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Stress-driven nonlinear behavior of curved nanobeams
International Journal of Engineering Science ( IF 6.6 ) Pub Date : 2022-06-24 , DOI: 10.1016/j.ijengsci.2022.103724
Mohammad Rezaiee-Pajand, Niloofar Rajabzadeh-Safaei

A nonlocal stress-driven model for geometrically nonlinear behavior of a shallow arch under radial pressure is presented. The analytical nonlinear equilibrium equation and also buckling equations by variational principles and virtual work are found. As it has been proven before, the strain-driven models encountered some contradictions with local equilibrium conditions, while stress-driven formulation has solved these difficulties. The simultaneous participation of the constitutive boundary conditions has led to this improvement. To obtain nonlocal strains, local nonlinear strains are incorporated in the nonlocal stress-based equations. In this way, nonlocal loads corresponding to the limit-load and bifurcation instabilities are exactly calculated by considering the effect of nanoscale and geometry parameters. In this article, the geometric limits which determine when and how the arch bifurcates, are found. The results in specific cases are compared with those available in the literature. These comparisons show the accuracy of the work. Finally, the 3D view of the equilibrium nonlinear paths, associated with the pinned curved nanobeam, are presented for different nanoscale and also geometry ratio parameters.



中文翻译:

弯曲纳米梁的应力驱动非线性行为

提出了一种非局部应力驱动模型,用于在径向压力下浅拱的几何非线性行为。通过变分原理和虚功求出了解析非线性平衡方程和屈曲方程。正如之前已经证明的那样,应变驱动模型与局部平衡条件存在一些矛盾,而应力驱动公式解决了这些困难。本构边界条件的同时参与导致了这种改进。为了获得非局部应变,将局部非线性应变结合到基于非局部应力的方程中。这样,通过考虑纳米尺度和几何参数的影响,可以精确计算出与极限载荷和分岔不稳定性相对应的非局部载荷。在本文中,找到确定拱形何时以及如何分叉的几何限制。将特定案例的结果与文献中的结果进行比较。这些比较显示了工作的准确性。最后,针对不同的纳米尺度和几何比参数,呈现了与固定弯曲纳米束相关的平衡非线性路径的 3D 视图。

更新日期:2022-06-26
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