김경종
15 KiB
All elements except variable node elements
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face 4 face 2 1 face 1 2 face 3 3 4
4 - node element
flowchart
graph TD
1 --> 5
1 --> 8
1 --> 1
2 --> 5
2 --> 2
3 --> 6
3 --> 3
4 --> 8
4 --> 4
5 --> 7
5 --> 5
6 --> 9
7 --> 9
8 --> 8
9 --> 10
10 --> 10
1 --> 4
2 --> 5
3 --> 3
4 --> 4
5 --> 5
6 --> 6
7 --> 7
8 --> 8
9 --> 9
10 --> 10
1 --> 1
2 --> 1
3 --> 3
4 --> 4
5 --> 5
6 --> 6
7 --> 7
8 --> 8
9 --> 9
10 --> 10
1 --> 1
2 --> 1
3 --> 1
4 --> 1
5 --> 1
6 --> 1
7 --> 1
8 --> 1
9 --> 1
10 --> 1
1 --> 1
2 --> 1
3 --> 1
4 --> 1
5 --> 1
6 --> 1
7 --> 1
8 --> 1
9 --> 1
10 --> 1
1 --> 1
2 --> 1
3 --> 1
4 --> 1
10 - node element
flowchart
graph TD
1["face 1"] --> 2["face 2"]
2 --> 3["face 3"]
3 --> 4["face 4"]
4 --> 5["face 5"]
5 --> 1
4 --> 4
3 --> 3
2 --> 2
1 --> 1
4 --> 4
5 - node element
flowchart
graph TD
A["face 1"] --> B["1"]
B --> C["2"]
C --> D["3"]
D --> E["4"]
E --> F["5"]
F --> G["6"]
G --> H["7"]
H --> I["8"]
I --> J["9"]
J --> K["10"]
K --> L["11"]
L --> M["12"]
M --> N["13"]
N --> O["14"]
O --> P["15"]
P --> Q["face 2"]
Q --> R["face 3"]
R --> S["face 4"]
S --> T["face 5"]
T --> U["face 6"]
U --> V["face 7"]
V --> W["face 8"]
W --> X["face 9"]
X --> Y["face 10"]
Y --> Z["face 11"]
Z --> A
15 - node element
flowchart
graph TD
1 --> 2
2 --> 3
3 --> 4
4 --> 5
5 --> 6
6 --> 4
4 --> 5
5 --> 6
6 --> 4
4 --> 3
3 --> 5
5 --> 6
6 --> 4
4 --> 3
3 --> 5
5 --> 6
6 --> 4
4 --> 3
3 --> 5
5 --> 6
6 --> 4
4 --> 3
3 --> 5
5 --> 6
6 --> face1
6 --> face4
4 --> face2
3 --> face1
5 --> face2
6 --> face4
6 - node element
flowchart
graph TD
1 -->|face 3| 2
2 -->|face 1| 3
3 -->|face 4| 4
4 -->|face 5| 5
5 -->|face 6| 6
6 -->|face 2| 8
8 -->|15| 7
7 -->|14| 6
6 -->|13| 5
5 -->|12| 4
4 -->|11| 3
3 -->|10| 2
2 -->|18| 1
1 -->|17| 5
5 -->|16| 8
8 -->|20| 6
6 -->|4| 4
4 -->|12| 5
20 - node element
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face 2 face 5 8 7 face 6 4 3 face 4 5 6 2 1 face 1 face 3
8 - node element
Tetrahedral element faces
| Face 1 | 1 - 2 - 3 face |
| Face 2 | 1 - 4 - 2 face |
| Face 3 | 2 - 4 - 3 face |
| Face 4 | 3 - 4 - 1 face |
Pyramid element faces
| Face 1 | 1 - 2 - 3 - 4 face |
| Face 2 | 1 - 5 - 2 face |
| Face 3 | 2 - 5 - 3 face |
| Face 4 | 3 - 5 - 4 face |
| Face 5 | 4 - 5 - 1 face |
Wedge (triangular prism) element faces
| Face 1 | 1 - 2 - 3 face |
| Face 2 | 4 - 6 - 5 face |
| Face 3 | 1 - 4 - 5 - 2 face |
| Face 4 | 2 - 5 - 6 - 3 face |
| Face 5 | 3 - 6 - 4 - 1 face |
Hexahedron (brick) element faces
| Face 1 | 1 - 2 - 3 - 4 face |
| Face 2 | 5 - 8 - 7 - 6 face |
| Face 3 | 1 - 5 - 6 - 2 face |
| Face 4 | 2 - 6 - 7 - 3 face |
| Face 5 | 3 - 7 - 8 - 4 face |
| Face 6 | 4 - 8 - 5 - 1 face |
Variable node elements
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12 6 10 11 4 13 18 5 15 16 17 9 3 1 7 14 8 2 X Y Z
15 to 18 - node element
16–18 are midface nodes on the three rectangular faces (see below for faces 1 to 5). These nodes can be omitted from an element by entering a zero or blank in the corresponding position when giving the nodes on the element. Only nodes 16–18 can be omitted.
Face location of nodes 16 to 18
| Face node number | Corner nodes on face |
| 16 | 1-4-5-2 |
| 17 | 2-5-6-3 |
| 18 | 3-6-4-1 |
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21 to 27 - node element
Node 21 is located at the centroid of the element.
(nodes 22–27) are midface nodes on the six faces (see below for faces 1 to 6). These \otimes nodes can be deleted from an element by entering a zero or blank in the corresponding position when giving the nodes on the element. Only nodes 22–27 can be omitted.
Face location of nodes 22 to 27
| Face node number | Corner nodes on face |
| 22 | 1 - 2 - 3 - 4 |
| 23 | 5 - 8 - 7 - 6 |
| 24 | 1 - 5 - 6 - 2 |
| 25 | 2 - 6 - 7 - 3 |
| 26 | 3 - 7 - 8 - 4 |
| 27 | 4 - 8 - 5 - 1 |
All elements except variable node elements
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1 ×1 2 3 4
4 - node element
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4 10 8 × 4 9 × 3 3 1 7 2× 5 6 2
10 - node element
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5 x5 4 x4 x3 3 1 x1 2 x2
5 - node element
flowchart
graph TD
1 -->|×1| 7
1 -->|×2| 8
1 -->|×3| 3
2 --> 3
2 --> 7
3 --> 8
3 --> 9
15 - node element
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3 ×1 1 2
6 - node element
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4 3 ×1 1 2
8 - node reduced integration element
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4 ×3 4× ×1 2× 1 2
8 - node element
flowchart
graph TD
1 -->|×1| 9
1 -->|×3| 11
1 -->|×1| 12
2 -->|2×| 9
2 -->|10| 10
3 -->|4×| 11
4 -->|11| 12
5 -->|3| 11
6 -->|4×| 12
2 0 - node reduced integration element
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4 11 3 ×7 ×8 ×9 ×4 ×5 ×6 ×1 ×2 ×3 12 9 10 2
2 0 - node element
This shows the scheme in the layer closest to the 1–2–3 and 1–2–3–4 faces. The integration points in the second and third layers are numbered consecutively. Multiple layers are used for composite solid elements.
For heat transfer applications a different integration scheme is used for tetrahedral and wedge elements, as described in “Triangular, tetrahedral, and wedge elements,” Section 3.2.6 of the Abaqus Theory Guide.
For linear triangular prisms in Abaqus/Explicit reduced integration is used; therefore, a C3D6 element and a C3D6T element have only one integration point.
For the linear bricks C3D8S and C3D8HS in Abaqus/Standard improved stress visualization is obtained through a 27-point integration rule, consisting of 8 integration points at the elements’ nodes, 12 integration points on the elements’ edges, 6 integration points on the elements’ sides, and one integration point inside the element.
For the general-purpose C3D10HS 10-node tetrahedra in Abaqus/Standard improved stress visualization is obtained through an 11-point integration rule, consisting of 10 integration points at the elements’ nodes and one integration point at their centroid.
For acoustic tetrahedra, pyramid, and wedges in Abaqus/Standard full integration is used; therefore, an AC3D4 element has 4 integration points, an AC3D5 element has 5 integration points, an AC3D6 element has 6 integration points, an AC3D10 element has 10 integration points, and an AC3D15 element has 18 integration points.
Variable node elements
flowchart
graph TD
1 -->|×1| 9
1 --> 7
1 --> 3
2 --> 8
2 --> 3
3 --> 8
3 --> 9
7 --> 8
7 --> 2
8 --> 3
9 --> 3
3 --> 8
8 --> 2
15 to 18 - node element
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4 ×7 11 ×8 ×9 3 12 ×4 ×5 ×6 10 ×1 ×2 ×3 1 9 2
21 to 27 - node element
This shows the scheme in the layer closest to the 1–2–3 and 1–2–3–4 faces. The integration points in the second and third layers are numbered consecutively. Multiple layers are used for composite solid elements. The face nodes do not appear.
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8 ×8 ×14 ×7 5 ×5 12 6 6 11 × × ×4 ×4 ×10 ×3 9 4 13 × ×1 2 1 3 1 2
21 to 27 - node reduced integration element
Node 21 is located at the centroid of the element.
28.1.5 CYLINDRICAL SOLID ELEMENT LIBRARY
Products: Abaqus/Standard Abaqus/CAE
References
• “Solid (continuum) elements,” Section 28.1.1
• *SOLID SECTION
Overview
This section provides a reference to the cylindrical solid elements available in Abaqus/Standard.
Element types
| CCL9 | 9-node cylindrical prism, linear interpolation in the radial plane and trigonometric interpolation along the circumferential direction |
| CCL9H | 9-node cylindrical prism, linear interpolation in the radial plane and trigonometric interpolation along the circumferential direction, hybrid with constant pressure in plane and linear pressure in the circumferential direction |
| CCL12 | 12-node cylindrical brick, linear interpolation in the radial plane and trigonometric interpolation along the circumferential direction |
| CCL12H | 12-node cylindrical brick, linear interpolation in the radial plane and trigonometric interpolation along the circumferential direction, hybrid with constant pressure in plane and linear pressure in circumferential direction |
| CCL18 | 18-node cylindrical prism, quadratic interpolation in the radial plane and trigonometric interpolation along the circumferential direction |
| CCL18H | 18-node cylindrical prism, quadratic interpolation in the radial plane and trigonometric interpolation along the circumferential direction, hybrid with linear pressure in plane and linear pressure in the circumferential direction |
| CCL24 | 24-node cylindrical brick, quadratic interpolation in the radial plane and trigonometric interpolation along the circumferential direction |
| CCL24H | 24-node cylindrical brick, quadratic interpolation in the radial plane and trigonometric interpolation along the circumferential direction, hybrid with linear pressure in plane and linear pressure in circumferential direction |
| CCL24R | 24-node cylindrical brick, reduced integration, quadratic interpolation in the radial plane and trigonometric interpolation along the circumferential direction |
CCL24RH 24-node cylindrical brick, reduced integration, quadratic interpolation in the radial plane and trigonometric interpolation along the circumferential direction, hybrid with linear pressure in plane and linear pressure in circumferential direction
Active degrees of freedom
1, 2, 3
Additional solution variables
The hybrid elements with constant pressure in plane have two additional variables relating to pressure, and the linear pressure hybrid elements have six additional variables relating to pressure.
Nodal coordinates required
X, Y, Z
Element property definition
| Input File Usage: | *SOLID SECTION |
| Abaqus/CAE Usage: | Property module: Create Section: select Solid as the section Category and Homogeneous as the section Type |
Element-based loading
Distributed loads
Distributed loads are specified as described in “Distributed loads,” Section 34.4.3.
| Load ID (*DLOAD) | Units | Description |
| BX | $FL^{-3}$ | Body force in global X-direction. |
| BY | $FL^{-3}$ | Body force in global Y-direction. |
| BZ | $FL^{-3}$ | Body force in global Z-direction. |
| BXNU | $FL^{-3}$ | Nonuniform body force in global X-direction with magnitude supplied via user subroutine DLOAD. |
| BYNU | $FL^{-3}$ | Nonuniform body force in global Y-direction with magnitude supplied via user subroutine DLOAD. |
| BZNU | $FL^{-3}$ | Nonuniform body force in global Z-direction with magnitude supplied via user subroutine DLOAD. |