Nonlocal large deflection analysis of a cantilever nanobeam on a nonlinear Winkler-Pasternak elastic foundation and under uniformly distributed lateral load

In this paper, the PDEs and BCs governing the large deflection of an Euler-Bernoulli cantilever nano-beam on a nonlinear Winkler-Pasternak elastic foundation and under uniformly distributed lateral load have been derived using Eringen’s nonlocal elasticity theory, considering the nonlinear and linear relationships of curvature-deformation, and then solved using finite difference method. The effect of changes of different parameters, including nonlocal parameter, load factor, linear/nonlinear and shear stiffness coefficients of the foundation on the deflection, bending slope angle of elastic curve and length change of the nano-beam, have been investigated. Results show that by increasing the nonlocal parameter, the bending slope angle and deflection of the free end of cantilever nano-beam are decreased and the dimensionless ratio of the final length of nano-beam is reduced. Also, the effect of nonlocal parameter on the nonlinear large deflection of the nano-beam is more significant at higher values of the applied lateral load.