Generalized Plane Strain Thermopiezoelectric Analysis of Multilayered Plates

Abstract

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.Smart structures, consisting of piezoelectric materials integrated with structural systems, have found widespread use in engineering applications. Piezoelectric materials are capable of altering the structure's response through sensing, actuation, and control. They exhibit two basic electromechanical phenomena that have led to their use as sensors and actuators in the control of structural systems. In sensor applications, an applied mechanical strain induces an electric potential in the material due to the direct piezoelectric effect; whereas in actuator applications, an applied electric field causes the material to deform. Of the 21 crystal classes that

Improved shell finite element for piezothermoelastic analysis of smart fiber reinforced composite structures

“…Görnandt and Gabbert [20] presented a general finite element concept based on a weak formulation of the equilibrium conditions and the coupled constitutive equations of this thermo-piezoelectric problem to solve such problems numerically. Vel and Batra [21,22] developed a three-dimensional analytical solution in terms of an infinite series for the thermopiezoelectric deformations of laminated thick plates with various support edges. Ganesan and Kadoli [23] analyzed the piezoelectric composite cylindrical shells operating in a steady state axisymmetric temperature using a semi-analytical finite element method.…”

Three-dimensional analysis of the coupled thermo-piezoelectro-mechanical behaviour of multilayered plates using the differential quadrature technique

“…The second example considered is a three-layered cross-ply plate (Vel and Batra, 2003). The two bottom layers are made of Gr/Ep material and the top is a thickness-poled PZT-5A layer.…”

Three-Dimensional transient heat conduction in a functionally graded thick plate with a higher-order plate theory and a meshless local Petrov-Galerkin method

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