This talk focuses on a new Topology Optimisation (TO) method, developed at the Institut de Mécanique et d’Ingénierie de Bordeaux (I2M) laboratory, which is based on a smart coupling between the well- established Solid Isotropic Material Penalisation (SIMP) strategy and the Non-Uniform Rational B-Splines (NURBS) geometric entities formalism. The resulting method is called “NURBS-based SIMP method” and it is implemented into the code SANTO (SIMP And NURBS for Topology Optimisation).
This TO method has been developed in order to go beyond the restrictions related to the classical SIMP approach : the accent is put on the general nature of the proposed strategy, on its robustness and, of course, on its advantages when compared to the classic SIMP method.
Among these advantages a special attention is dedicated to the intrinsic CAD compatibility of the solutions provided by the NURBS-based SIMP approach. This is due to the interesting properties of the NURBS entities and to the fact that, at each iteration, a geometric description of the topology boundary is always available. Moreover, unlike the SIMP approach, the optimised topology does not depend upon the quality of the mesh of the FE model and the continuity of the pseudo-density field is implicitly ensured by the NURBS blending function properties. Therefore no numerical artefacts, like filtering techniques, must be implemented to avoid topology discontinuity.
In particular the following features will be highlighted during the presentation :

• Topology representation. The topology description relies on a purely geometric entity (i.e. the NURBS surface/hyper-surface) defined over the computational domain and it is unrelated to the underlying mesh.
• Variables Saving and Implicitly Defined Filter Zone. Thanks to the local support property of NURBS blending functions, a single control point (and the respective weight) affects the fictitious density field only in a well-defined portion of the computational domain. Unlike to the classical SIMP approach, there is no need to define a further filter zone, because the NURBS local support establishes an implicit relationship among contiguous elements.
• Importance of the NURBS Weights. The influence of the NURBS weights on the final optimum topology is investigated. Including the NURBS weights among the design variables implies, on the one hand, improved quality of the solution (in terms of objective and constraint functions) and, on the other hand, a smoother boundary.
• Performances and Robustness. The presented algorithms systematically provides solutions, which exhibit equivalent or better performances, if compared to those obtained through a commercial software as Altair OptiStruct®.
• Results provision, consistency and CAD-compatibility. The advantages of NURBS entities are fully exploited in terms of their CAD compatibility : a suitable post-processing phase can be implemented and utilised in order to straightforwardly obtain the final optimised geometry for 2D and 3D problems.
• Effective handling of geometric constraints. Thanks to the properties of NURBS blending functions some important geometric constraints like the minimum and maximum length scale can be satisfied implicitly by tuning the discrete parameters involved into the definition of the NURBS entities without imposing further (often too complex) optimisation constraints.