Classical Theory of Plates

This chapter proposes a simple mode of deformation for the plate akin to that for deformation of beams which led to the technical theory of beams. As in the case of the technical theory of beams, there are obvious discrepancies in the classical theory of plates that has been presented. The chapter utilizes the variational approach to formulate a useful boundary-value problem for plates. Then uses variational methods to develop approximate solutions to these boundary-value problems. In fact, an alternative derivation of plate theory consists of expanding all quantities stresses and displacements into such Taylor series and then matching the coefficients of the corresponding powers of z. The chapter examines later a rectangular plate with four sections of smooth curves terminating in corners. In that case the integration may be carried out over each edge of the plate and so the closed integral would have contributions from the parenthetic expression at each corner.