Plates are initially flat structural elements, having thicknesses much smaller than their other dimensions. Many practical engineering problems fall into the categories, “plates in bending” or “shells in bending.” In this chapter, the elements of the plate-bending theory are introduced. The discussions include: historical development of plate and shell theory, behavior of plates, strain–curvature relations, stress and moment transformations, the governing equations for plate deflection, boundary conditions, methods for solution of plate deflection and stresses, and natural frequencies of plates.

Plate thickness is measured in a direction normal to the midplane. The flexural properties of a plate depend greatly on its thickness compared to its other dimensions. For a thin plate with which we are concerned, the ratio of the thickness to the smaller span length should be less than 1/20. The load-supporting action of plates resembles, to a certain extent, that of beams. Unless otherwise specified, it is assumed that plate and shell materials are homogeneous and isotropic. The distribution of stress and displacement for a plate subjected to a given set of forces requires consideration of the basic principles outlined in Chapter 1.