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CAE

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21 Jul 2022

All You Need to Know About Tria Elements

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Skill-Lync

Tria elements are the elements formed with 3 nodes. There are certain rules to be considered while handling Tria elements. These include:

  • The Tria elements should never be opposite to each other
  • No Tria elements should be connected back to back 
  • No Tria elements should be on the edge of the geometry 
  • No Tria elements should be near the holes
  • No Tria elements should be on the feature and the fillets.
  • There should be less Tria concentration, i.e., there should be a considerable distance between Tria elements.
     

The reason for a high degree of care for Tria elements is because of their stiffness. When the load is applied and if the stress concentration areas like the fillets, and holes are modelled with Trias then the results will not be accurate because of the Tria stiffness. This is also a reason why the holes which are in the stress concentration region are modelled with a washer i.e, a few layers of quads to extract an accurate result.

 

Few Examples of Tria Elements to Avoid

 

Below are the few Tria elements that we need to avoid.

 

 

Why Tria Elements are Stiffer?

 

Now comes the question of why the Tria is stiff, the reason is fairly simple: as we already know the elements will be formed in a plane and here it takes three points to define a plane, here it takes three nodes to form a Tria element this means that the Tria element will be formed in one plane only. But for a Quad element, there are four nodes by which 2 planes can be defined. This is the reason why Trias cannot bend and be stiff while Quads can bend. To break the explanation down and understand this visually, take a look at the below sketch.

 

 

Here the N1, N2, and N3 are the nodes of the Tria element. These three nodes form the planes X and Y. The nodes N1 and N2 are constrained in all d.o.f, now when a force (F) is applied to the node N3 since there are only three nodes available to define that plane, the N3 instead of bending and moving to the YZ plane, it is going to transfer the load to N1 and N2.

 

 

Isometric view : 

 

 

In this Quad element, all the nodes N1, N2, N3, and N4 are in the plane XY. The node N1, N2, and N4 are constrained in all d.o.f, now when a force F is applied at the node N3 this node can move in the YZ plane as node N1, N2, and N4 has already defined the XY plane. As a result, we have N1, N2, and N4 in XY along with N2, N3, and N4 in the other plane (N2, N3 in Z, and N4 in XY) thus having the nodes in 2 planes causes the bending in Quad elements.

 

Understanding the Stiffness in LST elements

 

There are two types of Tria elements, Constant Strain Triangle (CST) and Linear Stiffness Triangle (LST), or in simple terms, first-order (3 nodes)  and second-order elements (6 nodes), respectively. In the case of the second-order Tria element, there are 6 nodes so the element can be easily defined in more than one plane. This is the reason why the second-order Tria element can bend. 

 

But the disadvantage is that it is computationally expensive; this is also the reason why it is not widely used in industrial applications. The following sketch explains the bending in the second-order Tria element.

 

 

 

 

Here the N1, N2, N3, N4, N5, and N6 are the nodes that define a second-order Tria element. The nodes N1, N2, N4, N5, and N6 are constrained in all d.o.f. The force F is applied in node N3 since N6, N4, and N5 already define plane XY now node N3 is free to move in the Z plane resulting in bending.

 

This Stiffness of the CST element can also be explained experimentally using a Fixed-beam of the thickness of 5mm, a width of 20mm, and a length of 100mm with a concentrated load of 4 KN.

 

Here we are considering two cases:

Case 1: The beam has meshed with Quad elements and in 

Case 2: The beam has meshed with Tria elements. 

 

In both cases, the beam is expected to bend but how much it bends will be our area of interest in this experiment.

 

 

 

 

 

When we compare the displacement of both cases, the Tria elements showed less displacement when compared to the Quad elements. Hence, it is very evident that the Trias are stiffer than the Quads.

 

The Need for Tria Elements:

 

For analysis like the Crash, Drop, and Impact test, we need Tria elements in the mesh to ensure the mesh flow. Depending upon the geometry, even when we mesh with all quad elements sometimes we end up having rotating Quad elements. To avoid these rotating quad elements we need to smartly introduce the Tria elements but we should be careful about the thumb rules mentioned at the start.

 

On the other hand, when the geometry has a sharp edge or starts converging from one end to another, there is no option for the modeller other than introducing the Tria elements. Again we have to keep the thumb rulers in mind if we are doing so.

 

 

This is a classic example of converging geometry. In both ends, the geometry is converging and that is why it is ok to have the Tria elements. As mentioned earlier, we should always check on the Tria concentration. Even in this case, we have to reduce the Tria as much as possible but the mesh flow has to be maintained.

 

Tria Concentration

 

When the Tria elements lie close together, it is called the Tria concentration. Also if you notice the bottom, there is a Tria element that cannot be avoided. But in some cases, we can avoid dividing the geometry smartly. Dividing the geometry is the key to controlling the elements.

 

What are these Rotating Quads?

 

Rotating Quads are the elements that are avoided in the analysis like a crash, drop, and impact where the flow of energy is the main concern for the engineers. This is why the rotating Quad elements are avoided in the model as they distract or divert the flow of the energy in the model. 

 

But on the other hand, for Static analysis, like Fatigue, Durability analysis, etc., it is not required to have a Tria element so the Rotating Quads are preferred as the flow of the force does not make significant changes.

 

 

 

 The above image clearly explains how the force is getting diverted differently when there are rotating quads and Tria elements. Here the force F is applied to the bottom of the plate and if you follow the red line which is how the force will travel,  you can see the diversión that force takes when it is passing through quad elements and when it is passing through the Tria elements. 

 

If ‘what is going to happen with this force diversion?’ is your question, here is the answer to it. When energy flow is distracted by the rotating quads, the actual physics of the problem ( energy flow )  is being modelled wrongly and as a result, the simulation will also be not accurate.


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Navin Baskar


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