Three Dimensional Buckling — Lesson 3

This lesson covers the development of a three-dimensional buckling solution for a cylindrical shell. It delves into the governing equations for two-dimensional shell theories and first-order shear deformation shell theories. The lesson also explains the strain displacement relations and the governing partial differential equations in the lame parameters form. It further discusses the form of an equilibrium equation of stresses in curvilinear coordinate and the development of a three-dimensional solution for the case of a shell, plate, or beam. The lesson concludes with the study of the buckling of a composite cylindrical shell and the buckling of an angle ply cylindrical shell.

Video Highlights

01:53 - Three-dimensional equation of equilibrium governing equation.
07:53 - 3-D governing equations using the concept of principal virtual work done.
15:48 - Explanation of the buckling of a composite cylindrical shell.
17:08 - Buckling of a thin cylinder and angle ply cylindrical shell.
31:23 - Buckling of a multi-laminated angle ply cylindrical shell.

Key Takeaways

- Understanding the governing equations for two-dimensional shell theories and first-order shear deformation shell theories is crucial in developing a three-dimensional buckling solution for a cylindrical shell.
- The form of an equilibrium equation of stresses in curvilinear coordinate plays a significant role in developing a three-dimensional solution for different shell geometries.
- The buckling of a composite cylindrical shell can occur under various conditions, including due to a concentrated load, uniaxial under axial load, or due to normal pressure.
- Different mathematical techniques, such as the state space approach and the successive layer approach, can be used to solve the governing equations for the buckling of a cylindrical shell.