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Green's function for
symmetric loading of an elastic sphere with application to
contact problems
Alexey S. Titovich and Andrew N. Norris |
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Vol. 7 (2012), No. 7, 701–719
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Abstract |
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A compact form for the static Green’s function for symmetric loading of an elastic sphere is derived. The expression captures the singularity in closed form using standard functions and quickly convergent series. Applications to problems involving contact between elastic spheres are discussed. An exact solution for a point load on a sphere is presented and subsequently generalized for distributed loads. Examples for constant and Hertzian-type distributed loads are provided, where the latter is also compared to the Hertz contact theory for identical spheres. The results show that the form of the loading assumed in Hertz contact theory is valid for contact angles up to about ten degrees. For larger angles, the actual displacement is smaller and the contact surface is no longer flat. |
Keywords
Green's function, sphere, contact
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Milestones
Received: 18 April 2012
Revised: 4 August 2012
Accepted: 11 August 2012
Published: 4 January 2013
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Authors |
| Alexey S. Titovich | |
| Department of Mechanical and
Aerospace Engineering Rutgers University 98 Brett Road Piscataway, NJ 08854-8058 United States |
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| Andrew N. Norris | |
| Department of Mechanical and
Aerospace Engineering Rutgers University 98 Brett Road Piscataway, NJ 08854-8058 United States |
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