On the Generalization of the Timoshenko Beam Model Based on the Micropolar Linear Theory: Static Case
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-04-02
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
Three generalizations of the Timoshenko beam model according to the linear theory of micropolar elasticity or its special cases, that is, the couple stress theory or the modified couple stress theory, recently developed in the literature, are investigated and compared.
The analysis is carried out in a variational setting, making use of Hamilton’s principle.
It is shown that both the Timoshenko and the (possibly modified) couple stress models are based on a microstructural kinematics which is governed by kinosthenic (ignorable) terms in the Lagrangian.
Despite their difference, all models bring in a beam-plane theory only one microstructural material parameter.
Besides, the micropolar model formally reduces to the couple stress model upon introducing the proper constraint on the microstructure kinematics, although the material parameter is generally different.
Line loading on the microstructure results in a nonconservative force potential.
Finally, the Hamiltonian form of the micropolar beam model is derived and the canonical equations are presented along with their general solution.
The latter exhibits a general oscillatory pattern for the microstructure rotation and stress, whose behavior matches the numerical findings.
American Psychological Association (APA)
Nobili, Andrea. 2015. On the Generalization of the Timoshenko Beam Model Based on the Micropolar Linear Theory: Static Case. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-8.
https://search.emarefa.net/detail/BIM-1075038
Modern Language Association (MLA)
Nobili, Andrea. On the Generalization of the Timoshenko Beam Model Based on the Micropolar Linear Theory: Static Case. Mathematical Problems in Engineering No. 2015 (2015), pp.1-8.
https://search.emarefa.net/detail/BIM-1075038
American Medical Association (AMA)
Nobili, Andrea. On the Generalization of the Timoshenko Beam Model Based on the Micropolar Linear Theory: Static Case. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-8.
https://search.emarefa.net/detail/BIM-1075038
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1075038