Abstract Suppressing enclosed voids in topology optimization is an important problem in design for manufacturing. The method of Poisson equation-based scalar field constraint (i.e., Poisson method) can effectively address this problem. Nevertheless, the numerical performance of this method is not well understood. This paper investigates the numerical functionality and characteristics of the Poisson method. An electrostatic model is developed to describe this method instead of the previous temperature model. Moreover, an efficient constraint scheme is proposed, which combines density filtering, Heaviside projection, regional measure, and normalization techniques to overcome various numerical issues and difficulties associated with the method. Particularly, the key constraint relation between the constraint threshold and the optimized result in this method is clarified. Numerical examples are presented to assess the Poisson method and demonstrate the effectiveness of the proposed constraint scheme. It is shown that the choice of constraint boundary conditions affects the obtained design. And the constraint effect of the Poisson method depends on the constraint threshold. Besides, the approximation error variations have a significant impact on the constraint relation for the aggregation techniques-based constraint implementation. These findings are essential in obtaining reasonable designs by the Poisson method.

中文翻译：

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拓扑优化中限制封闭空隙的泊松方法的数值性能

摘要 在拓扑优化中抑制封闭空隙是制造设计中的一个重要问题。基于泊松方程的标量场约束方法（即泊松法）可以有效地解决这个问题。然而，这种方法的数值性能还不是很清楚。本文研究了泊松方法的数值功能和特性。开发了一个静电模型来描述这种方法，而不是以前的温度模型。此外，提出了一种有效的约束方案，该方案结合了密度过滤、Heaviside 投影、区域测量和归一化技术，以克服与该方法相关的各种数值问题和困难。特别，明确了该方法中约束阈值与优化结果之间的关键约束关系。给出了数值例子来评估泊松方法并证明所提出的约束方案的有效性。结果表明，约束边界条件的选择会影响获得的设计。而泊松方法的约束效果取决于约束阈值。此外，近似误差变化对基于聚合技术的约束实现的约束关系有重大影响。这些发现对于通过泊松方法获得合理的设计至关重要。结果表明，约束边界条件的选择会影响获得的设计。而泊松方法的约束效果取决于约束阈值。此外，近似误差变化对基于聚合技术的约束实现的约束关系有重大影响。这些发现对于通过泊松方法获得合理的设计至关重要。结果表明，约束边界条件的选择会影响获得的设计。而泊松方法的约束效果取决于约束阈值。此外，近似误差变化对基于聚合技术的约束实现的约束关系有重大影响。这些发现对于通过泊松方法获得合理的设计至关重要。