First-Order and Buckling Analysis of Thin-Walled Members with Deformable Cross-Section within the Generalized Beam Theory

Abstract

In this work, the Generalized Beam Theory (GBT) is used as the main tool to analyze the mechanics of thin-walled beams. After a brief introduction to the subject, the attention is focused on the constitutive relations both for the isotropic and the orthotropic cases. In particular, a novel approach based on energetic arguments , able to automatically select appropriate constitutive relations in accordance with the GBT kinematics, is presented. Furthermore, the concept of consistency of a GBT-based model is introduced and a consistency analysis is conducted. This provides a formal basis to investigate the effects of various families of cross-section deformation modes in terms of predictive capabilities of the GBT model. Later, a new finite element for GBT beams is presented. The element is based on the hybrid complementary energy functional, involving nodal displacements and equilibrating stresses within the element as indipendent variables. Assumed stresses are rationally derived basing on the stresses associated to analytical solutions of some particular cases. The numerical results show the high performance of the proposed element. Subsequently, in the framework of cold-formed stability verification, a verification approach called Embedded Stability Analysis is shown. The verification approach, based on the GBT, is an interesting alternative to the simplified procedures provided by current standards and it is applicable in a simple and general way. A synthetic parameter allows the designer to evaluate when it is more appropriate to consider the distortional effects in thin-walled stability check. Finally, in the framework of cold-formed stability analysis, a new version of the so-called approach ECBL (Erosion of the Critical Load Bifurcation), based on the GBT, is presented. The numerical results show an excellent agreement between the new version ECBL approach and the experimental results.