Non-linear analysis, P-delta analysis

[PatrickEC]

These settings are described in two places in the help:

http://docs.autodesk.com/RSA/2013/ENU/index.html?url=filesROBOT/GUID-539BF9B3-3DA5-4E07-8BC6-15284F8...

http://docs.autodesk.com/RSA/2013/ENU/index.html?url=filesROBOT/GUID-FB3C86D3-0E30-43A6-82D6-6C50F42...

I always use Non-linear analysis, because I tested that this is in fact what is usually called a second order or P-Δ analysis. I tested this on:

• a cantilever column with axial load and horizontal load applied at the top
• a column with pinned support at the bottom and a horizontal support at the top

In both cases the additional bending moments were as I expected.

Now, the second option is called P-delta analysis and it is supposed to account for third-order effects, so I am confused why it is called P-delta.

From the help:

"P-delta analysis - takes account of the third-order effects, such as the additional lateral rigidity and stresses resulting from deformation. This effect considers additional forces arising in a deformed structure such as a beam with fixed supports on both ends, loaded by a vertical load, longitudinal forces arise and the deflection decreases."

I modeled such a beam described above, see the attached file, but I do see any longitudinal forces.

[t.sautierr]

I re-read this post :http://forums.autodesk.com/t5/Robot-Structural-Analysis/Geometric-non-linear-analysis/td-p/4429165/h... where we were already discussing about these effect, so in addition to answer to I meant :

When you say that at each iteration the analysis is starting from non-deformed shape, you mean the deformed shape of the elements and not the deformed shape of the structure (the later is generated because of the displaced nodes of columns) don't you?

What I said above + I meant deformed shape of principal nodes (nodes at the end of the bars), with a structure like in my files : one structure, a column, but can be divided into smaller parts or with a whole structure.

Finally for pdelta (small delta), maybe robot restart calculations from the non deformed shape also but at least update the matrices stiffness and stresses because there is not point not keep the solution in the memory of the computer. or uses the solution at previous steps (deformed shape for principals nodes + added nodes along the elements), I don't know.

Let's see Pawel's comments and I'll make a sketch of what I assumes if it's not clear.

Good night.

[Pawel.Pulak]

Apologies for delay in my comments.

I preferred to contact developers before any answer.

Generally it is impossible to make such clear distinction like "geometry is updated" or "geometry is not updated" in specific situation.

The equation, which is solved, is K*d=f

Where:

K - stiffness matrix (not only the linear one)

d - displacement vector

f - force vector

During iterations solver tries to obtain equilibrium between the left and right side of this equation.

Considering 2nd and 3rd order effects influences both K and f.

During iterations K can be updated:

- after each load increment and after each iteration (full Newton-Raphson method)

- after each load increment and with additional BFGS corrections (BFGS method used by default)

- after each load increment (modified Newton-Raphson method)

- not updated at all (initial stiffness method)

Any of above methods can be used to consider 2nd and 3rd order effects - even the initial stress method, where the stiffness matrix is not updated at all. Of course the biggest chance of convergent solution is when using the most advanced (but usually the slowest) full Newton-Raphson method.

[Tuctas]

Interesting answer... 

Thanks

[t.sautierr]

oki doki!

thx pawel.

Please put on the wish list the idea of renaming the analysis because it so confusing .... to give you an example, I have recently be on a course where people (including the teacher) thought that P-Delta analysis in RSA was the same P-Delta than in the code (spare moment because of non centered vertical loads due to deformation) ...