On the equations of motion for curved slender beams using tubular coordinates
(2014) In Mathematics and Mechanics of Solids 19(7). p.758804 Abstract
 The equations of motion for a beam are derived from the threedimensional continuum mechanical point of view. The kinematics involve bending, torsion and shearing as well as crosssectional 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 bimomentum.... (More)
 The equations of motion for a beam are derived from the threedimensional continuum mechanical point of view. The kinematics involve bending, torsion and shearing as well as crosssectional 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 bimomentum. 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 VenantKirchhoff elastic material. Simplified stressstrain relations may be obtained using so called torsion free coordinates. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4659513
 author
 Lidström, Per ^{LU}
 organization
 publishing date
 2014
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Beam theory, principle of virtual power, equations of motion, crosssectional displacements, bimomentum, finite strains
 in
 Mathematics and Mechanics of Solids
 volume
 19
 issue
 7
 pages
 758  804
 publisher
 SAGE Publications
 external identifiers

 wos:000340114900003
 scopus:84905573422
 ISSN
 17413028
 DOI
 10.1177/1081286513487188
 language
 English
 LU publication?
 yes
 id
 5b1a40c085e645f4a11d7ca9711c6d33 (old id 4659513)
 date added to LUP
 20160401 10:08:11
 date last changed
 20220125 20:03:02
@article{5b1a40c085e645f4a11d7ca9711c6d33, abstract = {{The equations of motion for a beam are derived from the threedimensional continuum mechanical point of view. The kinematics involve bending, torsion and shearing as well as crosssectional 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 bimomentum. 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 VenantKirchhoff elastic material. Simplified stressstrain relations may be obtained using so called torsion free coordinates.}}, author = {{Lidström, Per}}, issn = {{17413028}}, keywords = {{Beam theory; principle of virtual power; equations of motion; crosssectional displacements; bimomentum; finite strains}}, language = {{eng}}, number = {{7}}, pages = {{758804}}, publisher = {{SAGE Publications}}, 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}}, doi = {{10.1177/1081286513487188}}, volume = {{19}}, year = {{2014}}, }