Finite-part integral and boundary element method to solve three-dimensional crack problems in piezoelectric materials

Using the hypersingular integral equation method based on body force method, a planar crack in a three-dimensional transversely isotropic piezoelectric solid under mechanical and electrical loads is analyzed. This crack problem is reduced to solve a set of hypersingular integral equations. Compare w...

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Bibliographic Details
Published in:International journal of solids and structures 2007-07, Vol.44 (14), p.4770-4783
Main Authors: Qin, T.Y., Yu, Y.S., Noda, N.A.
Format: Article
Language:English
Subjects:
Body force method
Boundary element method
Crack
Hypersingular integral equation
Piezoelectric
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Summary:Using the hypersingular integral equation method based on body force method, a planar crack in a three-dimensional transversely isotropic piezoelectric solid under mechanical and electrical loads is analyzed. This crack problem is reduced to solve a set of hypersingular integral equations. Compare with the crack problems in elastic isotropic materials, it is shown that for the impermeable crack, the intensity factors for piezoelectric materials can be obtained from those for elastic isotropic materials. Based on the exact analytical solution of the singular stresses and electrical displacements near the crack front, the numerical method of the hypersingular integral equation is proposed by the finite-part integral method and boundary element method, which the square root models of the displacement and electric potential discontinuities in elements near the crack front are applied. Finally, the numerical solutions of the stress and electric field intensity factors of some examples are given.
ISSN:0020-7683
1879-2146
DOI:10.1016/j.ijsolstr.2006.12.002