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**Localization limiters in transient problems.**
*(English)*
Zbl 0636.73021

In materials with strainThe emphasis in this paper is, however, on columns with a single axis of symmetry. The formulation is designed to take into account the simultaneous interaction of the purely flexural and flexural-torsion overall modes of buckling with local buckling. The local buckling deformations are described in terms of a primary local mode together with two secondary local modes of the same wavelength. The latter are triggered by the interaction of bending in two perpendicular planes with the primary localmode. The three eigenmodes and the six second-order in-plane displacement fields are all computed using a finite-strip technique. The modulation of the amplitudes of the local modes and the overall displacements are described in terms of a one- dimensional finite element model. Thus a new beam element which has embedded in it the local buckling information is developed.

It appears that the present analytical model is very versatile being applicable to members of arbitrary cross-section and end conditions. For columns with a single axis of symmetry, it is seen that there exists a nonlinear coupling between the purely flexural and the flexural-torsional modes of buckling via local buckling deformation. Typical examples of channel section columns are presented. It is shown that the channel section columns of commonly used proportions are highly imperfection sensitive in the context of combined interaction of the enumerated modes of buckling. This sensitivity remains even for columns with well separated overall and local critical stresses - a feature which is in stark contrast with the behavior of the Tvergaard panel.

It appears that the present analytical model is very versatile being applicable to members of arbitrary cross-section and end conditions. For columns with a single axis of symmetry, it is seen that there exists a nonlinear coupling between the purely flexural and the flexural-torsional modes of buckling via local buckling deformation. Typical examples of channel section columns are presented. It is shown that the channel section columns of commonly used proportions are highly imperfection sensitive in the context of combined interaction of the enumerated modes of buckling. This sensitivity remains even for columns with well separated overall and local critical stresses - a feature which is in stark contrast with the behavior of the Tvergaard panel.

### MSC:

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74S05 | Finite element methods applied to problems in solid mechanics |

74C99 | Plastic materials, materials of stress-rate and internal-variable type |