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Unformatted text preview: AE 321 – Practice Problems Chapter 3: Strain 1. The components of a displacement field are (in meters): u x = x 2 + 20 ( ) ! 10 " 4 , u y = 2 yz ! 10 " 3 , u z = z 2 " xy ( ) ! 10 " 3 , (a) Consider two points (2, 5, 7) and (3, 8, 9) in the undeformed configuration. Find the change in distance between these pints. (b) Compute the components of the Lagrangian and the infinitesimal strain tensors. (c) Compute the components of the rotation tensor. (d) Compute, and compare, the Lagrangian strains and the infinitesimal strains at location (2, 1, 3). (e) Does this displacement field satisfy compatibility? 2. The components of a strain tensor referred to the coordinate frame in the figure are ! ij [ ] = 0.02 " 0.003 0.01 0.02 sym . 0.01 # $ % % & ’ ( ( and are constant in the region shown. The direction cosines of AC are (1/ √ 2, 0, 1/ √ 2) and of BD are (1/ √ 6, √ 2/ √ 3, 1/ √ 6). A B C D O x x x 1 2 3 Find: (a) The extension ratios of lines AC and DB....
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 Fall '07
 waller
 Deformation, #, Finite strain theory, infinitesimal strain tensor

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