This lesson covers the in-depth analysis of plate buckling theories, focusing on the finite deflection theory. It explains the derivation of the governing differential equation in terms of stress function and displacement. The lesson also discusses the equilibrium approach, energy approach, and the Galerkin method used to solve the governing differential equation. It further elaborates on the concept of in-plane forces, the role of membrane action resulting from flexure, and the impact of mid-plane strain. The lesson concludes with the introduction of Von-Karman large deflection plate equations.

- The governing differential equation of plate buckling is derived based on small deflection plate theory.
- Finite deflection theory considers the membrane action resulting from flexure.
- The in-plane forces are a combination of the applied constant in-plane load and the membrane action resulting from flexure.
- The mid-plane strain is not considered in the small deflection plate theory.
- The Von-Karman large deflection plate equations are derived by substituting the constitutive relation in the compatibility condition and the equilibrium equation.

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