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Derivation of normal strain, stuck

  1. Nov 24, 2012 #1
    http://imgur.com/SnHyP

    What are the mathematical steps and assumptions to reach the conclusion that length(ab) ≈ dx + ∂u/∂x*dx ?

    If you consider the the squares of the gradients to be negligible, you still have a square root and multiplication by the constant "2". What other assumptions do we make to derive the final equation?
     
  2. jcsd
  3. Nov 24, 2012 #2

    arildno

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    You make a Taylor expansion of sqrt(1+e), where "e" is regarded to be small.
    Then, you have, approximately, sqrt(1+e)=1+e/2.
     
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