NDLI: Strain and velocity gradient theory for higher-order shear deformable beams

Content Provider	Springer Nature Link
Author	Yaghoubi, Saba Tahaei Mousavi, S. Mahmoud Paavola, Juha
Copyright Year	2015
Abstract	The strain and velocity gradient framework is formulated for the third-order shear deformable beam theory. A variational approach is applied to determine the governing equations together with initial and boundary conditions. Within the gradient framework, the strain energy is generalized to include strain as well as strain gradient. Furthermore, the kinetic energy is also generalized to include velocity and the velocity gradient. Such approach results in the introduction of the static and kinetic internal length scales. For dynamic analysis of beams, most of the gradient theories do not take the velocity gradient into account. The model developed in this paper depicts the influence of the velocity gradient on the governing equations and initial and boundary conditions of the third-order shear deformable theory. Through the assumption of the velocity gradients, kinematic quantities are distinguished on the microscale and on the macroscale. Finally, Timoshenko and Euler–Bernoulli beam theories are also presented by simplifying the third-order theory.
Starting Page	877
Ending Page	892
Page Count	16
File Format	PDF
ISSN	09391533
Journal	Archive of Applied Mechanics
Volume Number	85
Issue Number	7
e-ISSN	14320681
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2015-02-28
Publisher Place	Berlin/Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Dynamic analysis Shear deformable beam Strain gradient Velocity gradient Variational approach Theoretical and Applied Mechanics Mechanics
Content Type	Text
Resource Type	Article
Subject	Mechanical Engineering

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