基于离散变量的多材料结构拓扑优化设计

多材料结构拓扑优化相比于单材料结构优化具有更大的设计空间,展现出巨大的设计潜力和应用前景。本文基于离散设计变量研究多材料结构拓扑优化,通过建立有效的设计优化方法,获得轻质高效的结构设计。首先,根据离散变量的特点,建立多材料结构拓扑优化模型,由离散变量下约束函数和目标函数的灵敏度信息构造序列近似整数规划子问题,采用运动极限策略限制设计变量的改变量以保证整数规划子问题的近似精度。为了解决离散变量的组合复杂性,采用具有多项式复杂度的正则松弛算法来高效求解(和经典的连续变量算法效率相当)。本文利用多材料结构最小柔顺性优化问题以及最大传热效率优化问题研究离散变量方法的有效性。数值算例表明,离散变量优化方法可以获得稳定迭代收敛的多材料拓扑设计,优化构型中的材料界面清晰分明,有效避免了出现模糊区域。

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.