This lesson covers the concept of cylindrical shell buckling using finite deflection theory. It delves into the derivation of two coupled governing differential equations in terms of stress function F and displacement w, known as the F-w formulation. The lesson further discusses the modification of these equations by incorporating initial imperfections, which helps in resolving the discrepancy between theoretical and experimental results of shell buckling. The lesson also explains the importance of considering imperfections in the model for accurate results. For instance, a near-perfect specimen's experimental buckling load is very close to the theoretical critical load.

- The F-w formulation consists of two coupled governing differential equations derived using finite deflection theory.
- Initial imperfections significantly reduce the maximum load that an axially compressed cylindrical shell can support.
- Incorporating initial imperfections in the equilibrium and compatibility equations helps in achieving results closer to experimental values.
- The modified equilibrium and compatibility equations are used to analyze initially imperfect cylindrical shells.
- The governing differential equations for an initially imperfect cylindrical shell are solved simultaneously to find the critical load.

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