On the plastic bifurcation and post-bifurcation of axially compressed beams

Abstract

The paper presents two new results in the domain of the elastoplastic buckling and post-buckling of beams under axial compression. (i) First, the tangent modulus critical load, the buckling mode and the initial slope of the bifurcated branch are given for a Timoshenko beam (with the transverse shear effects). The result is derived from the 3D J 2 flow plastic bifurcation theory with the von Mises yield criterion and a linear isotropic hardening. (ii) Second, use is made of a specific method in order to provide the asymptotic expansion of the post-critical branch for a Euler-Bernoulli beam, exhibiting one new non-linear fractional term. All the analytical results are validated by finite element computations.

Investigation of the Torsional Effects on the Lateral Buckling of a Pipe-Like Beam Resting on the Ground under Axial Compression

“…In each case, the five numerical values have been plotted on the same graphs for completeness purposes. In Figure 3(c), the curve is piecewise linear, as expected by Equation (33). The same tendency is observed in Figure 3(a), even if Equation ( 22) does not display a linear form.…”

“…This approach is a general and efficient way to cope with the buckling of structures subjected to uniform pre-critical stress states. Among others, it was successfully applied to the cases of compressed homogeneous beams [33], sandwich beam-columns [34,35] and two-layer beams with partial interaction (with similar connections) [36,37], in earlier studies. The tube is represented by an Euler-Bernoulli beam model with an isotropic linear elastic material, and the ground-structure interaction is described using a uniform distribution of elastic lateral springs along the beam length, connected to the bottom line of the tube in contact with the soil.…”

Elastoplastic bifurcation analysis for the lateral–torsional buckling of straight beams

“…It is based on the 3D elastoplastic bifurcation theory, using the J 2 flow theory considering the von Mises yield criterion with linear isotropic hardening. This 3D approach has already been applied successfully to elastic/plastic Timoshenko beams [24], two-layer beams with partial interaction [25,26], or sandwich beams [27,28] under axial compression/pure bending, but also to the lateral buckling of offshore pipelines including twisting effects [29]. In Section 3, two particular cases are investigated: a beam with a thin rectangular cross-section and an I-beam.…”

Numerical analysis of highly deformable elastoplastic beams

“…In this context, several works can be cited as, for example, Hutchinson (1972), Cimetière and Léger (1996), Kounadis and Mallis (1987), Léger and Potier-Ferry (1993) and Grognec and Le van (2011). However, very few papers deal with the unloading and reloading phases, which is a topic that can be used, for instance, in the analyses of truss-like structures composed of elastoplastic materials.…”