This lesson covers the solution technique and mix type formulation of static bending of finite shell and free vibration of the finite shell under Levy type support conditions. It explains the displacement-based approach and the concept of eigenvalues and eigenvectors. The lesson also discusses the Pagano type solution and the three different ways to write a solution for a simultaneous first-order differential equation. It further elaborates on the mixed formulation technique, where displacement and stresses are taken as primary variables. The lesson concludes with a discussion on various techniques used to solve shell equations.

- The displacement-based approach is used to explain the static bending of Levy-type boundary conditions for the finite cylindrical shell.
- Eigenvalues and eigenvectors play a crucial role in defining new variables and converting them into first-order differential equations.
- The Pagano type solution is a standard solution used in higher engineering mathematics.
- The mixed formulation technique takes displacement and stresses as primary variables, leading to a first-order differential equation.
- Various techniques like DQM, FDM, SSDQM, Fourier transform, differential integral transform, EKM, Ritz, and finite element technique are used to solve shell equations.

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