Tetrahedral Element Topology

FEM Modeling > Patran Element Library > Tetrahedral Element Topology

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Patran contains eight different tetrahedral element topologies: Tet4, Tet5, Tet10, Tet11, Tet14, Tet15, Tet16, Tet40.

General Data

Shape = Tetrahedral

Element dimensionality= 3

Number of corner nodes = 4

Number of edges = 6

Number of faces = 4

Number of face edges = 3

General Shape

For Tet elements, volume coordinates [L1/L2/L3/L4] are commonly used. See Volume coordinate system for more information.

Tet elements can be obtained by degenerating Hex elements.

1. Hex corner nodes 2/3/4 collapse onto 1, and 6 collapses onto 5.

2. Tet corner nodes 1/2/3/4 match 1/5/7/8 for the Hex.

Table 15‑33
Face ID	Sense	Edge 1	Edge 2	Edge 3
1	‑1	1	2	3
2	1	1	5	4
3	1	2	6	5
4	1	3	4	6

Specific Data ‑ Tet4

Element name = Tet4

Number of nodes = 4

Order = linear

Degenerate element name = <none>

Table 15‑34
Edge Number	Node 1	Node 2
1	1	2
2	2	3
3	3	1
4	1	4
5	2	4
6	3	4

Table 15‑35
Node Number	Xi/Eta/Zeta or L2/L3/L4
1	0.0, 0.0, 0.0
2	1.0, 0.0, 0.0
3	0.0, 1.0, 0.0
4	0.0, 0.0, 1.0

To obtain a Tet4 by degenerating a Hex8, the following are corresponding nodes:


Tet4	Hex8
1	1
2	5
3	7
4	8

For more information, see Tet4.

Specific Data ‑ Tet5

Element name = Tet5

Number of nodes = 5

Order = linear

Degenerate element name = <none>

Table 15‑36
Edge Number	Node 1	Node 2
1	1	2
2	2	3
3	3	1
4	1	4
5	2	4
6	3	4

Table 15‑37
Node Number	Xi/Eta/Zeta or L2/L3/L4
1	0.0, 0.0, 0.0
2	1.0, 0.0, 0.0
3	0.0, 1.0, 1.0
4	0.0, 0.0, 1.0
5	1/4, 1/4, 1/4

To obtain a Tet5 by degenerating a Hex9, the following are corresponding nodes:


Tet5	Hex9
1	1
2	5
3	7
4	8
5	9

For more information, see Tet5.

Specific Data ‑ Tet10

Element name = Tet10

Number of nodes = 10

Order = Quadratic

Degenerate element name = <none>

Table 15‑38
Edge Number	Node 1	Node 2	Node 3
1	1	5	2
2	2	6	3
3	3	7	1
4	1	8	4
5	2	9	4
6	3	10	4

Table 15‑39
Node Number	Xi/Eta/Zeta or L2/L3/L4
1	0.0, 0.0, 0.0
2	1.0, 0.0, 0.0
3	0.0, 1.0, 0.0
4	0.0, 0.0, 1.0
5	0.5, 0.0, 0.0
6	0.5, 0.5, 0.0
7	0.0, 0.5, 0.0
8	0.0, 0.0, 0.5
9	0.5, 0.0, 0.5
10	0.0, 0.5, 0.5

To obtain a Tet10 by degenerating a Hex20, the following are corresponding nodes:


Tet10	Hex20
1	1
2	5
3	7
4	8
5	13
6	18
7	15
8	16
9	20
10	19

For more information, see Tet10.

Specific Data ‑ Tet11

Element name = Tet11

Number of nodes = 11

Order = Quadratic

Degenerate element name = <none>

Table 15‑40
Edge Number	Node 1	Node 2	Node 3
1	1	5	2
2	2	6	3
3	3	7	1
4	1	8	4
5	2	9	4
6	3	10	4

Table 15‑41
Node Number	Xi/Eta/Zeta or L2/L3/L4
1	0.0, 0.0, 0.0
2	1.0, 0.0, 0.0
3	0.0, 1.0, 0.0
4	0.0, 0.0, 1.0
5	0.5, 0.0, 0.0
6	0.5, 0.5, 0.0
7	0.0, 0.5, 0.0
8	0.0, 0.0, 0.5
9	0.5, 0.0, 0.5
10	0.0, 0.5, 0.5
11	1/4, 1/4, 1/4

To obtain a Tet11 by degenerating a Hex21, the following are corresponding nodes:


Tet11	Hex21
1	1
2	5
3	7
4	8
5	13
6	18
7	15
8	16
9	20
10	19
11	21

For more information, see Tet11.

Specific Data ‑ Tet14

Element name = Tet14

Number of nodes = 14

Order = Quadratic

Degenerate element name = <none>

Table 15‑42
Edge Number	Node 1	Node 2	Node 3
1	1	5	2
2	2	6	3
3	3	7	1
4	1	8	4
5	2	9	4
6	3	10	4

Table 15‑43
Node Number	Xi/Eta/Zeta or L2/L3/L4
1	0.0, 0.0, 0.0
2	1.0, 0.0, 0.0
3	0.0, 1.0, 0.0
4	0.0, 0.0, 1.0
5	0.5, 0.0, 0.0
6	0.5, 0.5, 0.0
7	0.0, 0.5, 0.0
8	0.0, 0.0, 0.5
9	0.5, 0.0, 0.5
10	0.0, 0.5, 0.5
11	1/4, 1/4, 0.0
12	0.5, 1/4, 1/4
13	0.0, 1/4, 1/4
14	1/4, 0.0, 1/4

To obtain a Tet14 by degenerating a Hex27, the following are corresponding nodes:


Tet14	Hex27
1	1
2	5
3	7
4	8
5	13
6	18
7	15
8	16
9	20
10	19
11	25
12	23
13	27
14	24

For more information, see Tet14.

Specific Data ‑ Tet15

Element name = Tet15

Number of nodes = 15

Order = Quadratic

Degenerate element name = <none>

Table 15‑44
Edge Number	Node 1	Node 2	Node 3
1	1	5	2
2	2	6	3
3	3	7	1
4	1	8	4
5	2	9	4
6	3	10	4

Table 15‑45
Node Number	Xi/Eta/Zeta or L2/L3/L4
1	0.0, 0.0, 0.0
2	1.0, 0.0, 0.0
3	0.0, 1.0, 0.0
4	0.0, 0.0, 1.0
5	0.5, 0.0, 0.0
6	0.5, 0.5, 0.0
7	0.0, 0.5, 0.0
8	0.0, 0.0, 0.5
9	0.5, 0.0, 0.5
10	0.0, 0.5, 0.5
11	1/4, 1/4, 1/4
12	1/4, 1/4, 0.0
13	0.5, 1/4, 1/4
14	0.0, 1/4, 1/4
15	1/4, 0.0, 1/4

To obtain a Tet15 by degenerating a Hex27, the following are corresponding nodes:


Tet15	Hex27
1	1
2	5
3	7
4	8
5	13
6	18
7	15
8	16
9	20
10	19
11	21
12	25
13	23
14	27
15	24

For more information, see Tet15.

Specific Data ‑ Tet16

Element name = Tet16

Number of nodes = 16

Order = Cubic

Degenerate element name = <none>

Table 15‑46
Edge Number	Node 1	Node 2	Node 3	Node 4
1	1	5	6	2
2	2	7	8	3
3	3	9	10	1
4	1	11	14	4
5	2	12	15	4
6	3	13	16	4

Table 15‑47
Node Number	Xi/Eta/Zeta or L2/L3/L4
1	0.0, 0.0, 0.0
2	1.0, 0.0, 0.0
3	0.0, 1.0, 0.0
4	0.0, 0.0, 1.0
5	1/3, 0.0, 0.0
6	2/3, 0.0, 0.0
7	2/3,1/3, 0.0
8	1/3, 2/3, 0.0
9	0.0, 2/3, 0.0
10	0.0, 1/3, 0.0
11	0.0, 0.0, 1/3
12	2/3, 0.0, 1/3
13	0.0, 1/3, 2/3
14	0.0, 0.0, 2/3
15	1/3, 0.0, 2/3
16	0.0, 1/3, 2/3

To obtain a Tet16 by degenerating a Hex32, the following are corresponding nodes:


Tet16	Hex32
1	1
2	5
3	7
4	8
5	17
6	21
7	27
8	28
9	23
10	19
11	20
12	32
13	29
14	24
15	31
16	30

For more information, see Tet16.

Specific Data ‑ Tet40

Element name = Tet40

Number of nodes = 40

Order = Cubic

Degenerate element name = <none>

Table 15‑48
Edge Number	Node 1	Node 2	Node 3	Node 4
1	1	5	6	2
2	2	7	8	3
3	3	9	10	1
4	1	11	14	4
5	2	12	15	4
6	3	13	16	4

Table 15‑49
Node Number	C(3)	Node Number	Xi/Eta/Zeta or L2/L3/L4
1	0.0, 0.0, 0.0	21	2/9, 0.0, 1/9
2	1.0, 0.0, 0.0	22	4/9, 0.0, 2/9
3	0.0, 1.0, 0.0	23	2/3, 2/9, 1/9
4	0.0, 0.0, 1.0	24	1/3, 4/9, 2/9
5	1/3, 0.0, 0.0	25	0.0, 1/9, 2/9
6	2/3, 0.0, 0.0	26	0.0, 2/9, 1/9
7	2/3, 1/3, 0.0	27	2/9,.074074,.037037
8	1/3, 2/3, 0.0	28	4/9, 148148,.074074
9	0.0, 2/3, 0.0	29	2/9, .296297,.148148
10	0.0, 1/3,0.0	30	1/9,.148148, .074074
11	0.0, 0.0, 1/3	31	1/9, 0.0, 2/9
12	2/3, 0.0, 1/3	32	2/9, 0.0, 4/9
13	0.0, 2/3, 1/3	33	2/3, 1/9, 2/9
14	0.0, 0.0, 2/3	34	1/3, 2/9, 4/9
15	1/3, 0.0, 2/3	35	0.0, 2/9, 4/9
16	0.0, 1/3, 2/3	36	0.0, 4/9, 2/9
17	2/9, 1/9, 0.0	37	2/9,.037037,.074074
18	4/9, 2/9, 0.0	38	4/9,.074074,.148148
19	2/9, 4/9, 0.0	39	2/9,.148148,.296297
20	1/9, 2/9, 0.0	40	1/9,.074074,.148148

To obtain a Tet40 by degenerating a Hex64, the following are corresponding nodes:


Tet40	Hex64
1	1
2	5
3	7
4	8
5	17
6	21
7	27
8	28
9	23
10	19
11	20
12	32
13	29
14	24
15	31
16	30
17	39
18	51
19	52
20	40
21	44
22	56
23	62
24	63
25	42
26	41
27	46
28	58
29	59
30	47
31	43
32	55
33	61
34	64
35	54
36	53
37	45
38	57
39	60
40	48

For more information, see Tet40.