The problem of an elastic layer with a cylindrical hole subjected to a nonuniform axisymmetric radial displacement

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1970

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Abstract

A problem in the linear theory of elasticity is considered wherein a layer with a circular cylindrical hole is subjected to a nonuniform radial displacement. The deformation is imposed on the cylindrical boundary such that axi-symmetric displacements and stresses result. The solution utilizes Navier"s equations of elasticity. These equations are solved by use of extended Hankel transforms to obtain displacements. Shear and longitudinal stresses are obtained by transformed stress-strain relationships. Radial and circumferential stresses, however, are obtained directly by use of stress-strain equations. The solution of a problem where the imposed radial displacement is a linear function of the axial coordinate is presented. Numerical results are given in graphical form for two different ratios of hole radius to layer thickness. The infinite integrals of the inversion formulas were evaluated numerically using Longman"s technique for computing infinite integrals of oscillatory functions.

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