Three-dimensional topology optimization considering overhang constraints with B-spline parameterization

In this paper, a B-spline parameterization based topology optimization method is presented to design 3D self-supporting structures for additive manufacturing (AM). B-spline parameterization being independent of the FE mesh is used to represent the density field characterizing the material layout of the structure. Heaviside projection and Boolean operations are applied to ensure the obtention of a clear topology configuration within a free-form design domain. Three specific constraints are formulated for AM: (i). The overhang angle constraint imposed on the structural boundaries in an integral form. (ii). The pyramid constraint aiming to avoid undesired inverted-cone features by constraining the values of density field at detection points uniformly distributed in the B-spline parameterized domain. (iii). The boundary gradient constraint imposed to deal with V-shaped cross-section features appearing on the boundary of the design domain by constraining the corresponding direction of the gradient of the B-spline density field. Meanwhile, the minimum feature size control is employed to deal with V-shaped cross-section features inside the design domain. Representative examples are dealt with to demonstrate the effectiveness of the proposed method. Numerical results show that the proposed method is effective to solve 3D problems.