Adaptive isogeometric multi-material topology optimization based on suitably graded truncated hierarchical B-spline

Abstract

A novel adaptive multi-material topology optimization (TO) is presented in this work based on suitably graded truncated hierarchical B-spline in the framework of isogeometric analysis (IGA). The isogeometric mesh is locally refined and coarsened during the topology process to achieve the analysis and design meshes for multi-material design problems. Adaptive marking strategy is established based on the summation of density variation indicators of all material phases, which plays a critical role in obtaining elements with different phases to be refined and coarsened. Besides, the graded constraint is imposed on the hierarchical isogeometric mesh to improve the numerical accuracy of multi-material problems solved by adaptive IGA and ensure the boundary quality of the converged multi-material structures. Through an alternating active-phase algorithm in a hierarchy form, the proposed isogeometric multi-material TO model can be divided into finite two-phase adaptive isogeometric optimization subproblems, of which the sensitivity analysis is derived in terms of an adaptively adjusted filter. Compared with the current isogeometric multi-resolution multi-material method, the proposed adaptive one can obtain optimized multi-material designs with much-improved efficiency. Several numerical examples are applied to verify the robustness and effectiveness of the proposed approach.