Snap through Stability Model and Model of Imperfect Geometry — Lesson 5

This lesson covers the concept of stability analysis and critical load in mechanical models. It delves into the energy and equilibrium methods used to analyze a system subjected to critical load. The lesson also discusses the effect of eccentricity on critical load and how to derive the critical load for perfect configuration by making the eccentricity approach zero. The lesson further explains the concept of snap through buckling and how to find the critical load using equilibrium and energy approaches. It also provides a detailed explanation of the total potential energy of a system when it gets deformed.

Video Highlights

00:38 - Discussion on mechanical model undergoing snap through buckling
05:20 - Finding the critical load
10:56 - Explanation of static equilibrium positions
27:10 - Derivation of the total potential energy in the deformed configuration
37:23 - Explanation of the critical condition

Key Takeaways

- The equilibrium method and energy method are used to analyze the system and determine the characteristics of the equilibrium configuration.
- The critical load for perfect configuration was derived by making the eccentricity approach 0.
- The total potential energy includes the strain energy stored in the spring and the external work done due to the load.
- The equilibrium positions are characterized by vanishing the first variation of the total potential energy.
- The characteristic of equilibrium is governed by the second variation of total potential energy.