Exploring Approximate Solutions for Finite Shells — Lesson 1

This lesson covers the development of approximate solutions for finite shells subjected to arbitrary support conditions. It delves into the Ritz method and Galerkin method, which are popular techniques for developing solutions for arbitrary support conditions. The lesson also discusses the extended Kantorovich method, which was first proposed in 1939 and has been used extensively in higher engineering mathematics. The lesson further explains the limitations of the Ritz or Galerkin method and introduces the concept of the Kantorovich method. It also provides an overview of how to develop a solution using the extended Kantorovich method for a cylindrical shell panel.

Video Highlights

03:10 - Limitations of the Ritz or Galerkin method
10:29 - Extended Kantorovich method for a cylindrical shell panel
16:46 - Boundary conditions for clamped, simply supported, and free cases
26:41 - Use of the Kantorovich method for solving the governing equations
36:19 - Intro to state space and differential quadrature method (SS DQM)

Key Takeaways

- The Ritz and Galerkin methods are popular techniques for developing solutions for arbitrary support conditions.
- The extended Kantorovich method, first proposed in 1939, is a significant method in higher engineering mathematics.
- The Ritz or Galerkin method has limitations, particularly in finding a function that satisfies other boundary conditions easily.
- The Kantorovich method was developed to improve the Ritz or Galerkin method.
- The extended Kantorovich method can be used to develop a solution for a cylindrical shell panel.