## 1 Introduction  
As a new family of advanced materials, carbon-based nanofiller reinforced composites have been gaining popularity in both academia and industry over the past decades [1]. Graphene, a two-dimensional single layer of carbon atoms, has been predicted to be a potential nanofiller due to the high thermal conductivity, superior mechanical properties and excellent electronic transport properties. These excellent properties, together with the interface chemistry and nanoscale effects, make graphene an opportunity as novel fillers in polymer nanocomposites [2; 3]. However, the pristine graphene is not suitable to form homogeneous composites with organic polymers [4]. Recently it has been theoretically and experimentally proven that the addition in very small quantities of graphene platelets (GPLs), a kind of graphene derivative, into a pristine polymer matrix can improve mechanical properties of the resulting nanocomposites significantly [3; 5]. Moreover, GPLs have a much larger specific surface area which provides much stronger bonding with the matrix, hence a greatly increased load transfer capability, and they are thus thought to be promising nano-fillers to develop high performance nanocomposites [6; 7]. Based on functionally graded materials (FGMs), [PERSON] and his co-workers proposed functionally graded graphene platelet reinforced nanocomposites (FG-GPLRCs), and they found that adding the nanofillers into polymer matrix at a certain gradient can promote the mechanical properties of the nanocomposite dramatically. [PERSON] et al. [8; 9] discussed the nonlinear static bending and free vibration of laminated beams reinforced with GPLs distributed non-uniformly by using the Timoshenko beam theory. [PERSON] et al. [10] studied the dynamic instability of FG-GPLRCs beams based on the first-order shear deformation theory (FSDT) considering the thermal effects. [PERSON] et al. [11]used the FSDT to examine the buckling and post-buckling of FG-GPLRC beam on a two-parameter elastic foundation. [PERSON] et al. [12; 13] utilized the generalized Mian and Spencer method to investigate the thermoelastic bending behaviors of rectangular, circular and annular plates reinforced with GPLs distributed non-uniformly along the thickness direction. [PERSON] et al. [14; 15] analyzed the free and forced vibrations, buckling and post-buckling characteristics of functionally graded multilayer graphene nanoplatelets reinforced polymer composite plates. [PERSON] et al. [16] examined the free vibration and static buckling of functionally graded porous nanocomposite plates reinforced with GPLs with the aid of the Chebyshev-Ritz method. [PERSON] et al. [17; 18] presented analytical solutions for free vibration and buckling of closed-cell metal foam cylindrical shell reinforced with GPLs. [PERSON] et al. [19] evaluated buckling and free vibration analyses of FG-GPLRC cylindrical shell under initially stresses from the view of three-dimensional elasticity. [PERSON] et al. [20] predicted dynamic response of a spinning functionally graded graphene reinforced cylindrical shell under the low-velocity impact. Following the pioneering work on FG-GPLRCs, [PERSON] and [PERSON] [21] examined the nonlinear instability of FG-GPLRCs nanoshells by considering the nonlocal effects. [PERSON] et al. carried out the nonlinear vibration [22; 23], nonlinear bending [24], thermal buckling and post-buckling [25] analyses of various structures, including beams, plates and shells, respectively. Composite and sandwich arches or curved beams are being used in various automotive, aerospace, bridge, medical and sports applications, to name a few, due to their high ratio of strength to weight. [PERSON] et al. [26] investigated the buckling behaviors of radial loaded FG-GPLRC shallow arches under the constraints of elastic rotations. [PERSON] et al. [27; 28] evaluated the in-plane nonlinear equilibrium, buckling and post-buckling of FG-GPLRC arches with fixed and pinned supports under a central point load and thermo-mechanical loading, respectively. [PERSON] al.