Elastic Deformations of Strips and Circular Plates Under Uniform Pressure

Abstract

A consistent theory for linear elastic behavior in which the strains are small but in which the displacements and rotations can be large is applied to the bending of a long rectangular plate and of a circular plate by uniform pressure. Within the range of small-strain, linear elastic behavior, the theory provides solutions for all slenderness ratios of the plates and magnitudes of the loading. Thus the theory bridges the gap between the classical theory and the nonlinear structural theory of Föppl and von Kármán. The results show that the von Kármán equations provide accurate solutions for thin plates for which deflections are not small.