Stress-based topology optimization through non-uniform rational basis spline hyper-surfaces

In this work, the Huber-Hencky-Von Mises criterion for isotropic materials is integrated into a special density-based algorithm for topology optimization (TO). The algorithm makes use of (a) Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces to represent the pseudo-density field describing the topology of the continuum and (b) the well-known Solid Isotropic Material with Penalization approach. The local behavior and the singularity of stresses are efficiently handled thanks to the NURBS blending functions properties and a suitable aggregation function. To this end, a dedicated strategy is proposed to properly update the parameters governing the behavior of the aggregation function during the iterations of the optimization process. Moreover, the gradient of the criterion is derived in closed form (in the most general case when both displacements and forces are applied as boundary conditions) by exploiting the local support property of NURBS entities. A sensitivity analysis of the optimized topology to the integer parameters of the NURBS hyper-surface is carried out. Furthermore, a manufacturing requirement related to the minimum allowable size is also integrated into the problem formulation. The effectiveness of the approach is proven on 2 D and 3 D benchmark problems taken from the literature.