The influence of the local postbuckling behaviour on the bending of thinwalled beams is studied. The analysis of the postbuckling behaviour of a prismatic column-beam subject to compression and bending is employed in order to determine the overall flexural stiffness of a beam after local buckling. The asymptotic Koiter method is used in the second order approximation. The determination of post-buckling coefficients enables one to find the beam's flexural stiffness without the necessity of using hypotheses on effective widths of eccentrically compressed plates. It is shown that the post-buckling equilibrium branch in a bending moment-global curvature coordinate system for a perfectly elastic thin-walled beam is rectilinear (in the second order approximation of' the asymptotic method). Simple analytical relations are presented between the slope of the post-buckling equilibrium branch of global bending and post-buckling coefficients for local buckling mode. The results obtained are compared with data reported by other authors.

Influence of local postbuckling behaviour on bending of thin-walled beams

Abstract A review of papers that investigate the static and dynamic coupled buckling and post-buckling behaviour of thin-walled structures is carried out. The problem of static coupled buckling is sufficiently well-recognized. The analysis of dynamic interactive buckling is limited in practice to columns, single plates and shells. The applications of finite element method (FEM) or/and analytical-numerical method (ANM) to solve interaction buckling problems are on-going. In Poland, the team of scientists from the Department of Strength of Materials, Lodz University of Technology and co-workers developed the analytical-numerical method. This method allows to determine static buckling stresses, natural frequencies, coefficients of the equation describing the post-buckling equilibrium path and dynamic response of the plate structure subjected to compression load and/or bending moment. Using the dynamic buckling criteria, it is possible to determine the dynamic critical load. They presented a lot of interesting results for problems of the static and dynamic coupled buckling of thin-walled plate structures with complex shapes of cross-sections, including an interaction of component plates. The most important advantage of presented analytical-numerical method is that it enables to describe all buckling modes and the post-buckling behaviours of thin-walled columns made of different materials. Thin isotropic, orthotropic or laminate structures were considered.

/pdf/coupled-static-and-dynamic-buckling-modelling-of-thin-walled-rrfj2musmw.pdf

Coupled Static and Dynamic Buckling Modelling of Thin-Walled Structures in Elastic Range Review of Selected Problems

Badania numeryczne i doświadczalne stateczności i nośności kompozytowych słupów cienkościennych poddanych ściskaniu

The paper contains an analysis of the influence of non-uniformity and eccentricity of compressive loads on global and local buckling, on interactive buckling, and on the load-carrying capacity of thin-walled columns. Isotropic and orthotropic tubular columns of regular hexagonal cross-section have been examined. Equilibrium equations for the first and the second order non-linear approximation have been solved using the asymptotic Byskov–Hutchinson method. Numerical calculations have been performed for numerous different loading modes of isotropic columns and also for several loading modes of orthotropic columns. The results are presented in diagrams with some conclusions.

Influence of load-non-uniformity and eccentricity on the stability and load carrying capacity of orthotropic tubular columns of regular hexagonal cross-section

In this paper, the dynamic responses of the open cross section columns with intermediate stifieners subjected to in{plane pulse loading of a rectangular shape were concerned. Columns made of isotropic material were assumed to be simply supported at both loaded ends. The problem of the interactive buckling was solved by flnite element method (FEM) { ANSYS 9. The critical dynamic load factors DLF has been determined using the most popular Budiansky{Hutchinson’s criterion and they have been verifled with author’s versions of the phase portraits criterion.

/pdf/application-of-different-dynamic-stability-criteria-in-case-23ns6u5idq.pdf

Application of different dynamic stability criteria in case of columns with intermediate stiffeners

A nonlinear finite element computer program has been developed to analyse thin-walled metal structural members. The program has the ability to handle both geometrical and material nonlinearities so that the post-buckling behaviour and ultimate strength of members can be predicted. A bending-membrane rectangular element with six degrees of freedom at each node forms the basic type of element used in the program. Marguerre's shallow shell theory is adopted for the strain-displacement relationships and hence the bifurcation point at buckling can be bypassed by providing an initial inperfection. The finite element formulation is based on the total Lagrange coordinate system and the flow theory of plasticity. Explicitly shown in the paper is the formation of the tangent stiffness matrix and the tridiagonal block form of solution procedure. Two problems of a square tube and a channel section beam subjected to pure bending were tested and found to be in close agreement with previous theoretical work.

Cheng-Tzu Thomas Hsu

Papers

A nonlinear finite element computer program for thin-walled members