Post Buckling Behaviour of an Imperfect Axially Compressed Cylindrical Shell Panel — Lesson 4

This lesson covers the F-w formulation, which is a type of formulation that involves two coupled governing differential equations in terms of stress function and displacement. The lesson also delves into the concept of shell buckling, explaining how initial imperfections can significantly affect the buckling characteristics of cylindrical panels. The lesson further illustrates these concepts through an example of finding the post-buckling behavior of an axially compressed cylindrical shell panel using the Galerkin method. The lesson concludes by discussing the implications of these findings, particularly how the maximum load an initially imperfect panel can support is considerably less than the critical load given by classical theory.

Video Highlights

00:42 - Explanation of the equilibrium equation and compatibility equation, known as F-w formulation.
06:15 - Discussion on the compatibility equation and its application in the example.
13:05 - Discussion on the particular solution and how it is derived.
20:50 - Explanation of how to use Galerkin's method to minimize the residue and find the value of P x.
33:26 - Discussion on the impact of small initial imperfection on the buckling behaviour of flat plate.

Key Takeaways

- The F-w formulation involves two coupled governing differential equations in terms of stress function and displacement.
- Initial imperfections can significantly affect the buckling characteristics of cylindrical panels.
- The Galerkin method can be used to solve the governing differential equations to find the post-buckling behavior of an axially compressed cylindrical shell panel.
- The maximum load an initially imperfect panel can support is considerably less than the critical load given by classical theory.