This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Coordination Transformations for Strain & Stress Rates To keep the presentation as simple as possible, we will look at purely twodimensional stressstrain rates. Given an original coordinate system ( x , y ) and a rotated system ( y x , ) as shown below: x x' y y' Recall that the strain rates in the xy coordinate system are: u 1 u v v = = = xx xy yy x 2 y + x y Or, in index notation: = ij 1 2 x u i j + u x i j Also, we note that the unit vectors for the rotated axes are: K i K = cos i K + sin j K K K j = sin i + cos j Thus, the location of a point in ( y x , ) is: cos sin x x = y y sin cos Similarly, the velocity components are related by: cos sin u u = v v sin cos For differential changes, we also have cos sin dx dx =...
View
Full
Document
 Fall '03
 willcox
 Dynamics, Aerodynamics

Click to edit the document details