Plastic Bifurcation of Thin-Walled Members: Thin Shell Elements vs. GBT-Based Beam Elements

In this paper, one compares plastic bifurcation results concerning thin-walled members made of non-linear elastic-plastic materials, which are obtained by means of two independent approaches, namely (i) a Total Lagrangian thin shell finite element formulation, developed by the second author, and (ii) a computationally efficient beam formulation based on Generalised Beam Theory (GBT), developed by the remaining two authors it is worth mentioning that the latter neglects the effect of pre-buckling deflections. Initially, one addresses the fundamental concepts, procedures and underlying assumptions involved in the application of the above two formulations, focusing on the similarities and differences existing between them. Then, one presents and thoroughly discusses a set of numerical results, determined through analyses based on the two alternative approaches and concerning (i) aluminium lipped channel and (ii) stainless steel rectangular hollow section (RHS) thin-walled columns (i.e., uniformly compressed members). In the first case, a very good correlation was found between the results (bifurcation loads/stresses and buckling mode shapes) yielded by the two formulations (e.g., see Fig. 1). In the second case, a non negligible discrepancy was observed, as the bifurcation loads provided by the shell formulation consistently lay below the GBT values and the differences, due to the combined influence of relevant pre-buckling deflection and a high imperfectionsensitivity, reached 19% however, the RHS buckling mode shapes exhibited again an excellent agreement.

Figure 1

Plastic distortional buckling mode shapes of a lipped channel column of length

L

=55cm (sheel FEA and GBT).