Buckling of centrosymmetric anisotropic beam structures within strain gradient elasticity

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Buckling of centrosymmetric anisotropic beam structures within strain gradient elasticity. / Tahaei Yaghoubi, Saba; Mousavi, S. Mahmoud; Paavola, Juha.

julkaisussa: International Journal of Solids and Structures, Vuosikerta 109, 15.03.2017, s. 84–92.

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Tahaei Yaghoubi, Saba ; Mousavi, S. Mahmoud ; Paavola, Juha. / Buckling of centrosymmetric anisotropic beam structures within strain gradient elasticity. Julkaisussa: International Journal of Solids and Structures. 2017 ; Vuosikerta 109. Sivut 84–92.

Bibtex - Lataa

@article{375088fc9af541c8af7e5462e31aa0a1,
title = "Buckling of centrosymmetric anisotropic beam structures within strain gradient elasticity",
abstract = "Buckling of centrosymmetric anisotropic beams is studied within strain gradient theory. First, the three dimensional anisotropic gradient elasticity theory is outlined. Then the dimension of the three dimensional theory is reduced, resulting in Timoshenko beam as well as Euler-Bernoulli beam theories. The governing differential equations together with the consistent (classical and non-classical) boundary conditions are derived for centrosymmetric anisotropic beams through a variational approach. By considering von K{\'a}rm{\'a}n nonlinear strains, the geometric nonlinearity is taken into account. The obtained nonlinear formulation can be used to study the postbuckling configuration. The analysis of size effect on anisotropic beam structures is missing in the literature so far, while the present model allows one to characterize the size effect on the buckling of the centrosymmetric anisotropic micro- and nano-scale beam structures such as micropillars. As a specific case, the governing buckling equation is obtained for the more practical case of orthotropic beams. Finally, the buckling loads for orthotropic simply supported Timoshenko and Euler-Bernoulli beams as well as a clamped Euler-Bernoulli beam are obtained analytically and the effect of the internal length scale parameters on the buckling load is depicted.",
keywords = "Anisotropic beam, Buckling, Euler-Bernoulli beam, Orthotropy, Strain gradient, Timoshenko beam",
author = "{Tahaei Yaghoubi}, Saba and Mousavi, {S. Mahmoud} and Juha Paavola",
year = "2017",
month = "3",
day = "15",
doi = "10.1016/j.ijsolstr.2017.01.009",
language = "English",
volume = "109",
pages = "84–92",
journal = "International Journal of Solids and Structures",
issn = "0020-7683",

}

RIS - Lataa

TY - JOUR

T1 - Buckling of centrosymmetric anisotropic beam structures within strain gradient elasticity

AU - Tahaei Yaghoubi, Saba

AU - Mousavi, S. Mahmoud

AU - Paavola, Juha

PY - 2017/3/15

Y1 - 2017/3/15

N2 - Buckling of centrosymmetric anisotropic beams is studied within strain gradient theory. First, the three dimensional anisotropic gradient elasticity theory is outlined. Then the dimension of the three dimensional theory is reduced, resulting in Timoshenko beam as well as Euler-Bernoulli beam theories. The governing differential equations together with the consistent (classical and non-classical) boundary conditions are derived for centrosymmetric anisotropic beams through a variational approach. By considering von Kármán nonlinear strains, the geometric nonlinearity is taken into account. The obtained nonlinear formulation can be used to study the postbuckling configuration. The analysis of size effect on anisotropic beam structures is missing in the literature so far, while the present model allows one to characterize the size effect on the buckling of the centrosymmetric anisotropic micro- and nano-scale beam structures such as micropillars. As a specific case, the governing buckling equation is obtained for the more practical case of orthotropic beams. Finally, the buckling loads for orthotropic simply supported Timoshenko and Euler-Bernoulli beams as well as a clamped Euler-Bernoulli beam are obtained analytically and the effect of the internal length scale parameters on the buckling load is depicted.

AB - Buckling of centrosymmetric anisotropic beams is studied within strain gradient theory. First, the three dimensional anisotropic gradient elasticity theory is outlined. Then the dimension of the three dimensional theory is reduced, resulting in Timoshenko beam as well as Euler-Bernoulli beam theories. The governing differential equations together with the consistent (classical and non-classical) boundary conditions are derived for centrosymmetric anisotropic beams through a variational approach. By considering von Kármán nonlinear strains, the geometric nonlinearity is taken into account. The obtained nonlinear formulation can be used to study the postbuckling configuration. The analysis of size effect on anisotropic beam structures is missing in the literature so far, while the present model allows one to characterize the size effect on the buckling of the centrosymmetric anisotropic micro- and nano-scale beam structures such as micropillars. As a specific case, the governing buckling equation is obtained for the more practical case of orthotropic beams. Finally, the buckling loads for orthotropic simply supported Timoshenko and Euler-Bernoulli beams as well as a clamped Euler-Bernoulli beam are obtained analytically and the effect of the internal length scale parameters on the buckling load is depicted.

KW - Anisotropic beam

KW - Buckling

KW - Euler-Bernoulli beam

KW - Orthotropy

KW - Strain gradient

KW - Timoshenko beam

UR - http://www.scopus.com/inward/record.url?scp=85009754081&partnerID=8YFLogxK

U2 - 10.1016/j.ijsolstr.2017.01.009

DO - 10.1016/j.ijsolstr.2017.01.009

M3 - Article

AN - SCOPUS:85009754081

VL - 109

SP - 84

EP - 92

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

ER -

ID: 10686572