28 Replies Latest reply on Aug 21, 2013 1:45 AM by Jared Conway

    Nonlinear buckling analysis and snap-through modeling of an arch

    P. B

      Hello,

       

      My name is Peter and I am working on a project to model snap-through buckling behaviour in an arch.

       

      I am wondering how I might be able to model a simple beam spring under a normal load as it is deflected and eventually buckles and undergoes snap-through buckling. I would like to have the spring (arch) fixtured on its outside edges so that there is no translation in the x, y or z directions, and the only motion allowed on the outside edges is rotation to allow the outer edges of the spring to rotate with the load. I would like to use a prescribed displacement on the uppermost part of the arch (-9mm) to cause the arch to buckle. This downward displacement should cause the spring to deflect and buckle, and eventually undergo snap-through behaviour as more load is applied. Since I have a fixture in the study which gives the prescribed displacement of the arch, I am using the force-length control method for solving the simulation. I tried using the arc-length control method to solve the simulation, but it ended in an error because it stated that solving for the prescribed displacement required that I use the force control method. I am wondering if this method is not the correct method to use since it cannot solve past the buckling point in the arch when the tangent to the force-displacement (equilibrium) curve is horizontal.

       

      Force

      riks-buckling.pngDisplacement

       

      I have completed the Solidworks tutorial problem on snap-through analysis, 'Snap-Through/Snap-back of a Cylindrical Sheet', and I am still in need of assistance. I have a result from the simulation as I currently have it set up, and I'm wondering if it's correct. I would also like to validate the snap-through behaviour of the arch using an equilibrium plot but I am unsure how to define the equilibrium plot after I have the results. I have included the model and results files of the example part which I would like to model.

       

      Any help on these problems would be greatly appreciated.

       

      Thank you,

      Peter

        • Re: Nonlinear buckling analysis and snap-through modeling of an arch
          Jerry Steiger

          Peter,

           

          I'm afraid I can't be of much assistance when it comes to the details of the solvers for snap-through analyses. But once you get that part worked out, I wanted to share a story from many years ago when I was designing calculators. This was back in the days when analysis was always done by specialists and a snap-through analysis was something that only one or two programs could handle. We had a professor in the local university analyze the Mylar snap domes on our keyboards. A big question was what the boundary conditions should be. We started out assuming that the edges  were fixed, but we got numbers about ten times higher than our measured values. We then assumed that the edges were free to rotate and got numbers much closer to what we expected. To help us understand what was going on, we had the model shop make a clamping fixture out of fairly stout steel plates with big screws. Now the measured values matched the analysis for fixed edges. So be careful when you assume fixed edges; it can take a lot more than you might expect to truly fix an edge.

           

          Jerry S.

          • Re: Nonlinear buckling analysis and snap-through modeling of an arch
            Bill McEachern

            You should use displacement control. Arc length would work you just have to use a load but it does get hard to know where you are at since they changed the settings in that method. I have no idea what they were thinking but it appears to me, at least baosed on the times I have used it recently,  that in the arc length method they will allow the arc step to reduce to get a solution started but then once it stiffens up it will not increase the load step and the solver window does not report the load factor anymore. All that leads to really long solution times and you have no idea if anything sensible is happening. Really sub optimal modification. They should have just left it as it was it when they used the old cosmos solver window. It is like product definition doesn't understand that Cosmos was developed through customer enhancement requests as well - go figure. Anyway displacement control works fine for this problem as long as you are only interested in the snap through part, snap back won't get handled though. For that you need the arc length method so set the steps to some really big number and wait. Force control can't get through the zero stiffness at the buckling point typically.

            • Re: Nonlinear buckling analysis and snap-through modeling of an arch
              Jared Conway

              Like bill says, displacement control and/or arc-length control is the way to go for this problem. This is covered in the nonlinear training class. If that does't work, update us and we'll see what the next step might be.

              • Re: Nonlinear buckling analysis and snap-through modeling of an arch
                P. B

                Ok I am trying to use the displacement control method and I have fixtured the model to mimic the conditions in which I will be using it, and I am seeing a new error which states:

                 

                "Error: Loading Pattern is not proper."

                 

                If I bring up the study properties by right-clicking the study icon in the simulation mode, I can enter the "Advanced Options" tab. I believe the error has something to do with the curve that I enter into the "Displacement Variation with time" option under the "Displacement Control Options". When I click the "Edit" button, I select "User-Defined" under Curve Information, and I enter for points 1 and 2 respectively: (0,0) and (1,-1). I would like the part to displace by 1mm downwards over the span of 1 second. I select a vertex of a split line on the part that I would like to displace by 1mm under the "select a vertex to control analysis" field. When I click ok and try running the study, the error comes up indicating that the study failed on the first step because the loading pattern is not proper. After I click enter onece, a new error message comes up saying:

                 

                Solution Failure in the First Step may be due to:

                1. Lack of Adequate fixtures for one or more parts

                2. Material properties may not be properly defined

                3. Load Increment may be too large or too small

                 

                The material of the part has been indicated, and the properties seem to be completely defined. I have tried using the same fixturing in a buckling analysis on the same part and it seemed to work ok. I have also tried varying the Step/Tolerance Options in the Advanced Options tab with no effect.

                 

                Would anyone be able to give an example of a Proper loading profile?

                • Re: Nonlinear buckling analysis and snap-through modeling of an arch
                  P. B

                  Ok it seems to be working now, thanks. I'm just modifying the parameters of the arch to see how each parameter changes the buckling load of the arch. I have the Donnell approximation equation for the buckling of an arch from the SolidWorks verification tutorial "Buckling of a quarter ring under a radial force" as:

                   

                  Pcr = 4*E*I/R^3

                   

                  Where:

                  Pcr = Critical (buckling) force

                  E = Modulus of elasticity

                  I = Moment of Inertia of the cross-section of the shell

                  R = Radius

                   

                  Does anyone know if there is a problem with using this equation for a point load instead of a distributed load across the whole arch? If so, are there any other equations I could use to estimate the buckling load of the arch under a point load? The tutorial uses a distributed load but I would like to use a point load for my application.

                  • Re: Nonlinear buckling analysis and snap-through modeling of an arch
                    P. B

                    Hey,

                     

                    I see what you mean about the asymmetrical mode of collapse. I created a model of the concept to observe the behaviour and I see that the physical model is exhibiting a flop-over behaviour due to asymmetrical properties of the steel. The arch I am modelling exhibits flop-over behaviour, where one side is bent unevenly compared to the other instead of completely symetrical buckling. I would like to verify that the buckling load factor I am getting from my simulation is equivalent to the buckling load I am reading from my model. I added a sensor to the model in the area of interest using a split line, but when I finished the simulation, the sensor had a warning stating: "Warning: Data not available". I was wondering if anyone knew how to get around this error?

                     

                    Thanks,

                    Peter

                    • Re: Nonlinear buckling analysis and snap-through modeling of an arch
                      P. B

                      Ok I think I found a way of getting what I want for now, I had to use a prescribed displacement instead of an applied force, and use the "List Result Force" option under results to plot the result force acting on a certain face of the part. I'm trying to pursue the prescribed displacement method using a different type of split line, where the displacement acts at a point instead of a circular face of the part. I believe there is a tutorial in Solidworks about this topic but I am unsure what it is called. Does anyone know what the name of this tutorial is?

                      • Re: Nonlinear buckling analysis and snap-through modeling of an arch
                        P. B

                        When I try to add the "Deformed Result" of a simulation study as a configuration in my part model, an error occurs, stating:

                         

                        Unable to sew faces together. Creation of deformed body failed.

                         

                        Does anyone know how to get around this error?

                         

                        Thanks,

                        Peter

                          • Re: Nonlinear buckling analysis and snap-through modeling of an arch
                            Jared Conway

                            there are a couple of posts on the forum about this. usually the mesh is too coarse or you have a large deformation that is either too large to create the deformed part OR you have a solver error that is causing it to be unrealistically too large. also, i think you're using shells which i'm not sure can be output as a deformed body.

                             

                            this one is one you would want to check with your reseller on after doing some checks on your model. for example other models, static vs nonlinear, lower loading conditions, improved mesh..etc.

                          • Re: Nonlinear buckling analysis and snap-through modeling of an arch
                            P. B

                            Ok I have got the deformed result the way I wanted it, thanks a lot for the helpful suggestions.

                             

                            I'm also trying to do another simulation in solidworks where I have a contact set between a dome-shaped actuator and an arch. The dome-shaped actuator is applying a downwards force to the arch using a prescribed displacment to simulate the actual conditions in which I am using the beam spring. For some reason the study is failing when I set the dome-shaped actuator to be rigid instead of a deformable body. The error reads:

                             

                            <Reference Geometry - 3> transfer failed

                             

                            Which refers to the prescribed downwards displacment of the dome-shaped actuator. Has anyone encountered this error before when working with rigid bodies?


                            Thanks a lot,

                            Peter

                            • Re: Nonlinear buckling analysis and snap-through modeling of an arch
                              P. B

                              How do I setup an elastic support in a nonlinear static study? For some reason I cannot select it in the drop-down menu for specifying the type of connector. In my study I have a spring connector, but it does not act the way I would like it to, so I would like to replace it with an elastic support. I have solidworks simulation premium, but for some reason the elastic support option does not appear in the drop-down menu.

                              • Re: Nonlinear buckling analysis and snap-through modeling of an arch
                                P. B

                                Here is an example of the problem I am encountering. In this assembly file, the spring plunger is initially in contact with a flat plate with a hole and there is an extension-only spring connection between the underside of the plate, and the top face of one of the flanges of the plunger, so I would like the spring plunger to be held up to the bottom face of the flat plate by the spring connector. I have applied a downwards force of 30 N to the top face of the spring plunger because I want it to force the plunger downwards. When I run this study by itself, an error occurs, stating that there is inadequate restraints on the parts. In order for this study to solve, I need to have a prescribed displacement on the underside of the spring plunger to restrain it in the vertical direction. The problem with this is that the prescribed displacement cannot be turned off at a certain time to allow the downward force to act on the plunger. When I add in a prescribed displacement to the bottom face of the spring plunger to restrain it in the vertical direction, the time curve does not go past 0.5 s, but there is a warning message that appears which states that the prescribed displacements will be extrapolated until the end of the study time, so the plunger is restrained vertically for the entire study.  I am wondering if there is any way for the prescribed displacement to be eliminated at a certain time, to allow the plunger to translate downwards due to the applied force instead of keeping the plunger at a displacement of 0 for the entire study. I need the prescribed displacement on the spring plunger for the study to solve, but I do not want the prescribed displacement to last for the entire duration of the study.

                                • Re: Nonlinear buckling analysis and snap-through modeling of an arch
                                  P. B

                                  In another similar study I have, the dome-shaped spring plunger comes into contact with a sheet metal part from above which buckles in snap-through beviour. Since I would like the sheet metal part not to penetrate the spring plunger, I specified a contact set between the plunger and the sheet metal part which is 'no penetration'. I also specified surface-to-surface contact in the advanced options of the contact set. When I run this study with the plunger as a deformable part, the result is a large gap between the sheet metal part and the plunger. Is there any way of minimizing this gap between the two parts appearing in the results of the studies? I have attached a picture showing what I am looking at when I view the results of the study. For some reason it seems like the actuator which comes down from above the beam spring is touching or is very close to touching the beam spring, but the spring plunger, which is located below the beam spring, is not touching. Both the actuator and the spring plunger have the same contact set definition, the only difference is that the actuator is defined as a rigid part, and the plunger is defined as deformable. Why does the gap between the beam spring and spring plunger exist, while it does not exist between the actuator and beam spring?

                                  • Re: Nonlinear buckling analysis and snap-through modeling of an arch
                                    P. B

                                    Here is the model with the gap condition occurring in the results. I believe that the gap may be ocurring due to the thickness of the beam spring shell mesh. I have been trying to play around with the mesh settings by making the mesh more fine on the spring plunger dome, hoping that the beam spring would be able to come closer to the spring plunger in the results. It does not appear to have any effect. I also may try playing around with the advanced settings of the mesh, by specifying node-to-surface contact instead of surface to surface contact.

                                    • Re: Nonlinear buckling analysis and snap-through modeling of an arch
                                      P. B

                                      I have modified the setup of the study slightly to reflect the new conditions in which I am testing the beam spring. In the new setup, I am using a cylindrical-shaped actuator instead of a dome-shaped actuator to test the beam spring with everything else remaining the same. After making this modification, I am having trouble with the study, because for some reason the beam spring is not shaped correctly when it is bent into position. It seems as though the ends of the beam spring are completely flat, whereas they should be arched. I have tried excluding the other components from the study to see what effect this has on the study, and it seems to allow the beam spring to bend correctly and the beam spring takes on the right arch shape as it is bent into position, but I am not sure why. There is no global contact condition defined for the study. I have attached pictures showing the beam spring in the regular arched shape and in the flattened shape. I would like the beam spring to bend into the right arch shape as seen in the second picture, while having the other components for the study present as seen in the first picture.