Variational formulations and isogeometric analysis for the dynamics of anisotropic gradient-elastic Euler-Bernoulli and shear deformable beams

Research output: Contribution to journalArticle

Standard

Variational formulations and isogeometric analysis for the dynamics of anisotropic gradient-elastic Euler-Bernoulli and shear deformable beams. / Tahaei Yaghoubi, Saba; Balobanov, Viacheslav; Mousavi, S. Mahmoud; Niiranen, Jarkko.

In: EUROPEAN JOURNAL OF MECHANICS A: SOLIDS, Vol. 69, 01.05.2018, p. 113-123.

Research output: Contribution to journalArticle

Harvard

APA

Vancouver

Author

Bibtex - Download

@article{af71330ea5404d86abb228f927c8b400,
title = "Variational formulations and isogeometric analysis for the dynamics of anisotropic gradient-elastic Euler-Bernoulli and shear deformable beams",
abstract = "A strain and velocity gradient framework is formulated for centrosymmetric anisotropic Euler-Bernoulli and third-order shear-deformable (TSD) beam models, reducible to Timoshenko beams. The governing equations and boundary conditions are obtained by using variational approach. The strain energy is generalized to include strain gradients and the tensor of anisotropic static length scale parameters. The kinetic energy includes velocity gradients and a tensor of anisotropic length scale parameters and hence the static and kinetic quantities of centrosymmetric anisotropic materials are distinguished in micro- and macroscales. Furthermore, the external work is written in the corresponding general form. Free vibration of simply supported centrosymmetric anisotropic TSD beams is studied by using analytical solution as well as an isogeometric numerical method verified with respect to convergence.",
keywords = "Anisotropic strain and velocity gradient, Shear-deformable beam, Centrosymmetric, Isogeometric analysis",
author = "{Tahaei Yaghoubi}, Saba and Viacheslav Balobanov and Mousavi, {S. Mahmoud} and Jarkko Niiranen",
year = "2018",
month = "5",
day = "1",
doi = "10.1016/j.euromechsol.2017.11.012",
language = "English",
volume = "69",
pages = "113--123",
journal = "EUROPEAN JOURNAL OF MECHANICS A: SOLIDS",
issn = "0997-7538",

}

RIS - Download

TY - JOUR

T1 - Variational formulations and isogeometric analysis for the dynamics of anisotropic gradient-elastic Euler-Bernoulli and shear deformable beams

AU - Tahaei Yaghoubi, Saba

AU - Balobanov, Viacheslav

AU - Mousavi, S. Mahmoud

AU - Niiranen, Jarkko

PY - 2018/5/1

Y1 - 2018/5/1

N2 - A strain and velocity gradient framework is formulated for centrosymmetric anisotropic Euler-Bernoulli and third-order shear-deformable (TSD) beam models, reducible to Timoshenko beams. The governing equations and boundary conditions are obtained by using variational approach. The strain energy is generalized to include strain gradients and the tensor of anisotropic static length scale parameters. The kinetic energy includes velocity gradients and a tensor of anisotropic length scale parameters and hence the static and kinetic quantities of centrosymmetric anisotropic materials are distinguished in micro- and macroscales. Furthermore, the external work is written in the corresponding general form. Free vibration of simply supported centrosymmetric anisotropic TSD beams is studied by using analytical solution as well as an isogeometric numerical method verified with respect to convergence.

AB - A strain and velocity gradient framework is formulated for centrosymmetric anisotropic Euler-Bernoulli and third-order shear-deformable (TSD) beam models, reducible to Timoshenko beams. The governing equations and boundary conditions are obtained by using variational approach. The strain energy is generalized to include strain gradients and the tensor of anisotropic static length scale parameters. The kinetic energy includes velocity gradients and a tensor of anisotropic length scale parameters and hence the static and kinetic quantities of centrosymmetric anisotropic materials are distinguished in micro- and macroscales. Furthermore, the external work is written in the corresponding general form. Free vibration of simply supported centrosymmetric anisotropic TSD beams is studied by using analytical solution as well as an isogeometric numerical method verified with respect to convergence.

KW - Anisotropic strain and velocity gradient

KW - Shear-deformable beam

KW - Centrosymmetric

KW - Isogeometric analysis

UR - http://www.scopus.com/inward/record.url?scp=85039801547&partnerID=8YFLogxK

U2 - 10.1016/j.euromechsol.2017.11.012

DO - 10.1016/j.euromechsol.2017.11.012

M3 - Article

VL - 69

SP - 113

EP - 123

JO - EUROPEAN JOURNAL OF MECHANICS A: SOLIDS

JF - EUROPEAN JOURNAL OF MECHANICS A: SOLIDS

SN - 0997-7538

ER -

ID: 16535931