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Nonlocal large deflection analysis of a cantilever nanobeam on a nonlinear Winkler-Pasternak elastic foundation and under uniformly distributed lateral load

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Abstract

In this paper, the PDEs and BCs governing the large deflection of an Euler-Bernoulli cantilever nano-beam on a nonlinear Winkler-Pasternak elastic foundation and under uniformly distributed lateral load have been derived using Eringen’s nonlocal elasticity theory, considering the nonlinear and linear relationships of curvature-deformation, and then solved using finite difference method. The effect of changes of different parameters, including nonlocal parameter, load factor, linear/nonlinear and shear stiffness coefficients of the foundation on the deflection, bending slope angle of elastic curve and length change of the nano-beam, have been investigated. Results show that by increasing the nonlocal parameter, the bending slope angle and deflection of the free end of cantilever nano-beam are decreased and the dimensionless ratio of the final length of nano-beam is reduced. Also, the effect of nonlocal parameter on the nonlinear large deflection of the nano-beam is more significant at higher values of the applied lateral load.

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Abbreviations

k 1 :

Linear stiffness coefficient of the foundation

k 2 :

Nonlinear stiffness coefficient of the foundation

k s :

Shear stiffness coefficient of the foundation

β :

Nonlocal parameter of cantilever nano-beam

α :

Dimensionless load parameter

φ :

Bending slope angle of cantilever nano-beam

η :

Dimensionless longitudinal distance of cantilever nano-beam

ξ :

Dimensionless nonlinear deflection of cantilever nano-beam

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Authors and Affiliations

  1. Department of Mechanical Engineering, Parand Branch, Islamic Azad University, Parand, Iran

    Ahmad Mamandi

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  1. Ahmad Mamandi
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Correspondence to Ahmad Mamandi.

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Additional information

Ahmad Mamandi is an Associate Professor of Aerospace Engineering, Parand Branch, Islamic Azad University, Parand, Iran. He received his Ph.D. in Aerospace Engineering from Science and Research Branch, Islamic Azad University, Tehran, Iran in January 2010. His research interests include nonlinear vibration, recent theories of beams, plates and shells, FSI phenomena, MEMS/NEMS, aeroelasticity, fracture mechanics and fatigue analysis of structures.

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Mamandi, A. Nonlocal large deflection analysis of a cantilever nanobeam on a nonlinear Winkler-Pasternak elastic foundation and under uniformly distributed lateral load. J Mech Sci Technol 37, 813–824 (2023). https://doi.org/10.1007/s12206-023-0124-3

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  • DOI: https://doi.org/10.1007/s12206-023-0124-3

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