Effective stiffness of sandwich panels

[Name:riley]

Homework Statement

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.

Homework 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

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.

 

[KataKoniK]

Thank you for your forum post. I would like to provide some feedback and suggestions for your equations and calculations.

Firstly, I would like to point out that the equations you have derived seem to be correct and in line with the given hints. However, I would like to clarify that the equation for E~ should be E~ = 6t/h * E, as the original equation for E~ should be E~ = 6t/h * E. This will also affect the subsequent equations for ρeff, which should be ρeff= 2ρ*t/h.

Additionally, I would like to suggest using consistent units throughout your equations. Since you are using SI units for density (kg/m3), it would be more appropriate to use SI units for the other variables as well, such as length (m), force (N), and stiffness (N/m2). This will also help in checking the dimensional consistency of your equations.

Furthermore, for the equation for ρeff, I would suggest using the volume of the entire sandwich panel (including the core) instead of just the volume of the face sheets. This will give a more accurate representation of the effective density of the panel.

As for estimating the effective stiffness of a wood face-sheet sandwich panel, I would suggest using the known values of E and ρ for wood (parallel direction) to calculate the value of E~ and ρeff, and then using those values in the equations to estimate the effective stiffness. This will give a more accurate estimation compared to using a generic value of 50 kg/m3 for the apparent density.

Finally, regarding the comment on whether the result falls in the 'desired' region of property space, I would suggest referring to the provided Figure 1 for the desired range of properties for sandwich panels. You can compare the estimated values of E~ and ρeff with the desired range to determine if the result falls within it.

I hope this helps in your analysis. Please let me know if you have any further questions or need any clarification.
Scientist