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TECHNICAL PAPERS

Partial Plane Contact of an Elastic Curved Beam Pressed by a Flat Surface

[+] Author and Article Information
Joseph M. Block

Department of Mechanical Engineering,  Northwestern University, 2145 Sheridan Road, Evanston, IL 60208

Leon M. Keer1

Department of Mechanical Engineering,  Northwestern University, 2145 Sheridan Road, Evanston, IL 60208l-keer@northwestern.edu

1

Corresponding author.

J. Tribol 129(1), 60-64 (Aug 31, 2006) (5 pages) doi:10.1115/1.2401212 History: Received April 06, 2006; Revised August 31, 2006

The normal contact of a frictionless, elastic curved beam 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. When the contact region is small compared to the radius of curvature of the beam, semi-analytical solutions are obtained by exploiting dual series equation techniques. The relation between the level of loading and the extent of contact, as well as stress on the surface, are found for plane strain. The elasticity results extend Hertz line contact to finite thickness, curved beams. As the beam becomes thin, beam theory type behavior is recovered. The results may have application to finite-thickness wavy surfaces, cylindrical structures, or pressurized seals.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Partial plane contact of an elastic, smooth curved beam pressed by a flat, rigid surface

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Figure 2

Surface stress for θc=5deg, θ0=15deg, ν=0.3

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Figure 3

Comparison of surface stress between Hertz theory and Elasticity solution for θc=3deg, θ0=90deg, ν=0.3,α=0

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Figure 4

Thin semi-circular beam in contact with flat surface with total load P, shown here for θ0=π∕2

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Figure 5

Normalized total load versus contact angle for (a) θ0=90deg, ν=0.3; and (b) θ0=45deg, ν=0.3

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