一个基于膜板比拟理论的四边形双线性薄板单元

A NEW QUADRILATERAL BI-LINEAR THIN PLATE ELEMENT BASED ON THE MEMBRANE-PLATE SIMILARITY THEORY

平面弹性与板弯曲的相似性理论为构造薄板单元提供了一条有效的新途径。根据这一理论,现有的平面弹性单元原则上可以转化为板弯曲单元。从平面弹性四节点双线性等参元Q4出发,根据相似性理论构造出一个新的四边形八自由度双线性薄板单元。该单元构造简单,节点自由度少,可以视为最简单的四边形薄板单元。数值结果表明,该单元能通过分片试验,满足坐标不变性,具有良好的收敛性和精度。是一个良好的低阶薄板单元。

A new effective way to formulate thin plate element can be realized by using the similarity theory between plane elasticity and plate bending. According to this theory, plane elasticity elements can be transformedinto plate bending ones. In this paper, starting with the 4-noded isoparametric element Q4, we present a newquadrilateral eight D.O.F (degree of freedom) bi-linear thin plate element on the basis of the similarity theory. The new plate bending element can be viewed as the simplest quadrilateral thin plate element. Numerical results for typical problems show that this new element can pass the patch test. It is independent of the orientation of the axesof coordinates and has a good convergence and a satisfactory precision. It is a low order thin plate element of high performance.