Solution of Donnell's Equation for Finding Critical Load — Lesson 2

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.

Video Highlights

01:03 - Introduction to the F-w formulation
08:51 - Explanation of the equilibrium equation in x theta coordinate
15:25 - Explanation of the single equilibrium equation
21:48 - Explanation of the equilibrium equation in terms of stress function

Key Takeaways

- 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.