Critical Load of Plate Using Energy Approach — Lesson 5

This lesson covers the concept of plate buckling using the energy method. It begins with a recap of the governing differential equation of plate buckling derived using the equilibrium approach. The lesson then delves into the energy method, using the example of a simply supported plate uniformly compressed in one direction. The lesson explains the strain energy of the plate due to bending and how to derive the strain energy in terms of displacement. It also discusses the boundary conditions for a simply supported plate and how to represent the deflection surface using a double trigonometric series. The lesson concludes by explaining how to calculate the total potential energy of the plate and derive the critical load by minimizing the total potential energy.

Video Highlights

00:35 - Explanation of the energy method for finding critical load
05:16 - Explanation of the strain energy due to bending
09:13 - Explanation of the boundary conditions for the problem
15:35 - Explanation of the critical load obtained by minimizing the total potential energy

Key Takeaways

- The energy method can be used to find the critical load of a simply supported plate uniformly compressed in one direction.
- The strain energy of the plate due to bending can be derived in terms of displacement.
- The deflection surface can be represented using a double trigonometric series.
- The total potential energy of the plate is the sum of the strain energy and the work done by the compressive force during buckling.
- The critical load is obtained by minimizing the total potential energy.