Decoupled formulation of piezoelectric elasticity under generalized plane deformation and its application to wedge problems

This paper presents the formulation of piezoelectric elasticity under generalized plane deformation derived from the three-dimensional theory. There are four decoupled classes in the generalized plane deformation formulation, i.e. when l3ðlÞ ¼ l 2ðlÞ ¼ 0, l3ðlÞ ¼ l 3ðlÞ ¼ 0, l 3ðlÞ ¼ l 2ðlÞ ¼ 0 or l3ðlÞ ¼ l 3ðlÞ ¼ l 2ðlÞ ¼ 0. Only the inplane fields of the first class and the antiplane field of the second class include the piezoelectric effect. Several examples of wedge problem often encountered in smart structures, such as sensors or actuators are studied to examine the stress singularity near the apex of the structure. The bonded materials to the PZT-4 wedge are PZT-5, graphite/epoxy or aluminum (conductor). The influencing factors on the singular behavior of the electro-elastic fields include the wedge angle, material type, poling direction, and the boundary and interface conditions. The numerical results of the first case are compared with Xu’s graphs and some comments are made in detail. In addition, some new results regarding the antiplane stress singularity of the second class are obtained via the case study. The coupled singularity solutions under generalized plane deformation are also investigated to seek the conditions of the weakest or vanishing singular stress fields