TOPOLOGY OPTIMIZATION WITH SELF-SUPPORTED ENCLOSED-VOIDS THROUGH ADVECTION-DIFFUSION EQUATIONS

In the additive manufacturing of structures with complex geometry, the auxiliary supports are generally required to fabricate surfaces with overhang angle smaller than the prescribed threshold. The fabrication of the support structures can lead to the increase of material waste and manufacturing cost. The support structures put on the enclosed voids are even difficult to remove after build. To solve this issue, this paper proposes an advection-diffusion equation based on topology optimization approach for designing self-supported enclosed voids. It can control the overhang angle of the enclosed voids in topology optimization without affecting the external surfaces. As a result, the internal support structures put on the enclosed voids can be eliminated without significant sacrifice of the structural performance. In the density-based topology optimization, due to the lack of explicit boundary representation, it is challenging to identify the enclosed voids and control their overhang angle. In this paper, by simulating the transport of light along the build direction through the advection-diffusion equation, we can identify the shadowed region as the inaccessible regions for machining tools. Combined with the spatial gradient of the density field, a global constraint is constructed to constrain the overhang angle of the enclosed voids in topology optimization. In addition, in order to exclude the external overhang boundaries from the inaccessible regions for machining tools, the intermediate density fields are eroded through the PDE-based density filtering and the Heaviside projection. Numerical examples are presented to demonstrate the efficacy of the proposed topology optimization method in the design of self-supported enclosed voids. The proposed method would help to further combine topology optimization and additive manufacturing in the generative design and fabrication of complex structures.