Stability analysis of nanobeams in hygrothermal environment based on a nonlocal strain gradient Timoshenko beam model under nonlinear thermal field

This article is dedicated to analyzing the buckling behavior of nanobeam subjected to hygrothermal environments based on the principle of the Timoshenko beam theory. The hygroscopic environment has been considered as a linear stress field model, while the thermal environment is assumed to be a nonlinear stress field based on the Murnaghan model. The size-dependent effect of the nanobeam is captured by the nonlocal strain gradient theory (NSGT), and the governing equations of the proposed model have been derived by implementing a variational principle. The critical buckling loads have been calculated for the hinged-hinged boundary condition by incorporating the Navier approach and considering other elasticity theories such as classical elasticity theory, Eringen nonlocal elasticity theory, and strain gradient theory along with the NSGT. The present model is also validated with the pre-existing model in exceptional cases. Further, a parametric investigation has been performed to report the influence of various scaling parameters like hygroscopic environment, thermal environment, length-to-diameter ratio, small scale parameter, and length scale parameter on critical buckling loads by considering both the linear and nonlinear temperature distributions.