基于重叠划分的自由网格四边形单元计算方法

Algorithm of free mesh quadrilateral element based on overlap division

提出了一种基于重叠划分的自由网格四边形单元计算方法。这一方法将四边形单元引入到自由网格计算方法中,不仅提高了计算的精度,同时还保留了自由网格计算方法的特点。方法首先对分析域内自动生成的每一个节点建立一套临时三角形单元,利用这些临时三角形单元组合生成四边形单元,以节点为单位进行计算。由于各矩阵的计算与组集均以节点为中心进行处理,因而特别适合于并行计算环境。在详细介绍自由网格四边形单元计算方法的基础上,利用数值算例证实了这一方法改善计算精度方面的有效性。

An algorithm of the free mesh quadrilateral element based on overlap division to achieve high accuracy is presented. The algorithm is not any different from the original free mesh method in the fundamental process. At first, create a set of temporary triangular element around every nodal point, and then for every temporary triangular element, generate the quadrilateral elements by using the triangular element and its adjacent triangular elements, finally, assemble matrices node-by-node. Because assembling matrices for the algorithm is carried out node-by-node, it is suitable for the paralleled calculation. The results of numerical examples indicate that the algorithm is more accurate than the original free mesh method.