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m15_ps12_fall03

m15_ps12_fall03 - 1 x 2 x 3 b The rigid body rotation about...

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Problem M15 (Materials and Structures) i) By considering the change in volume of an infinitessimal element undergoing small elongational strains show that the volumetric strain D V V ˆ = e 1 + 2 + 3 ii) A continuous body experiences a displacement field, u n that is described by: ( 2 2 u 1 = [ 0.5 x 1 - x 2 ) + 0.5x 1 x 2 ] 10 - 3 mm ( 2 2 u 1 = [ 0.25 x 1 - x 2 ) - x 1 x 2 ] 10 - 3 mm u 3 = 0 . Determine: a) The 6 components of the strain tensor as a function of position (i.e. in terms of x
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Unformatted text preview: 1 , x 2 , x 3 ) b) The rigid body rotation about x 3 as a function of position (i.e. in terms of x 1 , x 2 , x 3 ). c) The principal strains and the principal strain directions at x 1 = 5mm and x 2 =7 mm. d) The volumetric strain at x 1 = 5mm and x 2 =7 mm....
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