Large Deflection Theory for Stability Analysis of Rigid Body Stability Models — Lesson 3

This lesson covers the concept of large deflection theory in the context of stability analysis. It explains how to predict critical load for perfect geometry from an imperfect geometry using energy approach. The lesson also discusses the small deflection theory, which refers to small angles of rotation in bend configuration. It then delves into the large deflection theory, using a single degree of freedom system as an example. The lesson further explains how to calculate the total potential energy and how to determine whether a system is in stable or unstable equilibrium. For instance, if the load is greater than the spring constant squared divided by the length, the system is in equilibrium.

Video Highlights

00:56 - Explanation of small deflection theory
03:30 - Calculation of the spring force
10:51 - Explanation of the static equilibrium position
17:38 - Explanation of the stable and unstable equilibrium
24:47 - Explanation of the system's equilibrium when P is greater than k a square by l and theta is not equal to 0

Key Takeaways

- Small deflection theory refers to small angles of rotation in bend configuration.
- Large deflection theory is used for stability analysis of systems with significant angles of rotation.
- The total potential energy of a system can be calculated to determine its equilibrium state.
- A system is in equilibrium if the load is greater than the spring constant squared divided by the length.
- The magnitude of the load and the angle of rotation are interrelated; if one increases, the other also increases for equilibrium.