This paper presents the postbuckled configurations of simply supported and clamped-pinned nanorods under self-weight based on elastica theory. Numerical solution is considered in this work since closed-form solution of postbuckling analysis under self-weight cannot be obtained. The set of nonlinear differential equations of a nanorod including the effect of nonlocal elasticity are investigated. The constraint equation at boundary condition technique is introduced for the solution of postbuckling analysis. In order to solve the set of nonlinear differential equations, the shooting method is utilized, where the set of these equations along with boundary conditions are integrated by the fourth-order Runge-Kutta algorithm. Numerical results are obtained and the highlighting influences of the nonlocal elasticity on postbuckling behavior of nanorods are discussed. The obtained results indicate that the rotation angle and the postbuckled configurations of nanorods are varied by changing the nonlocal elasticity parameter. The effect of nonlocal elasticity shows the softening behavior in comparison with the Euler beam. The present formulation together with constraint boundary condition technique is an effective solution for postbuckling analysis of a nanorod under self-weight including the effect of nonlocal elasticity.

中文翻译：

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自重下非局部纳米棒的后屈曲分析

本文介绍了基于弹性理论的自重下简支和夹销纳米棒的后屈曲构型。由于无法获得自重下的后屈曲分析的闭合形式解，因此在这项工作中考虑了数值解。研究了包含非局部弹性效应的纳米棒非线性微分方程组。引入边界条件下的约束方程用于后屈曲分析的求解。为了求解非线性微分方程组，采用射击法，通过四阶龙格-库塔算法对这些方程组和边界条件进行积分。获得了数值结果，并讨论了非局部弹性对纳米棒后屈曲行为的突出影响。获得的结果表明，纳米棒的旋转角度和后屈曲构型通过改变非局部弹性参数而改变。与欧拉梁相比，非局部弹性的影响显示出软化行为。本公式与约束边界条件技术一起是一种有效的解决方案，用于在自重下对纳米棒进行后屈曲分析，包括非局部弹性的影响。与欧拉梁相比，非局部弹性的影响显示出软化行为。本公式与约束边界条件技术一起是一种有效的解决方案，用于在自重下对纳米棒进行后屈曲分析，包括非局部弹性的影响。与欧拉梁相比，非局部弹性的影响显示出软化行为。本公式与约束边界条件技术一起是一种有效的解决方案，用于在自重下对纳米棒进行后屈曲分析，包括非局部弹性的影响。