Adaptive isogeometric topology optimization using PHT splines

Abstract

This paper presents a novel adaptive isogeometric topology optimization methodology using the Geometry Independent Field approximaTion (GIFT) framework for Polynomial splines over Hierarchical T-meshes (PHT)-splines. Under the philosophy of the GIFT framework, industry-standard multi-patch Non-Uniform Rational B-Splines (NURBS) definition of the geometry is considered, and the adaptive discretization is achieved with the help of PHT-splines. The approach tracks the variation of density of an element, refining the sub-domains such that the boundary between the material and the non-material domain has a proper resolution. The proposed approach has threefold merits: (i) Complex multi-patch NURBS geometries could be constructed in any professional computer-aided design package and exported for analysis; (ii) The topology optimization problem could initially be solved on a relatively coarse mesh and refined progressively for substantial computational gains; (iii) Taking benefit of the GIFT framework, we can exactly represent conic sections in our computational model, thus altogether avoiding any geometric error during refinement. The accuracy and computational efficiency of the proposed framework are studied by comparing the adaptive solution to the non-adaptive solution. The proposed approach achieves a 30%–60% reduction in degree’s-of-freedom and an 80%–90% reduction in CPU time compared to the non-adaptive case.