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BEM for crack‐inclusion problems of plane thermopiezoelectric solids
Author(s) -
Qin Qing Hua,
Lu Meng
Publication year - 2000
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(20000710)48:7<1071::aid-nme917>3.0.co;2-w
Subject(s) - boundary element method , stress intensity factor , mathematics , mathematical analysis , electric displacement field , finite element method , plane (geometry) , boundary value problem , a priori and a posteriori , displacement (psychology) , boundary (topology) , piezoelectricity , structural engineering , geometry , materials science , engineering , composite material , psychology , philosophy , epistemology , psychotherapist
The problem of interactions between an inclusion and multiple cracks in a thermopiezoelectric solid is considered by boundary element method (BEM) in this paper. First of all, a BEM for the crack–inclusion problem is developed by way of potential variational principle, the concept of dislocation, and Green's function. In the BE model, the continuity condition of the interface between inclusion and matrix is satisfied, a priori , by the Green's function, and not involved in the boundary element equations. This is then followed by expressing the stress and electric displacement (SED) and elastic displacements and electric potential (EDEP) in terms of polynomials of complex variables ξ t and ξ k in the transformed ξ ‐plane in order to simulate SED intensity factors by the BEM. The least‐squares method incorporating the BE formulation can, then, be used to calculate SED intensity factors directly. Numerical results for a piezoelectric plate with one inclusion and a crack are presented to illustrate the application of the proposed formulation. Copyright © 2000 John Wiley & Sons, Ltd.