Research On Topological Optimization Method Of Microstructure And Integrated Design Of Structure And Material Based On Parametric Level Set

Meeting a specific performance requirement is the goal of Topology optimization,it is a process of finding the optimal distribution of materials,which is in a given design domain under the constraints of given loads and boundary conditions.In recent years,with the growing diversity and complexity of practical topology optimization problems and the increasing scale of the problems,multi-scale topology optimization design of structure and material has gradually begun to develop.Since the multi-scale topology optimization design method can break the limitation of traditional topology optimization design method,thus further realizing the structure lightweight and improving the structure performance.The structure material integrated optimization design has become a hot trend in the field of topology optimization.In this paper,firstly,we try to establish the material microstructure optimization model based on the parameterized level set method and the energy homogenization method,and then realize the structure material integrated topology optimization design.Finally,the two-dimensional and three-dimensional material microstructure topology optimization problem and the structure material integrated optimization design problem are in-depth studied.The basic idea of the parameterized level set method is to use radial basis function(RBF Function(RBF)to parameterize the introduced high-dimensional level set function ?.The zero isosurface or zero isoline of the level set function ? is used to define the boundary of structures,and the smoothness of RBF is used to separate the time and space derivatives to simplify the numerical solution process and realize the automatic generation of holes.In the next step,the energy homogenization method is proposed to solve the problems of periodic boundary conditions and numerical realization,which can be used to infer the macroscopic equivalent properties of materials.Based on the parameterized level set method and energy homogenization method,a topology optimization design scheme of material microstructure is proposed.The effectiveness of the scheme is verified by numerical examples of two-dimensional and three-dimensional bulk modulus maximization,shear modulus maximization and negative Poisson ratio problems.Then,the model of structure material integration optimization design is established based on the parameterized level set method and energy homogenization method.The two-dimensional and three-dimensional optimization design problems of structure material integration are realized.At the same time,the macro and micro optimization design elements are considered to jointly improve the overall performance of the structure on the macro and micro scales.Through two-dimensional and three-dimensional typical examples,the validity and generality of the model are discussed in detail,and the macro structure and micro structure topology with smooth and clear boundary are obtained,which provides convenience for the subsequent 3D printing and other additive manufacturing process.Based on the parameterized level set method and the energy homogenization method,this paper explores the microstructure topology optimization design and structure material integration design,further increasing the research content in the field of topology optimization design,and at the same time providing assistance for the application of topology optimization.