Strain Transformations, Strains in Polar Coordinates, Equilibrium Equations in 2-D — Lesson 4

This lesson covers the transformation of strain from one system of coordinates to another. It explains how to define strain in a new system using the transformation rules for second rank tension. The lesson also discusses the definition of strains in polar coordinates, particularly when dealing with circular geometries. It further elaborates on the components of displacement in radial and tangential directions. The lesson concludes with the derivation of equilibrium equations in two-dimensional rectangular coordinates, highlighting the importance of maintaining equilibrium in the system.

Video Highlights

03:44 - Definition of strains in polar coordinates.
08:23 - Definition of strains in terms of displacement in radial and tangential directions.
28:26 - Equilibrium equations in two-dimensional rectangular coordinates.
33:02 - Consideration of body forces at each point of the body.
46:54 - Moment equilibrium and the equality of tau x y and tau y x.
52:55 - Definition of strains in the case of a hollow cylinder pressurized by internal pressure .

Key Takeaways

- Strain can be transformed from one system of coordinates to another using the transformation rules for second rank tension.
- Strains in polar coordinates are particularly useful when dealing with circular geometries.
- Displacement in a system can occur in both radial and tangential directions.
- Equilibrium equations in two-dimensional rectangular coordinates are crucial for maintaining balance in the system.
- The transformation of strain works in tension irrespective of the field of application.