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Effective stiffness of sandwich panels

  1. May 3, 2016 #1
    1. The problem statement, all variables and given/known data

    Most sandwich panels are made up of two face sheets and a core. The core is often light, weak and

    contributes very little to the stiffness of the panel. This enables a very rough analysis to be made by
    assuming that the core is just air and that the cross‐section of the panel is equivalent to a rectangular crosssection tube. Using this assumption derive an equation for E~ in terms of the outer dimensions of the panel (b>>h) and the value of E for the face material. Hint: equate equations 1 and 2 for the same values of span,deflection, force and C1 and note that because b>>h the rectangular tube second moment of area can be given as I ~ h2tb / 2 . Note that you are not calculating a value here, just finding an expression in terms of the aforementioned variables.


    Use the assumption in the previous point to derive an approximate equation for the effective density, ρeff , of the panel. Hint: start by assuming the panel is b x b x h in size and calculate the volume of material in the two face sheets of thickness t (you can ignore the side strips). Your equation will be in terms of t/h.

    Use your equations to estimate the effective stiffness of a wood (parallel direction) face‐sheet sandwich
    panel (with a negligible weak light foam core). Assume the panel apparent density is 50 kg/m3. Comment on whether the result falls in the ‘desired’ region of property space in Figure 1.


    2. Relevant equations
    s= (L^3*F)/C*E*I and s=(L^3*F)/C*Eeff*Iouter
    Area box tube( neglecting sides) 2*t*b, Volume bt = 2*t*b^2
    3. The attempt at a solution
    Assuming L, F,S and C are the same we are left with E*I=Eeff*Iouter
    E*(h^2*t*b)/12=Eeff*(b*h^3/12)
    Eeff/E = 6t/h

    ρ=mass/volume
    ρeff=m/b*b*h and ρ=m/2*t*b^2
    m= ρeff*b^2*h=ρ*2*t*b^2
    ρeff= 2ρ*t/h

    50=2*ρ*t/h

    I think I have derived the equations correctly except for the E and the ρ stop the equation being used to find the desired values.

    Thanks in advance for any help.
     
  2. jcsd
  3. May 8, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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