一种用于有限元疏密过渡的新型十三节点单元

提出一种新型的十三节点单元,通过将母单元积分域分成四个子域,在各子域中分别建立线性化的插值函数并进行数值积分,确保了疏密单元之间的协调性,进而将四个子域的积分结果按自由度进行累加即可得到该单元的数值积分结果.该单元在保证疏密单元交界面位移协调的基础上,实现由一个粗(疏)单元向四个细(密)单元过渡.新型十三节点单元精度与普通六面体单元或四边形单元相当.若应用于大型工程结构的有限元分析,可在不损失精度的前提下有效减小计算量.算例表明该单元有良好的数值精度和实用性.

A thirteen-node element for transition between course and fine finite element meshes

This paper presents a kind of new-style 13-node element,in which the integration region is divided into four sub-regions,and linear interpolating functions are established in each sub-region.Numerical integration is performed in each sub-region,and the outcome is then assembled to form that of the original region.The accuracy of this 13-node element is the same as ordinary hexahedron or quadrilateral element.It realizes the transition from one coarse element to four fine elements while guaranteeing the matching of displacement on their interface.When applied to large-scale engineering practice,it can remarkably reduce computational effort without sacrificing accuracy.Numerical tests show the good precision and feasibility of this new-style thirteen-node element.