Finite Element Bending Analysis of Reissner Plates

A finite element plate bending analysis which includes the effects of transverse shear is described. A complete displacement formulation based on the governing equations of the Reissner theory is developed for application to the bending of rectangular plates. The finite element employed is a rectangle with 20 degrees of freedom which include both bending and shear deformation states and their interaction. Of primary importance is the ability of the finite element method to overcome certain of the anomalies found in classical plate theory. The presence of Kirchoff shear forces and concentrated corner reactions can be eliminated by the specification of more realistic boundary conditions. Results of several numerical examples are in excellent agreement with those of the Reissner theory for maximum displacements and for the distribution of shear stress resultants along plate edges. Also, the added transverse shear degrees of freedom allow shear deformations along an edge parallel to the edge. Thus, the vanishing edge twisting moment condition can be satisfied approximately. The formulation described offers a convenient method for approximating the Reissner theory with a discrete element approach.