Open Access

ARTICLE

Analytical Full-field Solutions of a Piezoelectric Layered Half-plane Subjected to Generalized Loadings

Chien-Ching Ma^1,2, Wen-Cha Wu²

1 Corresponding author. Tel.: +886-2-23659996; Fax: +886-2-23631755; E-mail: ccma@ntu.edu.tw
2 Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617, Re-public of China

Computers, Materials & Continua 2009, 11(2), 79-108. https://doi.org/10.3970/cmc.2009.011.079

Abstract

The two-dimensional problem of a planar transversely isotropic piezoelectric layered half-plane subjected to generalized line forces and edge dislocations in the layer is analyzed by using the Fourier-transform method and the series expansion technique. The full-field solutions for displacements, stresses, electrical displacements and electric fields are expressed in explicit closed forms. The complete solutions consist only of the simplest solutions for an infinite piezoelectric medium with applied loadings. It is shown in this study that the physical meaning of this solution is the image method. The explicit solutions include Green's function for originally applied loadings in an infinite piezoelectric medium and the remaining terms are image singularities which are induced to satisfy free surface and interface continuity conditions. The mathematical method used in this study provides an automatic determination for the locations and magnitudes of all image singularities. The locations and magnitudes of image singularities are dependent on the piezoelectric material constants of the layered half-plane and the location of the applied loading. With the aid of the generalized Peach-Koehler formula, the image forces acting on dislocations are derived from the full-field solutions of the generalized stresses. Numerical results for the full-field distributions of stresses and electric fields in the piezoelectric layered half-plane and image forces for edge dislocations are presented based on the available analytical solutions.

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