Generalized Plane Strain Thermopiezoelectric Analysis of Multilayered Plates

The generalized plane strain thermopiezoelectric deformations of laminated thick plates are analyzed using the Eshelby-Stroh formalism. The laminated plate consists of homogeneous laminae of arbitrary thicknesses. The three-dimensional equations of linear anisotropic thermopiezoelectricity simplified to the case of generalized plane strain deformations are exactly satisfied at every point in the body. The analytical solution is in terms of an infinite series. The continuity conditions at the interfaces and boundary conditions at the top and bottom surfaces and edges are used to determine coefficients in the series. The formulation admits different thermal, electrical, and mechanical boundary conditions at the edges of each lamina and is applicable to thick and thin laminated plates. Laminated plates containing piezoelectric laminae poled either in the thickness direction or in the axial direction are analyzed, and results are presented for plates with edges either rigidly clamped, simply supported, or traction-free.