目的 针对热力耦合拓扑优化中设计相关热载荷易在低密度区域引发寄生效应、导致拓扑边界模糊和优化稳定性不足的问题,建立一种兼顾物理合理性与计算效率的结构优化方法。方法 以结构柔顺度最小化为目标、材料体积分数为约束,构建热载荷与机械载荷共同作用下的热力耦合拓扑优化模型。分析弹性模量、热膨胀系数和热传导系数插值关系对优化结果的影响,提出多参数SIMP-RAMP混合惩罚插值模型。同时引入GPU自由度级无组装矩阵-向量乘方法,提高有限元分析与灵敏度计算效率。结果 算例表明,该插值模型能够削弱低密度区域的非物理热载荷贡献,减少灰度单元,使优化构型边界更加清晰。无组装并行计算方法可避免全局刚度矩阵显式装配,降低存储开销并提升迭代求解效率。结论 所提方法能够改善传统插值模型在设计相关热载荷作用下的不足,提高热力耦合拓扑优化的稳定性、物理合理性和计算效率,为复杂热环境下结构轻量化设计提供了有效途径。
Abstract
The work aims to develop a thermo-mechanical coupled topology optimization method which considers both physical rationality and computational efficiency to address the parasitic effect caused by design-dependent thermal loads in low-density regions, resulting in blurred topological boundaries and insufficient optimization stability. In the proposed framework, structural compliance was minimized under a prescribed material volume constraint. A thermo-mechanical coupled topology optimization model under both mechanical loads and thermal loads was established. The influence of the interpolation relationships among the elastic modulus, thermal expansion coefficient and thermal conductivity on the optimization results was investigated. A multi-parameter SIMP-RAMP hybrid penalization model was proposed. In addition, a GPU-based degree-of-freedom-level matrix-free matrix-vector multiplication strategy was introduced to improve the computational efficiency of finite element analysis and sensitivity calculation. The numerical examples showed that the proposed interpolation model could weaken the contribution of non-physical thermal loads in low-density areas, reduce gray elements, improve the clarity of optimized topologies. The matrix-free parallel computing strategy could avoid explicit assembly of the global stiffness matrix, reduce memory consumption and improve the efficiency iterative solutions. The proposed method can eliminate shortcomings of traditional interpolation models under the action of design-dependent thermal loads, and enhance the stability, physical rationality and computational efficiency of thermo-mechanical coupling topology optimization, providing an effective approach for lightweight structural design in complex thermal environments.
关键词
热力耦合 /
拓扑优化 /
设计相关热载荷 /
寄生效应 /
无组装矩阵计算
Key words
thermo-mechanical coupling (TMC) /
topology optimization (TO) /
design-dependent thermal load (DDTL) /
parasitic effect (PE) /
matrix-free computation (MFC)
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