# Principal of Minimum Complementary Energy

1. Oct 25, 2013

### TheFerruccio

1. The problem statement, all variables and given/known data

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

Therefore,

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