Catastrophic Influence of Global Distortional Modes on the Post-Buckling Behavior of Opened Columns

Andrzej Teter; Zbigniew Kolakowski

doi:10.3390/ma13153314

Catastrophic Influence of Global Distortional Modes on the Post-Buckling Behavior of Opened Columns

Materials (Basel). 2020 Jul 25;13(15):3314. doi: 10.3390/ma13153314.

Authors

Andrzej Teter¹, Zbigniew Kolakowski²

Affiliations

¹ Department of Applied Mechanics, Faculty of Mechanical Engineering, Lublin University of Technology (LUT), Nadbystrzycka 36, PL-20-618 Lublin, Poland.
² Department of Strength of Materials, Faculty of Mechanical Engineering, Lodz University of Technology, Stefanowskiego 1/15, PL-90-924 Lodz, Poland.

Abstract

The multimodal buckling of thin-walled isotropic columns with open cross-sections under uniform compression is discussed. Column lengths were selected to enable strong interactions between selected eigenmodes. In the case of short columns or very long ones subjected to compression, single-mode buckling can be observed only and the effect under discussion does not occur. In the present study, the influence of higher global modes on the load-carrying capacity and behavior in the post-buckling state of thin-walled structures with open cross-sections is analyzed in detail. In the literature known to the authors, higher global modes are always neglected practically in the analysis due to their very high values of bifurcation loads. However, the phenomenon of an unexpected loss in the load-carrying capacity of opened columns can be observed in the experimental investigations. It might be explained using multimode buckling when the higher global distortional-flexural buckling modes are taken into account. In the conducted numerical simulations, a significant influence of higher global distortional-flexural buckling modes on the post-buckling equilibrium path of uniformly compressed columns with C- and TH-shaped (the so-called "top-hat") cross-sections was observed. The columns of two lengths, for which strong interactions between selected eigenmodes were seen, were subject to consideration. Two numerical methods were applied, namely, the semi-analytical method (SAM) using Koiter's perturbation approach and the finite element method (FEM), to solve the problem. The SAM results showed that the third mode had a considerable impact on the load-carrying capacity, whereas the FEM results confirmed a catastrophic effect of the modes on the behavior of the structures under analysis, which led to a lack of convergence of numerical calculations despite an application of the Riks algorithm. All elastic-plastic effects were neglected.

Keywords: C-section; FEM; Koiter’s theory; TH-section; compression; distortional mode; interactive buckling; medium length.