Research On Topology Optimization Of Multi-material Structures Based On Equivalent Static Load Method

Topology optimization is a hot and difficult problem in the field of structural optimization.At present,topology optimization has been applied in various fields.With the development of topology optimization,the research of topology optimization is no longer limited to a single material,multi-materials topology optimization study has been developed.In reality,many structures work under dynamic loads,there are more and more researches on dynamic structural topology optimization.In view of this development direction,a multi-materials interpolation model is proposed based on the study of topology optimization modeling and solving methods of continuum structures,and an integration topology optimization model of multi-materials and structures based on variable density method is established.Then the interpolation models of SIMP and EAMP are compared by numerical examples,the optimization algorithm for the multi-materials model is determined,and analyzed the applicability of optimization criterion method and moving asymptotic algorithm.The specific contents are as follows:First of all,based on the study of the variable density method,a multi-materials interpolation model is proposed,and the multi-materials and structures integrated topology optimization models based on SIMP and EAMP material interpolation models are established.Secondly,the optimization criterion method and the moving asymptotic series algorithm are studied for the solving of topology optimization model based on the variable density method.The iterative formula of optimization criterion method based on SIMP and EAMP material interpolation models are derived,and the comparison analysis of SIMP and EAMP material interpolation model is made.The moving asymptotic series algorithm is used to solve the optimization model,and a comparative analysis is made with the optimization criterion method to determine the optimization algorithm applicable to the multi-materials optimization model proposed by the institute.The MMA method is not suitable for the optimization model proposed in this paper.The calculation process of GCMMA method is stable,but the calculation time is long.Finally,a dynamic topological optimization method,the equivalent static load method,is used to solve the dynamic structural topology optimization.The effectiveness and feasibility of this method are verified by the optimization examples.The numerical examples show that it is feasible to use the equivalent static load method to carry out the topological optimization calculation of dynamic structure,and the comparison with the topological optimization results under the static load shows that it is necessary to carry out the research of dynamic topology optimization.