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Archive of Applied Mechanics

, Volume 89, Issue 10, pp 1995–2003 | Cite as

Shear deformable rod theories and fundamental principles of mechanics

  • Dario Genovese
  • Isaac Elishakoff
Technical Note
  • 112 Downloads

Abstract

We discuss the role of the principle of virtual work, of the objectivity and of the energy balance in the formulation of planar static rod theories, in a large deformations framework and consider the effects of transverse shear. According to these principles, we also discuss the differences of Haringx approach to equilibrium and buckling over Engesser approach, as well as the advantages of choosing the curvature strain measure as the derivative of the rotation of the cross section with respect to the reference, rather than current, arc length.

Keywords

Rational mechanics Nonlinear elasticity Rod Shear 

List of symbols

\(u,v,\phi \)

Axial, transverse displacements and rotation of the cross section

fgm

Axial, transverse distributed body forces and body couple

\(\epsilon ,\gamma ,\kappa \)

Elongation, sliding, curvature (strains)

NQM

Axial force, shear and bending moment (stresses)

\(F_u,F_v,F_\phi \)

Boundary force in uv direction and boundary couple

sL

Reference abscissa and initial length of the rod (\(s\in [0;L]\))

\(()'\)

Derivative operator \(\mathrm {d}/\mathrm {d}s\)

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.AnconaItaly
  2. 2.Department of Ocean and Mechanical EngineeringFlorida Atlantic UniversityBoca RatonUSA

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