An isogeometric approach to topology optimization of spatially graded hierarchical structures

This paper presents an isogeometric approach to topology optimization of spatially graded hierarchical structures, which are assumed to be consisted of identical or spatially varying substructures. In this work, the isogeometric analysis (IGA) is adopted for an efficient and accurate performance assessment of spatially graded structures, especially for those with complex geometries. A multi-resolution topology optimization (MTOP) scheme with two distinct mesh discretization levels is used to achieve high-resolution topology representation. In specific, displacement field and topology field are approximated separately on two distinct levels of mesh discretization, where the IGA is performed on a coarse mesh and nodal-based topology design variables are defined on a refined mesh obtained by k-refinement scheme. A projection scheme with the use of non-uniform rational basis spline (NURBS) basis functions is employed to compute the densities at quadrature points from nodal densities variables. The proposed IGA-MTOP-based design framework has threefold merits: a) global structure and constituent substructures are strictly coupled with no assumption on the separation of scales as required in homogenization-based designs, which together with high continuous NURBS basis functions guarantee automatically smooth connection between substructures; b) high-resolution designs with detailed local structural features can be obtained in a computationally high-efficient manner; c) the substructures designed in the common parameter space can be freely transformed to conform the physical space. The effectiveness and robustness of the proposed method are validated by a series of benchmark designs.