Topology optimization of self-supporting structures for additive manufacturing with B-spline parameterization

Abstract This paper presents a B-spline based topology optimization method to design self-supporting structures for additive manufacturing (AM). The density field of the structure is represented by B-spline parameterization together with Heaviside function through Boolean operation. Two constraints are constructed for overhang control. One concerns the overhang angle constraint to structural boundaries and is formulated in an integral form within a narrowband region identified by the density gradient norm. The density gradient is obtained by directly computing the derivatives of the B-spline density field. The other concerns the constraint to avoid undesired V-shaped areas and is formulated by limiting the density values at detection points uniformly distributed in the design domain. Several examples are dealt with to demonstrate the effectiveness of the proposed method. It is shown that the proposed overhang control scheme is independent of the FE mesh with the help of B-spline parameterization and works well with free-form design domains.