Critical Load of Plate Using Equilibrium Approach — Lesson 4

This lesson covers the concept of plate buckling and the derivation of governing differential equations. It explains the assumptions made during the derivation process, such as small deflections compared to plate thickness and negligible membrane action resulting from flexure. The lesson also discusses the equilibrium approach, energy approach, and Galerkin method for solving these equations. For instance, the Galerkin method involves substituting an assumed shape function in the governing differential equation and minimizing the error in the complete domain of the plate. The lesson concludes with a problem-solving session where the critical load of a simply supported plate is calculated using the equilibrium approach.

Video Highlights

01:57 - Explanation of the process of deriving the governing differential equation
06:44 - Explanation of the governing differential equation for the given problem
15:07 - Substitution of the series solution into the governing differential equation and derivation of the expression for the critical load
23:12 - Explanation of how to find the number of half waves in the x direction corresponding to the minimum value of the critical load
29:40 - Plotting of the aspect ratio and the buckling stress coefficient

Key Takeaways

- Governing differential equations for plate buckling are derived based on certain assumptions.
- The equilibrium approach, energy approach, and Galerkin method are different methods to solve these equations.
- The Galerkin method involves substituting an assumed shape function in the governing differential equation and minimizing the error.
- The critical load of a simply supported plate can be calculated using the equilibrium approach.
- The buckling stress coefficient can be determined for any aspect ratio.