Non linearities in solving a structure

[binafem]

Hi to all of you,

we know that when we solve a structure we can have :

1) non linearity due to the material (read: reinforced concrete ...),

2) geometric non linearity , I would mean the section of the element doesn't remain plane due to the deformation;

3) non linearity due to big deformations, I would mean the case of a slender beam loaded normally to the transverse section.

I would like to know if there is an understandable book or a resource to study about all the themes above to get a glimpse into this branch of structural area.
Thank you very much in advance for your help.
Indo

 

[ESPcomposites]

There may be a few "problems" with your assumptions.

- Material nonlinearity : Just about any material can be treated as nonlinear, if you want. I am not sure why you specifically state reinforced concrete as a "nonlinear" material?

- Geometric nonlinear won't solve "plane sections not remaining plane". That has to do with the element formulation. For example, a simple beam element will not capture this effect, even if the geometric nonlinear switch is on.

- Large deformation IS a geometric nonlinearity. So item (3) should actually go under item (2).

These are really more "mechanics of materials" or "materials" questions than finite element questions. You can look at books related to those topics.

After that, there are two parts:

- How to incorporate a particular nonlinearity in the FEM.
- More importantly : When to recognize if the nonlinear effect is important to the solution and if simplifying assumptions can be made (this comes with experience).


Brian

http://www.espcomposites.com

 

[binafem]

Thank you Brian for your quickly reply.

Could you suggest which book or books to read to make clear these concepts?
Besides in the last part of your answer you have switched on a new light . May I ask you to mention a simply case when you had to leave the idea of linearity and, to avoid big mistakes, you had to embrace a non linearity behaviour?
Thank you very much in advance for your invaluable help.
Yours sincerely,
Binafem

 

[ESPcomposites]

There was a recent thread were some practical FEM books were suggested. I think it is OK to look over these since they have a blend of mechanics and FEM/nonlinear.

I like: Adams and Askenazi, "Building Better Products with Finite Element Analysis", but it is out of print (unfortunately).

Based on your original post, it would not hurt to also have a look at your mechanics of materials and materials books (which I assume you already own or did?) All of mine are probably out of print or outdated by today's standards, though anything with the name Timoshenko on it is pretty good.

Simple case: The deflection for a thin plate like structure was predicted to have excessive deflection via FEM. Since we did not want to increase thickness, we were able to rely on the edge constraints and the "stress stiffening" effect (a geometric nonlinearity) to demonstrate the actual deflection would be less. Usually it is the opposite though. You are trying to find ways to linearize a nonlinear problem (all real problems have "some" degree of nonlinearity). Even a simple beam is really nonlinear for small deflections. Its just that sin(theta) is approx (theta) and we linearize the problem (rightfully so).


Brian

http://www.espcomposites.com

 

[btrueblood]

"anything with the name Timoshenko on it is pretty good."

Yes. Yulia is pretty hot, imop.

 

[IDS]

I am not sure why you specifically state reinforced concrete as a "nonlinear" material?

Perhaps because within the normal working stress range it is by far the most non-linear of the commonly used engineering materials (and I include soil in that category).

For a comprehensive treatment of reinforced concrete stress/strain behaviour I recommend "Concrete Structures, Stress and Deformation" by Ghali, Favfe and Elbadry, but the important thing is being able to recognise when you need to use a non-linear analysis and when linear is adequate, and in the latter case, when to use an upper bound stiffness, and when a lower bound. To that end experimentation with the analysis of actual structures is essential.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[ESPcomposites]

Doug, I suspected something like that was the case. We try to minimize our use of concrete on the aerospace side.

But as you mention, you don't automatically classify a material as "nonlinear". This was the point that I was making and was not sure if the OP understood that. Just about all materials can be treated as linear or nonlinear, depending on the objectives of the problem.

Brian

http://www.espcomposites.com