Hostname: page-component-77c89778f8-9q27g Total loading time: 0 Render date: 2024-07-22T22:52:18.569Z Has data issue: false hasContentIssue false
  • English
  • Français

Elastic deformations of infinite strips

Published online by Cambridge University Press:  24 October 2008

H. G. Hopkins
H. G. Hopkins
Affiliation:
Department of MathematicsThe UniversityManchester
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, Fourier integrals are used to solve some elastic problems of generalized plane stress and small transverse displacements in infinitely long, rectangular, isotropic plates stressed only at their edges. The Airy stress function and the transverse displacement satisfy the two-dimensional bi-harmonic equation, and the basic mathematical problem is to solve this equation subject to different sets of boundary conditions. Little attention has been given hitherto to problems in which some of the boundary conditions depend directly upon displacements. Here the general problem is solved when one long edge is fixed, and stresses or displacements are arbitrarily prescribed at the other, with no stresses and displacements at infinity. The problem of a concentrated edge force is discussed in detail and numerical values of the stresses at the fixed edge are given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 46 , Issue 1 , January 1950 , pp. 164 - 181
Copyright
Copyright © Cambridge Philosophical Society 1950

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Filon, L. N. G.Philos. Trans. A, 201 (1903), 63.Google Scholar
(2)Howland, R. C. J.Proc. Roy. Soc. A, 124 (1929), 89.Google Scholar
(3)MacGregor, C. W.J. American Soc. Mech. Engrs. 57 (1935), 225.Google Scholar
(4)Coker, E. G. and Filon, L. N. G.A treatise on photo-elasticity (Cambridge, 1931).Google Scholar
(5)Timoshenko, S.Theory of plates and shells (New York and London, 1940).Google Scholar
(6)Titchmarsh, E. C.Theory of functions (Oxford, 1932).Google Scholar
(7)Titchmarsh, E. C.Theory of Fourier integrals (Oxford, 1937).Google Scholar