This lesson covers the derivation of the basic governing equations for a shell. It starts with a recap of the preliminary basic equations of shells and the theory of differential equations of shells covered in previous weeks. The lesson then delves into the strain energy or elastic strain energy of a shell, explaining how it can be written and sometimes known as internal work done. The lesson further breaks down the calculation of strain energy into sub integrals and explains the linear, non-linear, and curvature terms. The lesson also covers the external work done on a shell and how it contributes to the total work done. An example used in this lesson is the calculation of strain energy for a 3-dimensional shell.

- The basic governing equations for a shell are derived from the preliminary basic equations and the theory of differential equations of shells.
- The strain energy of a shell, also known as internal work done, is a crucial part of these equations.
- The strain energy is divided into linear, non-linear, and curvature terms.
- The external work done on a shell contributes to the total work done.
- The governing equations are used to analyze a shell resting on an elastic foundation with some damping coefficient.

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