Foudil Mohri

Theoretical and numerical stability analyses of unrestrained, mono-symmetric thin-walled beams

In this paper, a contribution to the overall stability of unrestrained thin-walled elements with open sections is investigated. A model is developed for beam lateral buckling stability analysis. According to the European steel code, Eurocode 3, an analytical solution is used for checking the stability of laterally unrestrained beams. It depends on bending distribution, on load height effect and on degree of the monosymmetry of the section called Wagner’s parameter. Coefficients C1, C2 and C3 are respectively affected to these parameters and are given for some selected load cases. Based on the present model, these coefficients are recomputed for simply supported beams. Ritz and Galerkin’s methods are applied. Following Galerkin’s method, the coefficients C1 and C2 are the same as those adopted in Eurocode 3, but some of Wagner’s proposed C3 coefficients are very different from those usually used. The different solutions are first discussed and then compared to finite element results. ABAQUS software is used in numerical simulations where three-dimensional beams with warping and shell elements are chosen in modelling lateral buckling phenomena. The presented results are close to shell element results but the regular solutions overestimate the lateral buckling resistance of mono-symmetric I beams.  2002 Elsevier Science Ltd. All rights reserved.

Lateral post-buckling analysis of thin-walled open section beams

Abstract Thin-walled beams with open sections are studied using a nonlinear model. This model is developed in the context of large displacements and small deformations, by accounting for bending-bending and bending-torsion couplings. The warping and shortening effects are considered in the torsion equilibrium equation. The governing coupled equilibrium equations obtained from Galerkin’s method are solved by a Newton–Raphson iterative process. It is established that the buckling loads are highly dependent on the pre-buckling deformations of the beam. The bifurcated branches are unstable and strongly influenced by shortening effects. Some comparisons are presented with the solutions commonly used in linear stability, like in the standard European steel code (Eurocode 3). The regular solutions appear to be very conservative, especially for I sections with large flanges.

Flexural-torsional post-buckling analysis of thin-walled elements with open sections

Abstract The post-buckling analysis of thin-walled elements under compression is investigated. A nonlinear model is developed by using nonlinear relationships between curvatures and bending moments. Warping and shortening effects are considered in the torsion equilibrium equation. Based on Galerkins method, a nonlinear algebraic system is obtained for simply supported boundary conditions. The three resulting equations in bending and torsion are highly coupled and the Newton–Raphson algorithm with displacement control is adopted for the solution. The post-buckling equilibrium curves are obtained for various sections shapes, such as bisymmetric and monosymmetric sections. The importance of the shortening effect is outlined.

Review and comparison of finite element flexural-torsional models for non-linear behaviour of thin-walled beams

The authors have developed a beam finite element model in large torsion context for thin-walled beams with arbitrary cross sections 1. In the model, the trigonometric functions of the twist angle ?x (c=cos ?x-1 and s=sin ?x) were included as additional variables in the whole model without any assumption. In the present paper, three other 3D finite element beams are derived according to three approximations based on truncated Taylor expansions of the functions c and s (cubic, quadratic and linear). A finite element approach of these approximations is carried out. Finally, it is worth mentioning that the promising results obtained in 1,2 encourage the authors to extend the formulation of the model in order to include load eccentricity effects. Solution of the non-linear equations is made possible by Asymptotic Numerical Method (ANM) 3. This method is used as an alternative to the classical incremental iterative methods. Many comparison examples are considered. They concern the non-linear behaviour of beams under twist moment and the post buckling behaviour of struts under axial loads or the beam lateral buckling under eccentric bending loads. The obtained results highlight the discrepancies between the various approximations often employed in thin-walled beams literature for the geometrically non-linear analysis of beams in flexural-torsional behaviour.