Explicit Isogeometric Topology Optimization Method with Suitably Graded Truncated Hierarchical B-Spline

This work puts forward an explicit isogeometric topology optimization (ITO) method using moving morphable components (MMC), which takes the suitably graded truncated hierarchical B-Spline based isogeometric analysis as the solver of physical unknown (SGTHB-ITO-MMC). By applying properly basis graded constraints to the hierarchical mesh of truncated hierarchical B-splines (THB), the convergence and robustness of the SGTHB-ITOMMC are simultaneously improved and the tiny holes occurred in optimized structure are eliminated, due to the improved accuracy around the explicit structural boundaries. Moreover, an efficient computational method is developed for the topological description functions (TDF) of MMC under the admissible hierarchical mesh, which consists of reducing the dimensionality strategy for design space and the locally computing strategy for hierarchical mesh. We apply the above SGTHB-ITO-MMC with improved efficiency to a series of 2D and 3D compliance design problems. The numerical results show that the proposed SGTHB-ITO-MMC method outperforms the traditional THB-ITO-MMC method in terms of convergence rate and efficiency. Therefore, the proposed SGTHB-ITO-MMC is an effective way of solving topology optimization (TO) problems.