Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Ovalisation or a ring: diferential equations

  1. Oct 2, 2005 #1

    I am looking for a book or a web site giving the differential equations for the ovalisation of a ring.
    In principle these are six differential equations:

    one for the compression force along the ring
    one for the shear force
    one for the bending moment
    one for the radial displacementof the ring
    one for the derivative of the radial displacement
    one for the longitudinal displacement

    these are similar to the equations of a beam, the difference is that it is a ring.
    I tried to write these equations by myself, but I have some doubts about signs and how bending moment and displacements relate to each other.

    I would also be interrested in the more general theory for shell deformations: where is there a good text on the web?
    With such a reference I hope to be able to work out such a particular problem in a more systematical way.

    Thank for your help !

    Appendix: the equations I would like to check

    [tex]\frac{dT}{d\Theta} = -F-R\ p_\bot[/tex]

    [tex]\frac{dF}{d\Theta} = T-R\ p_\|[/tex]

    [tex]\frac{dM}{d\Theta} = R\ T[/tex]

    [tex]\frac{dp}{d\Theta} = -w-\frac{MR²}{EI_z}[/tex]

    [tex]\frac{dw}{d\Theta} = p[/tex]

    [tex]\frac{dv}{d\Theta} = w[/tex]

    with the following meaning:

    T: shear stress
    F: compression stress
    M: bending moment
    w: radial displacement
    v: longitudinal displacement
    R: radius of the ring
    E: elastic modulus
    [tex]I_z[/tex]: moment of inertia of the material cross-section for the ring bending
    [tex]\ p_\bot[/tex]: radial force acting of the ring (depends on the angle)
    [tex]\ p_\|[/tex]: longitudinal force acting on the ring (depends on the angle)
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted

Similar Discussions: Ovalisation or a ring: diferential equations
  1. Newton rings ? (Replies: 0)

  2. Flying Ring (Replies: 5)

  3. Newton's rings (Replies: 3)