On nonlinear stability analysis of saturated embedded porous nanobeams

Abstract

In this work, the nonlinear stability behaviors of the saturated porous nanobeams embedded in an elastic foundation are investigated. The restrained nanobeam is modeled using geometrical nonlinear equations in conjunction with the constitutive law of saturation. Three patterns for saturation along the thickness of the nanobeam are considered as porous/monotonous, porous/ nonlinear symmetric, and porous/nonlinear non-symmetric distributions. The infinite terms of the power series are discretized thanks to Stokes' transformation and trigonometric series. Then, the effects of saturation and nonlinearity on buckling loads are studied by considering the restrained boundary conditions. Moreover, the nonlinear results are validated with the saturated nanobeam with the rigid supporting conditions.