16100lecture4_cg

16100lecture4_cg - Coordination Transformations for Strain...

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Unformatted text preview: Coordination Transformations for Strain & Stress Rates To keep the presentation as simple as possible, we will look at purely two-dimensional stress-strain 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 x-y 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 =...
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16100lecture4_cg - Coordination Transformations for Strain...

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