A thermo‐elastic topology optimization with stress and temperature constraints is proposed to attack the complex multiphysics problem in this paper. Based on the rational approximation of material properties (RAMP), the coupled equations of mechanic and temperature field are solved. Two optimization problems, volume minimization with temperature and stress constraints, and traditional compliance minimization with volume and temperature constraints, are discussed for comparison. The stress stabilizing control scheme (SSCS) combined with global stress measure is presented to tackle highly nonlinear and local nature of stress with thermal expansion in varying temperature field. The adjoint method is applied to achieve the sensitivity of multiphysics field and the density function is updated utilizing the method of moving asymptotes (MMA). Representative examples are investigated to demonstrate the effectiveness and utility of the proposed method. Clear topology and stable iterative process can be obtained for complex coupled problem by means of the SSCS. Meanwhile, the topology with stress and temperature constraints has obvious sensitivity to even subtle change in temperature. The optimization design considering several stress constraints under multithermal conditions can work well in different temperature ranges.

中文翻译：

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具有应力和温度约束的热弹性拓扑优化

为了解决复杂的多物理场问题，提出了一种具有应力和温度约束的热弹性拓扑优化方法。基于材料特性的有理近似（RAMP），求解了力学和温度场的耦合方程。为了进行比较，讨论了两个优化问题，即具有温度和应力约束的体积最小化以及具有体积和温度约束的传统顺应性最小化。提出了一种结合全局应力测度的应力稳定控制方案（SSCS），以解决温度场在变化的情况下应力的高度非线性和局部性。伴随方法被用来实现多物理场的灵敏度，并且密度密度函数使用移动渐近线（MMA）的方法进行了更新。研究了代表性实例，以证明所提出方法的有效性和实用性。借助SSCS，可以为复杂的耦合问题获得清晰的拓扑结构和稳定的迭代过程。同时，受应力和温度限制的拓扑对温度的细微变化也具有明显的敏感性。在多热条件下考虑多个应力约束的优化设计可以在不同的温度范围内很好地工作。