Exact solutions are derived for three-dimensional, anisotropic, linearly magneto-electroelastic, simply-supported, and multilayered rectangular plates under static loadings. While the homogeneous solutions are obtained in terms of a new and simple formalism that resemble the Stroh formalism, solutions for multilayered plates are expressed in terms of the propagator matrix. The present solutions include all the previous solutions, such as piezoelectric, piezomagnetic, purely elastic solutions, as special cases, and can therefore serve as benchmarks to check various thick plate theories and numerical methods used for the modeling of layered composite structures. Typical numerical examples are presented and discussed for layered piezoelectric/piezomagnetic plates under surface and internal loads.

https://blogs.uakron.edu/ernianpan/files/2014/09/046_2001JAMPanMEESimpleSupport.pdf

Exact Solution for Simply Supported and Multilayered Magneto-Electro-Elastic Plates

Three-dimensional exact analysis of a simply supported functionally gradient piezoelectric plate

On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates

This paper presents a single-domain boundary element method (BEM) analysis of fracture mechanics in 2D anisotropic piezoelectric solids. In this analysis, the extended displacement (elastic displacement and electrical potential) and extended traction (elastic traction and electrical displacement) integral equations are collocated on the outside boundary (no-crack boundary) of the problem and on one side of the crack surface, respectively. The Green's functions for the anisotropic piezoelectric solids in an infinite plane, a half plane, and two joined dissimilar half-planes are also derived using the complex variable function method. The extrapolation of the extended relative crack displacement is employed to calculate the extended `stress intensity factors' (SIFs), i.e., K I , K II , K III and K IV . For a finite crack in an infinite anisotropic piezoelectric solid, the extended SIFs obtained with the current numerical formulation were found to be very close to the exact solutions. For a central and inclined crack in a finite and anisotropic piezoelectric solid, we found that both the coupled and uncoupled (i.e., the piezoelectric coefficient e ijk =0) cases predict very similar stress intensity factors K I and K II when a uniform tension σ yy is applied, and very similar electric displacement intensity factor K IV when a uniform electrical displacement D y is applied. However, the relative crack displacement and electrical potential along the crack surface are quite different for the coupled and uncoupled cases. Furthermore, for a inclined crack within a finite domain, we found that while a uniform σ yy (=1 N m −2 ) induces only a very small electrical displacement intensity factor (in the unit of Cm −3/2 ), a uniform D y (=1 C m −2 ) can produce very large stress intensity factors (in the unit of Nm −3/2 ).

https://blogs.uakron.edu/ernianpan/files/2014/09/035_1999EABEPan2DPiezoBem.pdf

A BEM analysis of fracture mechanics in 2D anisotropic piezoelectric solids

A smart functionally graded plate consists of a plate made of a functionally gradient material and actuators made of an active material. The active material, a layer or set of patches, is bonded on the metal-rich surface of the functionally graded plate. When the ceramic-rich surface of the substrate is subjected to thermomechanical loadings, displacements, and stresses may be controlled, and vibration amplitudes may be suppressed by the actuators with supplied electric power. In the attempt towards a basic understanding of the new type of smart structural system, this study considers a benchmark problem, namely, the bending of a functionally graded rectangular plate with an attached piezoelectric actuator. The transfer matrix and asymptotic expansion techniques are employed to obtain a three-dimensional asymptotic solution. In numerical computations, the locally effective material properties of the functionally gradient material are estimated by the Mori-Tanaka scheme, The three-dimensional distributions of displacements and stresses for different volume fractions of the ceramic and metallic constituents could serve as benchmark results to assess approximate theories and numerical methods.

Jong S. Lee

Papers

Exact electroelastic analysis of piezoelectric laminae via state space approach