Under the influence of axial forces and uniform temperature variations, the thermal buckling and postbuckling of composite beams reinforced of functionally graded multilayer graphene platelets (GPLs) resting on nonlinear elastic foundations are examined. The Halpin-Tsai model is used to calculate the elastic modulus of each layer of GPL-reinforced composite (GPLRC). According to the virtual work principle, the nonlinear governing equations for the beam are obtained from the first-order shear deformation beam theory. The impact of axial force and nonlinear elastic foundation on thermal buckling and postbuckling is discussed using the differential quadrature method (DQM), and the analytical expression is given by the two-step perturbation method (TSPM). The effects of axial force, boundary conditions, slenderness ratio, GPL geometry, GPL weight fraction, GPL distribution pattern, and elastic foundation coefficient on thermal buckling and postbuckling are examined through parameter analysis.

The strict theory of the complex variable function method for the sextuple harmonic equation is given in detail, which is a development of the work on the quadruple harmonic equation of the authors. Both of the above mentioned works develop the well-known Muskhelishvili complex variable function method for solving the biharmonic equation used in the classical theory of elasticity. Meanwhile, some applications to the elasticity, plasticity, and fracture theories of quasicrystalline materials have shown that the theory and method are successful and effective.