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Exact solutions of the 2‐D frictional sliding contact problem of electrically insulated triangular and cylindrical punches on piezoelectric materials
Author(s) -
Zhou Y.T.,
Lee K.Y.
Publication year - 2013
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.201200030
Subject(s) - piezoelectricity , displacement (psychology) , electric displacement field , eigenvalues and eigenvectors , stress (linguistics) , mathematical analysis , coulomb's law , contact analysis , coulomb , electric potential , piezoelectric coefficient , contact mechanics , materials science , mechanics , mathematics , structural engineering , physics , composite material , engineering , finite element method , electrical engineering , voltage , psychology , linguistics , philosophy , quantum mechanics , psychotherapist , electron
The present paper performs an exact electro‐mechanical contact analysis for piezoelectric materials under a frictional sliding triangular or cylindrical punch. The Coulomb frictional law is used inside the contact region. Appropriate fundamental solutions that can lead to real solutions of electro‐mechanical quantities are derived for real and complex eigenvalues. A second kind singular integral equation of Cauchy type is obtained for the stated problem, whose exact solution can be found by using the excellent properties of Jacobi Polynomials. Closed‐form expressions of stress components and electrical displacement are obtained, which provide benchmark solutions for examining the frictional contact behaviors of piezoelectric materials. Numeric results are presented. The influences of the friction coefficient on the contact region, stress components and electric displacement are detailed.