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

Saba Tahaei Yaghoubi, Viacheslav Balobanov, S. Mahmoud Mousavi, Jarkko Niiranen

Research output: Contribution to journalArticleScientificpeer-review

36 Citations (Scopus)
209 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)113-123
Number of pages11
JournalEuropean Journal of Mechanics A: Solids
Volume69
DOIs
Publication statusPublished - 1 May 2018
MoE publication typeA1 Journal article-refereed

Keywords

  • Anisotropic strain and velocity gradient
  • Shear-deformable beam
  • Centrosymmetric
  • Isogeometric analysis

Fingerprint

Dive into the research topics of 'Variational formulations and isogeometric analysis for the dynamics of anisotropic gradient-elastic Euler-Bernoulli and shear deformable beams'. Together they form a unique fingerprint.

Cite this