On thermomechanical problems in a topology optimisation method based on non-uniform rational basis spline entities

This paper presents a new method to deal with thermomechanical topology optimisation (TO) problems based on a pseudo-density algorithm reformulated in the context of Non Uniform Rational Basis Spline (NURBS) entities. Specifically, a NURBS entity is used to represent the topological descriptor, providing an implicit filtering effect thanks to the local support propriety. The problem is formulated in the most general case of inhomogeneous Neumann-Dirichlet boundary conditions and design-dependent thermal sources and thermomechanical loads. In this context, a study on the combined effect of design-dependent heat sources, thermomechanical loads and applied forces and displacements on the optimal topologies is carried out. Furthermore, the influence of the penalisation schemes involved in the definition of the stiffness matrix, conductivity matrix, thermal loads and thermal sources on the optimised topology is investigated through a wide campaign of sensitivity analyses. Finally, sensitivity analyses are also conducted to investigate the influence of the integer parameters of the NURBS entity on the optimised solution. The effectiveness of the approach is tested on 2D and 3D benchmark problems.