Topology Optimization Design Of Material Microstructure And Structure Integration Based On Boundary Density Evolution Method

With the rapid development of modern industrial technology,the traditional structure optimization design has been unable to meet the needs of industrial product diversity,complexity,high performance,structural topology optimization as a kind of efficient combination of material design and mathematical science research methods in automobile manufacturing,biological,medical,construction,and many other fields have a wide range of applications.At present,how to give full play to the optimization potential of material design in mechanical properties and realize the integrated design of "material macroscopic distribution" and "material macroscopic equivalent properties" has become a hot and difficult topic in the field of structural topology optimization.Based on the boundary density evolution method and the energy homogenization method,this paper studies the material optimization design of the structure at the micro level,the integrated topology optimization design of the structure at the macro-micro scale and the application of the negative Poisson’s ratio material in the integrated design.This paper is divided into four chapters,and the main contents of each chapter are:The first chapter is the introduction.This paper mainly introduces several continuum topology optimization methods,the research status of microstructure and structure-material integrated topology optimization design at home and abroad,and gives the main research content and research significance of this paper.In chapter 2,topology optimization design of microstructure is studied based on boundary density evolution and energy homogenization.Firstly,the energy homogenization method and boundary density evolution method are introduced.Based on the two methods,the optimal design model of microstructure is established.Then,for the special performance design problem,different initial topologies and different volume fractions of all kinds of microstructure design with smooth boundary contour are obtained,and the correctness of the optimization algorithm is verified.In chapter 3,the integrated topology optimization design of structure and material is studied.Firstly,with the goal of maximizing the stiffness of continuum structure under volume constraints,the sensitivity analysis of macro structure and composite microstructure was carried out based on energy homogenization method and BDE method,and the structural and material integrated optimization design model was established.The effects of different optimization schemes,different working conditions,different initial topologies and different volume fractions on the optimization results are discussed.In chapter 4,the application of negative Poisson’s ratio material microstructure in the integrated design of tire structure is studied.In this chapter,the special mechanical properties of the material with negative Poisson’s ratio are verified firstly,and then the design and application of pneumatic tire are taken as the objective to explore the mechanical performance of the tire under different elastic modulus and different volume fraction of the material with negative Poisson’s ratio,and the tire topology optimization design is carried out.