A topology optimization formulation including a model of the layer-by-layer additive manufacturing (AM) process is considered. Defined as a multi-objective minimization problem, the formulation accounts for the performance and cost of both the final and partially manufactured designs and allows for considering AM-related issues such as overhang and residual stresses in the optimization. The formulation is exemplified by stiffness optimization in which the overhang is limited by adding mechanical or thermal compliance as a measure of the cost of partially manufactured designs. Convergence of the model as the approximate layer-by-layer model is refined is shown theoretically, and an extensive numerical study indicates that this convergence can be fast, thus making it a computationally viable approach useful for including AM-related issues into topology optimization. The examples also show that drips and sharp corners associated with some geometry-based formulations for overhang limitation can be avoided. The codes used in this article are written in Python using only open sources libraries and are available for reference.

拓扑优化考虑了包括逐层增材制造 (AM) 工艺模型的配方。该公式被定义为一个多目标最小化问题，它考虑了最终设计和部分制造设计的性能和成本，并允许在优化中考虑与 AM 相关的问题，例如悬垂和残余应力。该公式以刚度优化为例，其中通过增加机械或热柔顺性来限制悬伸，作为部分制造设计成本的衡量标准。理论上，随着近似逐层模型的细化，模型收敛，并且广泛的数值研究表明这种收敛速度很快，因此使其成为一种计算上可行的方法，可用于将 AM 相关问题纳入拓扑优化。这些示例还表明，可以避免与某些基于几何形状的悬垂限制公式相关的滴水和尖角。本文中使用的代码是用 Python 编写的，仅使用开源库，可供参考。