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Local strain energy density for a plate subjected to in-plane linear load

  1. Dec 5, 2011 #1
    Dear all,


    I would like to know from you the solution about this problem (which is not a homework, but a topic of my Master thesis!): I need the strain energy density related to a circle of radius r0 centered in an arbitrary point of a square plate, under the boundary conditions described in the attached picture (on the right edge a linear stress is applied, which ranges from 0 to S). The value I obtained, under the plain strain hypothesis, is:

    [itex]
    SED=\frac{1-\nu^2}{2\,E}\,\left(\frac{S}{h}\right)^2\,\left[\frac{r_0^2}{4}+(h+y_c)^2\right][/itex]

    where h is the edge of the square plate and yc the y coordinate of the center. The fact is that it doesn't match with the FEM solution (which is surely right, since it was obtained by my Supervisor :)).

    Can you please derive the equation and compare it with mine?


    Thanks for your help!


    Mattia
     

    Attached Files:

  2. jcsd
  3. Dec 5, 2011 #2
    Oops, I found the mistake! It was hidden inside the choose of the reference system :P

    Here's the correct formula:

    [itex]
    SED=\frac{1-\nu^2}{2\,E}\,\left(\frac{S}{h}\right)^2\,\left[\frac{r_0^2}{4}+(h-y_c)^2\right][/itex]


    Best regards,


    Mattia
     
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