This article proposes a new coupled meshless method, which can be called as coupled Carrera unified formulation (CUF)-meshless local Petrov–Galerkin (MLPG) method. Since no elements are required neither for interpolation of the trial and test functions nor for integration of governing equations, MLPG is known as a truly meshless method. Combining this method with the CUF with high expansion order offers an effective method for dynamic analysis of functionally graded multilayered graphene platelets (GPLs)-carbon nanotubes (CNTs) reinforced thick composite plates. The polynomial augmented radial point interpolation method (PA-RPIM) is used for constructing the shape function. The CUF is employed to facilitate the full 3D formulation into a 2D advanced model for plates. GPLs and CNTs are assumed to be uniformly dispersed in each individual layer while the nanofiller volume fraction of layers shows a continuous variation through the thickness direction. A modified Halpin–Tsai micromechanical model is used to evaluate the effective elasticity modulus of each GPL-CNT reinforced layer and the effective Poisson’s ratio, and mass density are evaluated by the rule of mixture. The results obtained by the proposed method are compared with the analytical and numerical results published in the literature. The influences of the key parameters such as aspect ratio of plate, GPL and CNT volume fraction, number of layers, and layer distribution patterns are demonstrated by several numerical examples. Results show that combining MLPG and CUF yields to a suitable method for dynamic analysis of thick multilayer functionally graded GPL-CNT reinforced plates.

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