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An axi-symmetric contact problem : the constriction of elastic cylinders under axial compression Allwood, Derek Anthony


The compression of fairly short solid cylinders under axial load is considered. A preliminary investigation examines the displacements produced by the superposition of a prescribed surface loading. This is followed by the more interesting problem in which the radial displacement is prescribed over part of the surface, the remaining part of the surface being stress free. Two types of elastic materials are considered; firstly, rubber-like materials governed by a strain energy function of the Mooney form, and secondly, metals which have a quadratic strain energy function. In the former case a finite axial compression is permitted prior to imposing any constraint on the outer curved surface of the cylinder. In all cases the irregularities introduced by the constraints are sufficiently small that they can be described by infinitesimal elasticity theory. The analysis utilizes displacement potential functions and the main problem is reduced to solving a set of dual cosine series. The particular case of the contact problem in which the cylinder height is equal to the radius is examined in detail and the contact stresses are given graphically.

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