This paper investigates the buckling and postbuckling behaviours of functionally graded multilayer nanocomposite beams reinforced with a low content of graphene platelets (GPLs) resting on an elastic foundation. It is assumed that GPLs are randomly oriented and uniformly dispersed in each individual GPL-reinforced composite (GPLRC) layer with its weight fraction varying layerwise along the thickness direction. The effective material properties of each layer are estimated by the Halpin-Tsai micromechanics model. The nonlinear governing equations of the beam on an elastic foundation are derived within the framework of the firstorder shear deformation beam theory then are converted into a nonlinear algebraic system by using the differential quadrature method. A detailed parametric study is carried out to examine the effects of the distribution pattern, weight fraction, geometry and size of GPL nanofillers, foundation stiffness parameters, slenderness ratio and boundary conditions on the buckling and postbuckling behaviours. The results show that GPLs have a remarkable reinforcing effect on the buckling and postbuckling of nanocomposite beams.

This paper studies the dynamic instability of functionally graded multilayer nanocomposite beams reinforced with a low content of graphene nanoplatelets (GPLs) and subjected to a combined action of a periodic axial force and a temperature change. The weight fraction of GPL nanofillers is assumed to be constant in each individual GPL-reinforced composite (GPLRC) layer but follows a layerwise variation across the beam thickness. The Halpin-Tsai micromechanics model is used to estimate the effective Young's modulus of GPLRC layers. The differential quadrature method is employed to convert the partial differential governing equations into a linear system of Mathieu-Hill equations, from which the principle unstable region of functionally graded multilayer GPLRC beams is determined by Bolotin's method. Special attention is given to the effects of GPL distribution pattern, weight fraction, geometry and dimension on the dynamic instability behaviour. The thermal buckling and free vibration are also discussed as subset problems. Numerical results show that distributing more GPLs near the top and bottom surfaces can effectively increase the natural frequency and reduce the size of the unstable region. The influences of GPL geometry and dimension tend to be insignificant when the GPL width-to-thickness ratio is larger than 10 3 .

This paper investigates the free vibration and elastic buckling of sandwich beams with a stiff core and functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets within the framework of Timoshenko beam theory. The material properties of FG-CNTRCs are assumed to vary in the thickness direction, and are estimated through a micromechanical model. The governing equations and boundary conditions are derived by using Hamilton's principle and discretized by employing the differential quadrature (DQ) method to obtain the natural frequency and critical buckling load of the sandwich beam. A detailed parametric study is conducted to study the effects of carbon nanotube volume fraction, core-to-face sheet thickness ratio, slenderness ratio, and end supports on the free vibration characteristics and buckling behavior of sandwich beams with FG-CNTRC face sheets. The vibration behavior of the sandwich beam under an initial axial force is also discussed. Numerical results for sandwich beams with uniformly distributed carbon nanotube-reinforced composite (UD-CNTRC) face sheets are also provided for comparison.

This paper deals with the thermal buckling and postbuckling of functionally graded multilayer nanocomposite plates reinforced with a low content of graphene platelets (GPLs). It is assumed that GPL reinforcements are randomly oriented and uniformly dispersed in each individual GPL-reinforced composite (GPLRC) layer but the concentration follows a layerwise variation across the plate thickness. The modified Halpin-Tsai micromechanics model that takes into account the GPL geometry effect is adopted to estimate the effective Young's modulus of GPLRC layers. Within the framework of the first-order shear deformation theory, the nonlinear governing equations are derived by applying the principle of virtual displacements and then solved by using a differential quadrature-based iteration technique. Parametric studies are conducted to examine the influences of GPL distribution pattern, concentration and geometry, as well as in-plane force on the thermal buckling and postbuckling behaviours. Our results show that distributing more GPLs near the surface layers is capable of reinforcing the thermal buckling and postbuckling performances of GPLRC plates. Whether the thermal buckling and postbuckling resistance increases or decreases with the increases in GPL weight fraction, aspect ratio and width-to-thickness ratio is highly dependent on the GPL distribution pattern.

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