Plane strain: the direct determination of stress

Abstract

(1) The advantages of the direct determination of the stresses in an elastic solid have been pointed out by Prof. J. H. Michell. The principal line of attack in the case of plane strain has been by aid of the well-known stress function method, by which the stresses are determined from a single stress function χ of x and y only, satisfying ∇ 1 4 χ = 0, where ∇ 1 2 = ∂ 2 /∂ x 2 + ∂ 2 /∂ y 2 (1) The lines along which further advance might have been expected, and the difficulties which have been met with, are discussed by Prof. A. E. H. Love. It seems to the writer, however, that a point of very considerable importance has been overlooked, viz., that the stress function method gives a set of stresses which can in most cases be resolved into two distinct sets, each of which leads to strains satisfying the identical relations between the strain components.