This lesson covers the in-depth understanding of shell theories and their formulations, focusing on the special cases of the shell of revolutions. It explains the governing equations for different types of shells, including cylindrical, spherical, and conical shells. The lesson also discusses the membrane theory and moment theory of shells, explaining when to use each theory. It further elaborates on the analysis of shell structures using these theories. The lesson also provides a detailed explanation of the governing equations for the membrane theory of shells and how to solve these equations. It concludes with a discussion on the moment theory of shells and its application in solving problems related to shell structures.

- Shell theories can be divided into two categories: membrane theory and moment theory.
- Membrane shell theory assumes no bending and no shear, while moment shell theory considers the effect of bending and moments.
- Governing equations for the shell of revolution are valid for all kinds of shells that can be generated through the shell of revolution.
- The shell of revolutions experiences both stretching and bending to resist an applied loading.
- The shell theories are more complex when the shell material is brittle like a composite, as bending deformation remains proportional to the applied load until failure.

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