An Edge-based Smoothed MITC3+ Plate Element for Analysis of Multilayer Functionally Graded Graphene Nanoplatelet-Reinforced Composite Plates Based on a Third-order Shear Deformation Theory

This study presents bending, frequency, and buckling analyses of multilayer functionally graded graphene nanoplatelets (GPLs)-reinforced composite (FG GPLRC) plates. To address these problems, an edge-based smoothed MITC3[Formula: see text] plate element is developed based on Reddy’s third-order shear deformation theory (TSDT). The proposed element utilizes a model of seven displacement variables, independently approximated using [Formula: see text]-type shape functions, and enhanced by a cubic function related to a bubble node at the centroid of a three-node triangular element. To reduce discrepancies in the in-plane strains among nearby elements, the in-plane strain fields are averaged over domains formed by segments connecting common edge nodes to the bubble nodes of neighboring elements, referred to as the edge-based smoothed (ES) method. The [Formula: see text]-type presented element can be applied to both thin and thick plates, as transverse shear strains are re-interpolated at six tying points to ensure spatially isotropic behavior, in accordance with the mixed interpolation tensorial component (MITC3[Formula: see text]) technique. Compared to other approaches, the proposed ES-MITC3[Formula: see text] element demonstrates excellent performance and potential for bending, free vibration, and buckling analyses of multilayer FG GPLRC plates with diverse graphene nanoplatelet (GPL) distribution patterns in the polymer matrix, varying GPL weight fractions, length-to-thickness ratios, geometries, and boundary conditions. Parametric studies indicate that GPLs significantly enhance the stiffness of functionally graded plates.