convergence algorithms

[ozzkoz]

Hi, I am new to mechanica (previously used cosmos and ansys WB) and admittedly a "project" level engineer with an interest in FEA more so than a pure structural engineer. Anyway, I've been reading through the help files trying to understand the convergence method of mechanica (primarily SPA) and am looking for either an explanation or conformation of my understanding. I should state I am using WF5.

I believe the SPA method generates a mesh and solution with p=3, computes the stresses two ways and based on the difference it estimates the error and modifies the p level to get what it calls a converged solution. The error is normalized by the max stress in the model and if you have singularities or an area with a very high stress you can get poor results in other areas. The program by default tries to choose the p order such that the global RMS value of the normalized stress errors is below a threshold.

My confusion is related to the exclude elements options and the advanced convergence options. When I select portions of the model to "exclude" from the convergence, I think means that the system will ignor stresses from these elements when normalizing the element errors across the mesh for p order modification. However the excluded elements will still count toward the global stress error. Is this correct and if so is the only effect basically to prevent the system from incorrectly using a low order p element on element edges away from the singularity by not artificially assuming a low normalized stress error?

The advanced options to have a section for local convergence criteria based on the "local stress error". I can't find anywhere what this "local stress error" is. Is it the raw stress error normalized by the maximum element stress (each element is normalized by it's own stress) or is it the element error normalized by the max stress amongst all the elements selected for local convergence?

If I want to get a high degree of accuracy over the entire mesh would it be best to exclude elements in the region of singularities and then use the advanced options to specify local convergence over the entire mesh? If I do this does excluding the elements around singularities have any effect or will the local convergence criteria override force the same solution whether the exclude option is used or not?

I know that was allot, thanks for anyone who read the whole thing and can help me. Right now I have results that I'm not sure I trust.

 

[seymours2571]

Ozz,

Take a look at the following TPIs from PTC:

https://www.ptc.com/appserver/cs/view/solution.jsp?n=111746

https://www.ptc.com/appserver/cs/view/solution.jsp?n=113256

https://www.ptc.com/appserver/cs/view/solution.jsp?n=33332

These TPIs will answer a lot of your questions regarding how convergence is obtained.

Your understanding of the SPA method is correct. When excluded elements are defined these elements will not have the shape functions adaptively increased (a.k.a. "refined"). However, according to PTC the global RMS values include these excluded elements, therefore rendering the Global RMS value useless if excluded elements are present in your model.

With respect to your accuracy question: the highest degree of accuracy comes when the entire model is converged upon. However, as you know converging on a singularity can be difficult to impossible. Thus, convergence in regions where singularities exist (e.g. point load on a surface) will never technically converge. The process of selecting exlcuded elements near regions of singularity doesn't necessarily improve the accuracy, but only serves to prevent the solver from trying to adaptively adjust the shape function polynomial order. By defining excluded elements you theoretically save computational time, memory usage, and solution file size by telling the solver to ignore these elements during the adaptation phase of the solution process (either SPA or MPA).

Regarding the "local stress error", I couldn't find a definition either in the supplied help files. I refered to some Ansys documentation which not only provides an explination, but also provides the equations used to determine the stress error. I am not sure if PTC uses the same algorithm, however it is a good place to start in understanding this mysterious quantity.

Hope this all helps. This is one of those situations where the more you dig....the more questions you find.

Good luck,

Steve



Stephen Seymour, PE
Seymour Engineering & Consulting Group

http://www.seymourecg.com