Topology Optimization Of Tensile And Compressive Heterogeneous Materials Based On SIMP-MM

Structural topology optimization is a process of finding the optimal force transfer path under given boundary conditions and constraints to obtain the optimal structural performance under limited materials.Variable density method is the most traditional topology optimization method,which has the advantages of high computational efficiency and fast iteration speed.However,the SIMP method(Solid Isotropic Material with Penalization Method)based on 0-1 material distribution model inevitably has some problems,such as serious sawtooth of final configuration boundary,gray cell phenomenon,implicit expression of design variables and checkerboard phenomenon.At present,the popular moving morphable component method has the characteristics of optimal configuration display and clear boundary,but the topological results depend on the initial layout of the components.In this paper,a topology optimization method based on SIMP and MMC is designed by combining the characteristics of SIMP and MMC.On this basis,this method is applied to the topology optimization design of materials with different modulus in tension and compression which is closer to the engineering practice.The method is successfully verified and has strong practical application.The main work and innovation of this paper are as follows:(1)According to the characteristics of SIMP method and MMC method,the theory of the two methods is deeply studied and related formulas are derived.The problems such as boundary zigzag phenomenon and checkerboard phenomenon of SIMP method are studied,and the dependence of the initial layout of components of MMC method and the reasons are analyzed.(2)Aiming at the characteristics of SIMP method and MMC method,a topology optimization algorithm based on SIMP-MMC is proposed.The algorithm has the characteristics of fast convergence speed,topology results can be displayed and expressed,and the problem of sawtooth and gray units can be eliminated.The main steps of the SIMP-MMC method include using the variable density method to quickly find the optimal force transfer path of the structure,the extraction and transformation of skeleton information,and the solution of the moving morphable component method.The iterative speed of this algorithm is 10%-30% faster than that of the traditional 188 line MMC method.(3)For the topology optimization of materials with different modulus in tension and compression,a finite element iterative format of principal stress criterion is adopted,combined with the SIMP-MMC method mentioned above.The rationality of the method is verified by the comparison of the simulation results with ANSYS.Topology optimization of materials with different modulus in tension and compression based on SIMP-MMC has a feature that other topology optimization methods do not have.It takes full advantage of the combination of topology optimization and size in MMC method.First,SIMP method is used to optimize the topology of linear elastic materials,and then MMC method is used to optimize the topology of materials with different modulus in tension and compression.The incongruity between topology iteration and finite element analysis is avoided.This provides a new idea for the study of correlative finite element extension in topology optimization.