Element Free Galerkin Method for Static Analysis of Thin Micro/Nanoscale Plates Based on the Nonlocal Plate Theory

In this article, element free Galerkin method is used for static analysis of thin micro/nanoscale plates based on the nonlocal plate theory. The problem is solved for the plates with arbitrary boundary conditions. Since shape functions of the element free Galerkin method do not satisfy the Kronecker’s delta property, the penalty method is used to impose the essential boundary conditions. Discrete form of the equilibrium equation is solved to obtain the plate deflection. Numerical results show that the number of nodes scattered in the plate domain, support domain radius, Gauss quadrature points affect the final results. So, before presentation of the results the element free Galerkin method is calibrated with the exact results. Finally, bending problem of nano graphene sheets as orthotropic thin nonlocal plates is solved for different boundary conditions.