In the present paper, a composite finite element is proposed using the assumed natural strain (ANS) method, which is based on the unified strain interpolations and the minimized potential energy. In the proposed formulation, the linearized weak form of compatibility and equilibrium equations is obtained for the geometrically nonlinear analysis. Additionally, the parabolic strain interpolation functions without any shear correction coefficient are imposed into the first-order shear deformation theory (FSDT) to verify the zero shear stresses condition at the top and bottom surfaces. The iterative arc-length method is applied to handle the post-buckling and free vibration responses. For the micromechanical part, the effective elasticity modulus based on the modified Halpin–Tsai micromechanical model is attained to analyze functionally graded graphene platelet-reinforced composite (FG-GPLRC) plates with and without hole. Furthermore, the effective mass density and the Poisson’s ratio are assessed via the rule of mixture. Therefore, the major novelty of this paper is in detecting the nonlinear thermomechanical behavior of GPLRC plates using robust strain-based interpolations. Hence, nonlinear equilibrium paths are plotted to illustrate the effects of different boundary conditions, weight fractions and distribution schemes on GPLRC plates.
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