Achieving self-supported enclosed voids and machinable support structures in topology optimization for additive manufacturing

This paper proposes a topology optimization formulation for additive manufacturing, in which the part, supports and their machining directions are simultaneously optimized. The part and supports are represented by two groups of density fields. The support structures are optimized for heat dissipation efficiency by solving a pseudo heat conduction problem under heat flux boundary loading and constraining the maximum temperature. The temperature constraint allows us to obtain self-supporting overhangs or non-self-supporting overhangs with support structures underneath. During the optimization, the support structures are further filtered by the solution fields from the advection-diffusion equations to ensure their accessibility to the machining tools. Based on the developed formulation, the optimized support structures would be distributed in the machinable regions of the part to enhance heat transfer in the manufacturing process. The unmachinable regions of the part, including enclosed voids, are self-supported for additive manufacturing. The sensitivity of the manufacturing constraint with respect to the design variables of the part, supports and the machining directions is derived through the adjoint method. We validate the effectiveness of the proposed formulation through several examples in 2D and 3D cases.