Abstract This article proposes two effective stabilizing control schemes for addressing the stress constrained thermo-elastic topology optimization in a non-uniform temperature field. Based on the density interpolation scheme, two linear elastic equations for coupling a thermo-elastic problem are considered. For comparison, different topology problem formulations for minimizing compliance or volume subject to stress constraints are solved. By virtue of a stabilization transform method, two stabilizing control schemes combined with the grouped aggregation method are developed to handle the challenging difficulties stemming from the local nature of highly nonlinear stress constraints. Moreover, the adjoint method is adopted to perform the sensitivity analysis. The design variables are updated by utilizing the method of moving asymptotes. The results of several typical numerical examples verify the validity of the proposed methodology, including the present stabilizing control schemes which can be employed to obtain clear topological design and fast convergence rate for thermo-elastic coupling problems. Meanwhile, compliance minimization design with stress constraints is appropriate to achieve balance between stress level and stiffness.

中文翻译：

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基于稳定控制方案的应力约束热弹性拓扑优化

摘要 本文提出了两种有效的稳定控制方案来解决非均匀温度场中应力约束的热弹性拓扑优化问题。基于密度插值方案，考虑了耦合热弹性问题的两个线弹性方程。为了比较，解决了用于最小化受应力约束的柔量或体积的不同拓扑问题公式。凭借稳定变换方法，开发了两种与分组聚合方法相结合的稳定控制方案，以解决高度非线性应力约束的局部性质所带来的挑战性难题。此外，采用伴随法进行敏感性分析。利用移动渐近线的方法更新设计变量。几个典型数值算例的结果验证了所提出方法的有效性，包括目前的稳定控制方案，可用于获得清晰的拓扑设计和快速的热弹性耦合问题收敛速度。同时，具有应力约束的柔量最小化设计适合实现应力水平和刚度之间的平衡。