Extension of Rayleigh-Ritz Method and Galerkin’s Method — Lesson 6

This lesson covers the concept of column buckling and the calculation of critical load. It delves into the Rayleigh-Ritz method, where a single sinusoidal function is assumed for the deformation of a simply supported column with a uniform cross-section. The lesson then moves on to discuss a column with variable cross-section and the derivation of equilibrium configuration and critical load. The Galerkin method is also introduced for deriving the critical load for a hinged fixed column using a governing differential equation. The lesson concludes with an example of calculating the critical load of a column using the Galerkin method.

Video Highlights

01:46 - Discussion on buckling of column with variable stiffness
08:36 - Calculation of potential energy of the applied load
13:10 - Discussion on non-trivial solution for critical load
29:37 - Introduction to Galerkin method and its application in finding critical load of a column

Key Takeaways

- The Rayleigh-Ritz method assumes a single sinusoidal function for the deformation of a simply supported column with a uniform cross-section.
- For a column with variable cross-section, more than one mode shape is considered for the assumed buckled shape.
- The Galerkin method is used to derive the critical load for a hinged fixed column using a governing differential equation.
- The total potential energy is minimized to derive the equilibrium equation and critical load.
- The Galerkin method minimizes the error in the complete domain by integrating the residue multiplied with the basis function.