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Homework Help: Homework help: anisotropic elasticity equations

  1. Jul 13, 2018 #1
    1. The problem statement, all variables and given/known data
    Hello, I'm studying anisotropic elasticity. One of the books I'm using is Lekhnitskii's. The book presents the general equations of the theory of elasticity for an orthotropic body as follows:

    2. Relevant equations
    upload_2018-7-13_9-56-33.png

    3. The attempt at a solution
    However, when I combine the strain-displacement equations and the Hook's Law and then replace them into the equilibrium equations I cannot get the same expression. My reasoning looks like this (for example, the first equation of the system):

    A11.Uxx + A12.Vyx + A13.Wzx + A66.(Uyy + Vyx) + A55.(Wzx + Uzz) = 0

    Obviously, I'm doing something wrong. What is my mistake?

    Many thanks for your kind help.
     
  2. jcsd
  3. Jul 13, 2018 #2
    Maybe they are able to eliminate the cross derivatives by combining the equations with the continuity equation.
     
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