  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.
