The paper studies how to control boundary slope of optimized parts in density-based topology optimization for additive manufacturing (AM). Boundary slope of a part affects the amount of support structure required during its fabrication by additive processes. Boundary slope also has direct relation with the resulting surface roughness from the AM processes, which in turn affects the heat transfer efficiency. By constraining the minimal boundary slope, support structures can be eliminated or reduced for AM, and thus material and post-processing costs are reduced; by constraining the maximal boundary slope, high surface roughness can be attained, and thus the heat transfer efficiency is increased. In this paper, the boundary slope is controlled through a constraint between the density gradient and the given build direction. This allows us to explicitly control the boundary slope through density gradient in the density-based topology optimization approach. We control the boundary slope through a single global constraint. Numerical examples on heat conduction problem, and coupled 2D and 3D thermoelastic problems demonstrate the effectiveness and efficiency of the proposed formulation in controlling boundary slopes for additive manufacturing.

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