Abstract

A highly accurate new quadrilateral thick plate element based on the Reissner–Mindlin theory is developed in this paper. The proposed element possesses nine nodes for improved accuracy, but the mid-sides and center nodes are condensed to form the element stiffness matrix so that it behaves as a four-node element externally, which is more convenient for practical engineering applications. The behavior of this new element, PLATE-Q9, is free from shear locking problems, and it can degenerate to the thin plate solution. The performance of this new plate element is compared with similar quadrilateral plate elements using static condensation under highly distorted mesh conditions. The numerical problems with some popular plate elements under adverse condition are highlighted, and some strange results are obtained. It is also demonstrated that the proposed quadrilateral element can still perform well under these special cases, and is able to pass through all the patch tests.

摘要

本文基于 Reissner-Mindlin 理论开发了一种高精度的新型四边形厚板单元。提出的单元具有九个节点以提高精度，但将中间节点和中心节点压缩形成单元刚度矩阵，使其对外表现为四节点单元，更便于实际工程应用。这种新元素 PLATE-Q9 的行为没有剪切锁定问题，并且可以退化为薄板解。将这种新板单元的性能与在高度扭曲的网格条件下使用静态冷凝的类似四边形板单元进行比较。突出了一些流行的板单元在不利条件下的数值问题，并得到了一些奇怪的结果。