The Origin of Imperfection Sensitivity in the Buckling of Cylindrical Shells
Abstract
Buckling of thin cylindrical shells under axial compression, a classical example of a subcritical instability, is highly sensitive to small imperfections, with minute geometric variations causing large changes in buckling threshold. To uncover the origin of this sensitivity, we use numerical continuation and bifurcation analysis while systematically varying the depth and size of a single localized Gaussian defect. We show that the instabilities of the imperfect shell originate from localized equilibria already present in the perfect shell. By breaking translation symmetry, the defect pins these equilibria and changes how they connect to the imperfect base state. Small changes in defect geometry can thereby switch the bifurcation that triggers buckling, producing non-monotonic and discontinuous changes in buckling threshold and abrupt changes in buckling mode. Imperfection sensitivity is therefore not simply sensitivity to imperfection magnitude, but sensitivity of the underlying bifurcation structure to imperfection geometry.
Related
- Payne's conjecture for buckling eigenvalues of odd index
- Element-dependent buckling loads of stiffened panels under cantilevered shear
- Buckling Prediction for Nonlinear Elastic Beams with Soft Inclusions
- Von Kármán theories for thin elastic shells subject to pressure
- Pólya's conjecture for Neumann eigenvalues of spherical shells
BibTeX
@misc{yang2026origin,
title = {{The Origin of Imperfection Sensitivity in the Buckling of Cylindrical Shells}},
author = {Tian Yang and Tobias M. Schneider},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19436},
eprint = {2609.19436},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19436},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Origin of Imperfection Sensitivity in the Buckling of Cylindrical Shells
AU - Tian Yang
AU - Tobias M. Schneider
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19436
UR - https://arxiv.org/abs/2609.19436
AB - Buckling of thin cylindrical shells under axial compression, a classical example of a subcritical instability, is highly sensitive to small imperfections, with minute geometric variations causing large changes in buckling threshold. To uncover the origin of this sensitivity, we use numerical continuation and bifurcation analysis while systematically varying the depth and size of a single localized Gaussian defect. We show that the instabilities of the imperfect shell originate from localized equilibria already present in the perfect shell. By breaking translation symmetry, the defect pins these equilibria and changes how they connect to the imperfect base state. Small changes in defect geometry can thereby switch the bifurcation that triggers buckling, producing non-monotonic and discontinuous changes in buckling threshold and abrupt changes in buckling mode. Imperfection sensitivity is therefore not simply sensitivity to imperfection magnitude, but sensitivity of the underlying bifurcation structure to imperfection geometry.
ER -