A twelfth-order theory of antisymmetric bending of isotropic plates

In this paper the transverse shear and normal strain and stress effects on antisymmetric bending of isotropic plates are considered. A set of twelfth-order partial differential governing equations as well as a set of fourth-order ordinary differential equations for f(z) and phi(z) which represent the transverse shear and normal effects, are derived from a mixed variational theorem. There exists coupling between the partial differential equations and the ordinary ones. In the homogeneous solutions for the former, besides an interior solution contribution there exist two types of edge-zone solution contributions. One of them is similar to the edge-zone solution in the Reissner-Mindlin theory. The other one is an edge-zone solution consisting of a pair of conjugate functions. Two sample examples are calculated using the present theory. In the former the present two-dimensional theory obtains the three-dimensional exact solution. The latter gives the stress couple and maximum-stress concentration factors at the free edge of a circular hole in a large bent plate. The numerical results still approximate to exact solutions.