Development of the plate elements based on the Hellinger-Reissner functional

Abstract

The finite element method has been an effective tool to analyze plate structures. Low-order plate elements still have accuracy problems compared to high-order plate elements, particularly triangular plate elements. The objective of this study is to design a 3-node plate element based on the Hellinger-Reissner functional to obtain better performance. The Hellinger-Reissner functional can make the displacements and the strains independent. The poor strain fields from the displacement-based formulation can be changed to the richer strain fields from interpolating the strains independently. Then we can use static condensation on the strain to get the stiffness matrix. Numerical tests and convergence curves of the present 3-node element has been carried out, which illustrate a favorable convergence rate of the present 3-node plate element.