and boundary operator, which plays the important role of decoding the genotype into the phenotype in the genetic algorithm, and is included in the string used in the genetic algorithm to represent the 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 analyzed by the finite element method.
