22 Replies Latest reply on Apr 22, 2016 3:12 PM by John Willett

    No Convergence in Simulation With No Sharp Corners

    John Willett

      I can't get this model to converge in spite of having filleted the presumed-relevant corner to remove the potential singularity.  It is shown here face-on to a symmetry cut after an h-adaptive loop of 8 cycles:

      Stud Test 5_16 Fillet Half Less Interf.jpg

      (The stress range for the plots was deliberately set to the yield level of the stud.)  This is intended to model a bolt threaded into a pair of test blocks, using a shrink fit to simulate the threaded joints.  A horizontal force is applied to the blocks, and vertical motion of the blocks is not allowed, so that the stud is bent into an "S" shape..  Only one quarter of the model is shown because I used symmetry across the X-Y plane and anti-symmetry across the middle of the stud to reduce the computational load.  The full model (before the symmetry cuts) is shown here for clarity:

      Stud Test 5_16 Plain Fillet.jpg

      Here's what happens when the mesh resolution is increased using the h-adaptive default settings:

      Stud Test 5_16 Fillet Half Less Interf Convergence.jpg

      This behavior is not caused by some instability of the h-adaptive method but has been replicated with manual mesh resolutions set by mesh controls.  It also has not improved by addition of the fillet; similar stress increases at the edge where the stud emerges from the block were observed without it.  The stress increases without limit on the compressed side of the stud here:

      Stud Test 5_16 Fillet Half Less Interf Stud.jpg

      ...and on the upper edge of the fillet inside the hole in the block here:

      Stud Test 5_16 Fillet Half Less Interf Block.jpg

      These stress maxima are near the location where the interference ends between the two parts.  Here are the study properties:

      Stud Test 5_16 Fillet Half Properties.jpg

       

      Stud Test 5_16 Fillet Half Properties 2.jpg

      (I haven't tried fiddling with the "Accuracy bias" setting, nor have I tried the p-adaptive method.)  Attached is a P&G in case you want to look in greater depth.

       

      Can anyone suggest what I'm doing wrong? -- John Willett

        • Re: No Convergence in Simulation With No Sharp Corners
          James Riddell

          I can't tell from the pictures, however, as a guess, I'll go out on a limb and ask if you are doing this as a non-linear solve?  If not, then once you approach the yield limit of the material all bets are off and you will likely never get to convergence.  (I tried a similar test with Hertzian contact - didn't work - nor did the answer approach the calculated value that it should have been.)

            • Re: No Convergence in Simulation With No Sharp Corners
              John Willett

              >>I'll go out on a limb and ask if you are doing this as a non-linear solve?  If not, then once you approach the yield limit of the material all bets are off and you will likely never get to convergence.<<

               


              James -- Thanks for your quick response.  No non-linear.  I should have mentioned that I'm using SW Premium 2015 SP5.0, so strictly linear static simulations.  It never occurred to me that it would actually care about the yield strength (except for computing the factor of safety)!

               

              Yikes!  Sounds like something I should take up with my VAR tech support.  Do you know of any documentation on the subject?

               

              If I want valid results near (or above) the true yield strength, should I just make up a fictitious material with much higher yield strength?  Is that a viable way to avoid this problem? -- John Willett

                • Re: No Convergence in Simulation With No Sharp Corners
                  James Riddell

                  I don't have a chance to look at your geometry but are your deflections higher than acceptable for linear analysis?  That would be another indicator.

                   

                  SW doesn't take into account the YS or UTS in a linear solve, just E & nu.  However, interpretation of your results would be where you can see that if you are near or above YS then it is no longer in the realm of a linear analysis.

                   

                  To get any meaningful results above that point you would have to use non-linear analysis, no question about that.

                    • Re: No Convergence in Simulation With No Sharp Corners
                      John Willett

                      >>To get any meaningful results above [the yield] point you would have to use non-linear analysis, no question about that.<<

                       

                       

                      James -- Agreed, but I believe (based on my geometry) that the solution should converge.  Since it isn't converging, I'm looking for a reason.  Your statement about a linear simulation breaking down (if I understand you correctly), not just exceeding its bounds of validity, might be one.

                       

                      In any case, there would seem to be reasons you might want to get valid results beyond the yield strength, if only to determine how much stronger a material you need or how much "beefier" to make the parts.  This is the stage I'm at with these simulations. -- John Willett

                  • Re: No Convergence in Simulation With No Sharp Corners
                    John Willett

                    >>I'll go out on a limb and ask if you are doing this as a non-linear solve?  If not, then once you approach the yield limit of the material all bets are off and you will likely never get to convergence.<<

                     

                     

                    James -- My VAR's tech support is telling me the same thing (if I understand you correctly): that the linear solver will "get confused" if the stresses go above the yield point and will cause convergence to fail.  So I did some tests with a much simpler model, driving the linear solver beyond the yield point in two different ways, but I could not reproduce the non-convergence:

                    Base Model.png

                    Here's the base solution of a single part with a 0.01" fillet, a curvature-based mesh with the minimum number of elements in a circle set to 12, and the iterative solver to make the solutions as fast as possible.  The chosen material has a yield point of about 36,000 psi, and in this case SW Premium calculates stresses that are well below that.  The maximum is only 2,432 psi.:

                    Wills Example Base.jpg

                    Then four more loops of h-adaptive solution on top of the above, which appear to converge to a maximum stress (in a different location) of 2,714 psi:

                    Wills Example Adaptive.jpg

                    h-Adaptive Convergence .jpg

                    Next I tried increasing the applied force by a factor of 14.4, calculated to drive the adaptive solution beyond the yield stress.  You will see that the maximum stress of 39,083 (and also the maximum displacement) is exactly a factor of 14.4 larger but the approach to convergence (above the yield point) is identical -- no indication of solver confusion or non-convergence:

                    Wills Example 143p4XForce Adaptive.jpg

                    h-Adaptive Convergence 14p4XForce.jpg

                    Finally I created a fictitious material, a copy of the original but with the yield point artificially reduced to 2500 psi -- just above the stress calculated in the base simulation.  Using that I re-ran the base solution and its adaptive sequel with the following results:

                    Wills Example Weak Steel Adaptive.jpg

                    h-Adaptive Convergence Weak Steel .jpg

                    Here the maximum stress is still 2,714 psi and the approach to convergence is still exactly the same.  (I've attached the model in case anyone wants to verify my conclusions.  All the studies run quickly in this model.)

                     

                    On the other hand, re-running my original problem (with the shrink fits and symmetries) with a factor of 10 less applied force still results in non-convergence.

                     

                    Conclusion:  The linear solver (at least the iterative version) behaves just fine beyond the material yield point.  Therefore the non-convergence observed in my original problem is probably due to something else.  My favorite candidate right now (at least with the h-adaptive method) is some kind of instability in the mesh refinement.  See below that the mesh resulting after 8 loops is "patchy," as though the mesher created flaws and then the adaptive algorithm "zoomed in" on them:

                    Stud Test 5_16 Fillet Half Less Interf Stud Mesh Zoom.jpg

                    Comments or rebuttal are eagerly invited. -- John Willett

                  • Re: No Convergence in Simulation With No Sharp Corners
                    Mike Pogue

                    This looks pretty straightforward to me. There is a discontinuous contact condition there and it is causing the non-convergence. If you choose strain energy as the convergence criteria, I think you'll see it converges.

                     

                    You can assume there will be some localized yielding in that small volume and, if that's acceptable, ignore it. If that's not acceptable, you can extract the linear portion of the stress there and apply the appropriate stress concentration factor.

                      • Re: No Convergence in Simulation With No Sharp Corners
                        John Willett

                        Mike -- I'm grateful for your response, but you're going a bit too fast for me.  (I was trained as a physicist, not an engineer, so I'm not as familiar with the terminology and rules of thumb as I should be.)  Sorry to be a pest, but could you please fill in some gaps?

                         

                        >>This looks pretty straightforward to me. There is a discontinuous contact condition there and it is causing the non-convergence.<<

                         

                             What do you mean by "discontinuous contact condition?"  The shrink fit and/or the adjoining surfaces included in each half of that contact set?  If so, does that inevitably produce unbounded stress as the mesh size decreases?  If so, is there some other kind of contact that I should be using to simulate a threaded joint?  (I think I know that bonded contact there, at least in the absence of a conventional fillet, produces a "re-entrant corner" that is guaranteed to result in unbounded stress.  I cannot have a conventional, concave fillet there, however, because the threaded joint must be adjustable.  I wanted friction between the faces of a shrink fit to allow some stretching of the stud inside the hole and, I hoped, to spread the stress -- it does seem to help.  When I found stress concentration around a square hole, I added the convex fillet to its edge in hopes of spreading that stress as well, but all it seems to do is move the stress concentration down to the bottom of the fillet...)

                         

                        >>If you choose strain energy as the convergence criteria, I think you'll see it converges.

                         

                             SW Help says under h-adaptive options, "Target accuracy -- Sets the accuracy level for the strain energy norm," so I thought I was already using that as the convergence criterion.  It is decreasing with decreasing mesh size -- red trace in the convergence plots -- but the fact that the stress is not approaching a constant value (as it does, for example, in my simple model immediately above) but is increasing apparently without bound is not helping me to assess failure of the threaded joint.

                         

                        >>You can assume there will be some localized yielding in that small volume and, if that's acceptable, ignore it. If that's not acceptable, you can extract the linear portion of the stress there and apply the appropriate stress concentration factor.<<

                         

                             Well, that is indeed the bottom line:  Localized yielding can be tolerated only as long as the threaded joint remains adjustable.  If it binds up, that is not acceptable. -- John Willett

                          • Re: No Convergence in Simulation With No Sharp Corners
                            Mike Pogue

                            I overlooked the fact that this was a threaded stud, I thought this was a press fit or shrink fit. Given this information, which going back I now see was in your OP, I can tell you with confidence that this stress you are calculating does not measure anything physical. you are not modeling a bolt. you are modeling a pin. And the local stresses in a pin are not related to the local stresses in a bolt in any interesting or predictable way. This should be a hand calculation. Calculate the moment in the bolt at the connection and check that it can resist the Moment as a circular beam with a cross section equal to the stress area or the bolt, which is available in Machinery's Handbook, or Google. Then add some appropriate safety factor and ship it. if this is fatigue, add another safety factor of 3 or 4, OR if you are super-dedicated, look up the stress concentration factor based on treating the thread as a notch. This last is conservative, though, because multiple adjacent notches tend to dissipate stress concentration.

                             

                            I say this should be a hand calculation, because you are trying to extract something from FEA that it cannot give you.

                             

                            If you are still interested, though, I'll go through you other questions.

                             

                            "What do you mean by "discontinuous contact condition?"  The shrink fit and/or the adjoining surfaces included in each half of that contact set?  If so, does that inevitably produce unbounded stress as the mesh size decreases?"

                            Discontinuous contact condition, because one element is touching the metal surrounding the hole, and the next is in space touching nothing. I don't know whether it's inevitable, as in re-entrant corner inevitable, but it's the least surprising thing since a lying politician. I am always very skeptical of contact stress results from FEA unless I know  the analyst very well. Also, if your stud is glued to the surrounding metal, the discontinuous Young's modulus will cause a singularity.

                             

                            I thought I was already using that as the convergence criterion

                            You are and it converged. That's why the solver stopped. Strain energy will frequently or usually converge even when stress diverges, as infinite strain becomes packed into infinitesimal volume. If you showed successive stress plots leading up to the singularity vs. decreasing element size, you'd see the series superficially resembles Gibbs phenomenon plotted vs. increasing n. What that shows is that your solution is converging to a divergent answer. It's not getting any better: your solution has converged even while your stress hasn't. Again, you can't see into the singularity, so you have to apply judgment.

                             

                            You can assume there will be some localized yielding in that small volume and, if that's acceptable, ignore it. If that's not acceptable, you can extract the linear portion of the stress there and apply the appropriate stress concentration factor

                            I'd be surprised if the screw were going to fail based on your results so far, assuming you've modeled the stress area or minor area and not the nominal area of the screw. If you are going to have more than, say, 100k cycles, though, look at fatigue.

                              • Re: No Convergence in Simulation With No Sharp Corners
                                John Willett

                                Mike -- Thanks for the very helpful responses.

                                 

                                >>Also, if your stud is glued to the surrounding metal, the discontinuous Young's modulus will cause a singularity.<<

                                 

                                Just to make sure I understand:  Are you saying that, even if two blocks of different materials were bonded (with compatible mesh and no overlap so no re-entrant corners), since the Young's moduli are different, a singularity would appear at the edge of the junction plane?

                                 

                                As you apparently concluded, I'm interested in both addressing the real problem and learning how to successfully execute SW linear simulations.  Thanks for addressing both!-- John Willett

                                • Re: No Convergence in Simulation With No Sharp Corners
                                  John Willett

                                  >>...check that it can resist the Moment as a circular beam with a cross section equal to the stress area or the bolt, which is available in Machinery's Handbook... Then... if you are super-dedicated, look up the stress concentration factor based on treating the thread as a notch. [Emphasis mine]<<

                                   

                                  Mike -- If you're still passing through, please answer two more specific questions re. the above quote:

                                   

                                  1) How would you specify the notch simulating a thread?  My uncertainty arises because the tensile-area diameter lies almost at the bottom of the thread groves, so any notch from there to the minor diameter would be very shallow.  Perhaps the stress concentration factor (SCF) should be based on a notch from the major diameter to the minor diameter?

                                   

                                  2) What does one do about the radius of the corner at the bottom of the notch?  One would expect the SCF to be very dependent on this radius.

                                   

                                  Thanks again for all your help on this. -- John Willett

                                    • Re: No Convergence in Simulation With No Sharp Corners
                                      Mike Pogue

                                      I'm concerned that I've given you too much to think about. Unless this application is really critical for some reason, and unless you really are in fatigue, say 100k cycles, You can skip the stress concentration analysis and apply a judicious safety factor directly to the nominal stress.

                                       

                                      Also, be advised that pounding this geometry into a Peterson stress concentration factor is going to require some heroic assumptions, and to defend those assumptions, you'd probably have to look at the sensitivity to each.

                                       

                                      Question 1 is a pretty good question. Yes, that's what I'd have done, but it seems really conservative to me and I'm not sure whether it's right, because this is not how bolted joints normally work and I haven't thought it through.

                                      Here is a screen from Peterson's stress concentration factors. I was not able to find "circular v-shaped groove in bending" (I did find it in torsion). So I'm posting the u-shaped groove and call it close enough if you choose a good effective groove width. This factor would be applied to the normal component of the bending stress at the outside diameter in addition to a whole host of fatigue factors (k_i) from Shigley, as well as your chosen factor of safety. These factors are all multiplied together to get the allowable stress. At any rate, this is conservative, because multiple adjacent notches tend to reduce stress concentration significantly.

                                       

                                      As to question 2, The concentration goes like sqrt(r/t), so the dependency is weaker than you'd guess until it gets pretty sharp. The radius at the bottom of the notch is documented in Machinery's Handbook.

                                       

                                       

                                    • Re: No Convergence in Simulation With No Sharp Corners
                                      John Willett

                                      >>...OR if you are super-dedicated, look up the stress concentration factor based on treating the thread as a notch. This last is conservative, though, because multiple adjacent notches tend to dissipate stress concentration.<<

                                       

                                       

                                      Mike -- You have been extremely helpful with this problem.  I just want to close the loop with some concrete results.  For what it's worth, I've now compared the Stress-Concentration Factor (SCF) calculated from formulae in Noda and Takase [1999] -- attached to my previous message -- with what Solidworks Premium 64bit SP5.0 gives and with a lab test on an actual physical bolt.  Here's what I found:

                                       

                                      1) For a single circumferential notch with a cross section equivalent to NF24 threads (having the largest possible notch-bottom radius that's tangent to the thread walls, .0060", and corresponding thread depth, .0256") cut into a rod with the major diameter of a 5/16" bolt, Noda and Takase give SCF = 3.54.  (For a factor-of-four smaller notch-bottom radius and correspondingly larger thread depth of .0301", SCF = 6.70.)  All I can say about this is that these are complicated calculations but I believe I did them correctly.

                                       

                                      2) In SW I set up a rod of the same diameter with the same notch shape in a case of "pure bending" -- stress in the extreme fiber is uniform along the length.  (This was achieved using equal and opposite "Remote Load (Direct transfer) Moments" applied to the opposing faces of the rod, with "Use inertial relief" stabilizing the model.)   The maximum stress in the extreme fiber away from the notch was the same as calculated for pure bending in the absence of a notch (either analytically or with SW).  The maximum stress at the bottom of the notch was found to be a factor of 6.1 larger than the pure-bending maximum.  This result is quite insensitive to mesh resolution over the three meshes I tried, so I tend to believe it.  (I haven't been able to figure out why this result is so different from the stress-concentration factor of 3.54 predicted by Noda and Takase.)

                                       

                                      3) From Machinery's Handbook for the conditions to which my bolt will be subjected ("Case 17," which I call "S-bending," with a transverse force of 100 lb between two parallel blocks 1.071" apart) I find that a smooth rod of ASTM A36 steel with 5/16" diameter should experience a maximum stress at either end of 17,900 psi.  (With some effort and no fixtures on the ends I can get essentially the same result from SW.)  Since the yield strength of this material is 36,300 psi, either SCF that I choose (assuming that the notch is located at the point of maximum stress, as it should be in a fully threaded bolt) should drive the material well beyond yield.  You had suggested that the notch approach would be overly conservative, but this seems like a serious overload!  Anyhow we were having trouble believing it.

                                       

                                      4) Now for the punch line:  We set up an actual test jig to apply "S-bending" (one end through a tight hole and the other end threaded into parallel sliding steel blocks separated by 1" rails) to a very similar bolt with up to 100 lb force exerted transversely between the blocks.  No yielding or cracking was observed.  In spite of the theoretical and FEM calculations, we conclude that the bolt is adequate for the task.

                                       

                                      I guess this wraps it up.  Thanks again! -- John Willett

                                        • Re: No Convergence in Simulation With No Sharp Corners
                                          James Riddell

                                          For your point #2 - perhaps this is due to the fact that the default stress reported is nodal stress (averaged) instead of elemental stress (which is not averaged) and thus tends to be higher (more conservative?).

                                            • Re: No Convergence in Simulation With No Sharp Corners
                                              John Willett

                                              >>For your point #2 - perhaps this is due to the fact that the default stress reported is nodal stress (averaged) instead of elemental stress (which is not averaged) and thus tends to be higher (more conservative?).<<I

                                               

                                              James -- That doesn't seem to be it.  I was plotting nodal values, but the element values are only slightly different, I guess because I have enough resolution.

                                               

                                              Actually I've been comparing the longitudinal component of normal stress (got into that to compare with results from Machinery's Handbook).  But when I compare von Mises stresses between the extreme fiber in the undisturbed shaft and the notch maximum, I get a ratio of about 5.0, still considerably larger than the predicted SCF.  Interestingly the element values are smaller in both cases.

                                               

                                              But maybe Mike has the answer...  (Or it still might be that I made some mistake in interpreting the formulae in Noda and Takase [1999], although I was able to get answers that agreed with their Figure 14.) -- John Willett

                                            • Re: No Convergence in Simulation With No Sharp Corners
                                              Mike Pogue

                                              Well, that is some good work there.

                                               

                                              One thing to remind you of above: SCFs do not apply unless you are in fatigue. Your test should correlate to the nominal stress, not the SCF*nominal stress. To compare to the SCF stress, you'd have to cycle this test rig to failure and compare to the SN curve.

                                                • Re: No Convergence in Simulation With No Sharp Corners
                                                  John Willett

                                                  >>SCFs do not apply unless you are in fatigue.<<

                                                   

                                                  OPS!  None of the material I have been reading explicitly says that (although the article I attached is indeed published in Fatigue Fract Engng Mater Struct).  So help me out here:  What if I want to look up the static stress enhancement of a notch (for example)?  I thought you had been suggesting the use of a "stress concentration factor" for that. -- John Willett

                                                    • Re: No Convergence in Simulation With No Sharp Corners
                                                      Mike Pogue

                                                      I did say that, but I said only if it is a fatigue situation (I checked back at what I wrote). The way to get the nominal stress at the notch (in bending) is to compute the moment at the notch and examine the ability of the section through the notch to resist that moment.

                                                       

                                                      The reason you can ignore stress concentrations in strength cases (non-fatigue), is that local yielding will relieve the highly concentrated stress. But this causes hardening. And if you keep repeating the motion, it can lead to cracks, and depending on [...2 years of college courses omitted for clarity]. It's all very, very complicated. None of it is individually hard to understand but there's just so damn much to take into account.

                                                       

                                                      I apologize again for getting so deep into it.