Symplectic model for piezoelectric wedges and its application in analysis of electroelastic singularities

In this paper, a symplectic model, based on the Hamiltonian system, is developed for analyzing singularities near the apex of a multi-dissimilar piezoelectric wedge under antiplane deformation. The derivation is based on a modified Hellinger-Reissner generalized variational principle or a differential equation approach. The study indicates that the order of singularity depends directly on the non-zero eigenvalue of the proposed Hamiltonian operator. Using the coordinate transformation technique and continuity conditions on the interface between two dissimilar materials, the orders of singularity for multi-dissimilar piezoelectric and piezoelectric-elastic composite wedges are determined. Numerical examples are considered to show potential applications and validity of the proposed method. It is found that the order of singularity also depends on the piezoelectric constant, in addition to the geometry and shear modulus.