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Dynamic buckling of an inextensible elastic ring: Linear and nonlinear analyses
Ousmane Kodio1,2, Alain Goriely1, Dominic Vella1
1Mathematical Institute, University of Oxford, Woodstock Rd, Oxford, OX2 6GG, United Kingdom.
Physical Review. E
|June 25, 2020
Summary
Dynamic buckling of elastic rings is explored. Inertia drives systems to higher modes not seen in static buckling, explaining experimental observations beyond linear stability analysis.
Area of Science:
- Mechanics of Materials
- Nonlinear Dynamics
- Fluid Dynamics
Background:
- Static buckling of slender objects is a well-understood bifurcation problem.
- Dynamic buckling shape evolution is complex and challenging to study.
- Elastic rings under normal pressure offer a model for dynamic buckling research.
Purpose of the Study:
- To theoretically analyze dynamic buckling of elastic rings under pressure.
- To understand the influence of inertia, material properties, and loading on buckling shapes.
- To explain experimental observations not covered by linear stability analysis.
Main Methods:
- Postbifurcation analysis of an elastic ring under pressure.
- Direct numerical solutions.
- Asymptotic analysis.
Main Results:
- Inertia drives the system towards higher buckling modes.
- These inertia-driven modes are inaccessible in static buckling scenarios.
- The theoretical model explains previously uncaptured experimental results.
Conclusions:
- Dynamic buckling of elastic rings is significantly influenced by inertia.
- Postbifurcation analysis provides deeper insights than linear stability.
- This work bridges theoretical understanding and experimental observations in dynamic buckling.
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