关于离散Kirchhoff薄板单元的研究

本文对离散Kirchhoff薄板单元进行了深入的分析。文中将用于建立离散Kirchhoff单元的泛函分为三部分,分别用应变第一不变量、绕Z轴的转动偶和有关的单元边界上的积分来表达,并阐明了各部分的作用。其中单元的收敛性质完全由第一、三部分所决定,而第二部分则控制了单元的计算精度。在此基础上,文中建议了一种提高离散Kirchhoff单元精度的新方法,并由此推导了一个任意四边形离散Kirchhoff单元。计算表明,本文的改进单元与原来的离散Kirchhoff单元及其改进型相比,计算精度有了显著提高。

STUDY OF DISCRETE KIRCHHOFF THIN PLATE BENDING ELEMENT

The discrete Kirchhoff thin plate bending element is deeply studied in this paper. The energy functional used in deriving discrete Kirchhoff elemente is divided into three parts, which are respectively expressed in the first strain invariant, a rotation couple and an integration round elemental boundary. It is pointed out that the first and third parts ensure the convergency of the element and the second part governs the computational accuracy. Based on the idea, a new way to improve the discrete Kirchhoff thin plate bending element is suggested and a new discrete Kirchhoff quadrilateral element is derived. Numerical examples show that the element presented here is obviously superior to existing similar elements in accuracy.