Lateral–torsional buckling of porous orthotropic thin-walled I-beams under non-uniform transverse loadings: a higher-order shear deformation approach

Abstract Porous orthotropic thin-walled I-beams (TWI-Bs) are commonly used in aerospace, civil, and mechanical applications due to their high stiffness-to-weight ratio. However, accurately predicting their lateral-torsional buckling (LTB) behavior remains challenging, especially under non-uniform loading and in the presence of material porosity and orthotropy. Classical beam theories often fail to capture essential deformation mechanisms, particularly shear deformation and warping effects, which become significant in porous and thin-walled configurations. This study develops a novel analytical model for evaluating the LTB response of porous orthotropic doubly symmetric I-beams subjected to non-uniformly distributed transverse loadings. To the author’s knowledge, this study is among the first to integrate an HSDT-based thin-walled beam formulation with porosity-dependent orthotropic constitutive modeling to the elastic lateral–torsional buckling of thin-walled I-beams under various non-uniform transverse loadings. Three trigonometric-based non-uniform porosity distribution patterns are considered. The solution is obtained using Galerkin’s method, and the model is validated against available benchmark solutions. The results reveal that neglecting higher-order shear deformation leads to a significant overestimation of critical buckling loads, especially for beams with high porosity or under non-uniform loading conditions. Among porosity patterns, NUDP1 yields the highest buckling resistance, whereas NUDP2 results in the lowest. The position of the applied load and its distribution type (e.g., TRL, TGL) substantially influence the LTB behavior, particularly in shear-sensitive configurations. Geometric parameters, such as flange and web thickness ratios and the orthotropy ratio, further interact with porosity and loading to affect buckling performance. These findings underscore the importance of incorporating advanced shear deformation models and realistic porosity distributions to ensure accurate LTB predictions and a robust structural design.