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Principal of Minimum Complementary Energy

  1. Oct 25, 2013 #1
    1. The problem statement, all variables and given/known data
    I am reading through this link:

    http://en.wikiversity.org/wiki/Introduction_to_Elasticity/Principle_of_minimum_complementary_energy

    I need to show that a certain thing follows from a previous thing. I will elaborate in the next section.

    2. Relevant equations
    I am stuck, specifically, at this point:

    "We can also show that
    4d52d86fda724c3d5b7869b19290223e.png
    Therefore,
    d391fb34b032ea2814f98bd2e067b106.png

    3. The attempt at a solution
    I know that I can represent ##\int \mathbf{t '}\cdot\mathbf{u}dA## as ##\int \mathbf{\sigma '\cdot n}\cdot\mathbf{u} dA## and then use divergence theorem to arrive at ##\int\mathbf{\nabla\cdot\sigma '}\cdot\mathbf{u}dV##

    But, I do not see where to go from here to arrive at where I need to be, the last statement at the end of line (2). Does anyone have any suggestions?

    I've been mulling over this for at least 4 hours and I have gotten nowhere with it. The method shown here is one of my many attempts to get to a solution.
     
    Last edited: Oct 25, 2013
  2. jcsd
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