Nonlocal strain gradient analysis of FG GPLRC nanoscale plates based on isogeometric approach

In this paper, a nonlocal strain gradient isogeometric model based on the higher order shear deformation theory for free vibration analysis of functionally graded graphene platelet-reinforced composites (FG GPLRC) plates is performed. Various distributed patterns of graphene platelets (GPLs) in the polymer matrix including uniform and non-uniform are considered. To capture size dependence of nanostructures, the nonlocal strain gradient theory including both nonlocal and strain gradient effects is used. Based on the modified Halpin–Tsai model, the effective Young’s modulus of the nanocomposites is expressed, while the Poisson’s ratio and density are established using the rule of mixtures. Natural frequencies of FG GPLRC nanoplates is determined using isogeometric analysis. The effects played by strain gradient parameter, distributions of GPLs, thickness-to-length ratio, and nonlocal parameter are examined, and results illustrate the interesting dynamic phenomenon. Several results are investigated and considered as benchmark results for further studies on the FG GPLRC nanoplates.