A conforming quadrilateral plate bending element with shear deformations

Abstract

A simple and accurate four nodes, 16 degrees of freedom (DOF) conforming quadrilateral finite element with shear deformations (NCQS) for the analysis of thin and moderately thick plates is presented. The assumed transverse displacement is described by slight modifications of bicubic polynomials which consist of a set of fundamental rigid-body and constant curvature modes plus a set of higher order modes. It has been shown that the requirements of the displacement functions may be greatly relaxed through slight modifications of the coupling stiffness between fundamental and higher order displacement modes. This alternation of stiffness terms has the advantage that the shear deformations, which are only associated with the higher modes of deformation, can be accounted for in a special way using the local equilibrium equations, kinematics, and the constitutive relations for shear. Therefore, there is no additional expansion for the shear deformations. To illustrate these concepts, several numerical examples of displacements and stresses for thin and moderately thick plate bending problems are presented and discussed. The NCQS element appears to be a simple and reliable 16 DOF conforming quadrilateral plate bending element.