Full-field analysis of three dimensional piezoelectric layered half-space with point loading

• Published in: European journal of mechanics, A, Solids Vol. 42; pp. 158 - 175
• Main Author: Lin, Ru-Li
• Format: Journal Article
• Language: English
• Published: Elsevier Masson SAS 01.11.2013
• Subjects: Electric fields; Half spaces; Image method; Layered half-space; Mathematical analysis; Mathematical models; Piezoelectricity; Singularities; Three dimensional; Transversely isotropic piezoelectric material; Layered half-space; Image method; Transversely isotropic piezoelectric material
• ISSN: 0997-7538; 1873-7285
• DOI: 10.1016/j.euromechsol.2013.05.001

In this study, a three dimensional transversely isotropic piezoelectric layered half-space subjected to concentrated loading and electric charge was analyzed. This paper provides an effective analytical methodology to obtain the explicit full-field solutions for this problem. Due to the dissimilar structures of the solutions, the applied loadings are separated into axis-symmetric loadings and non-symmetric loadings. By using the double Fourier transformation technique in conjunction with series expansion, the explicit closed-from solutions for displacements, stresses, and the electric field in the layered half-space are obtained. The analytical solutions are valid for loadings applied either in the interior or at the surface of the structure. It can be seen that the complete solutions obtained by the method used in this study comprise only the fundamental solutions of an infinite space with a concentrated loading. One of the fundamental solutions is the Green's function of an infinite space and the others are solutions induced to satisfy the boundary and interface conditions. The mathematical meaning of the method used in the study is in fact the image method or Mindlin's superposition method. Instead of finding image singularities manually, the intensity and locations of the image singularities are determined automatically from the mathematical technique used in this paper. Taking PZT materials as an example, the numerical computation for the full-field distributions of the displacement and electric field in the layered half-space medium subjected to a point force and a point charge was discussed. •We obtained the solution analytically of a three-dimensional piezoelectric body.•The case for the loading applied in the layer or in the half-space was considered.•Both axis-symmetric and non-symmetric loadings are investigated in the paper.•The mathematical meaning of the solution obtained in the study is the image method.•Numerical examples for the full-field distributions are shown in the Figures.