XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX''"> Tria Element Topology
Patran contains six different triangular element topologies: Tria3, Tria4, Tria6, Tria7, Tria9, Tria13.
General Shape
For Tri elements, area coordinates [L1/L2/L3] are commonly used. See
Area coordinate system for
more information.
Tri elements can be obtained by degenerating a Quad element.
1. Quad corner node 2 collapses onto 1.
2. Tri corner nodes 1/2/3 match 1/3/4 for the Quad.
General Data
Shape = Triangular
Element dimensionality= 2
Number of corner nodes = 3
Number of edges = 3
Number of faces = 1
Number of face edges = 3
Table 15‑7 Face ID | Sense | Edge 1 | Edge 2 | Edge 3 |
1 | 1 | 1 | 2 | 3 |
Specific Data ‑ Tria3
Element name = Tria3
Number of nodes = 3
Order = linear
Degenerate element name = <none>
Table 15‑8 Edge Number | Node 1 | Node 2 |
1 | 1 | 2 |
2 | 2 | 3 |
3 | 3 | 1 |
Table 15‑9 Node Number | Xi/Eta or L2/L3 |
1 | 0.0, 0.0 |
2 | 1.0, 0.0,0.0 |
3 | 0.0, 1.0 |
To obtain a Tri3 by degenerating a Quad4, the following are corresponding nodes
For more information, see
Tri3.
Specific Data ‑ Tria4
Element name = Tria4
Number of nodes = 4
Order = linear
Degenerate element name = <none>
Table 15‑10 Edge Number | Node 1 | Node 2 |
1 | 1 | 2 |
2 | 2 | 3 |
3 | 3 | 1 |
Table 15‑11 Node Number | Xi/Eta or L2/L3 |
1 | 0.0, 0.0 |
2 | 1.0, 0.0 |
3 | 0.0, 1.0 |
4 | 1/3, 1/3 |
To obtain a Tri4 by degenerating a Quad5, the following are corresponding nodes:
For more information, see
Tri4.
Specific Data ‑ Tria6
Element name = Tria6
Number of nodes = 6
Order = Quadratic
Degenerate element name = <none>
Table 15‑12 Edge Number | Node 1 | Node 2 | Node 3 |
1 | 1 | 4 | 2 |
2 | 2 | 5 | 3 |
3 | 3 | 6 | 1 |
Table 15‑13 Node Number | Xi/Eta or L2/L3 |
1 | 0.0, 0.0 |
2 | 1.0, 0.0 |
3 | 0.0, 1.0 |
4 | 0.5, 0.0 |
5 | 0.5, 0.5 |
6 | 0.0, 0.5 |
To obtain a Tri6 by degenerating a Quad8, the following are corresponding nodes:
For more information, see
Tri6.
Specific Data ‑ Tria7
Element name = Tria7
Number of nodes = 7
Order = Quadratic
Degenerate element name = <none>
Table 15‑14 Edge Number | Node 1 | Node 2 | Node 3 |
1 | 1 | 4 | 2 |
2 | 2 | 5 | 3 |
3 | 3 | 6 | 1 |
Table 15‑15 Node Number | Xi/Eta or L2/L3 |
1 | 0.0, 0.0 |
2 | 1.0, 0.0 |
3 | 0.0, 1.0 |
4 | 0.5, 0.0 |
5 | 0.5, 0.5 |
6 | 0.0, 0.5 |
7 | 1/3, 1/3 |
To obtain a Tri7 by degenerating a Quad9, the following are corresponding nodes:
Tri7 | Quad9 |
1 | 1 |
2 | 3 |
3 | 4 |
4 | 6 |
5 | 7 |
6 | 8 |
7 | 9 |
For more information, see
Tri7.
Specific Data ‑ Tria9
Element name = Tria9
Number of nodes = 9
Order = Cubic
Degenerate element name = <none>
Table 15‑16 Edge Number | Node 1 | Node 2 | Node 3 | Node 4 |
1 | 1 | 4 | 5 | 2 |
2 | 2 | 6 | 7 | 3 |
3 | 3 | 8 | 9 | 1 |
Table 15‑17 Node Number | Xi/Eta or L2/L3 |
1 | 0.0, 0.0 |
2 | 1.0, 0.0 |
3 | 0.0, 1.0 |
4 | 1/3, 0.0 |
5 | 2/3, 0.0 |
6 | 1/3, 2/3 |
7 | 1/3, 2/3 |
8 | 0.0, 2/3 |
9 | 0.0, 1/3 |
To obtain a Tri9 by degenerating a Quad12, the following are corresponding nodes:
Tri9 | Quad12 |
1 | 1 |
2 | 3 |
3 | 4 |
4 | 7 |
5 | 8 |
6 | 9 |
7 | 10 |
8 | 11 |
9 | 12 |
For more information, see
Tri9.
Specific Data ‑ Tria13
Element name = Tria13
Number of nodes = 13
Order = Cubic
Degenerate element name = <none>
Table 15‑18 Edge Number | Node 1 | Node 2 | Node 3 | Node 4 |
1 | 1 | 4 | 5 | 2 |
2 | 2 | 6 | 7 | 3 |
3 | 3 | 8 | 9 | 1 |
Table 15‑19 Node Number | Xi/Eta or L2/L3 |
1 | 0.0, 0.0 |
2 | 1.0, 0.0 |
3 | 0.0, 1.0 |
4 | 1/3, 0.0 |
5 | 2/3, 0.0 |
6 | 2/3, 1/3 |
7 | 1/3, 2/3 |
8 | 0.0, 2/3 |
9 | 0.0, 1/3 |
10 | 2/9, 1/9 |
11 | 4/9, 2/9 |
12 | 2/9, 4/9 |
13 | 1/9, 2/9 |
To obtain a Tri13 by degenerating a Quad16, the following are corresponding nodes:
Tri13 | Quad16 |
1 | 1 |
2 | 3 |
3 | 4 |
4 | 7 |
5 | 8 |
6 | 9 |
7 | 10 |
8 | 11 |
9 | 12 |
10 | 14 |
11 | 15 |
12 | 16 |
13 | 13 |
For more information, see
Tri13.