Closed Form Panel Buckling Solutions 1

[ESPcomposites]

I am looking for simple closed form initial buckling solutions for orthotropic plates (symmetric where =0 and D16=D26~0). Mil-17 has several cases, but nothing for shear loading and other boundary conditions for uniaxial loading.

I have found some solutions for these, but nothing that can be referenced in the public domain (i.e. DOD restricted access, etc.). The point there being that it possible.

Within the public domain resources, I have a lot of resources, but nothing that is a real improvement over what Mil-17 already offers (Jones, Whitney, Barbero, ASM 21, etc.). I am hoping there might be some other good resources or papers out there?

One interesting source is from Gay, "Composite Materialsesign and Applications". In the appendix, he shows curves similar to what you might see for a metallic, but normalized with properties from the [D] matrix. But they are just pulled out of thin air, without reference or equations. Any idea how to regenerate these?

Brian

http://www.espcomposites.com

 

[bellx1]

There seem to be a number of experimental sources that study plate buckling. Specifically what kind of improvements are you looking for? Accuracy or how broadness of application?

http://www.compositescentral.net

 

[ESPcomposites]

The ones I interested in would be for shear loading and other boundary conditions than SS for a/b < 4, etc. Mil-17 only has a handful of solutions.

I don't think the experimental data is necessary for this. I am looking for the classical bifurcation solution, which works well provided the transverse shear effect is not significant.

Brian

http://www.espcomposites.com

 

[RPstress]

ESDU 80023.

NASA TP 3159 and 3659 by Nemeth for interesting anisotropy effects on buckling load.

 

[ESPcomposites]

RPStress,

Thanks. ESDU 80023 has some pretty good info, but I don't know how they generate the curves for K0. I am looking for something closer to what Mil-17 has (i.e. in the form of an equation rather than curves). Though this may partially explain the curves presented by Gay and Hoa, which are a complete mystery to me. I wonder if in the ESDU, they use a computer program to solve for the critical load, then back out the K0 to generate the curves.

I had a look at the NASA reports as well and it looks like Nemeth has done a lot of work in this area. But that is probably more detail than what I am looking for. I am looking for "basic" solutions like Mil-17, but just for more load cases. Also, a few of the equations are incorrect in Mil-17. I have found references with the correct solution for some, but not for all of the errors.

Brian

http://www.espcomposites.com

 

[ESPcomposites]

It is interesting/odd that in ESDU 80023, D12 and D66 are not considered as part of the solution. For example, in figure 1, Nx can be solved with only D11 and D22 (D12 and D66 not considered and do not appear absorbed in K0 either). I am not sure how they reached this conclusion since every other source I have seen required these values (including Gay and Hoa's curves). Perhaps they have made an assumption about the material system. Also, it does appear that the curves are first generated via a computer algorithm. The problems here are that I cannot regenerate the curves and don't know/understand what additional assumptions appear to be made that others are not making.

Brian

http://www.espcomposites.com

 

[ESPcomposites]

RPstress,

If you are interested, I now provide a free stability analysis program, which uses the open source finite element solver CalculiX.

http://www.espcomposites.com/software/eStability.html

Brian

http://www.espcomposites.com

 

[RPstress]

Thanks ESP. That looks interesting. I'll have a good look when I have time.

 

[rybose]

Definitely check out:

Leissa (1985) - AFWAL-TR-85-3069 Buckling of Laminated Composite Plates and Shells

I think it will have what you are looking for. Unfortunately, very few cases have neat closed-form solutions. The report does a good job of explaining why.

 

[ESPcomposites]

Rybose,

Thanks a lot. I think this report contains the information/curves the Gay and Hoa published in their book. They did not reference it as far as I could tell, which is rather frustrating. I will have a further look, but it seems like good information.

Brian

http://www.espcomposites.com