Simultaneous optimization of build orientation and topology for self-supported enclosed voids in additive manufacturing

Abstract

The paper proposes a heat-flux based approach to optimize build orientation and topology simultaneously for self-supported enclosed voids in additive manufacturing. The enclosed overhangs that require supports in additive manufacturing are removed from the optimized design by constraining the maximum temperature of a pseudo heat conduction problem. In the pseudo problem, heat flux is applied on the non-self-supported open and enclosed surfaces. Since the density-based topology optimization involves no explicit boundary representation, we impose such surface slope dependent heat flux through a domain integral of a Heaviside projected density gradient. In addition, the solid materials and the void materials in the pseudo problem are assumed to be thermally insulating and conductive, respectively. As such, heat flux on the open surfaces can be successfully conducted to external heat sink through the void (or conductive) materials. However, heat flux on the non-self-supported enclosed surfaces is isolated by the solid (or insulating) materials and thus leads to locally high temperature. Hence, by limiting the maximum temperature of the pseudo problem, self-supported enclosed voids can be achieved, and the slope of the open surfaces would not be affected. Due to the differentiability of the heat flux loading in the pseudo problem, the calculated temperature and constraint on it are differentiable to both the build orientation and the density field. Numerical examples on 2D and 3D linear elasticity problems are presented to demonstrate the validity and effectiveness of the proposed approach in the design of self-supported enclosed voids.