利用 LDTM 和非局部弹性理论研究 CNT 的大弯曲行为

IF 2.8 3区 工程技术 Q2 MECHANICS
B.R.K.L.L. Mawphlang, P.K. Patra
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引用次数: 0

摘要

本文推导了均匀分布载荷下弯曲悬臂碳纳米管 (CNT) 的垂直挠度、水平位移和应变能的一般表达式。该推导采用了非局部弹性理论,这对理解纳米级力学的尺寸效应至关重要,并考虑了大弯曲条件下弯曲曲率与挠度之间的非线性关系,这是一项新贡献。在极限情况下,我们的大弯曲表达式给出了文献中报道的小弯曲的相应表达式。此外,我们首次引入了拉普拉斯微分变换法(LDTM),为探索长径比和小尺度因子等参数对 CNT 弯曲行为的影响提供了有效的解决方案。与分析方法的比较验证了拉普拉斯微分变换法的准确性和有效性,为非线性方程提供了快速解决方案。我们的研究结果表明,在高纵横比的 CNT 中,应变能更明显地偏离二次方行为,而小尺度参数则对较小纵横比的 CNT 有明显影响。这些结果将有助于设计和应用 MEMs/NEMs 中使用的纳米级悬臂 CNT。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Study of the large bending behavior of CNTs using LDTM and nonlocal elasticity theory

The general expressions for vertical deflection, horizontal displacement, and strain energy in a bent cantilevered carbon nanotube (CNT) are derived herein under a uniformly distributed load. This derivation employs nonlocal elasticity theory, crucial for understanding nanoscale mechanics due to size effects, and accounts for the nonlinear relationship between bending curvature and deflection under large bending conditions, a novel contribution. In the limiting cases, our expressions for large bending give the corresponding expressions reported in the literature for small bending. Additionally, we introduce the Laplace-Differential Transformation Method (LDTM) for the first time, providing efficient solutions to explore the influence of parameters like aspect ratio and small-scale factors on CNT bending behavior. Comparison with the analytical method validates the accuracy and efficacy of LDTM, offering a rapid solution for nonlinear equations. Our findings reveal that strain energy deviates more prominently from quadratic behavior in CNTs with high aspect ratios, while small-scale parameters have a pronounced effect on CNTs with smaller aspect ratios. These results will be relevant to designing and applying the nanoscale-sized cantilevered CNTs used in MEMs/NEMs.

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来源期刊
CiteScore
5.50
自引率
9.40%
发文量
192
审稿时长
67 days
期刊介绍: The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.
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