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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: 提出了一种基于混合变量的填充拓扑优化方法, 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相关载荷的挑战, 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, 导致结构边界模糊不便于加工制造. 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拓扑设计问题, 通过引入局部体积约束替代全局体积约束, 有效调控材料分布的局部密度, 避免优化后生成的多孔结构过于均匀. 设计优化首先在粗网格上进行连续变量拓扑优化, 然后在细化网格上生成离散变量填充设计. 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, 防止了设计结果因过于均匀而导致目标函数值显著增加. 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. 利用双固支梁的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对优化结果的影响. 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细网格下的离散变量多孔结构设计, 其几何特征清晰, 显著提升了设计的可制造性, 同时优化后的结构表现出优异的热变形抵抗能力和力学性能.

     

    Abstract: An infill topology optimization method based on a hybrid variable strategy is proposed for the lightweight design of porous structures under thermo-mechanical loads. Traditional topology optimization methods often face challenges in the topology optimization of thermoelastic structures, including design-dependent loads with complex sensitivity analysis, high computational costs, and gray regions in the optimization design results that blur structural boundaries and hinder manufacturability. To address these issues, this paper proposes a novel infill topology optimization method that combines continuous and discrete variables, specifically for topological optimization design of porous structures under thermo-mechanical loads. By replacing global volume constraints with local volume constraints, the local material density distribution is effectively controlled, avoiding excessive uniformity in the generated porous structures. The design optimization first performs continuous-variable topology optimization on a coarse mesh, followed by discrete-variable infill design on a refined mesh. The present local volume constraints not only facilitate the formation of substructures and guide the optimization process toward achieving an uniform material distribution, but also provide physical significance to the design variables in continuous variable topology optimization design through the connection between continuous and discrete variable methods, preventing a significant increase in the objective function value when the design optimization results are overly uniform. Furthermore, an improved sensitivity filtering strategy is developed to achieve superior topological designs with enhanced objective function values. The numerical examples on a bi-clamped beam model demonstrate the effectiveness of the present method and the effects of filter radius and temperature difference on optimal designs are investigated. It is shown that the proposed optimization method successfully converts continuous variable optimization design results under coarse mesh into discrete variable porous structure designs under fine mesh with clear geometric features to significantly enhance the manufacturability of topological design, while the optimized structures exhibit excellent thermal distortion resistance and mechanical performance.

     

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