Strength-based topology optimisation of anisotropic continua in a CAD-compatible framework

Abstract

In this paper, a new method to address strength-based topology optimisation (TO) problems is proposed. Specifically, failure criteria for anisotropic materials are integrated into a TO algorithm making use of Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces to represent the pseudo-density field describing the topology of the continuum, thus providing solutions that can be easily exported to any computer-aided design software. The notion of failure load factor is introduced to obtain optimised topologies that do not depend on the magnitude of the applied loads. A unified formulation of the main phenomenological criteria for anisotropic materials, i.e., Tsai–Wu, Hoffman and Tsai–Hill criteria, is used and typical issues related to stress-based TO problems, such as local behaviour and singularity of stresses, are handled thanks to: the properties of NURBS blending functions, a special adaptive χ-norm aggregation function that avoids overflow/underflow issues, and a modified pq relaxation approach. The effectiveness of the proposed approach is demonstrated on 2D and 3D problems. A sensitivity analysis of the optimised topologies to the integer parameters involved in the definition of the NURBS entity is performed. Moreover, the influence of the penalisation scheme used for the elasticity and the stress tensors, the failure criterion, and the orientation of the material on the optimal solution is also investigated.