Development and testing of a morphological geometric representation scheme for topology design optimization using a genetic algorithm

Abstract

This work describes a novel way of defining structural geometry for solving topology design optimization problems using a genetic algorithm (GA). It is a geometric representation scheme that works by specifying a skeleton which defines the underlying topology/connectivity of a structural continuum together with segments of material surrounding the skeleton. The required design variables are encoded in a chromosome which is in the form of a directed graph that embodies this underlying topology so that appropriate crossover and mutation operators can be devised to recombine and help preserve any desirable geometry characteristics of the design through succeeding generations in the evolutionary process. The overall methodology is first tested by solving a 'target geometry matching problem' - a simulated topology optimization problem in which a 'target' geometry is pre-defined as the optimum solution, and the objective of the optimization problem is to evolve design solutions to converge towards this 'target' shape. The second test problem is to design a complaint mechanism - a large-displacement flexural structure that undergoes a desired displacement path at some point when given a straight line input loading at some other point - by a process of topology/shape optimization.