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Axisymmetric interaction of a rigid disc with a transversely isotropic half‐space
Author(s) -
Katebi Amir Aabbas,
Khojasteh Ali,
Rahimian Mohammad,
Pak Ronald Y. S.
Publication year - 2010
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.854
Subject(s) - transverse isotropy , mathematical analysis , mathematics , isotropy , boundary value problem , displacement (psychology) , anisotropy , fredholm integral equation , representation (politics) , partial differential equation , integral equation , half space , space (punctuation) , equations of motion , physics , classical mechanics , computer science , psychology , quantum mechanics , politics , political science , law , psychotherapist , operating system
A theoretical formulation is presented for the determination of the interaction of a vertically loaded disc embedded in a transversely isotropic half‐space. By means of a complete representation using a displacement potential, it is shown that the governing equations of motion for this class of problems can be uncoupled into a fourth‐order partial differential equation. With the aid of Hankel transforms, a relaxed treatment of the mixed‐boundary value problem is formulated as dual integral equations, which, in turn, are reduced to a Fredholm equation of the second kind. In addition to furnishing a unified view of existing solutions for zero and infinite embedments, the present treatment reveals a severe boundary‐layer phenomenon, which is apt to be of interest to this class of problems in general. The present solutions are analytically in exact agreement with the existing solutions for a half‐space with isotropic material properties. To confirm the accuracy of the numerical evaluation of the integrals involved, numerical results are included for cases of different degrees of the material anisotropy and compared with existing solutions. Further numerical examples are also presented to elucidate the influence of the degree of the material anisotropy on the response. Copyright © 2009 John Wiley & Sons, Ltd.