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<p>This paper extends earlier work on the asymptotic reduction of buckling equations for beams, plates, and thin elastic shells, with a particular emphasis on configurations that develop localised compressive stresses under globally applied loads. Using a simplified model problem inspired by a cantilever cylindrical shell under vertical shear loading, we explore the role of degeneracy in the associated dispersion relation. The governing equations, derived in previous work, are modified through the introduction of two tunable parameters that allow precise control over the order of degeneracy. The resulting problems admit solutions exhibiting a rapidly oscillating spatial component modulated by a slowly varying envelope. Even in cases where the fast oscillations vanish, this framework remains analytically advantageous. A simplified multiple-scale asymptotic method is employed to derive reduced-order models, whose structure is shown to be intimately related to the degree of degeneracy in the dispersion relation. These findings provide a deeper understanding of when and why significant asymptotic simplifications are possible in static buckling problems of this kind.</p>

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Degenerate asymptotic phenomena in the buckling of inhomogeneously pre-stressed cylindrical shells

  • 期刊论文

  • 发表日期：

    2025年9月8日

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  • Ciprian D. Coman

摘要

This paper extends earlier work on the asymptotic reduction of buckling equations for beams, plates, and thin elastic shells, with a particular emphasis on configurations that develop localised compressive stresses under globally applied loads. Using a simplified model problem inspired by a cantilever cylindrical shell under vertical shear loading, we explore the role of degeneracy in the associated dispersion relation. The governing equations, derived in previous work, are modified through the introduction of two tunable parameters that allow precise control over the order of degeneracy. The resulting problems admit solutions exhibiting a rapidly oscillating spatial component modulated by a slowly varying envelope. Even in cases where the fast oscillations vanish, this framework remains analytically advantageous. A simplified multiple-scale asymptotic method is employed to derive reduced-order models, whose structure is shown to be intimately related to the degree of degeneracy in the dispersion relation. These findings provide a deeper understanding of when and why significant asymptotic simplifications are possible in static buckling problems of this kind.