A PDE-based approach to constrain the minimum overhang angle in topology optimization for additive manufacturing

Additive Manufacturing allows for considerably more form freedom compared to existing manufacturing technologies but still faces the limitation of building overhanging parts. The overhang limitation in additive manufacturing prevents the direct production of topology optimized parts. We present an overhang constraint that incorporates this manufacturing limitation into topology optimization. The overhanging regions in a design iteration are detected using front propagation and a global constraint is formulated by aggregating the local constraints within the design domain. Since the constraint is formulated in a continuous manner, it can be discretized for any type of mesh, and with an arbitrary minimum allowable overhang angle. Furthermore, it is easily extensible to 3D. The Ordered Upwind Method is used to solve the constraint, and adjoint sensitivities are used for efficient evaluation. The newly developed constraint is demonstrated on 2D examples having an unstructured mesh. Overhang free designs are obtained with smooth convergence behaviour.