Vol. 7, No. 7, 2012

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ISSN: 1559-3959
Green's function for symmetric loading of an elastic sphere with application to contact problems

Alexey S. Titovich and Andrew N. Norris

Vol. 7 (2012), No. 7, 701–719
Abstract

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
Milestones
Received: 18 April 2012
Revised: 4 August 2012
Accepted: 11 August 2012
Published: 4 January 2013
Authors
Alexey S. Titovich
Department of Mechanical and Aerospace Engineering
Rutgers University
98 Brett Road
Piscataway, NJ 08854-8058
United States
Andrew N. Norris
Department of Mechanical and Aerospace Engineering
Rutgers University
98 Brett Road
Piscataway, NJ 08854-8058
United States