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axisymmetricflexureofaninfiniteplaterestingonafinitely.PDF
hl. J. Solids Stnrcturrs, 1977. Vol. 13. pp 357-365. Pergamon Press. Printed in Great Britain
AXISYMMETRIC FLEXURE OF AN INFINITE PLATE
RESTING ON A FINITELY DEFORMED
INCOMPRESSIBLE ELASTIC HALFSPACE
A. P. S. SELVADUIW
Department of Civil Engineering, Carleton University, Ottawa, Canada
(Received 21 April 1976;revised 23 August 1976)
Abstract-This paper investigates the axisymmetric flexural behaviour of an infinite elastic plate resting on
an isotropic incompressible elastic halfspace which is initially deformed by a state of finite radial extension
or compression. The small axisymmetric flexural deformations of the infinite plate are due to forces which
act normal to the plane of radial deformation. The basic problem is of interest in connection with
geomechanics problems which deal with interaction analysis of the earth’s crustal plate and the underlying
mantle.
I. INTRODUCTION
The general theory of small deformations superposed on a finite deformation of an isotropic
elastic material was developed by Green, Rivlin and ShieldHI. This theory provides exact
solutions for problems of infinitesimal strains superimposed on an assigned and exact large
initial deformation. At the same time this theory offers a natural extension to the classical
theory of linear elasticity which takes into consideration the effects of initial stress. Detailed
accounts of the method of Green et al. [ 11together with references
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