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Loves rectangular contact problem revisited A complete solution.pdf
Tribology International 103 (2016) 331–342
Contents lists available at ScienceDirect
Tribology International
journal homepage: /locate/triboint
Loves rectangular contact problem revisited: A complete solution
Xiaoqing Jin a,n, Feifei Niu a, Xiangning Zhang a, Qinghua Zhou b, Ding Lyu a, Leon M. Keer c, Yumei Hu a
a State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing, China b School of Aeronautics Astronautics, Sichuan University, Chengdu, China c Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA
article info
Article history: Received 21 April 2016 Received in revised form 7 July 2016 Accepted 19 July 2016 Available online 20 July 2016
Keywords: Rectangular contact Elementary solution Greens function Response primitive function
abstract
Loves rectangular contact solution was recognized as the key ingredient in developing fast Fourier Transform related algorithms for computational contact analyses. This paper proposes an effective notation to simplify the analytical derivations, which are only carried out on the primitive functions. The complete solution of the stresses and displacements, together with the surface de?ection, produced by the both uniform normal and tangential loadings over a rectangular patch are solved in a more compact and consistent way, with explicit closed-form solutions optimized for computational ef?ciency and numerical stability. The correlation to the Greens functions due to Boussinesq and Cerruti is also noted. The present work complements the existing literature and provides a complete reference to the classical contact solution.
2016 Elsevier Ltd. All rights reserved.
1. Introduction
Contact analyses, which can be traced back to the work of Hertz [1], have a broad spectrum of applications in engineering ?elds, including wheel rail contact, as well as mechanisms of friction, wear and fatigue in bearings and gears. A basic problem in contact mechanics is to ?nd the stresses and de
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