Optimization of Geometrically Nonlinear Planar Frames Structures Using Genetic Algorithms

Abstract

The problem of choosing the sizes of the members in order to minimize the weight of structures while satisfying stress, displacement, stability, and other applicable constraints is complicated by the requirement of considering the non-linear structural behavior. The problem is further complicated if the members are to be chosen from a discrete set of commercially available sizes, which is often the case. Genetic Algorithms, inspired by Darwin’s theory of evolution by natural selection, are powerful and versatile tools in difficult search and optimization problems. In this paper a genetic algorithm is proposed to find the optimum discrete and continuous values of the cross-sectional areas of the members that minimize the weight of planar frame structures presenting geometrically non-linear behavior. Several computational experiments are discussed involving these structures.