Multi-Displacement Requirement in a Topology Optimization Algorithm Based on Non-uniform Rational Basis Spline Hyper-Surfaces

Abstract

This work proposes a general formulation of the design requirement on the structural displacements evaluated, simultaneously, at different points of the structure in the framework of a density-based algorithm for topology optimization. The algorithm makes use of Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces to represent the pseudo-density field describing the part topology and of the Solid Isotropic Material with Penalization approach. The proposed formulation takes advantage of the properties of the NURBS basis functions to ensure continuity between the pseudo-densities of adjacent elements, without the need of defining further filters. In particular, the multi-displacement requirement is formulated in the most general sense, by considering displacements on loaded and non-loaded regions. The gradient of structural displacements is evaluated in closed form by using the adjoint method and the properties of the NURBS blending functions. Moreover, a sensitivity analysis of the optimized topology to the integer parameters, involved in the definition of the NURBS hyper-surface, is carried out. The effectiveness of the proposed approach is proven through meaningful 2D and 3D benchmarks.