Governing Differential Equation of Shell Buckling by Using Small Deflection Theory - 2 — Lesson 5

This lesson covers the derivation and understanding of equilibrium equations for cylindrical shells using small deflection theory. It explains how the presence of initial curvature in a cylindrical shell results in membrane action due to secondary middle surface forces. The lesson further elaborates on how these forces are expressed in terms of mid-plane displacement components. It also discusses the equations of equilibrium for cylindrical shells in terms of displacement components. For instance, the lesson explains how compressive loads are considered negative as per sign convention. The lesson concludes with the derivation of Donnell's equation.

Video Highlights

00:53 - Explanation of the forces due to mid plane stretching in terms of mid plane displacement components
03:28 - Explanation of the moment resultants and force resultants expressed as displacement component
10:09 - Explanation of the curvature due to bending and secondary middle surface forces
21:08 - Explanation of the seventh and eighth equations of equilibrium
29:12 - Explanation of the reduced form of the seventh and eighth equations

Key Takeaways

- The equilibrium equations for cylindrical shells are derived using small deflection theory.
- The presence of initial curvature in a cylindrical shell results in membrane action due to secondary middle surface forces.
- These forces are expressed in terms of mid-plane displacement components.
- Compressive loads are considered negative as per sign convention.