离散剪切约束的4节点矩形弯曲单元

A Four-Noded Rectangular Bending Element by Discrete Kirchhoff Shear Constraints

提出一种基于Ｍｉｎｄｌｉｎ理论的４节点矩形薄板单元，该单元满足应变能正交准则下的收敛性充要条件，具有插值方式简单和相当二次数值精度等优点。在避免单元剪切自锁中，引入较严格沿单元边界法向剪切应变约束处理技术，使单元具有真实Ｋｉｒｃｈｈｏｆｆ单元的变形特点。

Based upon the Mindlin theory, a 4-noded rectangular element for thin plates is developed, which satisfies the necessary and sufficient conditions of convergence under energy orthogonal criterion and possesses features of simple interpolation scheme and equivalent quadratic accuracy. The element behaviour is greatly improved by the rigid discrete Kirchhoff constraint proposed herein for the treatment of transverse shear strains normal to the element boundaries. The DK technique is employed to keep the element bending deformation modes very close to those of real Kirchhoff type elements.