Open AccessPlane strain: the direct determination of stress
Publication year - 1920
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1920.0017
Subject(s) - plane stress , stress (linguistics) , function (biology) , plane (geometry) , set (abstract data type) , strain (injury) , line (geometry) , point (geometry) , stress–strain curve , mathematics , principal (computer security) , mathematical analysis , physics , computer science , geometry , philosophy , finite element method , thermodynamics , medicine , linguistics , evolutionary biology , biology , programming language , operating system
(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 functionχ ofx andy 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.