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Strain Energy and Entropy Based Scaling of Buckling Modes
1Institute of Structural Mechanics, Faculty of Civil Engineering, Brno University of Technology, 602 00 Brno, Czech Republic.
Entropy (Basel, Switzerland)
|December 23, 2023
Summary
Entropy is newly utilized to analyze structural buckling, connecting strain energy and entropy for pin-ended struts. This approach allows ranking buckling modes by deformation energy or entropy, with decreasing entropy modeling initial imperfections in steel frames.
Area of Science:
- Structural Mechanics
- Thermodynamics
- Computational Engineering
Background:
- Buckling analysis is crucial for structural stability.
- Initial imperfections significantly influence buckling behavior.
- Entropy's role in mechanical systems is underexplored.
Purpose of the Study:
- To introduce a novel application of entropy in buckling analysis.
- To establish a connection between strain energy and entropy for structural members.
- To develop a method for modeling initial geometric imperfections using buckling modes.
Main Methods:
- Deriving a relationship between strain energy and entropy for a pin-ended strut.
- Employing a surrogate model to decompose strain energy into entropy and virtual temperature.
- Analyzing buckling modes and their scaling factors in steel plane frames.
Main Results:
- A new concept linking strain energy and entropy in buckling is derived.
- Entropy provides a rational basis for ranking buckling modes.
- Decreasing entropy correlates with scaling factors of buckling modes, modeling initial imperfections.
- Entropy scales inversely with the square of the mode index for a given energy.
Conclusions:
- Entropy is a valuable complement to strain energy in structural mechanics.
- Scaled buckling modes, informed by entropy, can effectively model initial geometric imperfections in steel plane frames.
- This framework offers practical engineering applications for stability analysis.
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