Has automatic hexahedral meshing a future?

[69thbugler]

I have been working on the problem of automatic hexahedral meshing for the best of my engineering career, searching for the elusive “Holy Grail” of engineering analysis. After studying the behaviour of quadrilateral meshes in 2D and hexahedral meshes in 3D for years, I have identified a pattern that is found in all such meshes, the presence of irregular nodes, nodes where three or five elements meet. The pattern has been mathematized, and a simple, elegant solution emerges. I can at last say with confidence that I have solved the problem of automatic hexahedral meshing, a solution that is very different from any of the other approaches to solving the problem.

The findings can be used to manually create better quadrilateral and hexahedral meshes in existing FEA pre-processors, and a software implementation will make it possible to speed up the manual hexahedral meshing process by a factor of 10. Eventually, the process can be automated, but that is years away. I have now the challenge of finding financial backing to develop the algorithms for inclusion in or interfacing to existing FEA pre-processors.

However, tetrahedral elements have been successfully used for many years, and the work on creating meshable volumes for hexahedral meshing replaced by automatic tetrahedral meshing algorithms. Several vendors have launched the ultimate hexahedral meshing algorithm, but testing in the engineering community has left them wanting. The ultimate hexahedral meshing algorithm is still elusive. Engineers have stopped asking for it, because it is not available in the shops.

I am looking for advice from the structural engineering community on what I should do, forget the whole thing and get on with the rest of my life, or spend more time and money to develop a solution for automatic hexahedral meshing?

What are the application areas where hexahedral meshing will be highly desirable? Where can hexahedral meshing complement the tetrahedral meshing technology that is used successfully today?
What is the commercial opportunity for hexahedral meshing, the applications, the problems to solve, the end-users and vendors that want this, i.e., the substantial incentive necessary to invest in the development of this technology?

 

[fsi]

Does not ALGOR already have an automatic hexahedral meshing ?
I thought they did.
fsi

 

[bjpil]

69thbugler,
It seems that most FEA packages have some sort of automatic hex mesher. Some are better than other. The real problem I believe is developing good elements when there is a transition in the geometry. For example, tet meshes can easily transition from a three element through thickness to a six or more element through thickness. With a hex mesh you need to use other type of elements such as wedge elements to help make this transition, if you don't then your hex elements will be poor, along with your results. I prefer to use hex meshes because they solve faster but tet meshes let me refine my mesh more easily. The problem for me is do I spend more time meshing (hex mesh) so that the solve time is faster or do I quickly mesh the part (tet mesh) and let the solve time increase. If you could create a code that solves the transition problem, resulting in reducing the mesh time, then you would have something special.

BJP

 

[DickButkus]

Algor has automatic hex meshing -- good one. Now if only they could remember how many sides on a hex element... Maybe they have fixed this, but last time they tried this for me some of their "hex" elements onlt had five sides.

ABAQUS has put a lot of effort into developing a supertet so that you could do a lot of what could only be done with bricks in the past. The problem with this element is that it is CPU expensive.

ABAQUS does have a 2 1/2 D mesher, but not a fully automatic hex mesher.

If you want to make money of of this idea, you could code it in Python to work within the ABAQUS mesh module and sell it as a paid download off of your own web site. If it works you'll get the attention of the developers and they will probably want to talk to you about purchasing the technology. You may even be able to handle the licensing issues yourself.

If you really have an elegant solution to this problem you could end up making a LOT of money. I have seen many companies attempt this, but no one has a truley elegant solution yet.

 

[brad]

kf9ri--
The "five-sided" hex isn't limited to ALGOR--other commercial pre-processors have it (HyperMesh, FAME, and I belive Patran also). In fact, it is commonly known as a "pyramid" and can readily be formed in most solver codes by simply "collapsing" a six-noded solid (pentahedral) element. So instead of element connectivity 1-2-3-4-5-6 (where 1-3 and 4-6 form the triangular planes) the element nodal connectivity is 1-2-3-4-5-3 (hence 1-2-5-4 describe the "base" of the pyramid).

It processes very nicely, and passes the MacNeal-Harder continuum patch test.

Brad

 

[brad]

Back to the original question--
69thbugler, I apologize for my skepticism, as this is indeed a "holy grail" in FE pre-processing. If you truly have figured out a new, unique way of hexahedral meshing it would be very powerful. Tetrahedral meshing is pretty dominant today, but the dofs required for a 2nd-order tetrahedral mesh are significantly greater than what would be necessary for an equivalent first-order hexahedral.

If you truly do have such unique technology (which again I am skeptical of), by all means you should work to commercialize this. It would be worth a lot of money.

Brad

 

[sean01]

Within the analysis community I work - we tend to mainly use shell elements - if we are forced to use solid elements then we tend use 2nd order tetrahedrals rather than hexahedrals because they allow the mesh creation process to be speeded up within our chosen pre-processor.

The only disadvantage of this is the amount of nodes that it generates - but given the accessibility of low cost high performance computing - we haven't found any problems generating an analysis result.

best wishes


sean

 

[DickButkus]

Brad,

I don't know why this one irks me so, but I can't seem to just let it go. Sure you can collapse elements into pyramids, but if you're going to do this don't call it a hex mesher, call it a pent mesher instead, or a penthex mesher.

69thbugler, I wish you luck and I truly hope you have invented a pure automatic hex mesher. If you have all of our jobs will get easier!

 

[Irwin]

Try

http://www.avl.com!

I have seen some example of there software.

Irwin

 

[69thbugler]

Thank you for your feedback in this thread. Your responses have encouraged me to take the exchange of tips further: to explore how and where my automatic hexahedral meshing technology can be of use.

The problem of automatic hexahedral meshing has not yet found its definitive solution. A number of candidates exist, hundreds of man-years have gone into research and development to find the ”Holy Grail” in engineering analysis. When they have been put to the test by practising engineers, the hex meshers do not match expectations. Most of the solutions can be described by one word: “compromise”. However, sooner or later someone will come up with the answer to this problem. Will you recognise the solution when you see it for the first time?

I am convinced that I have solved the problem of automatic hexahedral meshing, calling it Dislocation Meshing. I need to find partners who can make use of my findings to solve their problems in FEA modelling, so we can understand when, where and how the research can be developed into well-structured engineering tools. I am now looking for practising engineers to give me feedback to define the best way forward.

How can I be so certain that I have found the solution to automatic hexahedral meshing?
[ul][li] Dislocation Meshing is not based on any of the existing schools of thought, it has developed independently over nearly two decades in isolation. No academic papers have been written to create a career, no promises made, no software written. I have focused on solving the problem.
[/li] [li] Dislocation Meshing is based on a thorough understanding of how meshes behave and a discovery of the mathematical principles that quadrilateral and hexahedral meshes adhere to.
[/li] [li] Dislocation Meshing works well when these principles are applied in manual mesh creation;
[/li] [li] The principles have been mathematized, i.e., a mathematical representation has been discovered and developed: simple, general, versatile, beautiful.
[/li] [li] Dislocation Meshing is a special application of a more general mathematical representation of geometric shapes, other applications are also useful in engineering analysis. (To be explained …)
[/li] [/ul]
The mathematical representation of hexahedral meshes can be used to describe any hexahedral mesh, i.e., any mesh with only hexahedra, independent of their origin.

Two overriding principles have been the driving force behind the search for a solution:
[ul][li] find the patterns – what rules do hexahedral meshes adhere to?
[/li] [li] only well-shaped hexahedral elements throughout: NO COMPROMISE !
[/li] [/ul]Dislocation Meshing is the outcome of this search. If this appeals to you, read on!

Dislocation Meshing is a disruptive technology, it will change the way people work by complementing existing knowledge and working practices. However, I have ambitions beyond augmenting what engineers know and do today, I want to open up to a hole new world of opportunities that have been blocked because automatic hexahedral meshing did not exist. Automatic hexahedral meshing is a small part of a comprehensive FEA programme, but it is a crucial little cog in a large machine. When in place it will change the way people work. I want to create a paradigm shift in finite element analysis, change the way engineering analysis is carried out. To make this happen, I need to do two things:
[ul][li] to let others learn as much as possible of what I know, so others can make use of the information and exploit it in whatever way they like;
[/li] [li] to develop practical engineering tools when working with positive forward-looking early adopters, practising engineers with no personal or commercial investments in this field to protect.
[/li] [/ul]
Therefore, I have set up an Engineering Tips Group to exchange experience, knowledge and insight away from the existing forums called “Hexahedral Tessellation of Solid Models – Dislocation Meshing”. The group is open, anyone can join and contribute within the rules. If you are interested, look it up on:

http://www.eng-tips.com/groups/dislocationmeshing

Why don’t you come along to check my findings, to work with me to see whether I have found the solution to this long-standing problem? I need verification from seriously interested practising engineers that Dislocation Meshing actually works away from my own workstation. There is a lot to do, most of it will be good fun and rewarding for all contributors.

By all means contribute to this thread for as long as you want to, but the main action will be in the group.

 

[sridharv]

Hi 69thbugler,

First of all accept my apologies for a late reply. I saw your posting and I wanted to reply. But because of work pressure I could not. Sorry. But better late than never....So here we go...

Auto heaxa meshing is a much sought out feature in any FE pre processor. Atlease myself and my colleagues and my company would be very much interested in having this tool. We tried for having this and had a brief look at tools like true grid and others. As on date we have no good tool for this. We use I-Deas NX for all our pre-processing needs. We like many others prefer to spend more time in meshing to have solve time less. Not only that our FE and fatigue procedures yield very good and reliable results with bricks than tets. So for any FE request that we get first choice is bricks. So an auto mesher for bricks would be the best thing and first thing that we would purchse in Y2004! Any way I also understand this may not happen so early but I would be more than happy to contribute my cents towards acheving this target! On a personal, non-commercial basis I am willing to extend all kind of help that I could do for your "dislocation meshing" Let us meet there!

Bye.
Sridharan

 

[69thbugler]

Dear sridharv

Thank you for your encouragement, you sound like the kind of serious engineer that I would like to interact with.
The best way would be for you to give feedback on the content in the Dislocation Meshing Forum, forum954
Please let me know what you want to know in addition when you have read the content of the Forum and seen the pictures.

The sooner I can work closely with a serious engineering partner or several, the sooner the theory can be turned into a working tool. The launch of a commercial product is years away, but Dislocation Meshing is a strategy that can be implemented in current FEA pre-processors and minor additions can make a BIG difference for effective hexahedral mesh generation. This may happen in 2004.

In the meantime, the theory of Dislocation Meshing needs exposure and dissemination, allowing “real engineers” to understand and use the techniques manually in existing FEA pre-processors. Currently, engineers like yourself know little or nothing about the behaviour of quadrilateral and hexahedral meshes, trying to make sense of the black box mesh generators that are available.
The Forum is my first attempt to give engineers an understanding that will transform the way they work. By raising the knowledge of how meshes behave, a “meshing engineer” can start designing meshes and get a pre-processor to deliver what (s)he wants.

However, the key to acceptance is not to replace the existing technology for “automatic anything meshing”, but to look at cases where existing technology cannot deliver. Dislocation Meshing is a general theory for quadrilateral and hexahedral meshing and currently a solution looking for a problem to solve.

I am looking for practical examples, the kind of shapes that engineers struggle to mesh with quadrilaterals and hexahedra, to demonstrate the versatility of the Dislocation Meshing strategy. Do you have anything that you could show me or let me have as a test example? Let me know.

Regards
69thbugler

 

[corus]

Why don't you simply draw an odd shape and try and mesh it with standard FE programs and then compare your method with it. There are methods by which you can compare the element shape to test if yours is truly better. A 2D shape would be a good way to start.

corus

 

[69thbugler]

Dear Corus and all hexahedral mesh designers

A sketch on a scrap piece of paper doesn’t really take us anywhere. We know what other systems can do, and the report back from the market is: “They do not match the user requirements”.
The fundamental problem is that existing mesh generators do not reflect the way hexahedral meshes behave, i.e., create meshes with dislocations in a controlled manner.

The question is: Which commercial FEA or CAE system allows a user to define meshes using the kernels, see

http://www.dislocationmeshing.com/downloads/KernelsVolumes.gif

and can deliver mid-point subdivision as shown in

http://www.dislocationmeshing.com/downloads/KernelsMeshes.gif

or anything like it?

Remember, Dislocation Meshing is a description of how hexahedral meshes behave, and they behave according to a law of nature, a law that has nothing to do with FEA or computing or engineering, but is an implicit property of the topology in geometric shapes. Like it or loath it, I am just the messenger!

I am making geometric models available for anyone who wants to learn how to make hexahedral meshes that reflect nature itself, see forum954 Use my models to test existing meshing technology if you like, the models are simple and should not cause any problems, or do they?

Let me know what happens …

Regards
69thbugler

 

[corus]

All of the simple shapes you mention I could mesh using Abaqus CAE by subdividing the regions into simpler shapes that could be hex-meshed. The program Marc, I believe, can also hex mesh odd shapes without subdivision. The problem with codes that proclaim they can mesh odd shapes with tetrahedrals or whatever, is that they look fine from the outside but internally generate badly shaped elements. A shape test on your overall mesh would recognize the worth of your technique. A true test, however, is when you are faced with a 3D CAD drawing of a complex casting with typical bolt holes, fillets, notches, etc. A reasonable hex-mesh can only be obtained by sub-division of the part into simpler regions or by generally tet-meshing the whole region. In most cases the latter option is best, and easiest, with a coarse tet mesh and then using a sub-model of a specific region, finely meshed using brick elements.
There is no doubt, however, that in general the current hex-meshing techniques could be improved upon.

corus

 

[Drej]

Just thought I would mention that ANSYS have a pre-proc and geometry healer product having a HEX-only mesher which is just truly amazing. Although still only relatively young in its development, the software evolves from ICEM CFD, and has been ported for use within ANSYS, and is able to HEX-mesh practically anything. The product is ANSYS AI*Environment.

http://www.ansys.com/ansys/aienvironment/index.htm

Meshing of difficult shapes mentioned above would be simply no problem with this software, as the user tells the program to "walk over" any geometry it considers irrelevant for meshing.

ANSYS have also introduced a HEX-dominant mesher as an add-on module into their AWE package, although it's quite pricey and, like any new functionality, requires time to mature. It appears, then, that since ANSYS are pushing HEX-meshing like never before - driven arguably by market demands for the product - that HEX-meshing is still very much in development and that market analysis has shown it to have a future.

-- drej --