A virtual layers-state-space method for 3D responses of arbitrary functionally graded magnetoelectroelastic plates

Abstract

In this paper, a methodological approach for the three-dimensional static behavior of functionally graded magnetoelectroelastic rectangular plates is elaborated. The state-space method is used to establish the set of state-space equations for arbitrary graded functionalities throughout the thickness direction of multilayered composite plates. To solve the resulting state-space equations, a numerical scheme that consists of dividing the heterogeneous plate into a number of virtual layers having homogeneous properties calculated in the thickness average sense within the corresponding layer is elaborated. In each virtual homogeneous layer the propagator matrix method is used and a recursive relationship is resulted. The proposed mathematical modeling has been validated and the convergence according to the number of virtual layers has been analyzed. The obtained results are in agreement with the available ones given by the pseudo-Stroh formalism, the finite elements method, the modified Pagano method and the three-dimensional asymptotic approach. Various types of graded properties can be easily considered. It has been revealed that the materials properties gradient index and the loading conditions remarkably influence the static response of functionally graded composites plates.