Thick rectangular plates—II: The generalized Lévy solution

Lévy's classical solution for the problem of a statically loaded, rectangular plate which is simply supported on two opposite edges and has arbitrary boundary conditions specified on the remaining edges is generalized so as to provide a solution for the problem when transverse shear deformation is taken into account. Such solutions are provided for both Mindlin's plate theory and a new plate theory, recently published, which does not require that normals to the undeformed midsurface of the plate remain straight after deformation of the plate. The results of these analyses are relatively uncomplicated generalizations of the classical results for the transverse displacement, or deflection, of the midsurface of the plate and equally simple expressions for the rotations of normals to the midsurface of the undeformed plate. Several particular examples are presented and numerical results are tabulated for several typical plate geometries in order to compare the predictions of the two theories considered. Pertinent observations and comments concerning the analytical and numerical results are made.