Research On A Topology Optimization Method Based On Memetic Algorithm And Its Key Technologies

Topology optimization is one of the structural optimization methods. Currently, foreign scholars have studied considerably in this area,and many results they got have been successfully applied into the engineering practice. At present, a few famous CAE softwares has added the topology optimization module, and the representative in them are TOSCA and Hyperworks. Chinese scholars have made some achievements in the field of theoretical research, but the achievements have not been transformed into engineering applications. They have not developt a successful topology optimization software by now. This paper tracked the current situation of international research closely, and made a more systematic study on the basis of topology optimization theory, algorithm and engineering application. The author proposed a topology optimization method based on Memetic algorithm, and have made a systematically research on the mathematical model, algorithm and engineering application, with some positive results have been achieved. Topology optimization is a NP-hard problem, which can be transformed into implicit non-linear equations to solve. Evolutionary algorithm has a strong global search ability. In the process of solving the problem, we just need to calculate the fitness function value, but not to concern the implicit non-linear constraints. The evolutionary algorithm is an important method in topology optimization for solving global optimization.This paper proposed the MATO's mathematical model and solution method firstly, and constructed the sub-list encoding scheme. This encoding can make MATO mixed a variety of mathematical expression models and associated algorithms of topology optimization methods. In this way, it can integrate the advantage of different methods, improve the search efficiency and solution quality. This paper proposed a mixed strategy which combined with global evolution and local search. On the one hand, it constructed the cross and variant operator for global evolution search; on the other hand,it advanced BBESO method for local search. MATO's hybrid search strategy inherited the advantages of genetic algorithm which can find global optimal solution and improved the search efficiency greatly.An important method for increasing the search efficiency of MATO is reducing the design space. This paper based on the variable density method, constructed the PDOC, which improve the convergence and quality of solutions; This paper also constructed the GSSPDOC to compress the middle material density of the solution, which makes the material density of the solution close to zero or one. This ensure the solution optimal. A reduce design space method based on GSSPDOC is constructed, which can reduce the search space of MATO, and can also improve the ability to find the global optimal solution and the search efficiency.The evolutionary operators and parameters of MATO are deeply studied in this paper, which provide the experimental evidence for operators and parameters setting. The parameters of MATO included N(the size of Population), G(the rate of memory), Pc(the rate of hybrid group), Pm(the rate of mutation), CO(crossover operator)and so on. The cantilever beam optimization example was also studied deeply. At the same time, we analyze the various parameters and operator through with numerical experiments. Finally, we get a group of proper parameters and operators. In the process of MATO problem solving, the checkerboard and isolate elements appear in the structure of the solution. This phenomenon will affect the efficiency of MATO solving process, and make the global optimal solution hard to found. The adjacent entropy filtering method is proposed to eliminate the numerical instability phenomenon. MATO method is improved by adding entropy filtering method to local search process. This strategy also improved the solving efficiency, and can avoid the checkerboard phenomenon and isolate elements. It is able to find a better solution.The author has developed a prototype system of topology optimization (TopOpt) using APDL language under the development platform of ANSYS. In this chapter, the author introduced the overall structure and function of TopOpt. Based on this system, the author finished the topology optimization of the mounting plate of the aerospace equipment through this system, and Completed an important component's characteristic frequency optimization of an Laser welding machine. Finally, the author validated the effectiveness and superiority of the proposed method through engineering practice.