Algorithm for yield-line prediction

[JoeH78]

Hi all,

I'm trying to implement the yield-line algorithm for the arbitrary polygonal slabs. I'm struggling with that for couple of days and as a result, net searching retrieved a two nice nomenclatures,"Systematic Prediction of Yield-Line Configurations for Arbitrary Polygonal Plates,J. Wust, W. Wagne" and "A computerised method for rigid-plastic yield-line analysis of slabs, A. Thavalingam, A. Jennings, J.J. McKeown *, D. Sloan". The theory assumes the collapse is reached when internal works is equal to exernal loads work along the YL. But accurately guessing the initial YL, iteration to find solution is very hard to implement due to fact that it heavily relies on math.
Any guidance to solve that programatically will be appreciated.

AFAIR somewhere in articles its also been mentioned that FEA can be used as an exact solution for YL. Actually how is that achieved? With trying to locate the bending moments where exceeding the plastic limit of material?

Regards,

 

[271828]

That's quite a challenge and I'm a little skeptical that it can be done for arbitrary geometry and loads.

My only idea is to start with a linear FEA to determine maximum positive and negative moments. The negative ones will probably be along supports, so then assume the YL spreads along that support to the next support. The positive ones are tougher, but perhaps a similar approach can be used.

Then again, if you're going to start with a FEA, the linear FEA could probably be extended into a spread-of-plasticity analysis and do a better job anyway.

 

[ishvaaag]

If I had to deal with this issue I would likely elect a Montecarlo approach (I am assuming initially a convex polygon platesupported at edges). By throwing points inside the plate I would directly generate a significantly big number of configurations by some rule or set of rules, then comparing the invested energies of deformation to select the one that shows the lesser energy of deformation and still is a mechanism, that would be the output.

 

[JoeH78]

Thanks for commenting,

The more I read, the more confused I get.
After reading throughly all day the ,"Systematic Prediction of Yield-Line Configurations for Arbitrary Polygonal Plates,J. Wust, W. Wagne" which I digested it to some extent, I'm convinced that YL can't be implemented via triangular subdivision, branching points chipering or some other method other than FEA, IMHO whole external factors should be taken into consideration.

For example, you may approximate the YLs geometrically and by DOF of edges and even radomization as isvaaag suggested, but if there is any point load(+ Line,+ UDL, etcc) acting on any arbitrary location on slab, that may change the whole mechanism, let alone to deal with the other inferiour factors that play important roles theoretically as well (e.g. for RC slab reinforcement direction , magnitude of loads)

I think that FEA with plasticity check is best option, the problem remains for how to assembly the plasticity zones to form the YLs?

 

[rapt]

I may be missing something here, but FEA and Yield Line are 2 compeltely different approaches.

FEA predicts the elastic response of the slab.

Yield Line completely ignores the elastic response.

 

[Guest262653]

Hi.

Just a small hint, as I've never really dwelved into yield line anaylis: There's this geotechnical software (LimitState Geo) that automatically selects the failure mechanism that corresponds to the minimum displacement energy. This is more or less what's happening on YLA as it is also an Upper Bound solution.

Check out their website and any related publications from the software authors as I think there are some technical publications which explain the general algorithm solution that was used. That may prove to be a path for the solution of your problem.

Regards,

 

[271828]

I think that FEA with plasticity check is best option, the problem remains for how to assembly the plasticity zones to form the YLs?

I've never programmed this approach, but I've heard it described as an event-to-event material nonlinear analysis. Something like the following:

1. Set your yield criterion. Probably using von Mises.
2. Run the linear analysis incrementally until some element has stress such that it yields per the criterion given in #1. This yielding is the "event" that your analysis is looking for, and results in a change in the stiffness.
3. Set the yielded element's flexural stiffness to zero and re-form the stiffness matrix. Every element, including the yielded one still holds whatever force effects were there at the event.
4. Run the analysis until some other element yields. Add the new force effects to the ones mentioned in the last sentence of #3.
5. Cycle through #2-#4 until no more load can be applied.

I'm sure this isn't exactly correct, but I think it's close. I think programs like Ansys and Abaqus already do this sort of thing. The advanced version of SAP2000 might also.

 

[paddingtongreen]

I tried this with STAAD in the early days when it was very crude compared with today. I set the matrix and the load to identify the highest stress line(s). Reasoning that they would stay that way as long as the behavior was linear, I changed the connections to pinned along that/those line(s) and reran to find the next failure lines(s).

It worked quite well, I experimented with some arbitrary solutions after, but couldn't find a lower energy solution.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[BAretired]

One method which I have used is to assume a yield line pattern, labelling the dimensions with letters, then writing the equation Internal Work = External Work.

For simple cases, the critical value of the dimensions can be found by setting the differential equal to zero. For more complex cases, this may not be so easily done.

BA