Wedge Element Topology

FEM Modeling > Patran Element Library > Wedge Element Topology

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Patran contains eight different wedge element topologies: Wedge6, Wedge7, Wedge15, Wedge16, Wedge20, Wedge21, Wedge24 and Wedge52.

General Data

Shape = Wedge

Element dimensionality= 3

Number of corner nodes = 6

Number of edges = 9

Number of faces = 5

Number of face edges = 4,3

General Shape

For Wedge elements, a combination of area and rectangular coordinates [L1/L2/L3/Zeta] are commonly used. Zeta values vary from -1 to 1 as in a Hex element. The area coordinates L1/L2/L3 represent the weighting with respect to the 3 edges along the Zeta direction:

edge number 8 (node 1-->4)

edge number 7 (node 2-->5)

edge number 9 (node 3-->6)

See Area coordinate system for more information.

Wedge elements can be obtained by degenerating Hex elements.

1. Hex corner node 2 collapses onto 1, and 6 collapses onto 5.

2. Wedge corner nodes 1:6 match 1/3/4/5/7/8 for the Hex.

Table 15‑50
Face ID	Sense	Edge 1	Edge 2	Edge 3	Edge 4
1	1	1	2	3	*
2	‑1	4	5	6	*
3	‑1	1	8	4	7
4	‑1	2	9	5	8
5	‑1	3	7	6	9

Specific Data ‑ Wedge6

Element name = Wedge6

Number of nodes = 6

Order = linear

Degenerate element name = Tet4

Table 15‑51
Edge Number	Node 1	Node 2
1	2	1
2	1	3
3	3	2
4	5	4
5	4	6
6	6	5
7	2	5
8	1	4
9	3	6

Table 15‑52
Node Number	Xi/Eta/Zeta or L2/L3/Zeta
1	0.0, 0.0, -1.0
2	1.0, 0.0, -1.0
3	0.0, 1.0, -1.0
4	0.0, 0.0, 1.0
5	1.0, 0.0, 1.0
6	0.0, 1.0, 1.0

To obtain a Wedge6 by degenerating a Hex8, the following are corresponding nodes:


Wedge6	Hex8
1	1
2	3
3	4
4	5
5	7
6	8

For more information, see Wedge 6.

Specific Data ‑ Wedge7

Element name = Wedge7

Number of nodes = 7

Order = linear

Degenerate element name = Tet5

Table 15‑53
Edge Number	Node 1	Node 2
1	2	1
2	1	3
3	3	2
4	5	4
5	4	6
6	6	5
7	2	5
8	1	4
9	3	6

Table 15‑54
Node Number	Xi/Eta/Zeta or L2/L3/Zeta
1	0.0, 0.0, -1.0
2	1.0, 0.0, -1.0
3	0.0, 1.0, -1.0
4	0.0, 0.0, 1.0
5	1.0, 0.0, 1.0
6	0.0, 1.0, 1.0
7	1/3, 1/3, 0.0

To obtain a Wedge7 by degenerating a Hex9, the following are corresponding nodes:


Wedge7	Hex9
1	1
2	3
3	4
4	5
5	7
6	8
7	9

For more information, see Wedge7.

Specific Data ‑ Wedge15

Element name = Wedge15

Number of nodes = 15

Order = quadratic

Degenerate element name = Tet10

Table 15‑55
Edge Number	Node 1	Node 2	Node 3
1	2	7	1
2	1	9	3
3	3	8	2
4	5	13	4
5	4	15	6
6	6	14	5
7	2	11	5
8	1	10	4
9	3	12	6

Table 15‑56
Node Number	Xi/Eta/Zeta or L2/L3/Zeta
1	0.0, 0.0, -1.0
2	1.0, 0.0, -1.0
3	0.0, 1.0, -1.0
4	0.0, 0.0, 1.0
5	1.0, 0.0, 1.0
6	0.0, 1.0, 1.0
7	0.5, 0.0, -1.0
8	0.5, 0.5, -1.0
9	0.0, 0.5, -1.0
10	0.0, 0.0, 0.0
11	1.0, 0.0, 0.0
12	0.0, 1.0, 0.0
13	0.5, 0.0, 1.0
14	0.5, 0.5, 1.0
15	0.0, 0.5, 1.0

To obtain a Wedge15 by degenerating a Hex20, the following are corresponding nodes:


Wedge15	Hex20
1	1
2	3
3	4
4	5
5	7
6	8
7	10
8	11
9	12
10	13
11	15
12	16
13	18
14	19
15	20

For more information, see Wedge15.

Specific Data ‑ Wedge16

Element name = Wedge16

Number of nodes = 16

Order = quadratic

Degenerate element name = Tet11

Table 15‑57
Edge Number	Node 1	Node 2	Node 3
1	2	7	1
2	1	9	3
3	3	8	2
4	5	13	4
5	4	15	6
6	6	14	5
7	2	11	5
8	1	10	4
9	3	12	6

Table 15‑58
Node Number	Xi/Eta/Zeta or L2/L3/Zeta
1	0.0, 0.0, -1.0
2	1.0, 0.0, -1.0
3	0.0, 1.0, -1.0
4	0.0, 0.0, 1.0
5	1.0, 0.0, 1.0
6	0.0, 1.0, 1.0
7	0.5, 0.0, -1.0
8	0.5, 0.5, -1.0
9	0.0, 0.5, -1.0
10	0.0, 0.0, 0.0
11	1.0, 0.0, 0.0
12	0.0, 1.0, 0.0
13	0.5, 0.0, 1.0
14	0.5, 0.5, 1.0
15	0.0, 0.5, 1.0
16	1/3, 1/3, 0.0

To obtain a Wedge16 by degenerating a Hex21, the following are corresponding nodes:


Wedge16	Hex21
1	1
2	3
3	4
4	5
5	7
6	8
7	10
8	11
9	12
10	13
11	15
12	16
13	18
14	19
15	20
16	21

For more information, see Wedge16.

Specific Data ‑ Wedge20

Element name = Wedge20

Number of nodes = 20

Order = quadratic

Degenerate element name = Tet14

Table 15‑59
Edge Number	Node 1	Node 2	Node 3
1	2	7	1
2	1	9	3
3	3	8	2
4	5	13	4
5	4	15	6
6	6	14	5
7	2	11	5
8	1	10	4
9	3	12	6

Table 15‑60
Node Number	Xi/Eta/Zeta or L2/L3/Zeta
1	0.0, 0.0, -1.0
2	1.0, 0.0, -1.0
3	0.0, 1.0, -1.0
4	0.0, 0.0, 1.0
5	1.0, 0.0, 1.0
6	0.0, 1.0, 1.0
7	0.5, 0.0, -1.0
8	0.5, 0.5, -1.0
9	0.0, 0.5, -1.0
10	0.0, 0.0, 0.0
11	1.0, 0.0, 0.0
12	0.0, 1.0, 0.0
13	0.5, 0.0, 1.0
14	0.5, 0.5, 1.0
15	0.0, 0.5, 1.0
16	1/3, 1/3, -1.0
17	1/3, 1/3, 1.0
18	0.5, 0.5, 0.0
19	0.0, 0.5, 0.0
20	0.5, 0.0, 0.0

To obtain a Wedge20 by degenerating a Hex26, the following are corresponding nodes:


Wedge20	Hex26
1	1
2	3
3	4
4	5
5	7
6	8
7	10
8	11
9	12
10	13
11	15
12	16
13	18
14	19
15	20
16	21
17	22
18	26
19	23
20	24

For more information, see Wedge20.

Specific Data ‑ Wedge21

Element name = Wedge21

Number of nodes = 21

Order = quadratic

Degenerate element name = Tet15

Table 15‑61
Edge Number	Node 1	Node 2	Node 3
1	2	7	1
2	1	9	3
3	3	8	2
4	5	13	4
5	4	15	6
6	6	14	5
7	2	11	5
8	1	10	4
9	3	12	6

Table 15‑62
Node Number	Xi/Eta/Zeta or L2/L3/Zeta
1	0.0, 0.0, -1.0
2	1.0, 0.0, -1.0
3	0.0, 1.0, -1.0
4	0.0, 0.0, 1.0
5	1.0, 0.0, 1.0
6	0.0, 1.0, 1.0
7	0.5, 0.0, -1.0
8	0.5, 0.5, -1.0
9	0.0, 0.5, -1.0
10	0.0, 0.0, 0.0
11	1.0, 0.0, 0.0
12	0.0, 1.0, 0.0
13	0.5, 0.0, 1.0
14	0.5, 0.5, 1.0
15	0.0, 0.5, 1.0
16	1/3, 1/3, 0.0
17	1/3, 1/3, -1.0
18	1/3, 1/3, 1.0
19	0.5, 0.5, 0.0
20	0.0, 0.5, 0.0
21	0.5, 0.0, 0.0

To obtain a Wedge21 by degenerating a Hex27, the following are corresponding nodes:


Wedge21	Hex27
1	1
2	3
3	4
4	5
5	7
6	8
7	10
8	11
9	12
10	13
11	15
12	16
13	18
14	19
15	20
16	21
17	22
18	23
19	27
20	24
21	25

For more information, see Wedge21.

Specific Data ‑ Wedge24

Element name = Wedge24

Number of nodes = 24

Order = Cubic

Degenerate element name = Tet16

Table 15‑63
Edge Number	Node 1	Node 2	Node 3	Node 4
1	2	8	7	1
2	1	12	11	3
3	3	10	9	2
4	5	20	19	4
5	4	24	23	6
6	6	22	21	5
7	2	14	17	5
8	1	13	16	4
9	3	15	18	6

Table 15‑64
Node Number	Xi/Eta/Zeta or L2/L3/Zeta
1	0.0, 0.0, -1.0
2	1.0, 0.0, -1.0
3	0.0, 1.0, -1.0
4	0.0, 0.0, 1.0
5	1.0, 0.0, 1.0
6	0.0, 1.0, 1.0
7	1/3, 0.0, -1.0
8	2/3, 0.0, -1.0
9	2/3, 1/3, -1.0
10	1/3, 2/3, -1.0
11	0.0, 2/3, -1.0
12	0.0, 1/3, -1.0
13	0.0, 0.0, -1/3
14	1.0, 0.0, -1/3
15	0.0, 1.0, -1/3
16	0.0, 0.0, 1/3
17	1.0, 0.0, 1/3
18	0.0, 1.0, 1/3
19	1/3, 0.0, 1.0
20	2/3, 0.0, 1.0
21	2/3, 1/3, 1.0
22	1/3, 2/3, 1.0
23	0.0, 2/3, 1.0
24	0.0, 1/3, 1.0

To obtain a Wedge24 by degenerating a Hex32, the following are corresponding nodes:


Wedge24	Hex32
1	1
2	3
3	4
4	5
5	7
6	8
7	11
8	12
9	13
10	14
11	15
12	16
13	17
14	19
15	20
16	21
17	23
18	24
19	27
20	28
21	29
22	30
23	31
24	32

For more information, see Wedge24.

Specific Data ‑ Wedge52

Element name = Wedge52

Number of nodes = 52

Order = Cubic

Degenerate element name = Tet40

Table 15‑65
Edge Number	Node 1	Node 2	Node 3	Node 4
1	2	8	7	1
2	1	12	11	3
3	3	10	9	2
4	5	20	19	4
5	4	24	23	6
6	6	22	21	5
7	2	14	17	5
8	1	13	16	4
9	3	15	18	6

Table 15‑66
Node Number	Xi/Eta/Zeta or L2/L3/Zeta	Node Number	Xi/Eta/Zeta or L2/L3/Zeta
1	0.0, 0.0, -1.0	27	2/9, 4/9, -1.0
2	1.0, 0.0, -1.0	28	1/9, 2/9, -1.0
3	0.0, 1.0, -1.0	29	1/3, 0.0, -1/3
4	0.0, 0.0, 1.0	30	2/3, 0.0, -1/3
5	1.0, 0.0, 1.0	31	2/3, 1/3, -1/3
6	0.0, 1.0, 1.0	32	1/3, 2/3, -1/3
7	1/3, 0.0, 1.0	33	0.0, 2/3, -1/3
8	2/3, 0.0, -1.0	34	0.0, 1/3, -1/3
9	1/3, 1/3, -1.0	35	2/9, 1/9, -1/3
10	1/3, 2/3, -1.0	36	4/9, 2/9, -1/3
11	0.0, 2/3, -1.0	37	2/9, 4/9, -1/3
12	0.0, 1/3, -1.0	38	1/9, 2/9, -1/3
13	0.0, 0.0, -1/3	39	1/3, 0.0, 1/3
14	1.0, 0.0, -1/3	40	2/3, 0.0, 1/3
15	0.0, 1.0, -1/3	41	2/3, 1/3, 1/3
16	0.0, 0.0, 1/3	42	1/3, 2/3, 1/3
17	1.0, 0.0, 1/3	43	0.0, 2/3, 1/3
18	0.0, 1.0, 1/3	44	0.0, 1/3, 1/3
19	1/3, 0.0, 1.0	45	2/9, 1/9, 1/3
20	2/3, 0.0, 1.0	46	4/9, 2/9, 1/3
21	2/3, 1/3, 1.0	47	2/9, 4/9, 1/3
22	1/3, 2/3, 1.0	48	1/9, 2/9, 1/3
23	0.0, 2/3, 1.0	49	2/9, 1/9, 1.0
24	0.0, 1/3, 1.0	50	4/9, 2/9, 1.0
25	2/9, 1/9, -1.0	51	2/9, 4/9, 1.0
26	4/9, 2/9, -1.0	52	1/9, 2/9, 1.0

To obtain a Wedge52 by degenerating a Hex64, the following are corresponding nodes:


Wedge52	Hex64
1	1
2	3
3	4
4	5
5	7
6	8
7	11
8	12
9	13
10	14
11	15
12	16
13	17
14	19
15	20
16	21
17	23
18	24
19	27
20	28
21	29
22	30
23	31
24	32
25	34
26	35
27	36
28	33
29	39
30	40
31	41
32	42
33	43
34	44
35	46
36	47
37	48
38	45
39	51
40	52
41	53
42	54
43	55
44	56
45	58
46	59
47	60
48	57
49	62
50	63
51	64
52	61

For more information, see Wedge 52.