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Deformation of a continuum element

  1. Apr 21, 2014 #1
    1. The problem statement, all variables and given/known data

    350qxj7.jpg

    The continuum element shown in Figure (a) deforms to figure (b)

    I'm looking to find the positions after deformation (x coordinates) by expressing them in terms of E coordinates.

    2. Relevant equations



    3. The attempt at a solution

    x1 = E1 + E2
    x2 = E1 + E2
    x3 = E3

    The first two equations for x I need help with, I'm not sure about the angles. I've done a previous question where the element deforms similarly (pure shear) but it stays within the same quadrant. The fact that this is flipped to the opposite quadrant is confusing me.

    When the element deforms but stays in the same quadrant the answer is:

    x1 = E1cosa + E2sina
    x2 = E1sina + E2cosa
    x3 = E3

    ftd5ed.jpg
     
  2. jcsd
  3. Apr 25, 2014 #2
    What are E1, E2, and E3 supposed to be?
     
  4. Apr 27, 2014 #3
    In your first figure, it doesn't look like the deformation is pure shear. Those parameters m and n look like stretches.

    Chet
     
  5. Apr 28, 2014 #4
    If the position vector between material points A and B is expressed as E1i in the original configuration of the body (figure a), and this vector stretches by an amount m to obtain the deformed configuration (figure b), what is the equation for the position vector between material points A and B in the deformed configuration?

    Chet
     
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