In additive manufacturing, the fabrication sequence has a large influence on the quality of manufactured components. While planning of the fabrication sequence is typically performed after the component has been designed, recent developments have demonstrated the possibility and benefits of simultaneous optimization of both the structural layout and the corresponding fabrication sequence. The simultaneous optimization approach, called space-time topology optimization, introduces a pseudo-time field to encode the manufacturing process order, alongside a pseudo-density field representing the structural layout. To comply with manufacturing principles, the pseudo-time field needs to be monotonic, i.e., free of local minima. However, explicitly formulated constraints are not always effective, particularly for complex structural layouts. In this paper, we introduce a novel method to regularize the pseudo-time field in space-time topology optimization. We conceptualize the monotonic additive manufacturing process as a virtual heat conduction process starting from the surface upon which a component is constructed layer by layer. The virtual temperature field, which shall not be confused with the actual temperature field during manufacturing, serves as an analogy for encoding the fabrication sequence. In this new formulation, we use local virtual heat conductivity coefficients as optimization variables to steer the temperature field and, consequently, the fabrication sequence. The virtual temperature field is inherently free of local minima due to the physics it resembles. We numerically validate the effectiveness of this regularization in space-time topology optimization under process-dependent loads, including gravity and thermomechanical loads.

翻译：在增材制造中，制造顺序对构件质量有重要影响。尽管制造顺序规划通常在构件设计完成后进行，但最新研究已证明同时优化结构布局及其对应制造顺序的可行性和优势。这种同时优化方法称为时空拓扑优化，它引入表征制造过程顺序的伪时间场，以及表征结构布局的伪密度场。为满足制造原理，伪时间场需保持单调性（即无局部极小值）。然而，显式约束对于复杂结构布局往往难以有效实施。本文提出一种在时空拓扑优化中对伪时间场进行正则化的新方法。我们将单调增材制造过程概念化为从构件逐层构建的起始表面开始的虚拟热传导过程。该虚拟温度场（需区别于实际制造过程中的温度场）可作为编码制造顺序的类比模型。在新公式中，我们采用局部虚拟热导系数作为优化变量来引导温度场，进而控制制造顺序。由于虚拟温度场遵循其模拟的物理规律，其本质上不存在局部极小值。我们通过数值验证证明了该正则化方法在考虑过程相关载荷（包括重力与热力载荷）的时空拓扑优化中的有效性。