Column buckling with shear deformations — A hyperelastic formulation

Mario M. Attard, Giles W. Hunt

Research output: Contribution to journalArticle

  • 27 Citations

Abstract

Column constitutive relationships and buckling equations are derived using a consistent hyperelastic neo-Hookean formulation. It is shown that the Mandel stress tensor provides the most concise representation for stress components. The analogous definitions for uniaxial beam plane stress and plane strain for large deformations are established by examining the virtual work equations. Anticlastic transverse curvature of the beam cross-section is incorporated when plane stress or thick beam dimensions are assumed. Column buckling equations which allow for shear and axial deformations are derived using the positive definiteness of the second order work. The buckling equations agree with the equation derived by Haringx and are extended to incorporate anticlastic transverse curvature which is important for low slenderness, high buckling modes and with increasing width to thickness ratio. The work in this paper does not support the existence of a shear buckling mode for straight prismatic columns made of an isotropic material.
LanguageEnglish
Pages4322-4339
Number of pages18
JournalInternational Journal of Solids and Structures
Volume45
Issue number14-15
DOIs
StatusPublished - Jul 2008

Fingerprint

Shear Deformation
buckling
Buckling
Shear deformation
shear
formulations
Formulation
plane stress
Plane Stress
Transverse
Curvature
curvature
Positive Definiteness
thickness ratio
plane strain
Plane Strain
Stress Tensor
stress tensors
Large Deformation
Straight

Keywords

  • beam theory
  • anticlastic curvature
  • column buckling
  • shear deformations
  • hyperelastic
  • elastica
  • finite strain
  • Mandel stress tensor

Cite this

Column buckling with shear deformations — A hyperelastic formulation. / Attard, Mario M.; Hunt, Giles W.

In: International Journal of Solids and Structures, Vol. 45, No. 14-15, 07.2008, p. 4322-4339.

Research output: Contribution to journalArticle

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