Non-linear bending analysis of multi-layer orthotropic annular/circular graphene sheets embedded in elastic matrix in thermal environment based on non-local elasticity theory

In this paper, the large deflection of multi-layer orthotropic annular/circular graphene sheets is investigated based on the non-local elasticity theory. The plate is considered to be in thermal environment. The equilibrium equations are derived in terms of generalized displacements and rotations considering the FSDT non-local elasticity theory and the van der Waals interaction between the layers. In order to solve the governing equations, the differential quadrature method (DQM) which is an accurate numerical method and a new semi-analytical polynomial method (SAPM) are applied. By applying DQM or SAPM, the ODE's would be converted to non-linear algebraic equations. In continue, the Newton–Raphson iterative scheme is applied to solve the obtained non-linear algebraic equations. The results of DQM and SAPM are compared. Although, the SAPM's formulation is considerably simpler than DQM, however, the results of two methods are so close to each other. The results are validated with the other available researches. The effect of small scale parameter, temperature effects on non-local results, the value of van der Waals interaction between the layers for bi-layer and triple layers graphene sheet, different values of elastic foundation matrix and load for various small scale parameters, the comparison between local and non-local deflections and linear to non-linear analysis are investigated.