Topology optimization design of multi-material structure based on discrete variables
Topology optimization of multi-material structures has a larger design space and shows great design potential and application prospect than optimization of single material structures optimization.This paper studies the topology optimization of multi-material structures based on discrete design variables,and obtains lightweight and efficient structure designs by establishing an effective design optimization method.Firstly,according to the characteristics of discrete variables,a multi-material structure topology optimization model is established.The sequence approximate integer programming subproblem is constructed from the sensitivity information of the constraint function and objective function with discrete variables.The move limit strategy is used to limit the change of design variables to ensure the accuracy of the integer programming subproblem.In order to overcome the combinatorial complexity of discrete variables,the canonical relaxation algorithm with polynomial complexity is employed to solve it efficiently(which is equivalent to the classical continuous variable algorithm).In this paper,the optimization problems of the minimum compliance and the maximum heat transfer efficiency of multi-material structures are utilized to study the effectiveness of the discrete variable method.Numerical examples show that the discrete variable optimization method can obtain a stable iterative convergence of multi-material topology design,and the material interface in the optimization configuration is clear,effectively avoiding the appearance of fuzzy region.
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