Critical load and Post Buckling Behaviour of Plate Using F-w Formulation — Lesson 3

This lesson covers the finite deflection theory of plate buckling, focusing on the derivation of governing differential equations in terms of stress function and displacement. It uses an example of a simply supported plate uniformly compressed in one direction to illustrate the calculation of critical load and post-buckling behaviour. The lesson also explains the Galerkin method for solving these equations and introduces the F-w approach. It further discusses the concept of membrane action resulting from flexure and how it influences the equations. The lesson concludes with a detailed explanation of the load-displacement curve and the concept of post-buckling strength.

Video Highlights

00:38 - Explanation of the example of a simply supported plate uniformly compressed in one direction.
07:31 - Explanation of the boundary conditions for the problem.
11:38 - Explanation of the complementary solution and the particular integral.
20:43 - Substitution of the stress function and transverse displacement in the equilibrium equation.
29:19 - Derivation of the critical load for column buckling.

Key Takeaways

- The governing differential equations for plate buckling are derived considering the membrane action resulting from flexure.
- The Galerkin method and F-w approach are effective methods for solving these equations.
- The concept of membrane action due to flexure plays a significant role in plate buckling.
- The load-displacement curve provides insights into the post-buckling behaviour of the plate.
- The plate's ability to resist axial loads in excess of the critical load after buckling is known as post-buckling strength.