Simplified numerical method for nonlocal static and dynamic analysis of a graphene nanoplate

In this paper, the dynamic analysis of single-layer rectangular armchair graphene nanoplates has been considered. The theory of nonlocal elasticity for small scale effects and the Kirchhoff's theory for plates have been used to obtain the dynamic equation of graphene nanoplates. Discrete Least Squares Meshless (DLSM) method has been used to examine the response of single-layer graphene nanoplates with various boundary conditions. The validation of the results has also been carried out using dynamic analysis of single-layer rectangular armchair graphene nanoplates under stationary loads. Results revealed that DLSM method is an efficient mean to solve the problems of structural mechanics in nano-dimensions. In addition, in nanostructures, the small scale effects have considerable impacts that should be considered as well. An increase in nonlocal coefficient increases the deflection. Higher nonlocal coefficient leads to higher deflection intensity and vibration amplitude.