Non-Local Thermo-Elastic Buckling Analysis of Multi-Layer Annular/Circular Nano-Plates Based on First and Third Order Shear Deformation Theories Using DQ Method

Document Type : Research Paper


1 Department of Mechanical Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran

2 Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran


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-layer sheets. The stability governing equations are obtained according to the adjacent equilibrium estate method. The constitutive equations are solved by applying the differential quadrature method (DQM). Applying the differential quadrature method, the ordinary differential equations are transformed to algebraic equations. Then, the critical temperature is obtained. Since there is not any research in thermo-elastic buckling analysis of multi-layer graphene sheets, the results are validated with available single layer articles. The effects of non-local parameter, the values of van der Waals interaction between the layers, third to first order shear deformation theory analyses, non-local to local analyses, different values of Winkler and Pasternak elastic foundation and analysis of bi-layer and triple layer sheets are investigated. It is concluded that the critical temperature increases and tends to a constant value along the rise of van der Waals interaction between the layers.


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