Transverse shear of plates 4

[haseg]

Hi all,
I have modeled honeycomb sandwich plates under uniform pressure in NASTRAN and have found that considering transverse shear deformation is important in modeling honeycomb sandwich structures. However,in many cases of treating solid plates , we can make the transverse shear stiffness infinity , because shear deformation is much smaller than bending deformation.
My questions are,
In what condition should I consider transverse shear deformation except honeycomb sandwich panels ?
And I'd like to know about somewhat "formulas" to calculate shear defomation of plates. I'd like to check NASTRAN results by hand calculation.

Any help would be nice. Thanks

 

[KSshopper]

Unless the thickness of the honeycomb is very large, I wouldn't think there would be much transverse shear deflection.

NASA has a good reference for modeling honeycomb plates:

http://femci.gsfc.nasa.gov/hcplate/honeycomb_pshell.html

 

[haseg]

Hi Philcondit,
Thanks for your reply.
I had refered to the NASA's page previously and it was very helpful.
My original model description is following.
* Size : 23.62"X11.81"
* Face : E=3094 ksi , t = 0.031"
* Core : G=2.1 ksi , h = 0.569"
* Linear analysis , and all materials are isotropic.

Here,I've changed "G" from 2.1ksi to 300ksi,then the deflection has become almost half of the original model's one.
I'm thinking that the ratio of D(Bending stiffeness) and G*h(Shear stiffeness) must influence the results.
I'd like to know the relationship between the ratio and the deflection. But,is it something empirical?

Thanks.

 

[RPstress]

A quick approximation for shear deflection of a cantilever beam of with a load on the end is
shear_delta = load * length / (GA)
where GA is shear stiffness, which is near enough shear modulus times area, or Gc * b*h for honeycomb ( Gc core shear modulus, b beam width, h facing centroidal separation). You can quite often approximate a more complicated situation with a combination of cantilever and simply supported beams.

For a rectangular plate under uniform pressure, Zenkert gives
shear_delta = K*pressure*b^2 / Dq
where Dq = Gc*h^2/tc ( Gc , h as above and tc is core thickness), b is plate minimum dimension and K is from:
a/b K
1.0 .0737
1.4 .0967
1.8 .1098
2.0 .1139
3.0 .1227
5.0 .1249
inf .1250

For a point load in the middle of a rectangular plate, Zenkert gives
shear_delta = K*load / Dq
where K is from:
a/b K
1.0 .613
1.4 .601
1.8 .581
2.0 .571
5.0 .456
Interestingly, this implies the shear deflection of a plate with a point load is independent of the plate's size...

You have to add these shear delfections to the bending deflection to get the total deflection, of course.

For the ratio of bending stiffness to shear stiffness for a plate, Allen (1969) gives
ratio rho = pi^2/b^2 * Ef*tf*h^2/2/(1-nuf^2) * tc/Gc/h^2
which boils down to
rho = pi^2/2/(1-nuf^2) * Ef/Gc * h*tf/b^2
for very thin facings (so that tc = h ).
Undefined symbols here: Ef facing E; tf facing thickness; nuf facing poisson's ratio.

Things get more complicated if your facings have different moduli and/or thicknesses and/or are orthotropic.

Dan Zenkert's "An Introduction to Sandwich Construction" is available in paperback for just 35 pounds UK from

http://www.amazon.co.uk

. It's not in

http://www.amazon.com

. Howard Allen's "Analysis and Design of Structural Sandwich Panels" is out of print.

 

[KSshopper]

RPStress gave you the ratio between shear and bending deflection. Running that calculation should tell you if you're in the ballpark.

Based on your problem description, I still think shear deflection would be small relative to bending deflection.

I recommend you use an orthotropic material property for the core. Core stiffness is different for each direction and in fact zero for in-plane shear. These stiffnesses should be available through the honeycomb manufacturer.

Finally, if you get unreasonable deflections due to pressure, try turning on stress stiffening during your solution.

 

[haseg]

Thanks very much for your helpful replies.
I appreciate excellent advices by RPstress.
I've checked NASTRAN results by hand calculation and reached good accordance 'in the ballpark'.
Tnank you.