Three Dimensional Bending — Lesson 1

This lesson covers the theory of composite shell, focusing on the development of a three-dimensional solution for a cylindrical shell. It delves into the explanation of doubly curved shells and singly curved shells using first-order shear deformation theories. The lesson also discusses the advantages of two-dimensional shell theories and the accuracy of three-dimensional shell theories. It further explains the displacement field, the importance of three-dimensional solutions as benchmark solutions, and the concept of angle ply cylindrical shell. The lesson concludes with the explanation of strain field relations, three-dimensional constitutive relations, and the equations of equilibrium.

Video Highlights

02:45 - 3-D shell theories and their purpose.
05:14 - Development of shell solutions for thermal loading.
16:01 - 3-D constitutive relations.
24:09 - Different approaches to solve the equations of equilibrium.
33:24 - Interface continuity conditions in layered panels.
38:14 - Non-dimensionalized coordinates and their use.

Key Takeaways

- Three-dimensional solution for a cylindrical shell can be developed, which provides a very accurate estimation of all stresses and displacement.
- Three-dimensional solutions can be used as benchmark solutions for assessing the accuracy of other two-dimensional solutions.
- The concept of angle ply cylindrical shell, use of the equation of motion, constitutive equations of linear 3D thermoelasticity and application of these in finite element solutions, finite different solutions, and DQM solutions.