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Elasticity theory, extracting the boundary conditions

  1. Mar 24, 2014 #1
    1. The problem statement, all variables and given/known data

    I am trying to extract the constant of integration after integrating the following stress equation (I got this by solving a system of ODEs for the upper and lower tablets (attached), quite tedious to paste it all here):

    σ = β * sinh(λx/2) * cosh( λ(L-x)/2 )

    Where σ is the stress in the upper tablet (see attached) which is Edu1/dx
    β = σ0 / sinh(λL/2)


    2. Relevant equations



    3. The attempt at a solution

    Separating the variables and integrating the above stress equation

    u1 = β/2E * [ 1/λ*cosh(λL/2 - λx) + sinh(λL/2)x + C ]

    Now, what displacement boundary condition can I apply here to extract that constant? Nothing is evident from the attached image. For the lower tablet (attached), this is simple as it's attached to a roller, and I managed to extract the constant of integration and a solution to the displacement of the lower tablet.
     

    Attached Files:

    Last edited: Mar 24, 2014
  2. jcsd
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