Snap-buckling of functionally graded multilayer graphene platelet-reinforced composite curved nanobeams with geometrical imperfections

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