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On the equations of motion for curved slender beams using tubular coordinates

Lidström, Per LU (2014) In Mathematics and Mechanics of Solids 19(7). p.758-804
Abstract
The equations of motion for a beam are derived from the three-dimensional continuum mechanical point of view. The kinematics involve bending, torsion and shearing as well as cross-sectional displacements. The transplacement of the beam from an arbitrary curved reference placement is considered. For slender beams so called tubular coordinates may be used as global coordinates in the reference placement. An explicit geometrical characterization of slender beams is given. The equations of motion for the slender beam are derived and some consequences of the power theorem are presented. Using the principle of virtual power the classical local beam equations are obtained along with equations representing the local balance of bi-momentum.... (More)
The equations of motion for a beam are derived from the three-dimensional continuum mechanical point of view. The kinematics involve bending, torsion and shearing as well as cross-sectional displacements. The transplacement of the beam from an arbitrary curved reference placement is considered. For slender beams so called tubular coordinates may be used as global coordinates in the reference placement. An explicit geometrical characterization of slender beams is given. The equations of motion for the slender beam are derived and some consequences of the power theorem are presented. Using the principle of virtual power the classical local beam equations are obtained along with equations representing the local balance of bi-momentum. Constitutive assumptions are introduced where the dependence of stress on the natural deformation measures for the beam is obtained by assuming that the beam consists of a St Venant-Kirchhoff elastic material. Simplified stress-strain relations may be obtained using so called torsion free coordinates. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Beam theory, principle of virtual power, equations of motion, cross-sectional displacements, bi-momentum, finite strains
in
Mathematics and Mechanics of Solids
volume
19
issue
7
pages
758 - 804
publisher
SAGE Publications Inc.
external identifiers
  • wos:000340114900003
  • scopus:84905573422
ISSN
1741-3028
DOI
10.1177/1081286513487188
language
English
LU publication?
yes
id
5b1a40c0-85e6-45f4-a11d-7ca9711c6d33 (old id 4659513)
date added to LUP
2014-09-25 08:12:50
date last changed
2017-04-16 03:05:32
@article{5b1a40c0-85e6-45f4-a11d-7ca9711c6d33,
  abstract     = {The equations of motion for a beam are derived from the three-dimensional continuum mechanical point of view. The kinematics involve bending, torsion and shearing as well as cross-sectional displacements. The transplacement of the beam from an arbitrary curved reference placement is considered. For slender beams so called tubular coordinates may be used as global coordinates in the reference placement. An explicit geometrical characterization of slender beams is given. The equations of motion for the slender beam are derived and some consequences of the power theorem are presented. Using the principle of virtual power the classical local beam equations are obtained along with equations representing the local balance of bi-momentum. Constitutive assumptions are introduced where the dependence of stress on the natural deformation measures for the beam is obtained by assuming that the beam consists of a St Venant-Kirchhoff elastic material. Simplified stress-strain relations may be obtained using so called torsion free coordinates.},
  author       = {Lidström, Per},
  issn         = {1741-3028},
  keyword      = {Beam theory,principle of virtual power,equations of motion,cross-sectional displacements,bi-momentum,finite strains},
  language     = {eng},
  number       = {7},
  pages        = {758--804},
  publisher    = {SAGE Publications Inc.},
  series       = {Mathematics and Mechanics of Solids},
  title        = {On the equations of motion for curved slender beams using tubular coordinates},
  url          = {http://dx.doi.org/10.1177/1081286513487188},
  volume       = {19},
  year         = {2014},
}