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The paper presents a formulation for simultaneous optimization of part and support in additive manufacturing. A pseudo heat conduction problem is solved to simulate heat transfer between the part and support. In the pseudo problem, a surface slope-dependent heat flux is applied on the part/support interfaces. The input heat is then transferred through the part and support to the build plate, which is treated as the heat sink. Since the density-based topology optimization does not involve explicit surface representation, the heat flux is implicitly imposed through a domain integration of a Heaviside projected density gradient. The proposed formulation has the inherent ability to control surface slope, which allows us to obtain self-supported enclosed voids and put removable external supports only on the open surfaces. Self-supporting supports can also be obtained by controlling the anisotropic thermal conductivity of the supports. Three different objective functions related to heat dissipation efficiency of the support are investigated. Both 2D and 3D numerical examples are presented to demonstrate the validity and efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

• Propose topology optimization formulation of thermophotonic problem for daytime passive radiative cooling. • Derive sensitivity of thermophotonic problem through adjoint method. • Propose density gradient based surface slope constraints for layer-wise design. • Demonstrate coupling effects between heat conduction, convection and radiation. Passive radiative cooling during the daytime requires efficient control of energy exchange in heat conduction, convection and radiation in the cooling system. In the paper, topology optimization formulations are proposed to design thermophotonic materials for passive radiative cooling. The first formulation solves pure photonic problem to achieve ideal absorption coefficients for radiation cooling. In the second formulation, we solve the coupled thermophotonic problem to maximize heat flux from the thermal load for efficient control of heat conduction, convection and radiation in passive radiative cooling. For better manufacturability, density gradient based boundary slope constraints are proposed to achieve layer-wise design. Sensitivity is derived through the adjoint method. While the objective function in the thermophotonic problem is independent of the density field, a derivation strategy is suggested to reduce the computational cost in sensitivity analysis. Numerical results demonstrate that passive radiative cooling can be achieved through topology optimization of thermophotonic materials. [ABSTRACT FROM AUTHOR]

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. • Topology optimization of self-supported enclosed voids for additive manufacturing. • Identification of enclosed voids with small surface slope through pseudo heat transfer problem. • Density gradient based formulations for surface slope dependent heat flux loading. • Differentiable to build orientation. • Applicable to both 2D and 3D problems. [ABSTRACT FROM AUTHOR]