Efficient worst-case topology optimization of self-supporting structures for additive manufacturing

In worst-case topology optimization, uncertain loads can result in complex internal structures and intricate printed details that challenge manufacturability. However, the impact of these features on manufacturing performance is often overlooked, potentially compromising the printability and quality of the final product in additive manufacturing (AM). This paper introduces a novel approach for generating 3D self-supporting structures under worst-case topology optimization. The proposed framework utilizes an implicit tensor-product B-spline (ITPBS) representation, directly adopting its coefficients as design variables to minimize compliance while enforcing selfsupporting constraints and minimal length scale. By reformulating AM constraints, we analytically derive a single geometric fabrication constraint that simultaneously addresses both overhang regions and the dripping effect. The solid-void boundary representation provided by ITPBS enables seamless integration of fabrication constraints into the worst-case optimization process. Worst-case compliance is evaluated by solving an eigenvalue problem, and sensitivity analysis is conducted using the adjoint variable method. Numerical experiments demonstrate that the proposed approach effectively produces self-supporting structures across various models.