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Bending of Euler-Bernoulli nanobeams based on the strain-driven and stress-driven nonlocal integral models: a numerical approach

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Acta Mechanica Sinica 2018年第5期34卷 871-882页

作者： M.Faraji Oskouie R.Ansari H.Rouhi Department of Mechanical Engineering University of GuilanP.O.Box 3756RashtIran Department of Engineering Science Faculty of Technology and EngineeringEast of GuilanUniversity of GuilanRudsar-Vajargah 44891-63157Iran

Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale *** studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases,such as bending analysis of cantilevers,and recourse must be made to the integral *** this article,a novel numerical approach is developed for the bending analysis of Euler-Bernoulli nanobeams in the context of strain-and stress-driven integral nonlocal *** numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential ***,the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential ***,in each case,the governing equation is obtained in both strong and weak *** solve numerically the derived equations,matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration *** is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned ***,it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.

关键词： Eringen's nonlocal theory Stress-driven model strain-driven model Euler-Bernoulli beam Numerical approach Paradox

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