Research On Multi Objective Topology Optimization Method Based On Average Distance Method

Mathematical programming is a branch of operations research,as a multi-objective optimization of main optimization algorithm,is widely used in engineering machinery,aircraft,automotive parts and other lightweight designs.Topology optimization is the main focus of research questions in the the structure optimization.In this paper,a generalized mean distance method based on mathematical programming is proposed to study the multi objective topology optimization.The main contents of this paper are as follows:(1)It has provided an overview of the development of structural optimization,the domestic and foreign research status and current problems are presented about topology optimization theory and algorithm.The necessity and feasibility of structure based on mathematical programming method for multi-objective topology optimization design have been put forward.(2)It has described the basic concepts and mathematical models of the structural multi-objective topology optimization problems.Based on evaluation function method and the average frequency characteristic value formula,the generalized mean distance formula is proposed.The principle of the common optimization algorithm for the topology optimization of continuum structures with the evolution of the average distance formula is studied,and the numerical instability in the iterative calculation is analyzed.(3)On the basis of the theory of the average distance formula,it has studied the effects of different parameters in the optimization process of topological optimization results.Using various optimization algorithm establishs the corresponding mathematical model and based on variable density method realizes multi state single target topology optimization.which are given the verification of typical examples.(4)Based on the formula and mathematical model of the average distance method of topology optimization,and the structure of the static stiffness and dynamic frequency established corresponding topological optimization mathematical model,it has established the multi-objective topology optimization of a typical automobile suspension control arm and obtained a corresponding optimization result.By comparing the results of the four models,the results showed that the application of average distance formula can effectively solve the multi-objective problem,and provide a new design idea for topology optimization.It also has some guiding significance for the practical engineering optimization problems in the future.