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

查看全文 作　　者：Aodi [1]YANG;Shuting [1]WANG;Nianmeng [1]LUO;Tifan [1]XIONG;Xianda [1]XIE 机构地区：[1]School of Mechanical Science and Engineering,Huazhong University of Science and Technology,Wuhan 430074,China 出　　处：《Frontiers of Mechanical Engineering》索引2022年第17卷第4期,共23页 基　　金：supported by the National Key R&D Program of China(Grant No.2020YFB1708300);China Postdoctoral Science Foundation(Grant No.2021M701310). 摘　　要：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. 关 键 词：topology optimization isogeometric analysis finite element analysis tensor product structure sensitivity analysis