Implementation of discrete least squares meshless method for nonlocal elastic graphene nanoplates

摘要

n this paper, armchair rectangular monolayer graphene nanoplates were analyzed based on the assumption of orthotropic properties with different boundary conditions. For this purpose, the nonlocal elasticity and Kirchhoff theories were applied to analyze the small-scale effects on the armchair monolayer graphene nanoplates and obtain the static equation of the graphene nanoplates, respectively. As there were no readily accurate answers to the analyses of all the problems associated with nanoplates of different boundary and geometrical conditions, numerical methods were employed for obtaining approximate responses. One of the capable approaches to the analyses of the differential equations governing these types of plates is the meshless method. In this research, the Discrete Least Squares Meshless (DLSM) method was employed for the static analysis of rectangular nanoplates with different boundary conditions besides assessing the effect of nonlocal coefficient amount on the nanoplate deflection. According to the results of this investigation, it could be concluded that the method utilized here was suitable for solving the problems of nano-dimensions compared to the analytical and Galerkin meshless methods.