HW4 - AE 321 Homework#4 Due Monday October 6 2008 Chapter 3...

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AE 321 – Homework #4 Due: Monday October 6, 2008 Chapter 3: Strain 1. The components of a displacement field are (in meters): u x = x 2 + 20 () ± 10 ² 4 , u y = 2 yz ± 10 ² 3 , u z = z 2 ² xy () ± 10 ² 3 , (a) Consider two points (2, 5, 7) and (3, 8, 9) in the undeformed configuration. Find the change in distance between these points. (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 ² 0.003 0 0.01 0.02 sym . 0.01 ³ ´ µ µ · ¸ ¸ 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

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This note was uploaded on 03/07/2011 for the course AE 311 taught by Professor Dutton,j during the Spring '08 term at University of Illinois, Urbana Champaign.

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HW4 - AE 321 Homework#4 Due Monday October 6 2008 Chapter 3...

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