김경종
13 KiB
13 KiB
12-node element
Face 1 (SPOS) 7 – 12 – 9 – 11 – 8 – 10 face
Face 2 (SNEG) 1 – 4 – 2 – 5 – 3 – 6 face
18-node element
Face 1 (SPOS) 9 – 16 – 12 – 15 – 11 – 14 – 10 – 13 face
Face 2 (SNEG) 1 – 5 – 2 – 6 – 3 – 7 – 4 – 8 face
Numbering of integration points for output
Link elements
text_image
1 2
2 - node element
Line elements
flowchart
graph TD
1 --> 2
1 --> 3
2 --> 3
2 --> 4
3 --> 4
4 - node element
flowchart
graph TD
1 --> 2
2 --> 3
3 --> 4
4 --> 5
5 --> 6
6 --> 1
1 -->|×| 2
2 -->|×| 3
3 -->|×| 4
4 -->|×| 5
5 -->|×| 6
6 - node element
Area elements
flowchart
graph TD
1 --> 2
1 --> 3
2 --> 3
2 --> 4
3 --> 4
3 --> 5
4 --> 5
5 --> 6
6 --> 4
5 --> 3
6 - node element
flowchart
graph TD
1 --> 2
2 --> 3
3 --> 9
9 --> 12
12 --> 7
7 --> 10
10 --> 8
8 --> 2
2 --> 5
5 --> 3
3 --> 11
11 --> 6
6 --> 8
8 --> 10
10 --> 11
11 --> 10
10 --> 10
10 --> 10
10 --> 10
10 --> 10
10 --> 10
10 --> 10
10 --> 10
10 --> 10
10 --> 10
10 --> 10
10 --> 10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
</details>
12 - node element
<details>
<summary>text_image</summary>
8
4
7
3
5
6
1
2
</details>
8 - node element
<details>
<summary>text_image</summary>
12
15
11
14
10
16
18
7
3
4
9
13
6
17
8
5
2
1
</details>
18 - node element
Integration points are indicated with an X and have the same numbers as the bottom face nodes, except that the point between nodes 17 and 18 in the 18-node gasket element is integration point number 9.
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# 32.6.9 AXISYMMETRIC GASKET ELEMENT LIBRARY
Products: Abaqus/Standard Abaqus/CAE
# References
• “Gasket elements: overview,” Section 32.6.1
• “Choosing a gasket element,” Section 32.6.2
• \*GASKET SECTION
# Overview
This section provides a reference to the axisymmetric gasket elements available in Abaqus/Standard.
# Element types
# Link elements
GKAX2 2-node, axisymmetric gasket element
GKAX2N 2-node, axisymmetric gasket element with thickness-direction behavior only
Active degrees of freedom
1 for gasket elements with thickness-direction behavior only.
1, 2 for other gasket elements.
Additional solution variables
# General elements
GKAX4 4-node, axisymmetric gasket element
GKAX4N 4-node, axisymmetric gasket element with thickness-direction behavior only
GKAX6 6-node, axisymmetric gasket element
GKAX6N 6-node, axisymmetric gasket element with thickness-direction behavior only
Active degrees of freedom
1 for gasket elements with thickness-direction behavior only.
1, 2 for other gasket elements.
Additional solution variables
None.
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# Nodal coordinates required
X,Y
# Element property definition
You must define the element’s initial gap and initial void. In addition, for link elements you must define the element’s width.
You can specify the thickness direction as part of the gasket section definition or by specifying a normal direction at the nodes; you can specify the element thickness as part of the gasket section definition. Otherwise, Abaqus/Standard will calculate the thickness direction and the thickness. For link elements the thickness direction is the direction from the first to the second node and the thickness is the distance between the nodes. For general elements the thickness direction is based on the midsurface of the element and the thicknesses at the integration points are based on the nodal positions. See “Defining the gasket element’s initial geometry,” Section 32.6.4, for more details.
Input File Usage: \*GASKET SECTION
Abaqus/CAE Usage: Property module: Create Section: select Other as the section Category and Gasket as the section Type
# Element-based loading
None.
# Element output
GKAX2 elements
<table><tr><td>S11</td><td>Pressure or thickness-direction force per unit length in the gasket element.</td></tr><tr><td>CS11</td><td>Contact pressure in the gasket element (only available if S11 is a force per unit length and the gasket response is not defined using a material model).</td></tr><tr><td>S22</td><td>Hoop stress.</td></tr><tr><td>S12</td><td>Shear stress or shear force per unit length.</td></tr><tr><td>E11</td><td>Gasket closure if the gasket response is defined directly using a gasket behavior model; strain if the gasket response is defined using a material model.</td></tr><tr><td>E22</td><td>Hoop strain.</td></tr><tr><td>E12</td><td>Shear motion if the gasket response is defined directly using a gasket behavior model; strain if the gasket response is defined using a material model.</td></tr><tr><td>NE11</td><td>Effective thickness-direction strain.</td></tr><tr><td>NE22</td><td>Hoop strain.</td></tr><tr><td>NE12</td><td>Effective shear strain.</td></tr></table>
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GKAX2N elements
<table><tr><td>S11</td><td>Pressure or thickness-direction force per unit length in the gasket element.</td></tr><tr><td>CS11</td><td>Contact pressure in the gasket element (only available if S11 is a force per unit length and the gasket response is not defined using a material model).</td></tr><tr><td>E11</td><td>Gasket closure if the gasket response is defined directly using a gasket behavior model; strain if the gasket response is defined using a material model.</td></tr><tr><td>NE11</td><td>Effective thickness-direction strain.</td></tr></table>
General elements with thickness-direction behavior only
<table><tr><td>S11</td><td>Pressure in the gasket element.</td></tr><tr><td>E11</td><td>Gasket closure if the gasket response is defined directly using a gasket behavior model; strain if the gasket response is defined using a material model.</td></tr><tr><td>NE11</td><td>Effective thickness-direction strain.</td></tr></table>
Other general elements
<table><tr><td>S11</td><td>Pressure in the gasket element.</td></tr><tr><td>S22</td><td>Direct membrane stress.</td></tr><tr><td>S33</td><td>Hoop stress.</td></tr><tr><td>S12</td><td>Shear stress.</td></tr><tr><td>E11</td><td>Gasket closure if the gasket response is defined directly using a gasket behavior model; strain if the gasket response is defined using a material model.</td></tr><tr><td>E22</td><td>Direct membrane strain.</td></tr><tr><td>E33</td><td>Hoop strain.</td></tr><tr><td>E12</td><td>Shear motion if the gasket response is defined directly using a gasket behavior model; strain if the gasket response is defined using a material model.</td></tr><tr><td>NE11</td><td>Effective thickness-direction strain.</td></tr><tr><td>NE22</td><td>Direct membrane strain.</td></tr><tr><td>NE33</td><td>Direct membrane strain.</td></tr><tr><td>NE12</td><td>Effective shear strain.</td></tr></table>
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# Link elements
<details>
<summary>text_image</summary>
1
×
2
</details>
2 - node element
# General elements
<details>
<summary>text_image</summary>
3
4
1
2
</details>
4 - node element
<details>
<summary>text_image</summary>
4
5
6
×
×
×
1
2
3
</details>
6 - node element
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# 32.7 Surface elements
• “Surface elements,” Section 32.7.1
• “General surface element library,” Section 32.7.2
• “Cylindrical surface element library,” Section 32.7.3
• “Axisymmetric surface element library,” Section 32.7.4
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# 32.7.1 SURFACE ELEMENTS
Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE Abaqus/Aqua
# References
• “General surface element library,” Section 32.7.2
• “Cylindrical surface element library,” Section 32.7.3
• “Axisymmetric surface element library,” Section 32.7.4
• \*SURFACE SECTION
• “Creating surface sections,” Section 12.13.9 of the Abaqus/CAE User’s Guide, in the HTML version of this guide
# Overview
Surface elements:
• are defined just like membrane elements—as surfaces in space;
• have no inherent stiffness;
• may have mass per unit area;
• may be used to define rigid bodies;
• may be used in the definition of surfaces and surface-based tie constraints;
• behave just like membrane elements with zero thickness;
• may be used with rebar layers;
• can be embedded in solid elements;
• can transmit only in-plane forces; and
• have no bending stiffness or transverse shear stiffness.
# Typical applications
Surface elements are useful in several special modeling cases:
• They are used to carry rebar layers to represent thin stiffening components in solid structures. The stiffness and mass of the rebar layers are added to the surface elements (see “Defining reinforcement,” Section 2.2.3). The reinforced surface elements can also be embedded in “host” solid elements (see “Embedded elements,” Section 35.4.1).
• They are used to bring additional mass into the model in the form of a mass per unit area; for example, to spread the mass of fuel in a tank over the tank surface, particularly when the tank is modeled with solid elements.
• They are used to specify a surface used in a constraint, when that surface does not have structural properties.
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• When used in conjunction with a surface-based tie constraint, they are used to specify distributed surface loading, such as incident wave loading, on beam elements.
• In Abaqus/Explicit (when used in conjunction with a surface-based tie constraint) they can be used to specify a complex surface on beam elements for use in general contact. The stiffness of the penalty springs used to enforce contact constraints is approximately proportional to the mass of the surface nodes. Contact will not be enforced if the surface nodes have no mass.
• In Abaqus/Explicit they can be used to define all or part of the boundary for a surface-based fluid cavity (for example, see “Hydrostatic fluid elements: modeling an airspring,” Section 1.1.9 of the Abaqus Example Problems Guide).
• In Abaqus/Aqua analysis they can be used to visualize gravity waves.
# Choosing an appropriate element
In addition to the general surface elements available in both Abaqus/Standard and Abaqus/Explicit, cylindrical surface elements and axisymmetric surface elements are available in Abaqus/Standard only.
# General surface elements
General surface elements should be used in three-dimensional models in which the deformation of the structure can evolve in three dimensions.
# Cylindrical surface elements
Cylindrical surface elements are available in Abaqus/Standard for precise modeling of regions in a structure with circular geometry, such as a tire. The elements make use of trigonometric functions to interpolate displacements along the circumferential direction and use regular isoparametric interpolation in the in-plane direction. They use three nodes along the circumferential direction and can span a segment between 0° and 180°. Elements with both first-order and second-order interpolation in the in-plane direction are available.
The geometry of the element is defined by specifying nodal coordinates in a global Cartesian system.
These elements can be used in the same mesh with regular surface elements. They can also be embedded in general solid and cylindrical elements.
# Axisymmetric surface elements
The axisymmetric surface elements available in Abaqus/Standard are divided into two categories: those that do not allow twist about the symmetry axis and those that do. These elements are referred to as the regular and generalized axisymmetric surface elements, respectively.
The generalized axisymmetric surface elements (axisymmetric surface elements with twist) allow a circumferential component of loading, which may cause twist about the symmetry axis. The circumferential load component is independent of the circumferential coordinate . Since there is no dependence of the loading on the circumferential coordinate, the deformation is axisymmetric.
The generalized axisymmetric surface elements cannot be used in dynamic or eigenfrequency extraction procedures.