Non linear analysis parameters definition 1

[ENGIRL]

Can someone explain to me the logic behind non linear analysis parameters in sap2000? mainly the total steps, null steps and convergence tolerence?
thank you

 

[Luceid]

Total steps is the number of times it iterates without reaching the convergence tolerance before it gives up. If you set it too low, it might not be able to converge in time. If you set it too high and the structure is pretty flexible, it might never converge and will take forever. You want this to be in a range where it converges before stopping, but don't just put it at 1000000000 since any problems with your model will keep you stuck in an analysis loop.

Convergence tolerance is what you tell the program to shoot for before considering the nonlinear analysis "complete." Essentially, after an iteration, SAP will total something like the net support reactions - and this will never be quite equal to 0 for most nonlinear cases. So you tell SAP, "as long as the total unbalanced force after the run is less than X force - I think we are close enough to call the analysis there and I trust the results within a few percent." I'm not sure what exactly the convergence tolerance input is for SAP, sometimes they let you put in a scalar and it takes the total applied load times that scalar as the convergence tolerance so you don't have to manually update it every time the load input changes. For example, if I apply 1000 kips of force to a model with a 0.05 convergence tolerance, once the unbalanced load comes out below 50 kips - the nonlinear analysis will consider itself "converged."

Null steps - not too sure. My guess is maybe that SAP skips steps that produce the same results as previous iterations?

 

[Luceid]

Based on how it reads in the SAP input - I think null steps is how many times an iteration result can be repeated before it gives up. If the unbalanced force just bounces back and forth between X and Y 50 times, the nonlinear analysis isn't going to converge, so this is a failsafe to tell you that you need to change some parameters or your iteration method in order to get it to solve.

 

[JoshPlumSE]

How a Null Step is defined depends somewhat on what kind of solution procedure was being used. Though, in general, it occurs when a) A frame hinge is trying to unload, b) an event (yielding, unloading) triggers another event, c) an iteration was attempted, but didn't converge so attempt can be made with a smaller step size.

 

[Celt83]

Josh:

Do you have any references you recommend for the nonlinear solution process, have the McGuire Gallagher and Ziemian book but always looking for more.

 

[JoshPlumSE]

Celt83 -

Not yet. I've got personal favorites for a lot of things:

Dynamics: Structural Analysis - Theory and Computation by Mario Paz
Response Spectra: Response Spectrum Method by AK Gupta
Frame FEM analysis: Matrix Structural Analysis by McGuire, Gallagher and Ziemian​

Unfortunately, I haven't found a favorite on non-linear analysis. At least not yet. In the past, I've mostly dug through various analysis references that came with software. Then I've looked up papers on the preferred methods used by that software.

The online book by Ed Wilson might be a decent place to start. We're getting to the point where more and more books can only be found in electronic form and not as print versions. Maybe that's part of the problem.

 

[Celt83]

Thanks for the feedback Josh. I need to find a chunk of time to carve out and really work through chapter 12 in the McGuire book, wish they would have included any examples to better illustrate some of the methods in section 12.3 but I imagine most of my struggle is just not devoting enough time to actually sit down and learn it.