Governing Differential Equation of Plate Buckling Using Small Deflection Theory - 2 — Lesson 3

This lesson covers the derivation of the governing differential equation of plate buckling using the equilibrium approach. It explains how to convert the equation from force and moment resultants to displacement components. The lesson also discusses how to find the unknowns in the equation by considering the deformation of the plate. It further elaborates on the moment displacement relation and the changes in the deflected middle surface. The lesson concludes by correlating the derived equation to the buckling expression of a column.

Video Highlights

00:36 - Explanation of the governing differential equation in terms of force and moment resultants
04:05 - Explanation of the moment displacement relation using a figure
11:55 - Explanation of how the moment develops and how to write the expression of the moment
17:30 - Calculation of M x, M y, and M xy
23:42 - Final expression of the governing differential equation of plate buckling under the action of in-plane forces

Key Takeaways

- The governing differential equation of plate buckling can be derived using the equilibrium approach.
- The equation initially derived in terms of force and moment resultants can be converted to displacement components.
- The unknowns in the equation can be found by considering the deformation of the plate.
- The moment displacement relation and the changes in the deflected middle surface play a crucial role in the derivation.
- The derived equation for plate buckling can be correlated to the buckling expression of a column.