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 orthotropic micro/nanoscale plates based on the nonlocal plate theory. Equilibrium equation is obtained based on the nonlocal Kirchoff plate theory. Weak form of the equilibrium equation is discretized based on the moving least square (MLS) approximation functions. Since MLS approximation functions do not satisfy the Kronecker’s delta property, the penalty method is used to impose the essential boundary conditions. Discrete form of the weak form is then solved and the plate deflection is obtained. Numerical results show that the number of nodes scattered in the plate domain, support domain radius and the number of Gauss quadrature points affect the results. Therefore, before presentation of the final results, the method is calibrated using some exact results. Finally, the plate deflection is obtained for various boundary conditions and the small scale effect is studied. In addition, as an example bending problem of nano graphene sheets is solved for different boundary conditions.