GA-FEM For Topological Optimization Of 2D-Continuum Structure

Topological optimization is considered as the most difficult problem among structural optimization problems. The idea of Evolutionary Structural Optimization (ESO) is utilized in this thesis to develop GA-FEM,which combines Genetic Algorithm (GA) and Finite Element Method (FEM),to solve the problem of topological optimization for 2D continuum structure. The main context includes the following work. (1) The feasibility of GA-FEM and its research status are summarized. (2) Binary chromosomes are used to represent the topology structures. (3) In order to analyze the structures by FEM,"exist/void" character for elements is set up in the topology structures represented by GA chromosomes. (4) Penalty function method is used to import the constrains into the objective function. (5) GA's operators are improved to reach better evolution effects,such as choosing proper fitness function,using 2D equal-block crossover and multi-bit mutation,expending the population size to reach better evolution effects. The structural results are effectively made better. (6) The idea of ESO is used to further improve the calculating efficiency and make the optimization results better. (7) OOP technology is used. The programs are easy to be used,developed and maintained. What's more,they are separately testified as FEM,GA and ESO. (8) FEM post process is used to review the stress changes in optimized structures. (9) The numerical results of a cantilever plate and a bicycle structure are given in this thesis. The evolution laws of structural weight,the best optimum fitness,average fitness,maximum nodal stress and displacement with increasing generations are discussed. And multi-result fact of the topology optimization can be obtained by GA-FEM. The research results in this thesis show that the developed method is successful in the topology optimization for 2D continuum structures under multi-load and multi-constrain conditions.