Nonlinear Bending Analysis of Sector Graphene Sheet Embedded in Elastic Matrix Based on Nonlocal Continuum Mechanics

The nonlinear bending behavior of sector graphene sheets is studied subjected to uniform transverse loads resting on a Winkler-Pasternak elastic foundation using the nonlocal elasticity theory.Considering the nonlocal differential constitutive relations of Eringen theory based on first order sheardeformation theory and using the von-Karman strain field, the equilibrium partial differential equations are derived. The nonlinear partial differential equations system is solved using the differentialquadrature method (DQM) and a new semi analytical polynomial method (SAPM). By using the DQMor SAPM, the partial differential equations are converted to nonlinear algebraic equations, then the Newton–Raphson iterative scheme is applied to solve the resulting nonlinear algebraic equationssystem. The obtained results from DQM and SAPM are compared. It is observed that the SAPM resultsare so close to DQM. The SAPM’s formulations are considerably simpler than the DQM. Different boundary conditions including clamped, simply supported and free edges are considered. The obtained results are validated with available researches, then the small scale effects is investigated on the results due to various conditions such as outer radius to thickness ratio, boundary conditions, linear to nonlinear analysis, nonlocal to local analysis ratio, angle of the sector and stiffness value of elastic foundation.

Keywords:

Nonlocal Elasticity Theory , Nano-graphene Sector Plates , Differential Quadrature Method , Semi Analytical Polynomial Method , Elastic Foundation