A semi-empirical modeling approach for predicting the deformational capacity of axially-compressed cylindrical shells based on a novel material stress-strain characterization method

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Adoption of cylindrical shell structures for various load-resistance applications has enjoyed wide-spread acceptance in the field of civil, mechanical and aerospace engineering, mainly due to the exceptional structural efficiency of cylindrical shells to withstand significant longitudinal and circumferential in-plane loading without bending. However, where such in-plane loading conditions are compressive, cylindrical shells are likely to exhibit an unstable response characterized by localized out-of-plane deformation. Computerized numerical simulation is often required for accurate and efficient estimation of the strains and resultant stresses in cylindrical shells under loading, especially where the thickness of the shell is sufficient to evoke an inelastic buckling response in the structure. The buckling behavior of thin-walled cylindrical shells subjected to uniform axial compression has been studied in this paper using the finite element (FE) simulation method to assign respective material, geometric, loading and boundary properties to computer-generated cylindrical shell specimens. Extensive parametric analysis, consisting of approximately 720 FE runs, was then conducted based on a full-factorial empirical design, applying ample variations of the relevant parameters that influence the buckling response of axially-compressed cylindrical-shell structures. Nonlinear multiple regression techniques were then employed to derive the coefficients of nonlinear mathematical expressions, each developed as an arithmetic product of appropriate variable functions related to the respective functional sensitivities of the investigated parameters. Strain-hardening properties were incorporated into the mathematical expressions based on the shape constants of the Ndubuaku stress-strain model; which has proven to be remarkably useful for accurate parameterization of the stress-strain behavior over the full range of strains for a wide range of metallic materials, including materials with a well-defined yield plateau. Excellent predictions of FEA-derived values for the critical limit strain limit were obtained, and a simple statistical approach was presented to increase the conservativeness of the semi-empirical model as required.