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L&L - Elasticity - couple questions on notation

  1. Jul 11, 2011 #1
    Edit - maybe I have the notaton figured out now and am just confused.

    1. The problem statement, all variables and given/known data
    The below relevant quotations come from Landau and Lifgarbagez, volume 7 : The theory of elasticity, chapter 1.

    2. Relevant quotations

    Page 2:
    where uik is the strain tensor, dl is the original distance between two points, and dl' is the deformed distance between the two points. xi are co-ordinates.

    ^^^Where, in the book, D is a squigly d (lower case delta?). Looks like the d used in variations.

    Page 5 (last paragraph):
    3. The attempt at a solution

    In quotation 2 - where did D come from? What is it?

    In quotation 3 - Is he using Einstiein summation notation still, because I don't understand why there would only be two components of the force, or two co-ordinates, because everything so far as been 3 dimensional. I don't understand how this is the moment tensor (it does make sense if its done for all 3 2d planes (xy, yz, zx), and Fi is a component of force in the i direction, then it's a scalar returned for the norm of the moment, directed in the direction normal to the plane - but then you get either a 2nd order diagonal tensor, or a first order tensor, neither of which is an antisymmetrical tensor of rank 2)

    Thanks for your help.
     
    Last edited: Jul 11, 2011
  2. jcsd
  3. Jul 11, 2011 #2
    Just got to this part:

    Where D is the same squigly D from quotation 2 above, and p is pressure.

    So I take it D is the identity tensor? Could somebody please explain quotation 2 to me. I can post more if you dont have the book.
     
  4. Jul 11, 2011 #3
    Another quick question - why are all the tensors (which seem to be 3x3 matrices) written as uik (only two subscripts)?

    EDIT - one last thing (to someone who has an older version of the book). Mine was printed kind of sloppily and I can't make out what it says above equation 2.9 (page 8 in my book). I'm trying to read the sentence that's starts out Substituting (2.8) in the first integral, we find.... what are the terms on the side of the equation opposite the surface integral? Thanks again.
     
    Last edited: Jul 11, 2011
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