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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
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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

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