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Basic solution of four 3‐D rectangular limited‐permeable cracks in piezoelectric materials
Author(s) -
Liu J.Y.,
Zhou Z.G.,
Zhou B.B.
Publication year - 2012
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.201100106
Subject(s) - electric displacement field , piezoelectricity , displacement (psychology) , materials science , permittivity , fourier transform , stress intensity factor , integral transform , mathematical analysis , crack tip opening displacement , mathematics , mechanics , fracture mechanics , composite material , dielectric , physics , psychology , optoelectronics , psychotherapist
Abstract The solution of four 3‐D rectangular limited‐permeable cracks in piezoelectric materials were given by using the generalized Almansi's theorem and the Schmidt method. At the same time, the electric permittivity of the air inside the rectangular crack was considered. The problem was formulated through Fourier transform as three pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Finally, the effects of the electric permittivity of the air inside the rectangular crack, the shape of the rectangular crack and the distance among four rectangular cracks on the stress and electric displacement intensity factors in piezoelectric materials were analyzed.