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Reverse Engineering Derivations - How?

  1. Mar 29, 2012 #1
    1. The problem statement, all variables and given/known data
    I have to reverse engineer a derivation in a paper and have no idea where to even start. The amount of terms are overwhelming and I can't imagine how the author even began.

    2. Relevant equations
    The following equations are known:
    http://img7.imagebanana.com/img/jpfqw5qj/Selection_001.png

    http://img7.imagebanana.com/img/v4cx2e07/Selection_009.png

    http://img6.imagebanana.com/img/ape27n0j/Selection_002.png

    Substituting them into the following equation gives an expression where [itex]r[/itex] needs to be isolated.

    http://img6.imagebanana.com/img/gayq1jb5/Selection_008.png

    The author makes many substitutions and results in the following simplified equation.

    http://img6.imagebanana.com/img/5gmnl628/Selection_007.png

    The substitutions are as follows:

    http://img6.imagebanana.com/img/36qfovp8/Selection_004.png

    http://img6.imagebanana.com/img/iinwallf/Selection_005.png

    http://img7.imagebanana.com/img/japtx4e8/Selection_006.png

    What I'm trying to do is figure out how he arrived at these coefficients [a], , [c], V, etc.

    3. The attempt at a solution
    I've substituted (1)--(5) into (6) but don't know where to go from here. The equation is huge and has many terms. I'm not sure how/where to begin.

    Any help will be much appreciated. Thanks.
     
  2. jcsd
  3. Mar 29, 2012 #2
    Out of interest, for what course is this?
     
  4. Mar 29, 2012 #3
    This is for a graduate level Fracture Mechanics course.

    The title of the paper is: The effect of T -stress on crack-tip plastic zones under mixed-mode
    loading conditions.
     
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