Shell Theories and Constitutive Relations — Lesson 1

This lesson covers the fundamental concepts of shell theories and constitutive relations. It begins with a recap of previous weeks' topics, including the basic concept of composites, the Theory of Surfaces, and governing equations for a doubly curved shell. The lesson then delves into the steps to obtain solutions for displacement and stress moments of a shell subjected to loading and boundary conditions. It explains the shell constitutive relations, the linear shell equations, and the generalized Hooke's law. The lesson also discusses the thermoelastic analysis of a shell, the concept of orthotropic material, and the importance of the reduced stiffness matrix. It concludes with an explanation of the membrane theory of shells and the conditions under which it can be applied.

Video Highlights

04:24 - Shell constitutive relations
08:27 - Reduced stiffness matrix
11:26 - Membrane stretching and bending in a shell
19:18 - Moment in a shell
24:00 - Shear forces in a shell
30:47 - Binomial expansion in shell theory
37:14 - Membrane theory of shells

Key Takeaways

- Shell theories and constitutive relations are fundamental in understanding the behavior of shells under various conditions.
- The shell constitutive relations and the generalized Hooke's law are essential in solving linear shell equations.
- The thermoelastic analysis of a shell is crucial when analyzing a composite shell under temperature loading.
- The concept of orthotropic material is significant when dealing with composite shells made of different materials.
- The membrane theory of shells is applicable under specific conditions, such as when the shell has a smooth varying and continuous surface, and when the loads applied to the shell boundaries lie in the plane that is tangent to the middle surface.