helix with hexahedral elements

[JasonNicholson]

Does anyone have any suggestions on how I could get or make a hexahedral mesh of a helix?

I am currently using Comsol MultiPhysics 3.2b. The problem that arises in Comsol is that I have a helix with a thin cross section but the height of the helix is very large. So to get good resolution across the cross section, I end up with a huge tetrahedral mesh (800,000+ elements). If I elongate the tetrahedrons, the quality of the elements decreases quickly. So I would like to use a hexahedral mesh so that I can elongate the elements along the axis of the helix but still maintain a high quality mesh.

 

[Stringmaker]

The first idea that comes to mind is does Comsol MP offer any sort of cyclic symmetry options? This would break the helix down from a number of sectors, N, into one sector thereby reducing model size by N times.

Another thing you could do is to do a test case which gives you an idea of what number of elements are needed throughout your cross section before an acceptable level of mesh convergence is shown. Make up a small 3D model of your helix but perhaps only a fraction of it's total length and see which number of elements in certain directions gives you this convergence.

Remember that hex meshes don't necessarily need to have 1:1 aspect ratios in all directions. While that would be ideal it isn't great for productivity or run time. You need to make sure that you have a sufficient number of nodes in the areas and directions of interest to capture stress gradients occuring there.

Good luck,
-Brian

 

[corus]

If the cross section is relatively thin then why not use a beam type element instead of a full three dimensional element?

corus

 

[johnhors]

Can you mesh the cross-section with quad elements, then extrude this 2D mesh into 3D using a combined rotation and translation to form the hex elements?

 

[crisb]

Depending on the program used it may be difficult or impossible to form an exact mathematical helix. I have resorted to forming a polyline on points with previously calculated coordinates and sweeping a (meshed) face (much as john suggests) round this polyline. Depending on the number of points this can form a very close approximation to the required geometry.

Not knowing the application...could this be a time to use substructuring (superelements)?

 

[Jordonlaw]

I do most of my modelling work on helical components with long pitches compared to their cross section dimensions; I only use Hex elements currently although beams can work depending on the application. I use Marc which will extrude from 2D meshes to 3D with suitable rotations and translations to form an exact helical path. I have also created these meshes by using a polyline as a driver curve and sweeping the mesh down it as suggested; both methods have their quirks. Cosmos can create helical meshes in this latter way; maybe other codes can as well.

The question was regarding the mesh dimensions. For my application I use elements that are 6 (six) times longer than their other dimensions and it works for me as the stress gradients along the helix length are not too high. As we haven't been told the application or loading its difficult to comment further without more information. The proposal to do a sensitivity analysis on, say, element dimension along the helix length on a small section of the helix sound a good first approach.

 

[JasonNicholson]

I am responding to all of you at once.

1. I am only modeling one gyre or turn of the helix. So symetry in the z direction is already been imposed.
2. Beam elements will not work for this case. I will not get enough information from them.
3. COMSOL Multiphysics (aka FEMLAB) does not allow sweeping or lofting of a quadralateral mesh. However, you can revolve and extrude a quadralateral mesh. If any of you can show me how to do this with some sort of trick, please tell me!
4. Super elements may help. However this is a last resort.
5. Helix dimensions: pitch: 249 mm
helix diameter: 35 mm
cross section: 3 mm
6. Loading: radial force pointing away from symetry axis of the helix. Like a spring loaded from the inside. Can be modified to a radial displacement away from symetry axis of the helix.
7. Scenarios I have tried with quadratic tetrahedral elements:
mesh setting: Normal
DOF: 5811
elements: 720
min. quality: .0443
elements across cross section: 2

mesh setting: Fine
DOF: 22539
elements:3600
min quality: 5371
elements across cross section: 4

mesh setting: Finer
DOF: 144273
elements: 11356
min qual: .2479
elements across cross section: 28

mesh setting Finer with tweaks
DOF: 144450
elements: 26955
min qual: .3382
elements across cross section: 28-30 ish


Finer with tweaks seems to be okay but I am not sure yet.

 

[Stringmaker]

If you're doing a static analysis and have any sort of decent computer I can't see why this would take a super long time to solve unless you're highly nonlinear with a large number of substeps or femlab has terribly slow solvers. Even with 144450 DOF that's a very small model relatively speaking. Can you quad mesh a face and rotate it about the central axis to get a hexahedal mesh instead of sweeping? Never used femlab before.

 

[JasonNicholson]

Stringmaker, the main point I am trying to make by showing you the mesh data is that even for a small amount of elements across the cross section the total amount of elements is much larger by order of a 1000.