Bézier extraction based isogeometric topology optimization with a locally-adaptive smoothed density model

Abstract

This paper presents a Bézier extraction based isogeometric topology optimization framework, in which the pseudo-densities and the weights at control points (CPs) are simultaneously treated as the design variables. A locally-adaptive smoothed density field, that is dynamically updated at each design iteration, is first proposed by utilizing the values of the non-uniform rational B-splines (NURBS) basis functions. The locally-adaptive density model can naturally handle the non-uniform CPs of the curvilinear edge Bézier elements, which enhances the smoothness of structural shape. In the Bézier extraction based topology optimization, the density surface of the optimized structure can be exactly described by NURBS. Then, the optimal shape can be achieved by slicing the density surface with a predefined level-set. The sensitivity analyses of the structural compliance and the compliant mechanism are derived with respect to the design variables and evaluated from the Gaussian quadrature points instead of each element centroid. Some advantages concerning the proposed isogeometric topology optimization are illustrated with several numerical examples that are widely used in recent literature of topology optimization. Meanwhile, the influences of the design parameters on the optimal solution are also discussed to assess the effectiveness of the method.