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Variational formulations and isogeometric analysis for the dynamics ofanisotropic gradient-elastic Euler-Bernoulli and shear-deformable beams
Aalto University, Finland.
Aalto University, Finland.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).ORCID iD: 0000-0001-8515-9907
Aalto University, Finland.
2018 (English)In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, ISSN 0997-7538, Vol. 69, p. 113-123Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Elsevier, 2018. Vol. 69, p. 113-123
Keywords [en]
Anisotropic strain and velocity gradient, Shear-deformable beam, Centrosymmetric, Isogeometric analysis
National Category
Applied Mechanics
Research subject
Mechanical Engineering
Identifiers
URN: urn:nbn:se:kau:diva-67108DOI: 10.1016/j.euromechsol.2017.11.012OAI: oai:DiVA.org:kau-67108DiVA, id: diva2:1199568
Available from: 2018-04-20 Created: 2018-04-20 Last updated: 2018-04-23Bibliographically approved

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Mousavi, Mahmoud

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