On the frictionless axi-symmetric contact of a thick elastic layer and the associated squeeze film problem

Abstract

The problem of the frictionless axi-symmetric indentation between a thick elastic layer (the contact radius does not exceed the layer thickness) and a rigid spherical indenter is investigated. The kernel of the governing integral equation was broken down into two parts. The first corresponds to the Hertzian solution and the second represents the contribution due to the finite layer thickness. The second part was approximated by an absolute and uniform convergent series. Hence, the governing elasticity equation was reduced to a set of linear equations.

A set of simple formulae for the contact pressure, total load, and penetration depth are presented. The obtained formulae were compared with the existing numerical results where good agreement was found. Furthermore, the associated squeeze film problem is examined. Expressions for the variation of the film thickness with time were derived using two different pressure conditions.

Keywords

Bessel function of the first kind spherical punch orthogonality modified Legendre polynomials squeeze film

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