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)ofMMC under the admissible hierarchicalmesh,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 3Dcompliance design problems.The numerical results show that the proposed SGTHB-ITO-MMC method outperforms the traditional THB-ITO-MMCmethod in terms of convergence rate and efficiency.Therefore,the proposed SGTHB-ITO-MMC is an effective way of solving topology optimization(TO)problems.

Massively efficient filter for topology optimization based on the splitting of tensor product structure

In this work,we put forward a massively efficient filter for topology optimization(TO)utilizing the splitting of tensor product structure.With the aid of splitting technique,the traditional weight matrices of B-splines and non-uniform rational B-spline implicit filters are decomposed equivalently into two or three submatrices,by which the sensitivity analysis is reformulated for the nodal design variables without altering the optimization process.Afterwards,an explicit sensitivity filter,which is decomposed by the splitting pipeline as that applied to implicit filter,is established in terms of the tensor product of the axial distances between adjacent element centroids,and the corresponding sensitivity analysis is derived for elemental design variables.According to the numerical results,the average updating time for the design variables is accelerated by two-order-of-magnitude for the decomposed filter compared with the traditional filter.In addition,the memory burden and computing time of the weight matrix are decreased by six-and three-order-of-magnitude for the decomposed filter.Therefore,the proposed filter is massively improved by the splitting of tensor product structure and delivers a much more efficient way of solving TO problems in the frameworks of isogeometric analysis and finite element analysis.