A Compatible Quadrilateral Finite Element for Plate Bending with Three-Nodal Degrees of Freedoms Each Node

Abstract

This paper describes the formulation of a four node quadrilateral finite element for the use in the analysis of thin plate structures and the stiffened folded structures. The element has three degrees of freedom at each node, these are the displacement perpendicular to the plane of the plate and the two in-plane rotations. The element ensures conformity and inter-element continuity. Expressions for the displacement and rotations along the edges of the element are first formulated. Depending on these expressions, the approximation functions of the two in-plane rotations are derived. The state of the strain for the plate element is defined by the two rotations and it is not necessary to have an explicit formula of the displacement function in order to derive the element stiffness matrix. The derived element is fully compatible, when combined with plane strain element previously derived in the mid 80th and the classical beam elements for the analysis of stiffened folded plate structures.