Principal stresses 2

1. Stresses don't depend on the way that the mesh is generated.
2. There is a convention on listing the three principal stresses which makes the first one the maximum of the three, and the third one the minimum, which can be the maximum compressive (negative) stress, but may actually be a positive stress.
3. For a shell element one of the principal stresses must be the pressure that is applied to the face.

What to do with it is a good question. I'd go back to the very first principles of stress and read up about the general theory and background.

corus

"1. Principal stresses are scalar or vector?"

- neither, its a tensor !


Suggest you follow Corus's very good advice.

1. why do you think a vector would be dependent on the mesh, but a scalar wouldn't be ? differing from the previous very knowledgable posters, i think it is slightly dependent on the mesh size (but then they know that too, and were possibly thinking in terms of mesh orientation, which is possibly where you were coming from).

2. in addition to normal pressure, transverse stress is also produced by poisson effects. a negative principal stress means there is compression without shear. principal stresses have the sign of the stress ... +ve for tension, -ve for compression.

3. i think you can have plane strain (3D stress) in a shell element ... this would represent a thick shell.

4. consider hydrostatic compression.

what's the issue with -ve principal stresses ?

Negative principle stress is often a stress that causes an element to become shorter. Therefore, you would be looking at a compressive stress in this sign convention. However, programs written specifically for concrete analysis and design consider compression on concrete to be a positive strain condition, so you have to make sure which sign convention the programmers used.

A well designed program will be able to find the principle stress and give you the orientation.

In my work, I rarely see a non-zero stress through the thickness of a shell.

Good luck.

Dinosaur,

At the risk of appearing to be petty, it's principal stress and not principle stress !

I think there might be another way to explain this. And please correct me if I'm wrong in the coming statements.

You have an element, 2D or 3D, and stresses are computed. For a 3D element (a cube) there will be 3 normal stresses and 3 shear stresses. They are often given in a global coordinat system.

Now imagine that you create a local coordinat system for each element. And imagine that you rotate the coordinate system so that there is no shear stresses on the cubes surfaces. The only stresses present for the rotated cube are "pure" normal stresses. Those are the principal stresses.

Another way is to say that to principal stress is the largest stress in any direction in the cube. Then you have two more stresses orthogonal to the largest. And zero shear on the surfaces of the cube.

You will also get three angles, how the principal angles are rotated in the global coordinate system.

Obviously this involves some math but nothing to bad. If I remember correct you need to solve a matrix equation for a 3D case. For 2D there are "formulas" based on the same matrix solution.

As for stresses being dependant on the mesh. They can be, and that is usually a very good indicator of a bad mesh. Consider that in real life there is no mesh and it's those "real life" stresses we are trying to reproduce with our software. So stresses can't be mesh dependant unless the mesh actually controls the stresses. And that is an unwanted "constraint".

As for thin shells and normal stresses. Well, a thin shell means plain stress and that means zero stress normal to the surface. However, this is in the element formulation and not always true in real life.

Maybe I added something to the discussion.
If not, let me know. I'm always interested in learning.

Thomas

I expect to read mohr about this.

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

Thanks for all replies and i am better now after reading info here and from other websites.

Johnhors, i was just referring to the orientation as rb1957 said. Anyway that was the wrong discription. Question arised due to confusion from the example from abaqus manual, which i have given at the end of this thread.

ThomosH, you summed it up the basics. To add further,

Max Principal stress = Max(Sigma_1, sigma_2, Sigma_3)

Min Principal stress = Min(Sigma_1, Sigma_2, Sigma_3)

Mid Principal Stress = A-Max-Min

A = Sigma_1 + Sigma_2 + Sigma_3.

As corus pointed out, Min principal could be positive. But is there any practical example?? If it is compressive, it must be comparted with compressive strenght of material. Again, no practical experience.

Regarding Thin shell example, i did not mention about plane stress problem. I mentioned for example loading in normal direction where bending involves.

As shown in the following example, stresses in the thickness direction(S33) is zero. But not necessaily zero third direction principal stress. (It was my earlier confusion and clear now)

Please refer the link below, and go to chaper 5 , shell element example called Skew plate. If you also could run to discuss further, we(I) may get more info for interpretation.


Thanks again.

johnhors,

Thanks. I had to look it up after your post. I always thought the "Principal" was a person and "Principle" had to do with science and ideas. Having mild dyslexia, I have to fight spelling all the time, but I'm always striving to get better because my customers don't care why I misspell a word. Coincidently, I was thinking of responding to another post about the prevelance of spelling and grammar errors as an indication of poor understanding of what computers can do for us. I might need to remove the beam from my own eye before helping my friend with the mote in his own.