Multiscale topology optimization of cellular structures using Nitsche-type isogeometric analysis

Abstract

This paper proposes a multiscale topology optimization method using Nitsche-type isogeometric analysis (IGA) for design of structures described by multiple non-uniform rational B-spline (NURBS) patches. In this method, at macroscale, unknown structural responses are calculated by Nitsche-type IGA, which not only ensures the consistency between geometric and analytical models, but also offers an effective way to enforce kinematic compatibility and mechanical equilibrium on interfaces between adjacent NURBS patches. At microscale, mechanical properties of microstructures are predicted by a Kriging metamodel at a low computational cost, which is constructed via some sample lattice unit cells (LUCs). In addition, analytical computation of sensitivities for coupled elements is developed. Finally, the structures are infilled by graded LUCs according to the density distribution within the design space. Some 2D and 3D numerical examples with conforming and non-conforming NURBS patches are presented to test the proposed method. Results indicate that the proposed method is effective for design of structures described by multiple NURBS patches.