Buckling analysis of graphene sheets embedded in an elastic medium based on the kp-Ritz method and non-local elasticity theory

Graphene finds application in nanoscale electronic devices, nano sensors and nanocomposites in which graphene sheets usually rest on an elastic medium. Buckling of graphene sheets can occur in such structures, which significantly influences its performance. Therefore, it is essential to investigate the buckling behavior of graphene for better engineering design and manufacture. The present work provides an element-free kp-Ritz framework to analyze the buckling behavior of graphene. The element-free kp-Ritz method is first implemented to investigate the buckling behavior of single-layered graphene sheets (SLGSs) embedded in elastic foundations, based on the classical plate theory (CLP), incorporating the non-local elasticity theory, which takes small effects into account when dealing with nanostructures. A Winkler-type model is adopted to simulate the functioning of the elastic medium. Numerical solutions for critical buckling loads of SLGSs are obtained by solving the governing differential equations derived from the principle of minimum potential energy using the element-free kp-Ritz method. The concepts of non-local parameter effects and non-local effects are distinguished. The influence of non-local parameters for both side length and aspect ratio on critical buckling loads of SLGSs is analyzed. Additionally, the effects of non-local parameters and the Winkler modulus parameter on the buckling patterns are discussed.