김경종
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Optimizing the transmission of energy out of the finite element mesh
For dynamic cases the ability of the infinite elements to transmit energy out of the finite element mesh, without trapping or reflecting it, is optimized by making the boundary between the finite and infinite elements as close as possible to being orthogonal to the direction from which the waves will impinge on this boundary. Close to a free surface, where Rayleigh waves may be important, or close to a material interface, where Love waves may be important, the infinite elements are most effective if they are orthogonal to the surface. (Rayleigh and Love waves are surface waves that decay with distance from the surface.)
For acoustic medium infinite elements, these general guidelines apply as well.
Defining an initial stress field and corresponding body force field
In many applications, especially geotechnical problems, an initial stress field and a corresponding body force field must be defined. For standard elements you define the initial stress field as an initial condition (“Defining initial stresses” in “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 34.2.1) and the corresponding body force field as a distributed load (“Distributed loads,” Section 34.4.3). The body force cannot be defined for infinite elements since the elements are of infinite extent. Therefore, Abaqus automatically inserts forces at the nodes of the infinite elements that cause those nodes to be in static equilibrium at the start of the analysis. These forces remain constant throughout the analysis. This capability allows the initial geostatic stress field to be defined in the infinite elements, but it does not check whether or not the geostatic stress field is reasonable. If the initial stress field is due to a body force loading (such as gravity loading), this loading must be held constant during the step. In multistep analyses it must be maintained constant over all steps.
You must remember that when infinite elements are used in conjunction with an initial stress condition, it is essential that the initial stress field be in equilibrium. In Abaqus/Standard any procedure that determines the initial static (steady-state) equilibrium conditions is suitable as the first step of the analysis; for example, static (“Static stress analysis,” Section 6.2.2); geostatic stress field (“Geostatic stress state,” Section 6.8.2); coupled pore fluid diffusion/stress (“Coupled pore fluid diffusion and stress analysis,” Section 6.8.1); and steady-state fully coupled thermal-stress (“Fully coupled thermal-stress analysis,” Section 6.5.3) steps can be used. To check for equilibrium in Abaqus/Explicit, perform an initial step with no loading (except for the body forces that created the initial stress field) and verify that the accelerations are small.
28.3.2 INFINITE ELEMENT LIBRARY
Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE
References
• “Infinite elements,” Section 28.3.1
• *SOLID SECTION
Overview
This section provides a reference to the infinite elements available in Abaqus/Standard and Abaqus/Explicit.
Element types
Plane strain solid continuum infinite elements
CINPE4 4-node linear, one-way infinite CINPE5R(S) 5-node quadratic, one-way infinite
Active degrees of freedom 1, 2
Additional solution variables None.
Plane stress solid continuum infinite elements
CINPS4 4-node linear, one-way infinite CINPS5R(S) 5-node quadratic, one-way infinite
Active degrees of freedom 1, 2
Additional solution variables None.
3D solid continuum infinite elements
CIN3D8 8-node linear, one-way infinite CIN3D12R(S) 12-node quadratic, one-way infinite CIN3D18R(S) 18-node quadratic, one-way infinite
Active degrees of freedom
1, 2, 3
Additional solution variables
None.
Axisymmetric solid continuum infinite elements
CINAX4
4-node linear, one-way infinite
CINAX5R(S)
5-node quadratic, one-way infinite
Active degrees of freedom
1, 2
Additional solution variables
None.
2D acoustic infinite elements
ACIN2D2
2-node linear, acoustic infinite
ACIN2D3(S)
3-node quadratic, acoustic infinite
Active degree of freedom
8
3D acoustic infinite elements
ACIN3D3
3-node linear, acoustic infinite triangular element
ACIN3D4
4-node linear, acoustic infinite quadrilateral element
ACIN3D6(S)
6-node quadratic, acoustic infinite triangular element
ACIN3D8(S)
8-node quadratic, acoustic infinite quadrilateral element
Active degree of freedom
8
Axisymmetric acoustic infinite elements
ACINAX2
2-node linear, acoustic infinite
ACINAX3(S)
3-node quadratic, acoustic infinite
Active degree of freedom
8
Nodal coordinates required
Plane stress and plane strain solid continuum elements: X, Y
2D acoustic elements: X, Y
3D solid continuum and acoustic elements: X, Y, Z
Axisymmetric solid continuum and acoustic elements: r, z
Normal directions are not specified at nodes used in acoustic infinite elements; they will be computed automatically. See “Infinite elements,” Section 28.3.1, for details.
Element property definition
For two-dimensional, plane strain, and plane stress elements, you must provide the thickness of the elements; by default, unit thickness is assumed.
For three-dimensional and axisymmetric solid elements, you do not need to specify a thickness.
For acoustic elements, you must specify the reference point in addition to the thickness.
Input File Usage: *SOLID SECTION
Abaqus/CAE Usage: Only acoustic infinite sections are supported in Abaqus/CAE.
Property module: Create Section: select Other as the section Category and Acoustic infinite as the section Type
Element-based loading
None.
Element output
Stress, strain, and other tensor components
No output is available from Abaqus/Explicit for infinite elements. Stress and other tensors (including strain tensors) are available from Abaqus/Standard for infinite elements with displacement degrees of freedom. All tensors have the same components. For example, the stress components are as follows:
S11 direct stress or radial stress for axisymmetric elements.
S22 direct stress or axial stress for axisymmetric elements.
S33 direct stress (not available for plane stress elements) or hoop stress for axisymmetric elements.
S12 shear stress or shear stress for axisymmetric elements.
S13 shear stress (not available for plane stress, plane strain, and axisymmetric elements).
S23 shear stress (not available for plane stress, plane strain, and axisymmetric elements).
Plane stress and plane strain solid continuum elements
Axisymmetric solid continuum elements
text_image
4 1 2 3
CINAX4
text_image
4 1 5 2 3
CINAX5R
Three-dimensional solid continuum elements
text_image
1 2 3 4 5 6 7 8
CIN3D8
line
| Point | Value |
|---|---|
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 8 | 8 |
| 9 | 9 |
| 10 | 10 |
| 11 | 11 |
| 12 | 12 |
CIN3D12R
scatter
| Point | X | Y |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 2 | 1 |
| 3 | 3 | 2 |
| 4 | 4 | 4 |
| 5 | 5 | 5 |
| 6 | 6 | 6 |
| 7 | 7 | 7 |
| 8 | 8 | 8 |
| 9 | 1 | 9 |
| 10 | 10 | 10 |
| 11 | 11 | 11 |
| 12 | 12 | 12 |
| 13 | 13 | 13 |
| 14 | 14 | 14 |
| 15 | 15 | 15 |
| 16 | 16 | 16 |
| 17 | 17 | 17 |
| 18 | 18 | 18 |
CIN3D18R
Two-dimensional and axisymmetric acoustic infinite elements
text_image
E1 1 SPOS 2 E2
ACIN2D2
text_image
E1 1 3 E2 2 SPOS
ACIN2D3
text_image
E1 1 SPOS E2 2
ACINAX2
text_image
E1 1 3 2 E2 SPOS
ACINAX3
Three-dimensional acoustic infinite elements
flowchart
graph TD
1 -->|E1| 2
1 -->|E2| 3
1 -->|E3| 3
2 -->|SPOS| 1
ACIN3D3
flowchart
graph TD
1 -->|E1| 2
1 -->|E4| 3
2 -->|E2| 3
3 -->|E3| 4
4 -->|E4| 1
ACIN3D4
flowchart
graph TD
1 -->|E1| 2
1 -->|E3| 3
1 -->|6| 4
2 -->|E2| 3
3 -->|5| 4
4 -->|E1| 1
ACIN3D6
flowchart
graph TD
1 -->|E1| 2
1 -->|E4| 3
1 -->|E1| 4
2 -->|E2| 3
2 -->|E3| 4
3 -->|E4| 4
4 -->|E3| 7
5 -->|E1| 2
6 -->|E2| 3
7 -->|E3| 3
8 -->|E4| 4
9 -->|E1| 5
10 -->|E2| 6
11 -->|E3| 7
12 -->|E4| 8
13 -->|E1| 5
14 -->|E2| 6
15 -->|E3| 7
16 -->|E4| 8
17 -->|E1| 5
18 -->|E2| 6
19 -->|E3| 7
20 -->|E4| 8
21 -->|E1| 5
22 -->|E2| 6
23 -->|E3| 7
24 -->|E4| 8
25 -->|E1| 5
26 -->|E2| 6
27 -->|E3| 7
28 -->|E4| 8
29 -->|E1| 5
30 -->|E2| 6
31 -->|E3| 7
32 -->|E4| 8
33 -->|E1| 5
34 -->|E2| 6
35 -->|E3| 7
36 -->|E4| 8
37 -->|E1| 5
38 -->|E2| 6
39 -->|E3| 7
40 -->|E4| 8
41 -->|E1| 5
42 -->|E2| 6
43 -->|E3| 7
44 -->|E4| 8
45 -->|E1| 5
46 -->|E2| 6
47 -->|E3| 7
48 -->|E4| 8
49 -->|E1| 5
50 -->|E2| 6
51 -->|E3| 7
52 -->|E4| 8
53 -->|E1| 5
54 -->|E2| 6
55 -->|E3| 7
56 -->|E4| 8
57 -->|E1| 5
58 -->|E2| 6
59 -->|E3| 7
60 -->|E4| 8
61 -->|E1| 5
62 -->|E2| 6
63 -->|E3| 7
64 -->|E4| 8
65 -->|E1| 5
66 -->|E2| 6
67 -->|E3| 7
68 -->|E4| 8
69 -->|E1| 5
70 -->|E2| 6
71 -->|E3| 7
72 -->|E4| 8
73 -->|E1| 5
74 -->|E2| 6
75 -->|E3| 7
76 -->|E4| 8
77 -->|E1| 5
78 -->|E2| 6
79 -->|E3| 7
80 -->|E4| 8
81 -->|E1| 5
82 -->|E2| 6
83 -->|E3| 7
84 -->|E4| 8
85 -->|E1| 5
86 -->|E2| 6
87 -->|E3| 7
88 -->|E4| 8
89 -->|E1| 5
90 -->|E2| 6
91 -->|E3| 7
92 -->|E4| 8
93 -->|E1| 5
94 -->|E2| 6
95 -->|E3| 7
96 -->|E4| 8
97 -->|E1| 5
98 -->|E2| 6
99 -->|E3| 7
100 -->|E4| 8
ACIN3D8
Plane stress and plane strain solid continuum elements
Axisymmetric solid continuum elements
text_image
4 ×3 ×4 ×1 ×2 1 2
CINAX4
text_image
4 ×3 ×4 3 ×1 ×2 1 5 2
CINAX5R