Research On A Topology Optimization Method Of Multi-phase Materials Structures Based On The Feasible Domain Adjustment

With the development of computer technology and the advanced manufacturing technology,the structural topology optimization method possesses important engineering application value.At present,the continuum topology optimization design is mainly involved in a single material,Really,to meet the requirements of a light structural weight and multi-function performances,most of structures are usually constructed of a variety of materials.Therefore,It is necessary to study the topology optimization design method of multiphase materials.This paper mainly research work for structures topology optimization method of multi-phase material under single load case and multiple load cases,program and numerical simulation.The relationships between the stiffnesses and the topology variables are built by using the rational approximation for material properties(RAMP)in this paper.Then,for single phase material,an optimization model of minimum compliance being the objective function with volume constraints is proposed in this work;Combining with the feasible domain adjustment scheme,an approximate topology optimization model is constructed;Then,the explicit approximate expressions of the compliance and its derivative are derived,based on the method of moving asymptotes(MMA).Finally,an optimization method of structural compliance with single phase material is proposed,and its simulation examples are given.To extend the proposed method to optimization problems of multi-phase materials,a interpolation model of any element stiffness is built by using the RAMP model;For a multi-phase material case,combining with the feasible domain adjustment scheme,an optimization model of the objective function being its compliance with volume constraints is proposed;Based on the MMA expressions,explicit approximate expressions of the compliance and its derivative are derived.The optimization problem of multi-phase materials is divided into some two phase topology optimization sub-problems by adopting an active phase alternating algorithm;Finally,an topology optimization method of multi-phase materials under single load case and multiple load cases is proposed,the preparation of the program and simulation of a large number of typical examples is completed.The results of given example simulations demonstrate that the proposed method can obtain a series of clear topology configurations during an optimization process,and an optimal topology with a clear black/white configuration.The example results also show that the proposed method is of the feasibility,efficiency,and good theoretical and engineering application value.