A twelfth-order theory of antisymmetric bending of isotropic plates (Q1905618)

The author presents a refined theory for the bending of thick isotropic elastic plates. The kinematical model contains six unknown functions, four with respect to the in-plane coordinates, and two with respect to the normal coordinate. These functions take into account the transverse shear and the normal strain and stress effects. Based on a mixed variational formulation, six governing differential equations and boundary conditions are derived. Two types of edge zone solutions are shown to exist besides the interior solution. The first example concerns a simply supported rectangular plate subjected to a sinusoidally distributed surface normal load, its solution is shown to be identical with the exact one for a three-dimensional layer. In the second example, the stress concentration factors at a cylindrical hole in a large bent plate are calculated; they agree very well with results based on the three-dimensional elasticity theory.