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.

中文翻译：

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非线性热场下基于非局部应变梯度Timoshenko梁模型的湿热环境纳米束稳定性分析

本文致力于根据Timoshenko束理论的原理分析在湿热环境下纳米束的屈曲行为。吸湿环境被认为是线性应力场模型，而热环境被认为是基于Murnaghan模型的非线性应力场。通过非局部应变梯度理论（NSGT）捕获了纳米束的尺寸依赖性效应，并通过实现变分原理推导了该模型的控制方程。通过结合Navier方法并考虑其他弹性理论（例如经典弹性理论，Eringen非局部弹性理论和应变梯度理论以及NSGT），已针对铰接铰接边界条件计算了临界屈曲载荷。在特殊情况下，还可以使用现有模型验证本模型。此外，已经进行了参数研究，以通过考虑线性和非线性温度来报告各种缩放参数（例如，吸湿环境，热环境，长径比，小缩放参数和长度缩放参数）对临界屈曲载荷的影响。分布。