Dear Pasha, I must correct my answer by replacing "residual vector" by "internal force > vector"
Ok, great. So this is a slightly different situation. I was going to say that I think that we're cross-talking here, and you saved me from sketching out a whole bunch of equations to clarify things :-) Yes, we can use internal forces for all situations. Hmm... I still don't think so. What about if you have body forces? Then the internal stresses balance both the externally applied loads plus the volume forces. Do you agree with this? However, one can of course compute the internal stress plus the body force loading... But then consider a cube with a non-uniform pressure on more than one side. How do I compute from this global vector the average or total load applied to any *individual* surface? You can't, because the values in the degrees-of-freedom shared by any two sides of the geometry contain load contributions from two faces. For reaction forces at constrained surfaces - no problem of course! Also, I think that one should consider which vectors one typically constructs during assembly. The most efficient way to do assembly (but I recognise that this is not universally followed - not even by me) is to compute the constrained RHS vector and tangent matrix in one shot during assembly. That means that you never need to actually construct the individual internal, external and body force vectors in order to solve your linear system because, well, they get bundled into the RHS and then further manipulated when imposing constraints. Dependent on what it is you want to achieve, I do concur that what you suggest may be perfectly plausible. But in general... I'm still unconvinced. To be introspective, what I suggest (and what Hamed has done here) might be overkill for plain elasticity alone since you can always recompute the traction vector itself as it is you that specified the loading at each time-/load-step. In coupled problems, however, external tractions are not always so easily defined and its actually sometimes easier to simply do this stress-type integration procedure. However, can we calculate internal force by integrating over boundary > surfaces when material model is history dependent and has internal state > variable such as plasticity Yes, you can - its just not very convenient. You could do this in one of two ways: 1. Extrapolate the internal variables to the faces and recompute the stresses with these values. Its clear that this might be problematic because one has to make an assumption about whether there is plastic yield at the extrapolated points (as can be attested to by the note in the ContinuousQuadratureDataTransfer <https://www.dealii.org/developer/doxygen/deal.II/classparallel_1_1distributed_1_1ContinuousQuadratureDataTransfer.html> class - we'd like to extend this at some point and we've already worked out a couple of options that may work for plasticity but simply haven't tried to implement them yet), so I would recommend option 2... 2. Simply create and track additional quadrature point data (with internal data) at the faces at which you'll be doing this post-processing. That way you can update the internal variables as necessary and they'll always be in sync with the solution field. You can then compute stresses etc. at these points whenever necessary. Its annoying if the local problem is expensive to compute, but the number of face QP data that you'd create is likely far less than those required for assembly etc. Best, Jean-Paul -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
