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IMA Journal of Applied Mathematics Advance Access originally published online on February 23, 2007
IMA Journal of Applied Mathematics 2007 72(2):180-190; doi:10.1093/imamat/hxl035
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© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Utilization of divergent integrals and a new symbolism in contact and crack analysis

V. I. Fabrikant**

Prisoner #167932D, Archambault Jail, Ste-Anne-des-Plaines, Quebec, Canada J0N 1H0

** Email: valery_fabrikant{at}hotmail.com


  Abstract

The main potential function, used for the complete solution of the contact and crack problems for elliptical domains, is presentable as an integral of an expression comprising a logarithm of a distance between two points. These integrals were considered to be impossible to compute, though various derivatives of these integrals were computed in the past. The new symbolism, introduced here, combined with utilization of divergent integrals, allows us to compute these integrals exactly and in a closed form. It also introduces a dramatic simplification in the final expressions and restores some mathematical symmetry and elegance.

Received on 15 June 2006. revised on 1 December 2006.


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