Electroelastic analysis of a piezoelectric finite wedge with mixed type boundary conditions under a pair of concentrated shear forces and free charges

The antiplane problem of a piezoelectric finite wedge with mixed type boundary conditions (i.e. traction free-electrically grounded or clamped-electrically insulated) assumed on the circular edge is studied in this paper. Using the first and second kinds of the finite Mellin transforms, the stress and electrical displacement in the piezoelectric finite wedge subjected to a pair of concentrated shear forces and free charges are derived analytically. The singularity orders and all generalized intensity factors can also be obtained. After being reduced to the crack problem, the energy density theory is applied to study the effects of the boundary conditions on the circular edge and the wedge radius on the fracture behaviors of the cracked piezoelectric medium. The problem can be further degenerated to several simple problems and the results agree well with those of previous studies.