Tet vs Hex - Handbags at Dawn!

​Hex and Tet are what you call frenemies, they are friends but are secretly jealous of each other and green with envy.
 
It was Saturday night and their boyfriends were watching football, so they decided to go on a girl’s night out.

Hex had put on few pounds and was a little self-conscious about it so she wore a modest outfit that accentuated her shape.
 
“You look fabulous, have you lost weight?” Tet says with a wry smile whilst looking Hex up and down and fluttering her eyelashes.
 
Tet used to have long flowing hair but recently tried a new shorter hair style, she didn’t really like it so she wore a fashionable hat to hide her mistake.
 
“No, you look fabulous, I love your new shorter hair style” Hex says flicking her long shiny locks of hair over her shoulders. She then twirls her hair around her fingers. “It must be so much easier to manage” she says with glee.
 
So, what’s all this got to do with finite elements…....................
 
There is a lot of debate and a bit of rivalry in the FEA Analysis world about which is better Tetrahedral or Hexahedral elements.
 
The ‘experts’ tend to favour Hex elements and like to build beautiful meshes.
 
The ‘novices’ usually favour Tet elements because they’re easy to mesh most CAD geometry.
 
I have listed the Pros and Cons of each and later compared the performance with worked examples.
 
Tetrahedral Elements
 Pros

• Easy to mesh a model without too much effort. Not all geometry can be easily divided into brick shapes, but most geometry can be divided into tetrahedral shapes.
• Reduced labour costs because of ease of meshing.

Cons

• Results can be poor for tets with bad aspect ratio and linear elements.
• Longer solver time because you need more of them.

 
Hexahedral Elements
 Pros

• Very good accuracy.
• The mesh looks aesthetically pleasing to the eye.
• Reduced solver time.
• Less demanding on hardware. Ideal for lower specification workstations.

Cons

• Higher labour costs for meshing, usually requires manual intervention.
• Not all CAD geometry will mesh without de-featuring.

 
 Worked Example Tet vs Hex
 
To put this to the test, consider a simply supported beam with pinned ends. The results are compared to about 99% convergence with Quadratic and Linear Hex and Tet elements.
 
The beam is 3000 mm long by 200 mm wide and 50 mm deep. The total distributed load is 40 kN.
 
The results are shown in Table 1.

The analysis was then repeated with a hole in the centre of the beam to save weight (bad joke 😊) and this is presented in Table 2.

​You can see from the results that both Hex and Tet elements have many similarities in performance, apart from Linear Tets which are best avoided if possible. I’m sure that some of you experts out there could mesh the models to create a different outcome but I didn’t have the time to optimise the meshing.
 
With highly non-linear models, it may be worth putting in the extra effort to create a beautiful Hex mesh because of hardware constraints or to reduce solver time for larger models.
 
On the other hand, geometry with lots of small features and fiddly bits may take too long to mesh with Hex elements. In those cases, Tet elements may prove to be a better option.
  
Back to Hex and Tets girls’ night out……..........
 
After all of the rivalry, Hex and Tet have more in common than they expected and they really enjoyed their night out.
 
Tet then pays a visit to the Ladies Loo and her phone rings. It was her other friend Tri.
 
“Hi Tri, guess what? I’m out with Hex” Tet says with a weary voice, slightly worse for wear.
 
Tet sighs, rolls her eyes, then says “She’s really getting on my TETS!”