Thin-walled structures are structural systems in which one dimension, the wall thickness, is substantially smaller than the other two geometric dimensions, typically by a ratio on the order of one hundred or more. The category encompasses plates, shells, built-up cold-formed sections, and tubular members whose structural behavior is governed by thin-wall theory rather than solid-mechanics assumptions ^[1]. The defining mechanical characteristic is that stresses through the thickness are essentially uniform, while bending and membrane action dominate the load-carrying mechanism. Thin-walled members exhibit distinctive instability phenomena, including local buckling, distortional buckling, flexural-torsional buckling, and shear buckling, which arise because the slender cross-sectional elements are prone to out-of-plane deformations under compressive stress ^[2]. The analysis of such structures requires shell theory or finite-element formulations that account for membrane stiffness, bending stiffness, and geometric nonlinearity, as classical beam theory based on Euler-Bernoulli assumptions is insufficient when cross-section deformation cannot be neglected ^[3]. The thin-wall geometric ratio is the fundamental parameter that determines whether plate-buckling, shell-buckling, or global member-buckling modes govern the structural response.