Static and dynamic analyses of FG-GNPs reinforced porous nanocomposite annular micro-plates based on MSGT

The metal foams are widely used in different areas of technologies due to their both, low specific weight and good stiffness. Adding nanofillers as reinforcement to metal foams makes them stiffer while keeping their lightweight. Graphene nanoplatelets (GNPs) are recently known as the best nanofillers due to their exciting features such as high Young's modulus and extremely high thermal conductivity. In the present article, bending, buckling, and free vibration analyses of micro-scaled functionally graded GNPs reinforced porous nanocomposite annular plate located on the bi-parameter elastic foundation exposed to hygro-thermo-mechanical loads are carried out. The GNPs reinforcement and also porous matrix properties are functionally graded along with the plate's thickness based on overall sixteen combination patterns. The Gaussian random field (GRF) scheme for closed-cell cellular solids is considered for the porous matrix properties, and the effective properties of the porous nanocomposite micro plate are determined via Halpin-Tsai and extended rule of mixture (ERM) micromechanics models. The modified strain gradient theory (MSGT) suggesting three material length-scale parameters is employed to cope with the size effect, and the shear deformation effects are taken into account using the first-order shear deformation theory (FSDT). The governing differential equations are derived using energy method and variational approach. The normalized, discretized equations are then solved using the generalized differential quadrature (GDQ) scheme for various boundary conditions. The reliability of the results is ensured by comparing with the previously published ones in the literature for simpler cases. The influence of the prominent parameters on the results is considered.