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中文核心期刊

热机械载荷下多孔结构的填充拓扑优化

Infill topology optimization of porous structures subjected to thermo-mechanical loading

  • 摘要: 提出了一种填充拓扑优化方法,应用于热机械载荷下多孔结构轻量化设计。传统优化方法在热弹性结构拓扑优化中常面临设计依赖载荷的挑战,灵敏度分析复杂且计算成本高,而且优化结果存在灰度区域不便于加工制造。为此,本文提出一种结合连续变量与离散变量的填充拓扑优化方法,应用于求解热机械载荷作用下的多孔结构设计问题,通过引入局部体积约束替代全局体积约束,避免优化后生成的多孔结构过度均匀。本文的局部体积约束不仅有助于子结构的形成,引导优化过程实现更均匀的材料分布,而且连续变量与离散变量方法之间的联系为连续变量拓扑优化中的设计变量赋予了物理意义,防止了设计结果过于均匀时目标函数值的显著增加。此外,发展了一种改进的灵敏度过滤策略,获得了目标函数值更优的拓扑设计。数值算例展示了方法的有效性,并研究了过滤半径和温度差的影响。结果表明,本文方法能够将粗网格下的连续变量优化结果转化为密网格下的离散变量多孔结构设计,同时显著提升设计的可制造性。

     

    Abstract: An infill topology optimization method is proposed for the lightweight design of porous structures under thermo-mechanical loading. Traditional optimization methods often face challenges in thermoelastic structural topology optimization, such as design-dependent loads, complex sensitivity analysis, high computational costs, and the presence of gray areas in the designs, which hinder manufacturing. To address these issues, this paper proposes an infill topology optimization method that combines continuous and discrete variables, applied to solve the design problems of porous structures under thermo-mechanical loading. By introducing local volume constraints to replace global volume constraints, the proposed method avoids excessive uniformity in the generated porous structures. The local volume constraints not only facilitate the formation of substructures and guide the optimization process toward more uniform material distribution but also provide physical significance to the design variables in continuous variable optimization through the connection between continuous and discrete variable methods, preventing a significant increase in the objective function value when the design results are overly uniform. Furthermore, an improved sensitivity filtering strategy is developed, resulting in topology designs with better objective function values. Numerical examples demonstrate the effectiveness of method and the effects of filter radius and temperature difference is investigated. It is shown that the present method can transform continuous variable optimization results under coarse mesh into discrete variable porous structure designs under fine mesh, significantly enhancing the manufacturability of the designs.

     

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