Partial Contact of an Elastic Coated Cylinder Pressed by a Rigid Flat Surface

Abstract

The normal contact of a frictionless elastic coated cylinder indented by a flat rigid surface is solved using a Michell–Fourier series expansion, which satisfies the mixed boundary value problem resulting from partial contact. The boundary conditions are chosen such that the elastic layer rests on the cylindrical substrate. When the contact region is small compared to the radius of curvature of the coated cylinder, semi-analytical solutions are obtained by exploiting dual series equation techniques. The stresses on the surface are evaluated for plane strain. The results may have application to coated cylindrical structures, bimaterial inclusions, or pin-joint contact.

Advancing contact of a 2D elastic curved beam indented by a rigid pin with clearance

“…The analytical approach adopted here is suggested by the studies [15][16][17], which investigated the plane contact problems of a circular inclusion embedded in an infinite elastic medium or in a thickwalled tube, as well as by the work [18], which addressed the problem of the indentation of an incomplete elastic ring by a rigid flat surface. By using a modified Michell solution for a biharmonic stress function in polar coordinates, these authors reduced the mixed boundary value problems with circular boundaries arising in the study of contact problems in 2D elasticity to dual trigonometric series and then to integral equations of the Fredholm type.…”

“…Since the loading condition is symmetric with respect to the vertical axis ( = 0), then following [18] and [21] we take the following cylindrical components of the stress, which are obtained by means of a biharmonic Airy stress function containing only even terms in , according to the Michell solution (for analytical details see Appendix A)…”

“…Then, we apply the procedure used in [18] for solving a set of dual series equations similar to eqns…”

“…The set of dual equations and (2.14) and (2.15) can now be solved by using the procedure proposed in [19] and adopted also in [18], based on the introduction of an auxiliary stress function  such that…”

“…where H denotes the unit step function. Then, the coefficients An of the Fourier cosine series expansion (2.18), for n ≥ 0, are given in [18,22]:…”