Strain Displacement Relations — Lesson 3

This lesson covers the classification of shell surfaces and the strain displacement relations in a curvilinear coordinate system. It explains the orthogonal curvilinear coordinate system and how to represent the strain displacement in this system. The lesson also discusses the cylindrical coordinate system and how to analyze it. It further explains how to represent a point in a 3-dimensional space and how to express the Cartesian system in terms of curvilinear parameters. The lesson concludes with the derivation of strain displacement relation in the curvilinear coordinate system and the explanation of different shell theories.

Video Highlights

01:56 - Representation of the cylindrical coordinate system.
04:04 - Spherical coordinate system and its representation in Cartesian coordinates.
10:34 - Derivation of strain displacement relation in the curvilinear coordinate system.
33:17 - Shell theories: Love’s and Kirchhoff Shell theory.
44:46 - Strain displacement relations in different shell theories.

Key Takeaways

- Strain Displacement Relations are crucial in understanding Shell Theories.
- The cylindrical coordinate system is ideal for solving problems related to singly curved surfaces.
- The transformation of the Cartesian system into curvilinear parameters is possible.
- A point in a 3-dimensional space can be defined in terms of curvilinear parameters.
- The derivation of strain displacement relation in the curvilinear coordinate system is complex but achievable with the right understanding.