In this paper, the direct one-dimensional beam model introduced by one of the
authors is refined to take into account nonsymmetrical beam cross-sections. Two
different beam axes are considered, and the strain is described with respect to both.
Two inner constraints are assumed: a vanishing shearing strain between the
cross-section and one of the two axes, and a linear relationship between the warping
and twisting of the cross-section. Considering a grade one mechanical theory and
nonlinear hyperelastic constitutive relations, the balance of power, and standard
localization and static perturbation procedures lead to field equations suitable to
describe the flexural-torsional buckling. Some examples are given to determine the
critical load for initially compressed beams and to evaluate their post-buckling
behavior.
Keywords
thin-walled beams, direct one-dimensional models,
flexural-torsional buckling