Governing Differential Equation of Plate Buckling Using Small Deflection Theory - 1 — Lesson 2

This lesson covers the in-depth understanding of plate buckling theory. It explains the concepts of local and global buckling, and the idealisations in small deflection theory of thin plate buckling. The lesson further elaborates on the derivation of the governing differential equation of plate buckling using the equilibrium approach. It discusses the concept of neutral equilibrium and the forces acting on a laterally bent plate. The lesson also explains the process of finding the equilibrium of in-plane forces and the resultant of middle surface forces. It concludes with the derivation of three equilibrium equations for plate buckling.

Video Highlights

00:29 - EDiscussion on local and global buckling
05:59 - Derivation of the equilibrium equation for in-plane forces
09:14 - Discussion on the concept of middle surface strains
14:10 - Explanation of the z direction component of forces
21:04 - Discussion on the moment of all forces about x-axis and y-axis
27:32 - Derivation of the equilibrium equations for plate buckling

Key Takeaways

- The small deflection theory is a concept where the membrane action resulting from flexure is negligible.
- The in-plane forces are solely due to applied constant in-plane loads and do not vary with x and y direction.
- The governing differential equation of plate buckling is derived using the equilibrium approach.
- The system is in neutral equilibrium at the critical load.
- The equilibrium of in-plane forces and the impact of transverse loading on the plate are crucial in understanding plate buckling.
- The equilibrium equations for plate buckling are derived by taking moments about the x-axis and y-axis.