# Corrugated tube (bellow) - problem with analytical verification **URL:** \ **Category:** Analysis issues\ **Created:** [February 9, 2026, 3:33pm UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774 "2026-02-09T15:33:01Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Calc\_em](https://avatars.discourse-cdn.com/v4/letter/c/43a26b/32.png) [@Calc\_em](https://calculix.discourse.group/u/Calc_em)\ **Post date:** [February 9, 2026, 3:33pm UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/1 "2026-02-09T15:33:01Z")
Hi, I’ve been struggling for a while with a seemingly simple case - stretching of a corrugated tube (bellow). Here’s my input data: - P = 2000 N (axial load) - a = 80 mm (distance from the axis of the tube to the center of the semicircular corrugation) - b = 42 mm (outer radius of the semicircular corrugation) - t = 4 mm (wall thickness) - n = 5 (number of corrugations) - E = 210 GPa (Young’s modulus) - v = 0.3 (Poisson’s ratio) [Geometry (for an axisymmetric model)](https://www.dropbox.com/scl/fi/5ej6mk6tdh4gx5o63bid0/Bellow-axi-sym.step?rlkey=uvpcirzuca5wgjfxw7qewpa4m&st=bms2jxnj&dl=0) **CalculiX model:** [Input deck](https://www.dropbox.com/scl/fi/eetvelk23srs1c4woi2vp/bellow.inp?rlkey=fmsnh164o3x3m7vknld2xmw2p&st=mh6pyrn0&dl=0) FEA results: - max von Mises stress: around 14.5 MPa - max displacement (symmetric model): 0.0407 mm (total stretch: 0.0814 mm) ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/b/b143ffabec5de2a6ae3ac7a878a513be1ccc5d05.png) ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/2/262cf921b61774ad3b9e2421f7c0d584b01be08c.png) **Hand calcs based on Roark’s:** ![Roark bellow](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/a/a94502cfbba31ba6c29841ffdb852bcd45c50fb1.png) ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/c/c26c60896ed27a5757d5df66413129328bc0a18f.png) So, rather far from the simulation results. However, if I make this assumption (from the paper on which Roark’s case is based - “On the Theory of Thin Elastic Toroidal Shells” by R.A. Clark): > For the section AO it may be shown that the maximum direct stress and the maximum bending stress occur at similar locations but are opposite in sign. and add minus to the equation for σ\_h (as in the article), then I get σ\_vM = **13.26 MPa** , so much closer to the expected result ( **9% error** ). I even tried stress linearization to check the values and signs of both stresses. The results were not helpful. But more importantly, **the stretch is still off (by 17%)**. I also tried symmetric and full models (with and without the straight tips), axisymmetric and 3D, as well as different BCs, but I haven’t managed to improve the accuracy of the results. Any ideas what else could help ? ---
**Author:** ![xyont](https://yyz2.discourse-cdn.com/free1/user_avatar/calculix.discourse.group/xyont/32/3553_2.png) [@xyont](https://calculix.discourse.group/u/xyont)\ **Post date:** [February 9, 2026, 10:24pm UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/2 "2026-02-09T22:24:21Z")
can analytical plot deformed shapes and shown its magnitude? i suspect the model FE is over constrained. ---
**Author:** ![Calc\_em](https://avatars.discourse-cdn.com/v4/letter/c/43a26b/32.png) [@Calc\_em](https://calculix.discourse.group/u/Calc_em)\ **Post date:** [February 9, 2026, 11:49pm UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/3 "2026-02-09T23:49:33Z")
> [@xyont](#): > > can analytical plot deformed shapes and shown its magnitude? The only analytical solution I have for the displacement is just the total stretch value from a formula. But I can try different BC configurations (so far none helped) later and share the screenshots of the corresponding deformed shapes. > [@xyont](#): > > i suspect the model FE is over constrained I also suspect that. After all, if stiffness is too high, it’s almost always a fault of overconstraining BCs. Maybe I will try with symmetry in a 3D model and try to figure out the assumptions made by the author of the original paper. ---
**Author:** ![xyont](https://yyz2.discourse-cdn.com/free1/user_avatar/calculix.discourse.group/xyont/32/3553_2.png) [@xyont](https://calculix.discourse.group/u/xyont)\ **Post date:** [February 10, 2026, 12:22am UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/4 "2026-02-10T00:22:30Z")
i imported the model in PrePoMax to view and removes some of boundary conditions but complaining to run in material properties. the bottom support needs to release in radial movement to make the pipe shrink due to tensions. ---
**Author:** ![Disla](https://yyz2.discourse-cdn.com/free1/user_avatar/calculix.discourse.group/disla/32/3548_2.png) [@Disla](https://calculix.discourse.group/u/Disla)\ **Post date:** [February 10, 2026, 12:37am UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/5 "2026-02-10T00:37:38Z")
Hint: The Stretch formula is linearly proportional to n. It suggest formula assumes all your sections Stretch the same. You can check if your set up suits that condition. ![imagen](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/8/80e14ea5a31af115f9ab032b3601601323b123cc.png) There is also a solved problem “A corrugated-steel tube” in Roarks which states: “The ends are rigidly fixed”. and later rafers to this same formulas. Ends are probably fixed. ---
**Author:** ![Calc\_em](https://avatars.discourse-cdn.com/v4/letter/c/43a26b/32.png) [@Calc\_em](https://calculix.discourse.group/u/Calc_em)\ **Post date:** [February 10, 2026, 3:07pm UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/6 "2026-02-10T15:07:30Z")
Thanks for the comments. I’ve tried interpreting BCs from the paper: ![bellow paper](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/c/c27f879d6a85b060e231020f4fba0ea521a09833.png) And this is my updated setup: ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/7/784fdd577402bded1f212dea35dae6ae9b3b355b.png) The result I get is: ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/f/f1bcc1fe9731439df28dc2065fa348a24f6bdc45.png) I don’t think I can give it more flexibility. The straight ends are removed to make it easier to constrain and closer to the paper. [PrePoMax file for this configuration](https://www.dropbox.com/scl/fi/3qvdxspfsmjm7t2bsbrlq/Bellow-axi-symm.pmx?rlkey=k4inyp134tfdqfqne8l8z7lm4&st=8lekmdp6&dl=0) [Input file for the same configuration](https://www.dropbox.com/scl/fi/5b8rc6t7l1ll02jrh1ew7/Bellow-axi-symm.inp?rlkey=48g0umaj1ug7vtmfp349ld1kn&st=guh83s0z&dl=0) ---
**Author:** ![Disla](https://yyz2.discourse-cdn.com/free1/user_avatar/calculix.discourse.group/disla/32/3548_2.png) [@Disla](https://calculix.discourse.group/u/Disla)\ **Post date:** [February 11, 2026, 12:16am UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/7 "2026-02-11T00:16:57Z")
The problem is not simple at all, and I have not yet been able to rule out any of the possible errors: mine, the formula’s, or ccx’s. Assumptions or BC behind the formula are not clear too. In my case, I am using Saint Venant’s principle to minimize the effects of boundary conditions. I’m using a 9-wave spring and focus on the central section. By other hand, seems like according to the formula overall stretch should be the sum of the individual stretches of each section like Springs in series. Note that your bellow doesn’t satisfy the t/b condition of less than 1/10. According to the formula Stresses should not depend on “n” value and in ccx it does right now for me. (Specially Membrane) ¿?¿? ![imagen](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/9/9e8ebd79366a1feebd2478e62b9b99b040f0a3f6.png) EDITED. Just noticed an unnexpected behaviour in ccx. Maybe my intuition fails but I would expect the bellow should srink in the middle section and not expand as it does. ¿?¿. ---
**Author:** ![Calc\_em](https://avatars.discourse-cdn.com/v4/letter/c/43a26b/32.png) [@Calc\_em](https://calculix.discourse.group/u/Calc_em)\ **Post date:** [February 11, 2026, 9:05am UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/8 "2026-02-11T09:05:31Z")
> [@Disla](#): > > The problem is not simple at all, and I have not yet been able to rule out any of the possible errors: mine, the formula’s, or ccx’s. Yeah, I’ve been struggling with it for quite some time already and it’s one of the last few cases that I’ve never managed to validate analytically despite several attempts and apparent simplicity of the problem. I’ve tried using different kinds of models (full/symmetry, 2D/3D), various BC configurations and even solvers, but there’s still a significant discrepancy. > [@Disla](#): > > Assumptions or BC behind the formula are not clear too. I only know some assumptions from the R.A. Clark’s paper, but they just mention the conditions at point B (and partially at point O) and in a rather enigmatic way (my interpretation is shared above). > [@Disla](#): > > In my case, I am using Saint Venant’s principle to minimize the effects of boundary conditions. I’m using a 9-wave spring and focus on the central section. I was also thinking about simulating only a small segment corresponding to the one shown in the figure from Clark’s paper attached before. Or a single corrugations. But either way, the expected BCs are not clear. > [@Disla](#): > > Note that your bellow doesn’t satisfy the t/b condition of less than 1/10. Why ? In my case t = 4 mm and b = 42 mm so t/b≈0.0952 \< 0.1 > [@Disla](#): > > According to the formula Stresses should not depend on “n” value Right, the paper says: > Away from the ends of the pipe the state of stress may be assumed to be periodic in the axial direction so that it is necessary to obtain a solution only for a portion of the shell such as AOB. > [@Disla](#): > > Specially Membrane Are you using stress linearization in Mecway ? Does it confirm the assumption about the sign of the stress components ? ---
**Author:** ![Disla](https://yyz2.discourse-cdn.com/free1/user_avatar/calculix.discourse.group/disla/32/3548_2.png) [@Disla](https://calculix.discourse.group/u/Disla)\ **Post date:** [February 12, 2026, 6:58pm UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/9 "2026-02-12T18:58:52Z")
I have solved the problem with MECWAY as it has true shell elements (You probably did that with ABAQUS too). I have managed to get the periodic solution, and the Hoop Stress is fully uniform all around the 1/4 of the modeled section. (That’s a good indicator that the Symmetry BC is working properly. Mesh is pretty good quality too after some geometry adjustments. My best solution deviates up to a 15% in the worst case. ![screenshot.23](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/9/9a59b072c131a95468c38a91af2eea1c31e2dd02.jpeg) ![imagen](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/d/d477d87e2e339ef0c37d7e6fcc04e8ff08277adb.png) My guess on why this deviation: -From my point of view the formula assumptions are restrictive. Especially when it is stated that one only needs to solve for section OB because the OA is symmetric. I don’t think that’s the case for the bellow. That’s true for Lambda\<\<1. Yours is .525. Also recall this is an axisymmetric problem. ![imagen](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/d/d86376043c327589861e7ff7d76a21203dbbff48.png) (You could maybe focus on the OB section when comparing to the formula). -Axisymmetric shell problems normally disregard one of the principal stress components. In this case it is not negligible. -Inner section is stiffer than the external one. -When solving complex differential equations, one needs to assume certain conditions that narrow down the range of validity of the solution. Those assumptions sometimes are too strong and there is not an equivalent BC combination. -Deflection (v) is not solved in the original paper. Only an order of magnitude is provided. Solution is given for the horizontal component . Don’t read me grong. Obtaining an anlytical solution is remarkable considering the complexity of the problem and has probably been very useful for a long time. Applause to MrCLARK. 🙇‍♂️ Maybe I’m wrong and someone finds the right set up that fulfill all the assumptions behind the formul a. Regards ---
**Author:** ![Calc\_em](https://avatars.discourse-cdn.com/v4/letter/c/43a26b/32.png) [@Calc\_em](https://calculix.discourse.group/u/Calc_em)\ **Post date:** [February 12, 2026, 7:21pm UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/10 "2026-02-12T19:21:55Z")
> [@Disla](#): > > I have solved the problem with MECWAY as it has true shell elements (You probably did that with ABAQUS too). I have managed to get the periodic solution, and the Hoop Stress is fully uniform all around the 1/4 of the modeled section. (That’s a good indicator that the Symmetry BC is working properly. Mesh is pretty good quality too after some geometry adjustments. My best solution deviates up to a 15% in the worst case. Can you show your BCs ? My stretch deviation is around 17%. For the stress, it’s ≈ 9%. > [@Disla](#): > > -Deflection (v) is not solved in the original paper. Only an order of magnitude is provided. Solution is given for the horizontal component . Right, I wonder how Roark’s got it. And maybe we should check the horizontal displacement too, then. I should also add for other readers that my geometry had a flaw - the internal and external corrugations (semicircles) had different radii because I used offset in FreeCAD to draw this: ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/8/854850298e39928799dfc21fa80f94b9fd302ebf.png) I should have used mirroring and translation instead: ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/7/740bbb05b6526254a3c135aafb61c06b60932648.png) However, this somehow doesn’t really change the result. ---
**Author:** ![Disla](https://yyz2.discourse-cdn.com/free1/user_avatar/calculix.discourse.group/disla/32/3548_2.png) [@Disla](https://calculix.discourse.group/u/Disla)\ **Post date:** [February 13, 2026, 1:03am UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/11 "2026-02-13T01:03:59Z")
I’m now using this geometry which is closer to fullfill all the assumptions, at least in terms of Numerical values. There are still some uncertainties in the BC considered in the formula. ![imagen](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/5/579d93ccc73cd0e5ff762eb12dea53dce00d167e.png) With those values , the quantities I can extract more clearly are Sigmav0 and Hoop Stress . They both agree very. My BC are ![imagen](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/4/494df96686a73ae16f26eb4c4231016d2181f91e.png) Y on the base, Symmetry on the sides and pressure on a thin line on top. Reactions are fine. I’m using full 5 waves so BC are far from the center section which is the one used for inspection. ![imagen](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/8/82afa4a1fbae2214d5bccfa744a41fd4eb8de995.png) I don’t think you can do that on Prepomax. Only Mecway can constrain rotations aligned with the shell plane of a curved shell. ---
**Author:** ![JuanP74](https://avatars.discourse-cdn.com/v4/letter/j/b5a626/32.png) [@JuanP74](https://calculix.discourse.group/u/JuanP74)\ **Post date:** [February 15, 2026, 3:04pm UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/12 "2026-02-15T15:04:06Z")
the report referenced by Roark says: Example 4: Corrugated pipe subject to axial load. Consider a pipe with a cross section as shown in figure 8a subject to a uniform axial load. **Away from the ends of the pipe** the state of stress may be assumed to be periodic in the axial direction so that it is necessary to obtain a solution only for a portion of the shell such as AOB. bold marking is mine, but solution may not be accurate for such a reduced number of corrugations. ---
**Author:** ![Calc\_em](https://avatars.discourse-cdn.com/v4/letter/c/43a26b/32.png) [@Calc\_em](https://calculix.discourse.group/u/Calc_em)\ **Post date:** [February 16, 2026, 11:23am UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/13 "2026-02-16T11:23:52Z")
> [@Disla](#): > > With those values , the quantities I can extract more clearly are Sigmav0 and Hoop Stress . They both agree very. Thank you very much, I’ll have a closer look at it. > [@Disla](#): > > I don’t think you can do that on Prepomax. Only Mecway can constrain rotations aligned with the shell plane of a curved shell. Considering the issue with symmetry on CalculiX’s curved shell edges (due to drilling DOF), it would indeed be tricky and at least require local CSYS: [Inconsistent result with CalculiX on a shell model of a plate in bending · Issue #64 · Dhondtguido/CalculiX · GitHub](https://github.com/Dhondtguido/CalculiX/issues/64) So I’ve tried without symmetry (full model) for now, but it might be overconstrained: ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/6/6a45a674ca509f1efea8d8e04c5aae2df8a69926.jpeg) ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/1/16385ff7eeb4060137dd9617b45c83f3b83d362e.jpeg) I’ll also check with symmetry in Abaqus. ---
**Author:** ![Disla](https://yyz2.discourse-cdn.com/free1/user_avatar/calculix.discourse.group/disla/32/3548_2.png) [@Disla](https://calculix.discourse.group/u/Disla)\ **Post date:** [February 16, 2026, 12:47pm UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/14 "2026-02-16T12:47:44Z")
The far the BC are from your area of interest the smaller will be its impact on the result. That’s useful if there is some uncertainty on the BC of your problem. In this case it can be used just extending the number of corrugations. ---
**Author:** ![Calc\_em](https://avatars.discourse-cdn.com/v4/letter/c/43a26b/32.png) [@Calc\_em](https://calculix.discourse.group/u/Calc_em)\ **Post date:** [February 16, 2026, 1:17pm UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/15 "2026-02-16T13:17:08Z")
Do you check the displacement at the top edge or somewhere below ? Because the top edge sort of unfolds. Perhaps it should have some constraints too. Symmetric model in Abaqus: ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/1/155f6334c5eaf1d53466a7d4c5525491014b8b84.png) And full model: ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/d/d57a8267761c61447a7c04f7cb2e84a17074644f.png) ---
**Author:** ![Calc\_em](https://avatars.discourse-cdn.com/v4/letter/c/43a26b/32.png) [@Calc\_em](https://calculix.discourse.group/u/Calc_em)\ **Post date:** [February 16, 2026, 4:32pm UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/16 "2026-02-16T16:32:45Z")
I even tried with axisymmetric shell elements (they are applied to lines like beam elements, but they utilize axial symmetry): ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/c/c9dc321564e7afffb11f4caf8fe3432826d72b2f.png) Now if I fix the bottom end completely: ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/8/83bc3dd5563b816791abdeba45c1800a290a55cf.png) And if I leave only U2 free at the top: ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/a/ab9b87f49a272c47873239097e6240ecd505cfa3.png) ---
**Author:** ![Calc\_em](https://avatars.discourse-cdn.com/v4/letter/c/43a26b/32.png) [@Calc\_em](https://calculix.discourse.group/u/Calc_em)\ **Post date:** [February 16, 2026, 4:55pm UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/17 "2026-02-16T16:55:58Z")
> [@Calc\_em](#): > > And if I leave only U2 free at the top: Based on that, I’ve tried: ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/8/8e42c7e8defeadc6b4c13f77d2c237457eb0f3f1.jpeg) And the displacement is really close: ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/e/e360296c7e70c1504c7f9bbb420204b7e3f0c2da.jpeg) But the stresses are off: ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/6/6be89681623eaf0a249f4eb3e13cc2ae07ed28b5.jpeg) I even tried with: ```auto *Shell section, Elset=Internal_Selection-1_Shell_Section-1, Offset=0, Composite 0.075,,Steel 0.075,,Steel 0.075,,Steel 0.075,,Steel ``` but it didn’t help. I feel that I’m closer now, but again running out of ideas. ---
**Author:** ![Disla](https://yyz2.discourse-cdn.com/free1/user_avatar/calculix.discourse.group/disla/32/3548_2.png) [@Disla](https://calculix.discourse.group/u/Disla)\ **Post date:** [February 16, 2026, 7:41pm UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/18 "2026-02-16T19:41:19Z")
Paper doesn’t provide Von Misses. Hoop and bending. ¿Is your Hoop Stress right.? ---
**Author:** ![Calc\_em](https://avatars.discourse-cdn.com/v4/letter/c/43a26b/32.png) [@Calc\_em](https://calculix.discourse.group/u/Calc_em)\ **Post date:** [February 16, 2026, 7:52pm UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/19 "2026-02-16T19:52:58Z")
Yeah, but I calculate it from these components (the last equation in my original post). I would have to do the transformation to get the components, but probably also perform linearization because it’s supposed to be meridional bending stress and hoop membrane stress, specifically. Pure transformation to cylindrical CSYS on the results where I got U2 = 11.48 mm: ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/7/726b45fed3b255969ed199ea0e5ac1ebc3fd428e.jpeg) ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/0/003841450ef5ee05be5cbed6a088f9ac03485015.jpeg) ![image](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/1/1ef9d47cf26ed8e4573e874012f15c9ae9059edd.jpeg) ---
**Author:** ![teeps](https://avatars.discourse-cdn.com/v4/letter/t/58f4c7/32.png) [@teeps](https://calculix.discourse.group/u/teeps)\ **Post date:** [February 16, 2026, 10:13pm UTC](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774/20 "2026-02-16T22:13:43Z")
To whom it may concern/interest I modeled the Roark case with your (@Calc_em) dimensions and analysed in 2 1/2 D with Code-Aster. By 2 1/2 D I mean 1/4 sector (for ease of symmetry constraints application) and approached by shell elements on the mid-plane. Axial displacement of the unconstrained, loaded end is 0,086mm and Von Mises stress of the highest loaded zones is 14MPa. ![Bellow](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/5/5baee65d7dc67266b8537ccade963398585d5976.jpeg) [Next page](https://calculix.discourse.group/t/corrugated-tube-bellow-problem-with-analytical-verification/3774.md?page=2)