摘要
相对于传统的有限元法,基于几何样条的等几何方法可以保证几何模型与物理模型的一致性,但细分依然会导致模型刚度矩阵较大时求解效率不高的问题,因此可以采用多重网格法加速等几何分析中的迭代求解。文章研究等几何法中的k细分方法并构建了基于k细分的多重网格映射矩阵,加快求解效率,探讨了不同k细分策略的收敛速度。算法计算结果表明:多重网格法能够有效提高基于k细分等几何分析方法求解的收敛速度。
Compared with the traditional finite element method, isogeometric analysis method(IGA for short) based on spline geometric can keep the consistency between the geometric model and the physical model. But the subdivision still leads to the solving efficiency problem with huge stiffness matrix. Therefore, the multiple grid method was introduced to the iterative progress in IGA. This paper studied the k-subdivision in IGA and constructed a multiple grid reflecting matrix based on k-subdivision to improve the solution efficiency, and also the convergence speed of different k-subdivision strategies was studied. The results show that: the convergence speed of IGA based on k-subdivision was improved effectively using the multiple grid method.
作者
魏志鹏
罗会信
左兵权
费建国
WEI Zhi-peng;LUO Hui-xin;ZUO Bing-quan;FEI Jian-guo(Key Laboratory of Metallurgical Equipment and Control Technology Ministry of Education,Wuhan University of Science and Technology,Wuhan 430081,China;Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering,Wuhan University of Science and Technology,Wuhan 430081,China)
出处
《组合机床与自动化加工技术》
北大核心
2020年第7期30-35,共6页
Modular Machine Tool & Automatic Manufacturing Technique
基金
武汉科技大学冶金装备及其控制教育部重点实验室开放基金项目(2015B14)
湖北省教育厅科学研究计划指导项目(B2019003)。
关键词
等几何法
多重网格法
映射矩阵
k细分
isogeometric method
multigrid method
reflecting matrix
k-subdivision
