Topology and anisotropy optimisation of continua using non-uniform rational basis spline entities

Abstract

This paper presents a novel method to address the challenge of concurrent topology and anisotropy optimisation of variable-stiffness anisotropic structures with variable thickness from additive manufacturing technologies. The proposed methodology relies on the multi-level optimisation strategy based on non-uniform rational basis spline (NURBS) entities, density-based method for topology optimisation and the polar formalism to describe the anisotropy of the continuum. Specifically, NURBS entities are used to describe both the density field and the distribution of the polar parameters and the thickness across the design domain. Furthermore, the properties of NURBS entities are efficiently exploited to derive the gradient of the physical responses involved in the problem formulation. The proposed method is applied to the problem of maximising the structural stiffness, while fulfilling design requirements on the lightness and on the feasibility of the polar parameters. In this context, the problem is formulated in the most general case considering inhomogeneous Neumann–Dirichlet boundary conditions. The effectiveness of the approach is tested on benchmark problems taken from literature subjected to both in-plane and out-of-plane loads. Particularly, a large campaign of sensitivity analyses has been carried out to examine the impact of integer parameters of the NURBS entity, the penalty scheme used for the element stiffness matrix, inhomogeneous Neumann–Dirichlet boundary conditions, optimisation strategy (sequential versus concurrent) and initial guess on the optimised solution.