Nonlocal elasticity and boundary condition paradoxes: a review
Nonlocal elasticity and boundary condition paradoxes: a review
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DOI：
10.1007/s11051-020-05107-y
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发表时间：
2021-03
影响因子：
2.5
通讯作者：
S. Ceballes;K. Larkin;E. Rojas;S. Ghaffari;A. Abdelkefi
中科院分区：
文献类型：
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作者：
S. Ceballes;K. Larkin;E. Rojas;S. Ghaffari;A. Abdelkefi
非经典连续介质力学理论在过去几年中由于对微/纳机电系统（MEMS/NEMS），微/纳谐振器，碳纳米管（CNT）等的研究增加而在实施中有所增加。有几种可用的理论可以捕捉纳米结构固有的现象。在现有的理论中，研究人员最常使用埃林根的非局部理论，因为它易于实现，并且对于特定的载荷条件和边界条件似乎是准确的结果。Eringen的积分非局部理论，导致一组积分偏微分方程，是很难解决的，因此，积分形式减少到一组奇异偏微分方程使用格林型衰减函数。然而，一个所谓的悖论之间出现的积分和微分公式的埃林根的非局部弹性。对于某些边界和载荷条件，而不是预期的软化效应固有的非局部颗粒相互作用，一些研究人员已经发现了一个硬化效应。尽管如此，其他人发现与使用经典理论发现的结果没有变化。因此，积分形式和微分形式之间的差异已经成为近二十年来辩论的主题，近年来发表了几项决议。本文旨在回顾和巩固现有的非局部弹性理论，沿着与选定的理论在非经典连续介质力学，利用埃林根的非局部弹性梁，壳和板，现有的差异和建议的解决方案，并建议为今后的工作。
Nonclassical continuum mechanics theories have seen a rise in implementation over the past several years due to the increased research into micro-/nanoelectromechanical systems (MEMS/NEMS), micro-/nanoresonators, carbon nanotubes (CNTs), etc. Typically, these systems exist in the range of several nanometers to the micro-scale. There are several available theories that can capture phenomena inherent to nanoscale structures. Of the available theories, researchers utilize Eringen’s nonlocal theory most frequently because of its ease of implementation and seemingly accurate results for specific loading conditions and boundary conditions. Eringen’s integral nonlocal theory, which leads to a set of integro-partial differential equations, is difficult to solve; therefore, the integral form was reduced to a set of singular partial differential equations using a Green-type attenuation function. However, a so-called paradox has arisen between the integral and differential formulations of Eringen’s nonlocal elasticity. For certain boundary and loading conditions, instead of the expected softening effect inherent in nonlocal particle interactions, some researchers have found a stiffening effect. Still, others have found no variation from those results found using classical theories. As such, the discrepancies between the integral and differential forms have been the subject of debate for nearly two decades, with several proposed resolutions published in recent years. This paper serves to review and consolidate existing theories in nonlocal elasticity along with selected theories in nonclassical continuum mechanics, the utilization of Eringen’s nonlocal elasticity in beams, shells, and plates, the existing discrepancies and proposed solutions, and recommendations for future work.