混合物统一梯度纳米梁弯曲时的非标准界面条件

IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
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引用次数: 0

摘要

工程科学中具有应用价值的结构方案经常会遇到错综复杂的不连续性现象。本研究拟采用一种抽象的变分方案来解决弹性纳米梁弯曲过程中的不连续性问题。引用弹性的混合统一梯度理论来实现超小尺度的尺寸效应。从已建立的静态变分原理出发,细致地提出了界面条件的一致形式。适当封闭了平衡的边界值问题,并对弹性纳米梁的横向位移场进行了分析求解。作为一种替代方法,还利用特征函数展开法仔细研究了所提出的变分公式在解决具有不连续的弹性纳米梁弯曲问题中的有效性。对具有不同运动学约束的混合统一梯度梁的弯曲特性进行了数值说明和深入讨论。长度尺度特征参数的预期纳米特征得到了证实。所展示的数值结果可作为分析和设计开创性超灵敏纳米传感器的基准。所建立的与尺寸相关的变异一致性框架为纳米力学的发展铺平了道路,并激发了对超小尺度弹性梁断裂力学的进一步研究。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Non-standard interface conditions in flexure of mixture unified gradient Nanobeams

Structural schemes of applicative interests in Engineering Science frequently encounter the intricate phenomenon of discontinuity. The present study intends to address the discontinuity in the flexure of elastic nanobeam by adopting an abstract variational scheme. The mixture unified gradient theory of elasticity is invoked to realize the size-effects at the ultra-small scale. The consistent form of the interface conditions, stemming from the established stationary variational principle, is meticulously set forth. The boundary-value problem of equilibrium is properly closed and the analytical solution of the transverse displacement field of the elastic nanobeam is addressed. As an alternative approach, the eigenfunction expansion method is also utilized to scrutinize the efficacy of the presented variational formulation in tackling the flexure of elastic nanobeams with discontinuity. The flexural characteristic of mixture unified gradient beams with diverse kinematic constraints is numerically illustrated and thoroughly discussed. The anticipated nanoscopic features of the characteristic length-scale parameters are confirmed. The demonstrated numerical results can advantageously serve as a benchmark for the analysis and design of pioneering ultra-sensitive nano-sensors. The established variationally consistent size-dependent framework paves the way ahead in nanomechanics and inspires further research contributing to fracture mechanics of ultra-small scale elastic beams.

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来源期刊
International Journal of Engineering Science
International Journal of Engineering Science 工程技术-工程:综合
CiteScore
11.80
自引率
16.70%
发文量
86
审稿时长
45 days
期刊介绍: The International Journal of Engineering Science is not limited to a specific aspect of science and engineering but is instead devoted to a wide range of subfields in the engineering sciences. While it encourages a broad spectrum of contribution in the engineering sciences, its core interest lies in issues concerning material modeling and response. Articles of interdisciplinary nature are particularly welcome. The primary goal of the new editors is to maintain high quality of publications. There will be a commitment to expediting the time taken for the publication of the papers. The articles that are sent for reviews will have names of the authors deleted with a view towards enhancing the objectivity and fairness of the review process. Articles that are devoted to the purely mathematical aspects without a discussion of the physical implications of the results or the consideration of specific examples are discouraged. Articles concerning material science should not be limited merely to a description and recording of observations but should contain theoretical or quantitative discussion of the results.
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