Understanding Shell Governing Equations — Lesson 4

This lesson covers the development of Shell Governing Equations, focusing on Love's first approximation theory and the first-order shear deformation theory. It explains the process of choosing a suitable displacement field and strain displacement field. The lesson also discusses the concept of geometrical nonlinearity, Von Karman nonlinearity, and the importance of strain displacement relations. It further elaborates on the definition of stress resultants and the derivation of governing equations based on Sander’s shell theory. The lesson concludes with an explanation of the Hamilton principle and the calculation of kinetic energy for a shell element.

Video Highlights

03:12 - Von Karman nonlinearity and its effects
07:30 - Concept of stress resultant and its definition
13:33 - Hamilton principle and its application in deriving governing equations
14:39 - kinetic energy for a shell element
20:50 - Concept of internal work done
24:13 - Concept of external work done
31:55 - Concept of non-linear terms

Key Takeaways

- The development of Shell Governing Equations involves choosing a suitable displacement field and strain displacement field.
- Geometrical nonlinearity is crucial for the buckling of the shell.
- Von Karman nonlinearity considers the nonlinearity effect through deflection.
- Stress resultants are defined per unit of arc length on the reference surface.
- Governing equations are derived based on Sander’s shell theory and considering the Von Karman nonlinearity.
- The Hamilton principle states that the sum of total energy and dt is zero.
- The kinetic energy for a shell element is calculated using the Hamilton principle.