On the use of bubble complex finite strip method in the nonlocal buckling and vibration analysis of single-layered graphene sheets

Abstract

In the present work, the buckling and vibration of rectangular single-layered graphene sheets is analyzed based on the nonlocal theory of elasticity which takes the small scale effects into account. The graphene sheet is assumed as a thin plate, and the classical plate theory is applied to obtain the differential equation of the sheet. For the first time, the complex finite strip method is employed to study the vibration and buckling behavior of graphene sheets. The weighted residual method is employed to obtain the stiffness, stability and the mass matrices of the graphene sheet which is assumed to be an isotropic nanoplate. A sinusoidal displacement function is used for the longitudinal direction , which satisfies the simply supported boundary condition , while piecewise interpolation polynomials including the Hermitian and bubble functions are assumed for the other direction. A matrix eigenvalue problem is solved to find the vibration frequency and buckling load of graphene sheets subjected to different types of in-plane loadings including the uniform and non-uniform uniaxial and biaxial compressions as well as shear loading. The accuracy of the proposed model is validated by comparing the results with those reported by the available references. Furthermore, a number of examples are presented to investigate the effects of various parameters (e.g., boundary conditions, nonlocal parameter, aspect ratio, and type of loading) on the results. The bubble complex finite strip method is proposed to study the buckling and vibration characteristics of rectangular single-layered graphene sheets, based on the nonlocal classical plate theory. • Buckling and free vibration and of single layered graphene sheets are considered. • The bubble complex finite strip method is applied to study the GS׳s problems for the first time. • Nonlocal continuum mechanics is employed to include the small scale-effects. • Contrary to the most of the studies, different boundary conditions are considered.