Introduction

Often times, plates and panels are subject to in-plane loads. Their dynamic characteristics are influenced in ways not dissimilar to those of axially loaded beams. However, the modeling of these 2D systems is more challenging, involving for example more boundary conditions. Typical plates also exhibit considerable postbuckled stiffness, even to the extent that buckled plates can fulfill useful design purposes, that is, the elastic critical load and ultimate failure load are quite different.

This chapter introduces some basic concepts from the theory of thin, rectangular plates. The bending of plates has received considerable attention over the years and is well established in the literature. In its simplest context, we might consider a long plate supported on only two opposite sides as analogous to a wide beam. More sophisticated analyses would then incorporate large deflections of relatively thick plates including various shapes and higher-order effects. It is assumed that the reader is somewhat familiar with simple plate bending theory, both in terms of the governing differential equations and energy considerations. Thus this chapter will focus on the interaction of in-plane forces, large deflections, and dynamic response.

Brief Review of the Classical Theory

Consider a flat rectangular plate as shown in Fig. 10.1. The plate has a uniform thickness h, and coordinates x and y describe the middle surface of the plate. The z coordinate is directed vertically upward from this plane.