assn3 - 4. Justify our step in the derivation of the local...

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16.21 - Techniques of structural analysis and design Homework assignment # 3 Handed out: 2/25/05 Due: 3/4/05 February 24, 2005 Warm-up exercises (not for grade) Problem 3.23 from textbook Problem 3.24 from textbook Problem 3.25 from textbook (Compliments of C. Graff. ) Create a solid model of the flat plate in the ±gure using Solidworks (you may turn in your ±le electronically for feedback purposes). 1
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Problems for grade 1. Problem 3.26 from textbook 2. Problem 3.27 from textbook: (a) Find the linear strains corresponding to the following displacement ±eld: 0 u 1 = u 1 ( x 1 , x 2 ) + x 3 φ 1 ( x 1 , x 2 ) 0 u 2 = u 2 ( x 1 , x 2 ) + x 3 φ 2 ( x 1 , x 2 ) 0 u 3 = u 3 ( x 1 , x 2 ) (b) Verify that the resulting strain ±eld is compatible for any choice 0 of functions u i , φ i . 3. Problem 3.30 from textbook
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Unformatted text preview: 4. Justify our step in the derivation of the local form of the rst law of thermodynamics for deforming bodies where we assumed: u i ij = ij ij u j i.e., demonstrate that the double scalar product (full contraction) of a symmetric tensor A = A T , with an arbitrary tensor B amounts to contracting A with the symmetric part of B : 1 B sym = B + B T 2 (Hint: Decompose B into its symmetric and antisymmetric parts and show that the contraction of a symmetric tensor A with the antisym-metric part of B : 1 B antisym = B B T 2 is zero. 5. Obtain the relationships between the engineering elastic constants ( E, ) and the Lam e constants ( 1 , 2 ). 2...
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This note was uploaded on 11/07/2011 for the course AERO 16.21 taught by Professor Dffs during the Fall '10 term at MIT.

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assn3 - 4. Justify our step in the derivation of the local...

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