On the Bending of Isotropic Plates

Abstract

The analogies existing between the mathematical formulations of the bending of elastic plates and two dimensional stress problem has been well known, and so it is quite natural that we can apply the analytical methods which have been used in the latter to the former. In this paper the complementary function of the fundamental equation of the bending of isotropic plates is represented by means of the so-called Goursat's stress function. By the use of derived formulae and relations, several fundamental solutions are obtained. As examples, bending of a clamped circular plate under a concentrated load, bending of a simply supported circular plate under a concentrated load, bending of a circular plate under several concentrated loads on the boundary and bending of an infinite plate with an elliptic hole are treated.