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Nonlinear buckling behaviour of spherical shells: barriers and symmetry-breaking dimples
John W Hutchinson1, J Michael T Thompson2
1School of Engineering and Applied Sciences, Harvard University, Cambridge 02138, MA, USA jhutchin@fas.harvard.edu.
Summary
This study analyzes the post-buckling behavior of elastic spherical shells under external pressure. We detail how dimples form and affect shell volume, offering insights into shell stability and nonlinear mechanics.
Area of Science:
- Solid mechanics
- Materials science
- Nonlinear dynamics
Background:
- Elastic spherical shells are critical structural components.
- Understanding their post-buckling behavior under external pressure is essential for design and safety.
- Previous studies often simplify the complex nonlinear responses observed.
Purpose of the Study:
- To characterize the nonlinear axisymmetric post-buckling behavior of perfect, thin, elastic spherical shells under external pressure.
- To investigate the asymmetric bifurcations occurring in the post-buckling regime.
- To provide detailed results for a structure/loading combination exhibiting exceptionally nonlinear buckling.
Main Methods:
- Analysis of nonlinear axisymmetric post-buckling behavior.
- Characterization of asymmetric bifurcations.
- Determination of relationships between pressure, dimple amplitude, and volume change.
- Evaluation of criteria like the Maxwell condition.
Main Results:
- Buckling mode localizes into a polar dimple immediately after buckling onset.
- Established relationships between pressure, dimple amplitude, and volume change over a wide range of deflections.
- Identified non-axisymmetric bifurcations into multi-lobed dimples deep in the post-buckling regime.
Conclusions:
- The study provides a comprehensive characterization of post-buckling phenomena in elastic spherical shells.
- Accurate evaluation of stability criteria and loading effects (pressure vs. volume-controlled) is enabled.
- The findings contribute to understanding pattern formation through instabilities in complex media.
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