Rectangular Finite Element for Plate Bending Analysis Based on Hellinger-Reissner's Variational Principle

Abstract

Based on Hellinger-Reissner's variational principle, a rectangular finite element for plate bending is derived with bilinearly varying deflection and incompletely linear moments. This method is an example of the mixed method first proposed by Herrmann, where both displacement and stress are adopted simultaneously as fundamental variables. Because continuity conditions required on the fundamental variables are much relaxed compared with compatible models, suitable shape functions can be easily derived and calculation of the element matrix can be performed by hand. The explicit expression of the element matrix for general orthotropic plates is presented in this paper. A few simple test problems are computed in order to demonstrate the accuracy of the present model, and it is shown that it gives improved results compared with Herrmann's triangular element. Convergence is also assured when suitably small mesh sizes are adopted, and this element can be utilized in general practical problems.