Abstract

This paper proposes a topology optimization method for a multi-physics problem considering weight minimization with compliance, stress, and temperature constraints. Two static equations for thermal and structural problems are solved. A novel topology optimization formulation, i.e., lightweight design involving compliance, stress and temperature limits, is established using the rational approximation of material properties. A corrected P-norm function is employed to exactly evaluate the maximum stress and temperature of the structure. Moreover, iteration oscillations stemming from the high non-linearity of stress constraint are alleviated by means of a stabilizing control scheme based on the stability transformation method. The sensitivity analysis of the coupled multi-physics field is performed utilizing the adjoint method. Some numerical examples are adopted to demonstrate the validity and robustness of the proposed methodology. It is indicated that the topology considering the above three constraints simultaneously can achieve good mechanical and thermal performances, while the compliance constraint can accelerate the rate of convergence. The stricter compliance limit leads to a heavier structure and more uneven stress distribution but less iterations. The optimized topologies are dependent on the temperature range due to the effect of thermal expansion.

摘要

本文提出了一种多物理场问题的拓扑优化方法，该方法考虑了具有柔顺性、应力和温度约束的权重最小化。解决了热和结构问题的两个静态方程。一种新颖的拓扑优化公式，即涉及顺应性、应力和温度限制的轻量化设计，是使用材料属性的合理近似来建立的。采用修正的 P 范数函数来准确评估结构的最大应力和温度。此外，通过基于稳定性变换方法的稳定控制方案，缓解了由应力约束的高度非线性引起的迭代振荡。耦合多物理场的灵敏度分析是利用伴随方法进行的。通过一些数值例子来证明所提出方法的有效性和稳健性。表明同时考虑以上三个约束的拓扑结构可以获得良好的力学和热性能，而柔度约束可以加快收敛速度​​。更严格的柔度限制导致更重的结构和更不均匀的应力分布，但迭代次数更少。由于热膨胀的影响，优化的拓扑取决于温度范围。更严格的柔度限制导致更重的结构和更不均匀的应力分布，但迭代次数更少。由于热膨胀的影响，优化的拓扑取决于温度范围。更严格的柔度限制导致更重的结构和更不均匀的应力分布，但迭代次数更少。由于热膨胀的影响，优化的拓扑取决于温度范围。