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Structural Engineering and Mechanics Volume 67, Number 4, August25 2018 , pages 417-425 DOI: https://doi.org/10.12989/sem.2018.67.4.417 |
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Bending analysis of bi-directional functionally graded Euler-Bernoulli nano-beams using integral form of Eringen\'s non-local elasticity theory |
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Mohammad Zamani Nejad, Amin Hadi, Arash Omidvari and Abbas Rastgoo
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| Abstract | ||
| The main aim of this paper is to investigate the bending of Euler-Bernouilli nano-beams made of bi-directional functionally graded materials (BDFGMs) using Eringen\'s non-local elasticity theory in the integral form with compare the differential form. To the best of the researchers\' knowledge, in the literature, there is no study carried out into integral form of Eringen\'s non-local elasticity theory for bending analysis of BDFGM Euler-Bernoulli nano-beams with arbitrary functions. Material properties of nano-beam are assumed to change along the thickness and length directions according to arbitrary function. The approximate analytical solutions to the bending analysis of the BDFG nano-beam are derived by using the Rayleigh-Ritz method. The differential form of Eringen\'s non-local elasticity theory reveals with increasing size effect parameter, the flexibility of the nano-beam decreases, that this is unreasonable. This problem has been resolved in the integral form of the Eringen\'s model. For all boundary conditions, it is clearly seen that the integral form of Eringen\'s model predicts the softening effect of the non-local parameter as expected. Finally, the effects of changes of some important parameters such as material length scale, BDFG index on the values of deflection of nano-beam are studied. | ||
| Key Words | ||
| bending; Euler-Bernoulli nano-beams; Bi-directional functionally graded material (BDFGM); integral form; non-local; Rayleigh-Ritz method | ||
| Address | ||
| Mohammad Zamani Nejad: Department of Mechanical Engineering, Yasouj University, P.O. Box: 75914-353, Yasouj, Iran Amin Hadi: School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran Arash Omidvari: Department of Mechanical Engineering, Shiraz University, Shiraz, Iran Abbas Rastgoo: School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran | ||