in present study, thermo-elastic buckling analysis of multi-layer orthotropic annular/circular graphene sheets is investigated based on eringen’s theory. the moderately thick and also thick nano-plates are considered. using the non-local first and third order shear deformation theories, the governing equations are derived. the van der waals interaction between the layers is simulated for multi-...

The di culty encountered when solving singularly perturbed differential equations is that errors introduced in layers pollute the solution in smooth regions. Since a priori control of the errors in layers is di cult, special methods must be designed to reduce or eliminate polluting errors. Successful methods add dissipation to a computational scheme to enlarge layers to the mesh spacing. We foc...

In this article we have considered a non-standard finite difference method for the solution of second order  Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the Fredholm integro-differential equation into a system of equations. We have also developed a numerical met...

In this paper, nonlinear bending analysis of bilayer orthotropic annular/circular graphene sheets is studied based on the nonlocal elasticity theory. The equilibrium equations are derived in terms of generalized displacements and rotations considering the first-order Shear deformation theory (FSDT). The nonlinear governing equations are solved using the differential quadrature method (DQM) whic...

This paper investigates natural frequencies of free transverse vibrations prestressed beams, and the governing equations vibration in related literatures are discussed corrected. The differential quadrature methods (DQ) applied directly to corrected get values frequency numerically. Under simple supported boundary conditions, model beam numerically studied, physical parameters analyzed respecti...