Uncertainty in transient simulations

[Kevin071586]

Hi All,
I'm doing some work that involves calculating the transient structural response (acceleration, displacement) in a system-level model that is subject to impulsive loading. Let's assume that everything is strictly linear, small rotations for the purposes of discussion. I would like the acceleration traces primarily for looking at things like shock response spectra and vibration characteristics. Discretizing any continuous domain always introduces numerical dispersion, which of course can be minimized by further mesh refinement. In this case, it's simply not possible to further refine the mesh and there is absolutely no hope to resolve wave motion in the structure. Therefore, the acceleration I record at any point in the mesh is almost entirely qualitative.

Does anybody has some experience, guidelines, or rules-of-thumb for interpreting or improving results like this? Can a statistical argument be made regarding the quality of the results, given the inherent numerical dispersion and mesh-dependency for a transient structural dynamics simulation run?

Thanks
Kevin

 

[jameslamb]

Hi Kevin,

Afraid I have no answers for you but I have been encountering the same problem.

I am finding that the shock attenuates as expected through any spring elements I have placed in my assembly but increases in magnitude through each solid part as if energy is being added somehow (this is not due to any whipping effects). Have you got anywhere with your problem?

Apologies again for not providing any sort of solution.

James

 

[Kevin071586]

James, what I have found is that there really isn't a very good answer to this issue right now. I've asked several of the 'experts' that are around me, as well as some basic literature searches. We can take much more liberty with refining mesh in high-detail regions for static solutions; but with transient simulations this isn't the case. Any region of low refinement is going to have much more dramatic effects in a transient solution vs. static solution. It's possible to understand and quantify these effects on simple problems with structured meshes. But with more complex geometry, it becomes an issue for the analyst to interpret properly. The best solution I've come across is to deal with uncertainty by varying parameters within a reasonable range and then quantifying the sensitivity of those results. One might also re-mesh certain parts to see how sensitive results are to the mesh. It's more qualitative than qualitative, but it's one approach.

For your problem, when you refer to the 'shock' are you talking about a shock response spectra or the actual motion measured at a point in your structure? Either of those can vary pretty significantly throughout an assembly as vibrations/waves go in and out of phase with each other. Maybe you can look at the total energy in the structure to be sure that no energy is being added?

 

[shaun8567]

Kevin, can you provide more information was to why you can't refine your mesh further? Can you also provide some more information about what type of simulation you're doing? Are you trying to do a drop/impact test? Is the event highly non-linear, requiring non-linear dynamics? Maybe I'm not understanding your situation correctly, but if you're concern is whether your results have converged, and you cannot (for whatever reason) refine the mesh further, then maybe start with a coarser mesh and plot the change in your results as you refine the mesh and look at how they converge.

 

[Kevin071586]

shaun, the main reason I can't refine the mesh further is because convergence would require a

 

[Kevin071586]

shaun, the main reason I can't refine the mesh further is because convergence would require an excessively large model (memory, storage, etc.). The simulation involves a drop/impact type testing on a system-level model. Components are connected with contact constraints and may experience highly non-linear conditions.

The main problem lies in the many nuances that need to be taken care of for mesh convergence in transient simulations (either linear or non-linear). The motion measured at a point in response to some forcing function is highly-dependent on the mesh for frequency content with wavelengths on the same order as the elements. Various frequencies travel at different speeds (dispersion), and lower-frequency components tend to converge faster than higher-frequency components. This means the various frequency components combine in such a way that the resultant transient signal can be significantly different due to "random" phase relationships. Further discretization problems associated with reflection/transmission arise at parts of model where mesh transitions from fine to coarse. The mesh would have to become impossibly small to converge on a transient signal, with the exception of a "low" frequency range ("low" being relative to the model dimensions and material properties).

I agree with you, though. For lack of a better solution, starting with a coarser mesh and then refining various components may be the way to go. The transient signal measured at a particular point in each case will be significantly different in the time domain. They may be similar in the frequency-domain for some frequency range. The approach will end up being experience-based, but at least somewhat rational and methodical. I was originally hoping that there was some standardized method of quantifying the error/variation in the time domain signal, but I don't think there is.

 

[Elabbasi]

Drop/impact events introduce very high frequency content in a system. Capturing that response in finite element simulations requires both a fine mesh and a small time step size. The FEA response will include high frequency content that is physical and another part results purely from numerics (such as the contact formulation). It will also include physical damping and numerical damping (needed to stabilize the solution). The physical damping is also frequently hard to measure and is sometimes neglected in this type of simulations.

That is why even reducing element size and time step size in impact problems does not always lead to solution convergence (with respect to say the peak acceleration). It instead creates higher frequency content that may be either numerical or physical with a high damping rate that is not accounted for!

Nagi Elabbasi
Veryst Engineering

Nagi Elabbasi

http://www.veryst.com