Abstract Currently, most works on layout optimization problem of continuum structure embedded with movable holes are all carried out to maximize the stiffness of the overall system. In this work, the embedding problem is solved for minimum stress design for the first time. To this end, we propose an effective hybrid methodology under SIMP-based computational framework. The material density characterizing the topology of the load transfer path and the geometric parameters defining the rigid body motion (translation and rotational) of the embedded holes are considered as design variables and are optimized simultaneously to minimize the aggregated maximum stress. To unite these two seemingly different representations into an optimization model, we mapped the embedded holes into a density field on a fixed grid using a Sigmoid activation function. Then, a new SIMP-like material interpolation scheme that considers embedding holes is introduced for stiffness penalization and stress penalization. The optimization model for solving the minimum stress problem embedded with movable holes and its sensitivity analysis are detailed. Finally, two typical examples are performed to illustrate the effectiveness of the proposed methodology.

中文翻译：

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带嵌入式活动孔的最小应力设计的拓扑优化

摘要 目前，大多数关于嵌入活动孔的连续结构布局优化问题的工作都是为了使整个系统的刚度最大化。在这项工作中，首次解决了最小应力设计的嵌入问题。为此，我们在基于 SIMP 的计算框架下提出了一种有效的混合方法。表征载荷传递路径拓扑的材料密度和定义嵌入孔的刚体运动（平移和旋转）的几何参数被视为设计变量，并同时进行优化以最小化聚合最大应力。为了将这两种看似不同的表示联合到一个优化模型中，我们使用 Sigmoid 激活函数将嵌入的孔映射到固定网格上的密度场。然后，引入了一种新的类似 SIMP 的材料插值方案，该方案考虑了嵌入孔的刚度惩罚和应力惩罚。详细介绍了嵌入活动孔的最小应力问题的优化模型及其敏感性分析。最后，通过两个典型的例子来说明所提出方法的有效性。