Non-linear static stability of bi-layer carbon nanosheets resting on an elastic matrix under various types of in-plane shearing loads in thermo-elasticity using nonlocal continuum

Abstract

In this research, the shear and thermal buckling of bi-layer rectangular orthotropic carbon nanosheets embedded on an elastic matrix using the nonlocal elasticity theory and non-linear strains of Von-Karman was studied. The bi-layer carbon sheets was modeled as a double-layered plate, and van der Waals forces between layers were considered. The governing equations and boundary conditions were obtained using the first order shear deformation theory. For calculation of critical temperature and critical shear load, the equations were divided for two states via adjacent equilibrium criterion, pre-buckling and stability. The stability equations were discretized by differential quadrature method which is a high accurate numerical method. The equations were solved for various boundary conditions, such as free edges. Finally, the small scale parameter effect due to length to the width ratio, stiffness of elastic medium on the critical load was considered. The shear buckling results showed that the effect of type of shear loading on the nonlocal results is more than local results. Also, in thermal buckling analysis, the most important results being that whether the boundary conditions have more flexibility, by increasing the dimensions ratio, the results of critical temperature were tightly close together in nonlocal and local analysis.