An exact Peano Series solution for bending analysis of imperfect layered functionally graded neutral magneto-electro-elastic plates resting on elastic foundations

In this article, a three-dimensional solution is presented for the bending analysis of functionally graded and layered neutral magneto-electro-elastic plates resting on two-parameter elastic foundations, considering imperfect interfacial bonding. The equations of motion, Gauss's equations for electrostatics and magnetostatics, and boundary and interface conditions are satisfied exactly regardless of the number of layers. No assumptions on deformations, stresses, and magnetic and electric fields along the thickness direction are introduced. The interfacial imperfection is modeled using a generalized spring layer. The state-space method is employed for solving the governing partial differential equations. Effects of a two-parameter elastic foundation, gradient index, bonding imperfection, and applied mechanical and electrical loads on the response of the functionally graded magneto-electro-elastic plate are discussed. The obtained exact solution can serve as a benchmark for assessing the accuracy of layered functionally graded magneto-electro-elastic plate theories.