有限元网格的拓扑分析

有限元网格生成及节点编号优化是有限元分析的关键技术之一。在有限元计算过程中,可通过优化节点编号来减少整体刚度矩阵的带宽,从而节约存储空间,减少有限元分析的计算时间。通过分析有限元网格的拓扑关系,依据单元节点相关性,提出了构造单元节点拓扑阵和组装有限元网格整体节点拓扑阵的有效方法,为优化有限元网格节点编号,减小有限元方程组中总体刚度矩阵的带宽奠定了基础。

Topology Analysis of Finite Element Meshes

Mesh generation and node-numbering optimization are key techniques in finite element analysis.In finite element analysis,the bandwidth of the whole stiffness matrix is reduced by optimizing the node numbering,thereby the needed memory space is saved and the calculation time is reduced.Topological relationship of the element meshes is analyzed.The useful methods for constructing element-node topology matrix and assembling the whole topology matrix are presented on the basis of the element-node relativity,which provides the basis for optimizing the numbering of the nodes and reducing the bandwidth of the whole stiffness matrix.