7 Replies Latest reply on Mar 11, 2009 8:06 PM by Bill McEachern

    Flange and dished head

    Ben Floan

      I'm curious if anyone has played around with non-linear predictions for snap-through load of flange and dished heads given an external pressure load?

      My initial assumption was that the code can handle this simulation, especially a very simplified shell element symmetric case, however after trying I am not sure.

      I'm modeling the crown portion only with external pressure, shell elements using manually defined sym. constraints along edges, non-linear-static study, plastic material, assumed non-conservative force update for normal pressure, large displacement formulation, and arc-length control method.

      New to GNL and I'm hoping I may be missing something that is obvious to others.

      Attached are response graph of center point and displacment profile.

      Thanks for the help,
        • Flange and dished head
          Bill McEachern
          Why do you feel your results are NFG?

          Also, sometimes it is not obvious that the buckling response will be symmetrical so the symmetry assumption may not be right in all cases. This is particularily true in dome type structures of which this is obviously one.
            • Flange and dished head
              Ben Floan
              Bill,

              Appreciate the feed back (NFG?)....being somewhat new to the game, I think it is only the paranoia of "how do you know solution is correct?" of what is driving me here.

              Good point on the sym. assumption for buckling in free tet mesh/ non-linear case... would it be correct to assume a mapped uniform mesh would respond symmetrically in theory?

              Before assuming symmetry I noted differences in buckling response from full dome to sym. model... full model seems to be prone to dimpling in location off center which I still don't believe. I suppose much like actual material... small variations in localized stress, or material imperfections invalidate symmetry assumption.

              Also, do you have any advice on selection of # of steps in arc-control... is it a function of having a good idea of actual solution looks so one knows how long to run?

              Thanks again,

              Ben
                • Flange and dished head
                  Bill McEachern
                  (NFG?) No F___king Good....

                  You said:
                  Good point on the sym. assumption for buckling in free tet mesh/ non-linear case... would it be correct to assume a mapped uniform mesh would respond symmetrically in theory?

                  I don't think this has anything to do with the mesh or element selection - these things just have a non-symmetical buckling mode so to capture it you have to include the whole model. In my experience what happens is that the dome moves off to one side as it buckles.

                  You said:
                  Before assuming symmetry I noted differences in buckling response from full dome to sym. model... full model seems to be prone to dimpling in location off center which I still don't believe.

                  I would't be to quick to dismiss this. You should do some research on the buckling of domes. They often buckle asymmetically.

                  You said:
                  I suppose much like actual material... small variations in localized stress, or material imperfections invalidate symmetry assumption.

                  Very often the case. Non-linear analysis provides real world responses because the the shapes computed in the various inital loads steps allow the non in-plane loads to develop (even though they can be very small) which can provide the initiation forces for the proper modes to manifest themselves. It is insightful if you try to load a column axially and do a post buckling analysis on a beam element model. What you get is that the beam just gets shorter - it doesn't buckle. If you apply a very slight load in the center of the column length normal to the beam length the beam will buckle at the pridicted Euler load. The small load (could be a small displacement - like 0.001") acts like real world imperfections which is what allows the real world behavior to manifiest itself.

                  You said:
                  Also, do you have any advice on selection of # of steps in arc-control... is it a function of having a good idea of actual solution looks so one knows how long to run?

                  The automatic loads stepping works fine. Not every problem will solve in a post buckling analysis - that is to say it won't get to the post buckling phase. This typically happens in Simulation when problems are shear dominated (say a wagner tension field is the mode) or when there are so many potential load paths that all buckle nearly simultaneously the analysis can't discriminate and fails. In these cases a dynamic analysis can get beyond the buckling point as the inital forces provide the direction to select a path in the potentially bifurcating response.

                  Hope all that helps.
                    • Flange and dished head
                      Ben Floan
                      Bill,

                      Thanks again for the insight, very helpful...

                      In your opinion, how does SW code compare to other software for these types of advanced problems? I have access to Abaqus and other codes at school and I'm thinking of trying the same simulation for comparison. I guess what I am asking is if there are known deficiencies in SW for NL numeric calc. relative to other commercial codes... assume theory is the same but implementation of theory is not always the same.

                      Ben
                        • Flange and dished head
                          Bill McEachern
                          for this class of problem I would suspect that similar answers would be delivered by ABAQUS - I used to be a user of that code and actually did that beam element model I mentioned in ABAQUS. You can export the meshed model out of cosmos and into an ABAQUS inpuut deck though I have to admit I haven't used the translator before but it exists. The other thing is the Cosmos tet 10 is a very good element , at least in my opinion. Ciao.
                            • Flange and dished head
                              Ben Floan
                              Bill,

                              I recently came accross this and thought it was interesting and relevent to our discussion.. quoted here for your reference:

                              "The deep arch example,.... can be categorised as a large displacement/large rotation/small strain problem. For an exactly circular arch the deflected shap is symmetric and the load deflection path exhibits a limit load. But if the radius is perturbed slightly... then a bifurcation emerges in the equilibrium path and an asymmetric deflected shape develops. Clearly manufacturing errors would make the latter lower elastic critical load the practical case.

                              If the arch were exactly circular and if a symmetric deflected shape were attained beyond the bifurcation point then the arch would be in a position of unstable equilibrium. In practice, ...this unstable position would not be maintained and a 'snap through' to a stable equilibrium position would result."

                              NAFEMS Intro to NFEA, E. Hinton
                                • Flange and dished head
                                  Bill McEachern
                                  It sounds pretty consistent with what I have said though the subtle detail is nice. I would surmise that the full FEA model behave as per the asymmetic as small pertubations would exist due the shape descritization and round off errors - which didn't happen in the straight line beam element model. There wasnothin in the aforementioned beam element model to generate out of plane loads.