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[FlexPDE] Not sure if displacement equations are right

  1. Oct 3, 2013 #1
    Hi guys, I'm recently using FlexPDE to find the resonant frequencies of a torsional oscillator, but it does not match the analytic solution. It uses a Finite Element Method to find solutions.

    Is there something wrong with the equations I'm using?

    simple_oscillator2.png



    C11 = G*(1-nu)
    C12 = G*nu
    C13 = G*nu
    C22 = G*(1-nu)
    C23 = G*nu
    C33 = G*(1-nu)
    C44 = G*(1-2*nu)/2

    Strains

    ex = dx(U)
    ey = dy(V)
    ez = dz(W)
    gxy = dy(U) + dx(V)
    gyz = dz(V) + dy(W)
    gzx = dx(W) + dz(U)

    VARIABLES

    U { X displacement }
    V { Y displacement }
    W { Z displacement }



    Stresses

    Sx = C11*ex + C12*ey + C13*ez
    Sy = C12*ex + C22*ey + C23*ez
    Sz = C13*ex + C23*ey + C33*ez
    Txy = C44*gxy
    Tyz = C44*gyz
    Tzx = C44*gzx

    EQUATIONS

    U: dx(Sx) + dy(Txy) + dz(Tzx) + lambda*rho*U = 0 { the U-displacement equation }
    V: dx(Txy) + dy(Sy) + dz(Tyz) + lambda*rho*V = 0 { the V-displacement equation }
    W: dx(Tzx) + dy(Tyz) + dz(Sz) + lambda*rho*W = 0 { the W-displacement equation }
     
  2. jcsd
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