This lesson covers the derivation of the governing differential equation for cylindrical shell buckling using finite deflection theory. It introduces the F-w formulation, which consists of two coupled governing differential equations in terms of stress function F and displacement w. The lesson also explains the middle surface strain displacement relations and the equilibrium equation in the xy coordinate system. It further discusses the forces due to mid-plane stretching and applied edge loading. The lesson concludes with the introduction of the stress function that satisfies the equilibrium equations and the derivation of the compatibility equation.

- The governing differential equation for cylindrical shell buckling is derived using finite deflection theory.
- The F-w formulation consists of two coupled governing differential equations in terms of stress function F and displacement w.
- The middle surface strain displacement relations and the equilibrium equation in the xy coordinate system are crucial in this derivation.
- Forces due to mid-plane stretching and applied edge loading are considered in the equilibrium equation.
- The stress function that satisfies the equilibrium equations is introduced, leading to the derivation of the compatibility equation.

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