Comparison between 3D Beam and Laminate Plate

eric_c

Hello,
I've modelised in two way a sandwich beam made of two carbon skin(top bottom) with foam in the center.

The first way was using full 3D geometry
The second one was using a plate with laminate material

The result are very divergent, I'm probably doing something very wrong.

Then I've decide to make it all foam on both case (no laminate for the plate). The results are much better but still different

Any Idea ? I suspect it has something to do with G12 G23 G31( I extrapolate value from unidirectionnal carbon data)

The liml files are here:
https://www.dropbox.com/s/slnrsrcuuxelek6/sandwich_test1.rar?dl=0

Best,

Eric

VMH

Eric,
I don't know much on laminate material, but for solid elements, quadratic elements (with midside nodes) may give you a better results for bending because linear solid element (without midside nodes) you are using may be too "stiff" for bending.

From the pictures attached, you can see that quadratic solid elements deflected more.

eric_c

VMH,
Thanks for pointing out this. I was not refining enough with linear. I've tried quadratic on my side and I realize that much less refinement was necessary to reach the converging result.
Curiously the hand formula for sandwich beam gave me a stiffer result (0.47mm bending) than 3D shape but softer result than laminate plate. So I don't know what is the best way to model this. Is the 1.2 mm skin too small in comparison of the core for 3D volume ?

Victor

That's definitely an important point about hex8, VMH. But, Eric, I'm curious how you got the results to converge. When I converted the solids to hex20 or refined them, the displacement increased, getting even further from the shell result.

I also suspect it has something to do with the shear modulii, but not sure how to calculate them off hand.

By the way, the zig-zag displacement of the shell is partly caused by what's really a zig-zag force distribution. To get a uniform force, you need to apply 19.5N to the middle node, and a total of 19.5N to the two edge nodes (9.75N each). I used a face load for this instead to avoid calculating that strange distribution.

eric_c

Sorry I mean comparing convergence between hex20 and linear. Yes, with the plate it is diverging, unfortunately.

Thanks for the force distribution advice, much better.

Victor

I think you're running into a limitation of the thick shell theory and that's why it's overly stiff. The deformation of the solid mesh shows that the cross-section is deforming into a kind of "Z" shape. This violates an assumption that the normal to the midsurface remains straight. http://en.wikipedia.org/wiki/Plate_theory#Mindlin.E2.80.93Reissner_theory_for_thick_plates

The shell model performs much better when it isn't carrying shear forces - for example in bending as shown in the 2nd picture.

eric_c

Thanks for the information Victor. The article say that it should be no more than 0.1 the size of planar shape, I'm definetly out of the scope.