A Calibrated Rayleigh–Ritz–Euler Screening Framework for Linear Axial Buckling of Closed Lenticular CFRP Booms

Thin-walled carbon fiber-reinforced polymer (CFRP) members with closed lenticular cross-sections are suitable for lightweight load-bearing and deployable aerospace structures. Their axial buckling may be governed by competition between finite-length local or cross-sectional deformation branches and long-member global flexural branches. This competition increases the computational cost of parametric sweeps and complicates rapid identification of the transition length. This study develops a combined Rayleigh–Ritz–Euler screening framework to address this challenge. A finite-length Rayleigh–Ritz (RR) model predicts local and mixed buckling branches and the governing half-wave number, while an Euler model provides the global flexural buckling load scale. The intersection of the predicted load–length curves defines an engineering transition length, and shell finite element (FE) analyses are used to check selected configurations. The RR model incorporates an effective closure coefficient for the geometric stiffness, calibrated solely on the baseline configuration (BASE). Against Abaqus linear buckling results, excluding BASE, RR and Euler yield root-mean-square relative errors of 11.6% and 1.3% in the local and global buckling regimes, respectively. Across all 13 configurations, including BASE, the engineering transition length has a mean absolute relative error of 2.4% and a maximum of 11.1%. The framework captures transition-length trends under the investigated variations in cross-sectional scale, thickness, and layup, but shows larger deviations for variations in the circular-arc subtended angle. Within the tested parameter range, it supports preliminary screening of candidate designs and identification of parameter regions for targeted FE verification. However, it cannot replace high-fidelity FE analysis or experiments as the basis for final design decisions.