Unified Formulations of the Shear Coefficients in Timoshenko Beam Theory

Faghidian, S. Ali

doi:10.1061/(asce)em.1943-7889.0001297

Cited by 34 publications

(28 citation statements)

References 35 publications

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“…The parameters of SWCNT are listed in Table 1, and the results of simply supported SWCNTs with different SSPs α are listed in Table 2. There are several methods for computing the shear coefficient [48,49]. In this paper, the value of k 0 can be obtained by…”

Section: Comparison Examplementioning

confidence: 99%

Vibration Analysis of Fluid Conveying Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory by Spectral Element Method

Wang

2019

Nanomaterials

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In this work, we applied the spectral element method (SEM) to analyze the dynamic characteristics of fluid conveying single-walled carbon nanotubes (SWCNTs). First, the dynamic equations for fluid conveying SWCNTs were deduced based on the nonlocal Timoshenko beam theory. Then, the spectral element formulation was established for a free/forced vibration analysis of fluid conveying SWCNTs by introducing discrete Fourier transform. Furthermore, the proposed method was validated using several comparison examples. Finally, the natural frequencies and dynamic responses of a simply-supported fluid conveying SWCNTs were calculated by the SEM, considering different internal fluid velocities and small-scale parameters (SSPs). The effects of fluid velocity and SSPs on the dynamic characteristics of SWCNTs conveying fluid were revealed by the numerical results. Compared with other methods, the SEM shows high accuracy and efficiency.

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Section: Comparison Examplementioning

confidence: 99%

Vibration Analysis of Fluid Conveying Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory by Spectral Element Method

Wang

2019

Nanomaterials

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“…Diversos autores propuseram uma grande variedade de fórmulas para o parâmetro do coeficiente de cisalhamento, conforme abordado em Faghidian (2017), algumas formulações são apresentadas em sequência.…”

Section: Coeficiente De Cisalhamentounclassified

“…É interessante notar que os valores do coeficiente de cisalhamento para seção circular e retangular, quando admitido coeficiente de poisson nulo, chegam ao mesmo valor obtido pelas expressões de Cowper, apud Faghidian (2017).…”

Section: Coeficiente De Cisalhamentounclassified

“…Existem outras formulações semelhantes à equação 10 que levam em consideração a relação entre a base e a altura da seção. Podem-se citar as formulações de Stephen, apud Faghidian (2017) e Hutchinson, apudFaghidian (2017), contudo há pouca discrepância de valores para tais formulações, principalmente para uma elevada razão entre a base e a altura da seção.…”

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Estudo analítico das teorias de viga de Bernoulli e Timoshenko para condições de contorno variadas

Silva

2019

REC

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Neste artigo é analisado a diferença que ocorre nos deslocamentos utilizando as teorias de viga de Bernoulli e Timoshenko variando-se a relação entre o vão e a altura da seção transversal e alterando a condição de contorno do elemento estrutural. As análises efetuadas ficaram restritas a vigas de seção retangular, foi demonstrado que para vigas isostáticas o efeito da distorção devido ao cisalhamento (teoria de Timoshenko) tem pouca influência no aumento dos deslocamentos, em vigas continuas esse efeito passa a ter uma maior contribuição, enquanto que para viga biengastada esse efeito contribui de maneira significativa para o aumento dos deslocamentos na estrutura. Foram propostas relações limites de tamanho de vão e altura da seção transversal em função da condição de contorno para a consideração da distorção por cisalhamento.

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“…In the above equation, is the shear correction factor which is present due to an error caused by the assumption of the constant distribution of the transverse shear stress in the thickness of the beam, [53] defined in various papers [54][55][56][57] as: = 5(1+ ) ∕ 6+5 for rectangular sections, = 6(1+ ) 2 ∕ 7+12 +4 2 for circular sections and = 6(1+ ) 2 (1+ 2 ) 2 ∕ (7+12 +4 2 )(1+4 2 + 4 )+6 2 for hollow sections. In these relationships, and m are the Poisson's ratio and the ratio of the outer radius to the inner radius, respectively.…”

Section: Bending Of Timoshenko Nanobeamsmentioning

confidence: 99%

Doublet mechanical analysis of bending of Euler‐Bernoulli and Timoshenko nanobeams

2018

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By taking the effect of the scale parameter explicitly into account, bending behavior of Euler‐Bernoulli and Timoshenko nanobeams is studied using doublet mechanics. In addition, the effect of chirality on the softening or hardening behavior of an Euler‐Bernoulli nanobeam in bending is studied by taking the effect of the chiral angle explicitly into account. For the bending of the Timoshenko nanobeam the effect of the scale parameter and chirality on the axial and shear stresses is studied and the results are compared with the gradient and Eringen‐like models. It is shown that as the chiral angle increases, a simply supported Timoshenko nanobeam under a uniform loading changes from a softening to a hardening nanobeam indicating that chirality has a pronounced effect on the bending response of the nanobeams.

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Unified Formulations of the Shear Coefficients in Timoshenko Beam Theory

Cited by 34 publications

References 35 publications

Vibration Analysis of Fluid Conveying Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory by Spectral Element Method

Vibration Analysis of Fluid Conveying Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory by Spectral Element Method

Estudo analítico das teorias de viga de Bernoulli e Timoshenko para condições de contorno variadas

Doublet mechanical analysis of bending of Euler‐Bernoulli and Timoshenko nanobeams

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