Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-19T09:34:25.725Z Has data issue: false hasContentIssue false
  • English
  • Français

A moment theory of elastic plates

Published online by Cambridge University Press:  26 February 2010

R. Tiffen  and
F. P. Sayer
R. Tiffen
Affiliation:
Birkbeck College, University of London
F. P. Sayer
Affiliation:
Birkbeck College, University of London
Get access

Summary

This paper is concerned with infinitesimal transverse displacements of homogeneous isotropic elastic plates. The method uses moments of the fundamental equations of orders 0, 1, 2, 3. Assuming a form for the shear stresses tα3, these equations enable one to determine the mean values of the transverse displacements instead of the weighted mean values associated with plate theories of all but the classical type. The relevant moments of the stresses and displacements are expressed in terms of three functions satisfying three differential equations of the fourth order, the solutions of which may be expressed in terms of six independent functions. Thus six boundary conditions may be satisfied. Equating two, three and four of the above functions to zero in turn gives plate theories involving four, three and two boundary conditions respectively. The method is illustrated by assuming that the shear stresses are quadratic functions of the distance from the mid-plane of the material.

Type
Research Article
Information
Mathematika , Volume 9 , Issue 1 , June 1962 , pp. 11 - 24
Copyright
Copyright © University College London 1962

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

1.Love, A. E. H., Math. theory of elasticity, 4th ed. (Cambridge, 1934).Google Scholar
2.Stevenson, A. C., Phil. Mag. (7), 33 (1942), 639.CrossRefGoogle Scholar
3.Stevenson, A. C., Phil. Mag. (7), 34 (1943), 766.CrossRefGoogle Scholar
4.Coker, E. G. and Filon, L. N. G., Photoelasticity (Cambridge, 1931).Google Scholar
5.Muskhelishvili, N. I., Some basic problems of the math, theory of elasticity, 3rd ed. (Moscow, 1949). Eng. ed. (Groningen-Holland, 1953).Google Scholar
6.Reissner, E., J. Math. Phys., 23 (1944), 184.CrossRefGoogle Scholar
7.Reissner, E., J. Appl. Mech., 12 (1945), 68.Google Scholar
8.Reissner, E., Quart. Appl. Math., 5 (1947), 55.CrossRefGoogle Scholar
9.Green, A. E., Quart. Appl. Math., 7 (1949), 223.CrossRefGoogle Scholar
10.Green, A. E. and Zerna, W., Theoretical elasticity (Oxford, 1954), 215–253.Google Scholar
11.Green, A. E., Proc. Roy. Soc. A, 195 (1949), 533–552.Google Scholar
12.Tiften, R., Quart. J. Mech. and Appl. Math., 14 (1961), 59–74.Google Scholar