Topology Optimization of Continuum Structures Using HPM Encoded Genetic Algorithms

Abstract

[Abstract] This work investigates the use of genetic algorithms (GA) in solving discrete continuum topology optimization problems. Traditional approaches encode structural designs into GA bit strings using element volume fractions. Numerical issues such as checkerboard patterns, one-node hinges, and mesh dependence of solutions are then addressed through penalty functions. The proposed approach encodes designs into GA bit strings using reduced design variable fields. These variables are extracted onto element space using the Heaviside Projection Method (HPM) to topology optimization. The new bit string contains far fewer design variables for a given mesh, translating into computational savings. Additionally, as HPM is used to extract the design from the encoding, solutions are inherently checkerboard-free and satisfy user-prescribed minimum length scale constraints, providing a means to introduce manufacturing constraints and theoretically ensuring mesh dependence. With careful selection of design variable locations, one-node hinges can also be eliminated. Simple examples are considered and limitations are discussed.