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A three-dimensional (3D) Peano series solution is presented for the static analysis of functionally graded (FG) and layered magneto-electro-elastic (MEE) plates resting on elastic foundations with considering imperfect interfacial bonding. The interfacial imperfection is modeled using a generalized spring layer. Regardless of the number of layers, the equations of motion, Gauss’ equations for electrostatics and magnetostatics, the boundary and interface conditions are satisfied exactly. No assumption on deformations, stresses, magnetic and electric field along the thickness direction is introduced. The governing partial differential equations are finally solved using the state-space method. The present formulation has been validated through comparison with other similar works available in the open literature. Effects of two-parameter elastic foundation, gradient index, bonding imperfection, applied mechanical and electrical loads on the static and dynamic response of the functionally graded magneto-electro-elastic (FGMEE) plate are discussed. It is worthy to note that the present novel exact formulation includes all previous solutions, such as piezoelectric, piezomagnetic, purely elastic solution, elastic foundation and interlayer slip problems, as special cases. The obtained exact solution can be used to assess the accuracy of layered FGMEE plate theories and/or validating finite element codes.

Keywords: Functionally materials, Exact solution, Magneto-electro-elastic plates

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