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

Abstract

Exact solutions are derived for three-dimensional, anisotropic, linearly magneto-electro-elastic, 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.

Modeling and analysis of loaded multilayered magnetoelectroelastic structures composite materials: Applications

“…The Eshelby-Stroh solution for the macroscale analysis of laminated piezo-electric composite structures has been used in earlier studies [12,13,14] …”

Exact Solutions for Simply Supported and Multilayered Piezothermoelastic Plates with Imperfect Interfaces

“…Three-dimensional analytical solutions for simplysupported plates continue to attract investigators' attention [1][2][3][4][5][6][7][8][9]. Various techniques including the asymptotic expansion scheme [7], the state space formulation [4,7], the Stroh formalism [6], the pseudo-Stroh formalism [8,9], and the transfer matrix (or propagator matrix) [2,[7][8][9] have been proposed in these studies.…”

Analytical Solution for Free Vibration of Multilayered Circular Plate

“…Among those structures, the composites made of piezoelectric (PE) and piezomagnetic (PM) layers were most frequently considered and some full-field exact solutions of these structures under certain boundary conditions were obtained. Pan and colleagues [1,2] derived the static and free vibration solutions for multilayered rectangular plates under simply-supported boundary conditions by using the Stroh formulism and propagation matrix methods. By applying the state vector approach and propagation matrix method, Wang et al [3] derived the exact solution of the multilayered plate under static deformation, Chen et al [4] extended the static solution to the vibration case, and Chen et al [5] discussed the modal analysis of the multilayered plates.…”