Locking-free variational formulations and isogeometric analysis for the Timoshenko beam models of strain gradient and classical elasticity

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2018-09-01
Major/Subject
Mcode
Degree programme
Language
en
Pages
23
137-159
Series
Computer Methods in Applied Mechanics and Engineering, Volume 339
Abstract
The Timoshenko beam bending problem is formulated in the context of strain gradient elasticity for both static and dynamic analysis. Two non-standard variational formulations in the Sobolev space framework are presented in order to avoid the numerical shear locking effect pronounced in the strain gradient context. Both formulations are shown to be reducible to their locking-free counterparts of classical elasticity. Conforming Galerkin discretizations for numerical results are obtained by an isogeometric Cp−1-continuous approach with B-spline basis functions of order p≥2. Convergence analyses cover both statics and free vibrations as well as both strain gradient and classical elasticity. Parameter studies for the thickness and gradient parameters, including micro-inertia terms, demonstrate the capability of the beam model in capturing size effects. Finally, a model comparison between the gradient-elastic Timoshenko and Euler–Bernoulli beam models justifies the relevance of the former, confirmed by experimental results on nano-beams from literature.
Description
Keywords
Isogeometric analysis, Shear locking, Size effect, Strain gradient elasticity, Timoshenko beam, Variational formulation
Other note
Citation
Balobanov, V & Niiranen, J 2018, ' Locking-free variational formulations and isogeometric analysis for the Timoshenko beam models of strain gradient and classical elasticity ', Computer Methods in Applied Mechanics and Engineering, vol. 339, pp. 137-159 . https://doi.org/10.1016/j.cma.2018.04.028