Global–Local–Distortional Buckling of Shear-Deformable Composite Beams with Open Cross-Sections Using a Novel GBT–Ritz Approach

This paper explores the application of the generalized beam theory (GBT) in analyzing the buckling behavior of isotropic and composite thin-walled beams with open cross-sections, both with and without branching. The composite beams are composed of orthotropic laminate layers arranged in arbitrary symmetrical orientations. By integrating GBT with the Ritz method and solving the associated generalized eigenvalue problem (GEP), an efficient and robust semi-analytical framework is developed to assess the stability of such isotropic and orthotropic members. The novelty of this work is not the GBT cross-sectional formulation itself, but its implementation at the beam level using a Ritz formulation leading to a generalized eigenvalue problem for the critical buckling loads and mode shapes that capture coupled global, local, and distortional modes in isotropic and orthotropic composite members. This makes the method suitable for early-stage design studies and parametric investigations, where many design variants (geometry, laminate lay-up, and aspect ratios) must be screened quickly without building large-scale high-fidelity finite element (FE) models for each case. The preliminary outcomes, when compared with those obtained using FE, confirm the approach’s effectiveness in evaluating buckling responses, particularly for open-section composite beams. Ultimately, the combined use of GBT and the Ritz method delivers both physical insight and computational efficiency, allowing engineers and researchers to address complex stability issues that were previously difficult to solve. In summary, the methodology can be correctly used for stability assessment of thin-walled composite members prone to interacting global–local–distortional buckling, especially when rapid, mechanistically transparent predictions are required rather than purely numerical FE output.