Governing Differential Equation of Shell Buckling by Using Small Deflection Theory - 1 — Lesson 4

This lesson covers the concept of buckling in shells, specifically focusing on the buckling of cylindrical shells under axial compression. It delves into the differences between small deflection theory and finite deflection theory, and how these theories apply to shell buckling. The lesson also discusses the derivation of shell equations, the role of mid-surface forces, and the impact of initial curvature on shell buckling. It further explains the derivation of governing differential equations, the equilibrium of forces in different directions, and the relationship between middle surface force and displacement. The lesson concludes with the stress-strain relation used for thin plates and shells.

Video Highlights

00:50 - Discussion on small deflection theory and finite deflection theory in plate analysis
04:15 - Explanation of the use of circumferential coordinate in comparing the shell with the plate
09:42 - Discussion on the derivation of the equation for forces in the z direction considering curvature
16:33 - Explanation of the derivation of the equation for all forces in the z direction
20:13 - Explanation of the derivation of the middle surface force displacement relation for shells with small deflection theory
27:27 - Discussion on the derivation of the stress strain relation used for thin plate and thin shell

Key Takeaways

- Buckling of shells, particularly cylindrical shells under axial compression, is a complex process influenced by various factors.
- Both small deflection theory and finite deflection theory are considered in shell buckling analysis.
- The presence of initial curvature in shells significantly impacts the buckling process.
- Governing differential equations are derived considering displacements in different directions.
- The equilibrium of forces in different directions plays a crucial role in understanding shell buckling.
- The relationship between middle surface force and displacement is essential in shell buckling analysis.
- The stress-strain relation used for thin plates is also applicable to thin shells.