Multi-material isogeometric topology optimization in multiple NURBS patches

Abstract

In design optimization of structures, design domains are often described by multiple non-uniform rational B-spline (NURBS) patches. To perform multi-material topological design in such design domains, an effective Nitsche-based multi-material isogeometric topology optimization (ITO) method is proposed in this paper. Specifically, the Nitsche's method is utilized to effectively couple the interfaces between adjacent NURBS patches. In order to preserve the coercivity of the bilinear form, the stabilization parameters are estimated locally according to the element size. Meanwhile, the discrete material optimization (DMO) approach is employed to describe the mixing of candidate materials. Analytical computation of sensitivities for coupled elements is developed as well. The effectiveness of the proposed method is demonstrated via several 2D and 3D numerical examples, where the design domains are constituted by conforming and non-conforming NURBS patches, respectively.