Analysis of a piezoelectric finite wedge under antiplane concentrated loads

• Close form solutions of the antiplane problems of a finite piezoelectric wedge subjected to concentrated loads is obtained.
• Four different boundary conditions on the radial edge and the circular edge are investigated and the concentrated loads can be located in the full domain of the finite wedge.
• The derived solutions can be further employed as kernel functions to analyze the corresponding piezoelectric problems under distributed loads.

This paper analyzes the antiplane problem of a finite piezoelectric wedge subjected to concentrated loads. The piezoelectric wedge is assumed to be transversely isotropic with the poling direction along the x3x3 direction. The concentrated loads considered here involve screw dislocations with the Burgers vectors parallel to the poling direction. In addition, a line force and a line charge are applied at the core of the dislocation. Four different boundary conditions on the radial edge and the circular edge are investigated and the concentrated loads can be located in the full domain of the finite wedge. The analytical derivation is based on the complex variable, analytical continuation and the conformal mapping methods. The derived complex potentials show that the stress and electric displacement fields display r1−λr1−λ type of singularity near the wedge crack-tip when the wedge angle is larger than ππ. The obtained solutions then are used to calculate the electric-elastic fields and the crack-tip stress and electric displacement intensity factors. The results are further degenerated to several specific cases and are agreed well with existing ones.