One-dimensional finite element model based on a higher-order framework for efficient post-buckling analysis of stiffened cylindrical structures

This article introduces a one-dimensional finite element model based on a higher-order framework for efficient post-buckling analysis of stiffened cylindrical structures. The model accurately captures both beam and 3D behavior, significantly reducing computational costs while maintaining high accuracy. The research focuses on the post-buckling behavior of axially loaded elastic, circular hollow structures with rib and stringer stiffening. The nonlinear governing equations are derived using the principle of virtual work, and the analysis includes elastic fundamental nuclei using the Carrera Unified Formulation (CUF). The study derives complete expressions for the secant stiffness matrices and the tangent stiffness matrix for the unified beam element. The Newton–Raphson linearized incremental scheme with an arc-length constraint relationship is applied to solve the nonlinear algebraic system accurately. The results demonstrate that higher-order expansions yield more accurate post-buckling solutions and that the model is computationally efficient compared to traditional 3D finite element models. The incorporation of stringers and ribs enhances the post-buckling behavior, confirming the reliability of the proposed approach. The study concludes that the model is capable of capturing 3D structural behavior through cross-sectional expansions, making it a valuable tool for analyzing the post-buckling behavior of cylindrical structures.