Structural optimization under overhang constraints imposed by additive manufacturing technologies

Abstract

This article addresses one of the major constraints imposed by additive manufacturing processes on shape optimization problems -that of overhangs, i.e. large regions hanging over void without sufficient support from the lower structure. After revisiting the 'classical' geometric criteria used in the literature, based on the angle between the structural boundary and the build direction, we propose a new mechanical constraint functional, which mimics the layer by layer construction process featured by additive manufacturing technologies, and thereby appeals to the physical origin of the difficulties caused by overhangs. This constraint, as well as some variants, are precisely defined; their shape derivatives are computed in the sense of Hadamard's method and numerical strategies are extensively discussed, in two and three space dimensions, to efficiently deal with the appearance of overhang features in the course of shape optimization processes.

Continuous front propagation-based overhang control for topology optimization with additive manufacturing

“…20, where the final objective values are plotted. Although oscillatory boundaries develop under the main structural beams for small density filter radii, the presence of these detailed features is not a manifestation of the sawtooth patterns observed when the overhang is only locally evaluated (Allaire et al 2017a;Qian 2017): in our results the cusps of any sawtooth are at all times sufficiently supported, and thus manufacturable. Exact control over the length scale is lost, since members can be positioned such that they are partially overhanging, resulting in thinner members in the overhang filtered design.…”

“…Both (Qian 2017) and (Allaire et al 2017a) proposed a geometrical overhang constraint by constraining the angle between the normal vector at the perimeter and the build direction. Qian (2017) uses density-based topology optimization in combination with a non-discreteness constraint to suppress intermediate densities, while in Allaire et al (2017a) level-set-based topology optimization is used. Although both methods reduce the overhang, unmanufacturable sawtooth patterns are generated, due to the local nature of the methods.…”

Taking into account thermal residual stresses in topology optimization of structures built by additive manufacturing

“…More precisely, we follow an approach initiated in [2], [3] for structural optimization. The equations are still the same as in Section 2 but we add the fact that the solid part is evolving in time during the building process.…”

“…Although, in principle, additive manufacturing can build any kind of shapes, there remain some explicit or implicit constraints on their geometries and topologies. Let us quote a few of them: overhang limitations [2], [3], [11], [26], [27], alloy anisotropy [40], [45], orientation with respect to the build direction [28], no closed holes (in order to remove the powder inside), and finally thermal residual stresses or thermal deformations.…”

“…We follow the approach of [2], [3] to model the layer by layer construction. If the final solid structure is called Ω, there are a sequence of intermediate structures Ω(t i ) corresponding to an increasing sequence of discrete times t i , each corresponding to the addition of a new layer in the building process.…”