A simple shear deformation theory for nonlocal beams

Son Thai; Huu-Tai Thai; Thuc Vo; Vipulkumar Ishvarbhai Patel

doi:10.1016/j.compstruct.2017.03.022

A simple shear deformation theory for nonlocal beams

Son Thai, Huu-Tai Thai, Thuc Vo, Vipulkumar Ishvarbhai Patel

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Abstract

In this paper, a simple beam theory accounting for shear deformation effects with one unknown is proposed for static bending and free vibration analysis of isotropic nanobeams. The size-dependent behaviour is captured by using the nonlocal differential constitutive relations of Eringen. The governing equation of the present beam theory is obtained by using equilibrium equations of elasticity theory. The present theory has strong similarities with nonlocal Euler–Bernoulli beam theory in terms of the governing equation and boundary conditions. Analytical solutions for static bending and free vibration are derived for nonlocal beams with various types of boundary conditions. Verification studies indicate that the present theory is not only more accurate than Euler–Bernoulli beam theory, but also comparable with Timoshenko beam theory.

Original language	English
Pages (from-to)	262-270
Journal	Composite Structures
Volume	183
Early online date	16 Mar 2017
DOIs	https://doi.org/10.1016/j.compstruct.2017.03.022
Publication status	Published - 1 Jan 2018

Keywords

nanobeam
nonlocal elasticity theory
shear deformation beam theorys bending
vibration

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10.1016/j.compstruct.2017.03.022

Thai et al - A simple shear deformation theory for nonlocal beams AAMAccepted author manuscript, 2.05 MBLicence: CC BY-NC-ND

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title = "A simple shear deformation theory for nonlocal beams",

abstract = "In this paper, a simple beam theory accounting for shear deformation effects with one unknown is proposed for static bending and free vibration analysis of isotropic nanobeams. The size-dependent behaviour is captured by using the nonlocal differential constitutive relations of Eringen. The governing equation of the present beam theory is obtained by using equilibrium equations of elasticity theory. The present theory has strong similarities with nonlocal Euler–Bernoulli beam theory in terms of the governing equation and boundary conditions. Analytical solutions for static bending and free vibration are derived for nonlocal beams with various types of boundary conditions. Verification studies indicate that the present theory is not only more accurate than Euler–Bernoulli beam theory, but also comparable with Timoshenko beam theory.",

keywords = "nanobeam, nonlocal elasticity theory, shear deformation beam theorys bending, vibration",

author = "Son Thai and Huu-Tai Thai and Thuc Vo and Patel, \{Vipulkumar Ishvarbhai\}",

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doi = "10.1016/j.compstruct.2017.03.022",

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journal = "Composite Structures",

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TY - JOUR

T1 - A simple shear deformation theory for nonlocal beams

AU - Thai, Son

AU - Thai, Huu-Tai

AU - Vo, Thuc

AU - Patel, Vipulkumar Ishvarbhai

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In this paper, a simple beam theory accounting for shear deformation effects with one unknown is proposed for static bending and free vibration analysis of isotropic nanobeams. The size-dependent behaviour is captured by using the nonlocal differential constitutive relations of Eringen. The governing equation of the present beam theory is obtained by using equilibrium equations of elasticity theory. The present theory has strong similarities with nonlocal Euler–Bernoulli beam theory in terms of the governing equation and boundary conditions. Analytical solutions for static bending and free vibration are derived for nonlocal beams with various types of boundary conditions. Verification studies indicate that the present theory is not only more accurate than Euler–Bernoulli beam theory, but also comparable with Timoshenko beam theory.

AB - In this paper, a simple beam theory accounting for shear deformation effects with one unknown is proposed for static bending and free vibration analysis of isotropic nanobeams. The size-dependent behaviour is captured by using the nonlocal differential constitutive relations of Eringen. The governing equation of the present beam theory is obtained by using equilibrium equations of elasticity theory. The present theory has strong similarities with nonlocal Euler–Bernoulli beam theory in terms of the governing equation and boundary conditions. Analytical solutions for static bending and free vibration are derived for nonlocal beams with various types of boundary conditions. Verification studies indicate that the present theory is not only more accurate than Euler–Bernoulli beam theory, but also comparable with Timoshenko beam theory.

KW - nanobeam

KW - nonlocal elasticity theory

KW - shear deformation beam theorys bending

KW - vibration

UR - https://www.scopus.com/pages/publications/85015829775

U2 - 10.1016/j.compstruct.2017.03.022

DO - 10.1016/j.compstruct.2017.03.022

M3 - Article

SN - 0263-8223

VL - 183

SP - 262

EP - 270

JO - Composite Structures

JF - Composite Structures

ER -

A simple shear deformation theory for nonlocal beams

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