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We in this paper dedicate to study the snap-buckling of functionally graded multilayer graphene platelet-reinforced composite curved beams with geometrical imperfections on the nanometer length. It is supposed that graphene platelets (GPLs) are uniformly distributed and randomly oriented in each layer, while its weight fraction varies from one layer to another based on various functionally graded patterns. The effective material properties of functionally graded multilayer GPLRC beams are evaluated via the model of the Halpin-Tsa. In the theoretical framework of the nonlocal strain gradient theory (NSGT) and the surface elasticity theory, a generalized nonlinear size-dependent curved beam model is established. The novel model includes not only a nonlocal parameter and a material length scale parameter of NSGT but also three surface constants of the surface elasticity theory, which can explore the coupling effect of nonlocal stress, strain gradient and surface energy on the snap-buckling of nanoarches. Furthermore, the present model can be transformed into the Euler-Bernoulli shallow arch model, the Timoshenko shallow arch model as well as the Reddy's higher-order shear deformation shallow arch model by choosing the appropriated shape function. Next, On the basis of the principle of Hamilton, the nonlinear governing equations of curved nanobeams are derived. Then to obtain the analytical solution of snap-buckling of curved beams, the nonlinear equations are solved by a two-step perturbation method. Finally, a detailed parametric study is carried out based on the analytical solution, aiming at analyzing the influences of respective physical parameters on the snap-buckling of such nanostructure. • A generalized nonlinear size-dependent curved beam model is established. • The governing equations are derived based on nonlocal strain gradient theory incorporating surface effects. • Obtaining the size-dependent post-buckling equilibrium paths of perfect and imperfect curved nanobeams. • The coupling effect of nonlocal stress, strain gradient and surface energy on the snap-buckling of curved nanobeams is studied. [ABSTRACT FROM AUTHOR]

We in this article put forward a novel size-dependent beam model for static bending deformation of a functionally graded bi-semi-tube subjected to different boundary conditions based on the nonlocal strain gradient theory. The tube is formed by bonding together a ZrO 2 /Ti–6Al–4V functionally graded lower semi-tube and a Si 3 N 4 /SUS304 functionally graded upper one. The effective material properties P f of FG bi-semi-tubes are assumed to vary along the radius of tube. We propose a refined shear model without requiring a shear correction factor for bars with circular cross section. Next the model is used to derive the governing equations of the tube based on the Hamilton's principle. The obtained equations form present a detailed analysis include a nonlocal parameter as well as a material length scale parameter, so much that they can account for the size-dependent in static bending of FG bi-semi-tubes. Later, these equations are resolved analytically by using an improved perturbation method. The analytical solutions are used to discuss the influence of various physical parameters on static mechanical performance of nanotubes, such as double volume fraction indexes, inner radius, the variation of temperature, strain gradient parameter, nonlocal parameter, scale parameter ratio. At last, compared with the conventional approaches, the novel approach is suggested in such work to lead to more accurate bending deformation in the same dimensionless size of tubes. • Nonlinear bending of nano-tubes made of functionally graded bi-semi-tubes has n been studied in detail. • We put forward a novel displacement function without acquiring a shear correction factor. • Nonlocal strain gradient theory is used to characterize size-dependent of nanostructures. • The perturbation method is used for solving the problem to obtain an analytical solution. • In contrast to conventional approach, the present approach results in more accurate bending control in the same conditions. [ABSTRACT FROM AUTHOR]