Mathematical help with structural analysis.

[ENgez]

In the attached equation from structural analysis, I don't understand the transition between the second and third equal signs. I think that $u_{j,l}da_l = u_{j,1}da_1+u_{j,2}da_2+u_{j,3}da_3$, so doesn't equating $da_j\delta_{lj} = da_l$ assume that $l=j$. can anyone help me see why this assumption is justified?

 

[afreiden]

Are they just changing variables?
Maybe just ignore the third line. Start with the second line and carry through the algebra... For example, consider the first term in the second line:

First term in second line: $u_{j,l}da_l da_i\delta_{ij}=u_{i,l}da_l da_j$

Just replace $i$ with $j$ and replace $l$ with $i$ and presto! But that might be cheating... what text is that from?

More simple derivation here, btw: http://utsv.net/solid-mechanics/2-strain/strain-tensors -- middle of page

 

[ENgez]

thanks, this is from mit ocw. i had to resort to it because my lecturer is truly terrible at conveying this stuff...