Eigen-frequencies and harmonic responses in topology optimisation: A CAD-compatible algorithm

The formulation of Topology Optimisation (TO) problems related to dynamics is particularly challenging, due to some intrinsic difficulties of mathematical and numerical nature. This paper deals with the integration of specific physical quantities, such as eigen-frequencies and dynamic compliance, in a special TO algorithm, which combines a classical pseudo-density field with Non-Uniform Rational Basis Spline (NURBS) entities. In this framework, wherein some of the NURBS continuous parameters (i.e. control points and weights) are the new design variables, important advantages can be exploited. In particular, beyond the reduction of the number of design variables and the definition of an implicit filter zones, the post-processing phase involving the CAD reconstruction of the optimised geometry is immediate for 2D problems and it needs few operations in 3D. Classical TO problems dealing with structural dynamics, as the maximisation of the first eigen-frequency and the minimisation of the dynamic compliance, are formulated in the NURBS framework. Accordingly, the analytical expressions of the gradients of the considered physical quantities are derived in closed form. In order to show the effectiveness of the proposed approach, an exhaustive numerical campaign is proposed and the algorithm is applied to both 2D and 3D benchmarks. Moreover, a sensitivity analysis of the final optimised solutions to the NURBS discrete parameters is provided as well.