NURBS hyper-surfaces for 3D topology optimization problems

A general topology optimization strategy is presented in this study for three-dimensional applications. The approach is based on the combination of a well-established density-based method and the Non-uniform rational basis spline (NURBS) hyper-surfaces formalism. The topology of the structure to be optimized can be embedded in a reference domain and it is opportunely described by means of a suitable NURBS hyper-surface. This choice implies several advantages. On the one hand, the number of design variables (control points and weights of the NURBS hyper-surface) is drastically reduced, when compared to classical density-based approaches, and it is unrelated to the mesh of the finite element model. On the other hand, the topology is described through a purely geometrical entity, while the mesh is utilized only to perform the computation of the relevant physical quantities for the problem at hand. A sensitivity analysis with respect to the new variables set is carried out. The effectiveness of the method as well as the effects of some discrete parameters tuning the NURBS hyper-surface shape are investigated on meaningful benchmarks and results are compared with those provided by the classical Solid Isotropic Material with Penalization approach.