Bending behavior of FGM-coated and FGM-undercoated plates with two simply supported opposite edges and two free edges

Abstract This investigation analyzes laminated plates with two simply supported opposite edges and two free edges subjected to transverse loads. Two situations are considered. The first involves a two-layer plate in which an FGM layer is coated on a homogeneous substrate, simply called an FGM-coated plate; the other involves a three-layer plate in which an FGM is employed for the inter-medium layer and different homogeneous materials are in the top and bottom layers; this is called an FGM-undercoated plate. The Young’s modulus of FGM plates is assumed to vary in the thickness direction and the Poisson’s ratio to remain constant throughout the FGM plate. The material gradations in FGM portion of the laminate structures follow sigmoid functions. Even though the FGM-coated or undercoated plates are formed from composite materials, the bending and in-plane problems in these FGM plates with constant Poisson’s ratio and varying Young’s modulus in the thickness direction under transverse loads only are uncoupled. For the multi-layer structures of interest, the calculations of the quantities, A 11 , B 11 , C 11 , Q 11 , S 11 , defined herein become very complex. Therefore this study proposes an alternative approach for easily and efficiently calculating them. The results reveal that the analytical solution to the bending problem of FGM plates obtained using a Fourier series expanding is strongly consistent with the finite element calculation. The deflections, strains, and stresses of FGM-coated and undercoated plates are evaluated and under discussion. The differences between the flexibility behaviors of FGM-coated and undercoated plates are investigated.