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Complete solution to elastic field around an elliptic punch
Author(s) -
Roy A.,
Basu U.
Publication year - 2011
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201000068
Subject(s) - cartesian coordinate system , mathematical analysis , elliptic integral , indentation , bessel function , half space , transverse isotropy , isotropy , mathematics , displacement (psychology) , exact solutions in general relativity , plane (geometry) , stress field , displacement field , coordinate system , geometry , physics , finite element method , materials science , optics , psychology , composite material , psychotherapist , thermodynamics
The problem of a rigid flat indentor resting on a transversely isotropic medium under external forces is reexamined. The contacting surface is an elliptic region. Both normal and tangential indentation are considered. Unlike the usual approach, we do not use ellipsoidal co‐ordinate system. The integral equations for prescribed normal and tangential indentation are first solved in cartesian co‐ordinate system for the unknown stress on the contact plane. A series of transformation and known results of integrals involving Bessel functions are then used to derive exact and complete solutions to the displacement and stress inside the half space. The result is exact in the sense that it involves a finite integration which must be evaluated numerically. Such a complete solution to the elliptic punch problem in cartesian co‐ordinate has not been obtained before. We also obtain the asymptotic form of the field near the border of the contact region. The corresponding result for an isotropic medium is obtained by a limiting process.