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Fully localized post-buckling states of cylindrical shells under axial compression
Tobias Kreilos1, Tobias M Schneider1
1Emergent Complexity in Physical Systems Laboratory (ECPS), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.
Proceedings. Mathematical, Physical, and Engineering Sciences
|October 10, 2017
Summary
Researchers identified edge states in thin cylindrical shells under compression. These edge states, or single dimple deformations, evolve into complex patterns, potentially explaining shell buckling triggers.
Area of Science:
- Solid Mechanics
- Structural Engineering
- Nonlinear Dynamics
Background:
- Thin cylindrical shells are susceptible to buckling under axial compression.
- Understanding the nonlinear behavior and stability limits is crucial for structural integrity.
- Previous studies often focused on linear stability or simplified nonlinear models.
Purpose of the Study:
- To compute nonlinear force equilibrium solutions for clamped thin cylindrical shells under axial compression.
- To identify and characterize the 'edge state' deformation within the stability boundary.
- To investigate the evolution of deformation patterns, including dimple formation and propagation.
Main Methods:
- Numerical computation of nonlinear force equilibrium solutions.
- Analysis of dynamic instability and stability boundaries.
- Identification of attractors for dynamics restricted to the stability boundary.
Main Results:
- Dynamically unstable equilibrium solutions were found on the stability boundary.
- A single localized dimple deformation was identified as the edge state.
- Homoclinic snaking led to the formation of multiple dimples and complex patterns under varying axial loads.
Conclusions:
- The identified nonlinear solutions represent critical shape deformations.
- These edge states and their evolution may provide insights into the triggering mechanisms of shell buckling and collapse.
- The study advances the understanding of post-buckling behavior in thin cylindrical shells.
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