摘要
本文提出构造厚薄板通用四边形单元的一种合理方法：先按Timoshenko厚梁理论导出单元各边的转角和剪应变公式，然后进行合理插值，导出单元的转角场、曲率场和剪应变场。当板的厚度变小时，厚梁理论自动退化为薄梁理论，各边剪应变以及单元剪应变插值函数自动退化为零，厚板单元自动退化为薄板单元，彻底消除了剪切闭锁现象。此单元对厚板和薄板都给出了高精度的结果。
A rational approach to formulate Reissuer-Mindlin quadrilateral element is proposed in this paper. Firstly, the variation functions of rotation and shear strain along each side of the element are determined based on the Timoshenko beam theory. Secondly, the rotation, curvatUre and shear strain fields in the domain of the element are determined with improved interpolation. The resulting element is free of shear locking in the thin limit. Numerical examples show that the element, called TMQ, is a high-performance element for thick and thin plates.
出处
《工程力学》
EI
CSCD
北大核心
1999年第4期1-15,共15页
Engineering Mechanics
基金
国家自然科学基金
高校博士点基金
关键词
有限元
厚板元
四边形单元
厚梁
剪应变
转角
finite element, thick plate element
quadrilateral element
timoshenko beam theory
