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김경종
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<!-- source-page: 281 -->
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# Using MPC type LINK
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MPC type LINK provides a pinned rigid link between two nodes to keep the distance between the nodes constant, as shown in Figure 35.2.2–11. The displacements of the first node are modified to enforce this constraint. The rotations at the nodes, if they exist, are not involved in this constraint.
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<details>
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<summary>flowchart</summary>
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```mermaid
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graph TD
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a -->|L| b
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a -->|L| b
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b -->|L| a
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```
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</details>
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Figure 35.2.2–11 MPC type LINK.
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Input data
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Give the nodes a and b as shown in Figure 35.2.2–11.
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Input File Usage: \*MPC
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LINK, a, b
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Abaqus/CAE Usage: Use one of the following options:
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Interaction module: Create Connector Section: select MPC as the Connection Category and Link as the MPC Type
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Interaction module: Create Constraint: MPC Constraint; select Link as the MPC Type
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<!-- source-page: 282 -->
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# Using MPC type PIN
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MPC type PIN provides a pinned joint between two nodes. This MPC makes the global displacements equal but leaves the rotations, if they exist, independent of each other, as shown in Figure 35.2.2–12.
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<details>
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<summary>text_image</summary>
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Diagram illustrating vector relationships in 3D coordinate systems with labeled axes and unit vectors
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</details>
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Figure 35.2.2–12 MPC type PIN.
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Input data
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Give the nodes a and b as shown in Figure 35.2.2–12.
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Input File Usage: \*MPC
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PIN, a, b
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Abaqus/CAE Usage: Use one of the following options:
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Interaction module: Create Connector Section: select MPC as the Connection Category and Pin as the MPC Type
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Interaction module: Create Constraint: MPC Constraint; select Pin as the MPC Type
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<!-- source-page: 283 -->
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# Using MPC type REVOLUTE
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This MPC type is available only in Abaqus/Standard.
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A revolute joint is a joint in which relative rotation is allowed between two nodes about an axis that rotates during the motion (see Figure 35.2.2–13). The axis of the joint is defined in the initial configuration as the line from node b to node c. If these nodes are coincident, the axis is assumed to be the global z-axis. The rotation of the joint axis is that of node b.
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The relative rotation in the joint is a single variable and is stored as degree of freedom 6 at node c. This degree of freedom can be used with other members in the model, but caution should be used because of the nonstandard use of degree of freedom 6. For example, a SPRING1 element (a spring to ground) might be attached to this degree of freedom. Since the degree of freedom measures a relative rotation, this spring would then be a torsional spring between nodes a and b.
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The displacements at node a are not constrained by the REVOLUTE MPC to be the same as the displacements at node b. Thus, the joint definition must usually be completed either by using a PIN type MPC between nodes a and b or by using suitable stiffness members between these two nodes.
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An example of a revolute joint and application of the REVOLUTE MPC is provided in “Revolute MPC verification: rotation of a crank,” Section 1.3.8 of the Abaqus Benchmarks Guide. See “Revolute joint,” Section 6.6.3 of the Abaqus Theory Guide, for more details on revolute joints.
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<details>
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<summary>text_image</summary>
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a
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c
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b
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</details>
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Figure 35.2.2–13 Revolute joint.
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# Input data
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Give the nodes a, b, and c as shown in Figure 35.2.2–13. Degree of freedom 6 at node c defines the relative rotation between nodes a and b; therefore, this degree of freedom does not obey the standard convention for degrees of freedom in Abaqus.
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Input File Usage: \*MPC
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REVOLUTE, a, b, c
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Abaqus/CAE Usage: Revolute joint multi-point constraints are not supported in Abaqus/CAE.
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<!-- source-page: 284 -->
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# Using MPC type SLIDER
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MPC type SLIDER keeps a node on a straight line defined by two other nodes but allows the possibility of moving along the line and allows the line to change length.
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When transitioning from multiple layers of solid elements to shells, it is often desirable to constrain the nodes on the free edge of the solid elements to remain in a straight line. (This constraint is consistent with shell theory.) The SLIDER MPC can perform this function without restraining the “thinning” behavior of the solid layers. The SS LINEAR MPC is then used to attach the shell element to this edge.
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In Abaqus/Standard when a SLIDER MPC is used with one of the shell-solid MPCs—SS LINEAR, SS BILINEAR, or SSF BILINEAR—it must be given following the shell-solid MPCs.
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# Input data
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For each node p shown in Figure 35.2.2–14 and Figure 35.2.2–15, give the nodes p, a, and b for each line of nodes that should remain straight. For each node q shown in Figure 35.2.2–14, give the nodes q, c, and $d ,$ and so on for each line of nodes that should remain straight.
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<table><tr><td>Input File Usage:</td><td>*MPC</td></tr><tr><td></td><td>SLIDER, p, a, b</td></tr><tr><td></td><td>SLIDER, q, c, d</td></tr></table>
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Abaqus/CAE Usage: Slider multi-point constraints are not supported in Abaqus/CAE.
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<!-- source-page: 285 -->
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Figure 35.2.2–14 SLIDER type MPC used at a shell-solid intersection.
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<!-- source-page: 286 -->
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<details>
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<summary>text_image</summary>
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a, b are nodes on the outer pipe
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p¹, p² are nodes on the inner pipe
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</details>
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Figure 35.2.2–15 SLIDER type MPC used to model a telescoping beam.
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<!-- source-page: 287 -->
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# Using MPC type TIE
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MPC type TIE makes the global displacements and rotations as well as all other active degrees of freedom equal at two nodes. If there are different degrees of freedom active at the two nodes, only those in common will be constrained.
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MPC type TIE is usually used to join two parts of a mesh when corresponding nodes on the two parts are to be fully connected (“zipping up” a mesh). For example, when a mesh is generated on a cylindrical body, the solution at the nodes at 0° and those at 360° must be the same. This can be done either by renumbering the nodes on one of the mesh extremes or by using this MPC for each pair of corresponding nodes, as shown in Figure 35.2.2–16.
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<details>
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<summary>text_image</summary>
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a¹
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b¹
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a²
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b²
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a³
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b³
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</details>
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Figure 35.2.2–16 Example of use of TIE MPC.
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# Input data
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Give the nodes a and b as shown in Figure 35.2.2–16.
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Input File Usage: \*MPC
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TIE, a, b
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Abaqus/CAE Usage: Use one of the following options:
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Interaction module: Create Connector Section: select MPC as the Connection Category and Tie as the MPC Type
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Interaction module: Create Constraint: MPC Constraint; select Tie as the MPC Type
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<!-- source-page: 288 -->
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# Using MPC type UNIVERSAL
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This MPC type is available only in Abaqus/Standard.
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A universal joint is a joint in which relative rotation is allowed between two nodes, about two axes that are connected rigidly, and each of which rotates with the rotation of one end of the joint (see Figure 35.2.2–17). Such a joint might be used to couple two shafts that have an angular misalignment. The first axis of the joint, which is attached to node b, is defined in the initial configuration as the line from node b to node c. If these nodes are coincident, the axis is assumed to be the global z-axis. The second axis of the joint is at right angles to the first axis and is in the plane defined by the first axis and node d.
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The relative rotations in the joint are stored as degree of freedom 6 at the nodes c and d. These degrees of freedom can be used with other members in the model, but caution should be used because of the nonstandard use of degree of freedom 6. For example, a SPRING1 element (a spring to ground) might be attached to one of these degrees of freedom. Since the degree of freedom measures a relative rotation, this spring would then be a torsional spring, restraining that component of relative rotation.
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The displacements at node a are not constrained by the UNIVERSAL MPC to be the same as the displacements at node b. Thus, the joint definition must usually be completed either by using a PIN type MPC between nodes a and b or by using suitable stiffness members between these two nodes.
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See “Universal joint,” Section 6.6.4 of the Abaqus Theory Guide, for more details on universal joints.
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<details>
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<summary>text_image</summary>
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a
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b
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c
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d
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</details>
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Figure 35.2.2–17 Universal joint.
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# Input data
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Give the nodes a, b, c, and d as shown in Figure 35.2.2–17. Degrees of freedom 6 at nodes c and d define the relative rotation in the joint; therefore, these degrees of freedom do not obey the standard convention for degrees of freedom in Abaqus.
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Input File Usage: \*MPC
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UNIVERSAL, a, b, c, d
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Abaqus/CAE Usage: Universal joint multi-point constraints are not supported in Abaqus/CAE.
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<!-- source-page: 289 -->
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# Using MPC type V LOCAL
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This MPC type is available only in Abaqus/Standard.
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As shown in Figure 35.2.2–18, MPC type V LOCAL constrains the velocity components associated with degrees of freedom 1, 2, and 3 at a first node (a) to be equal to the velocity components at a third node (c) along local, rotating directions. These local directions rotate according to the rotation at a second node (b). In the initial configuration the first local direction is from the second to the third node of the MPC (from b to c, as indicated by the arrows in Figure 35.2.2–18), or it is the global z-axis if these nodes coincide. The other local directions are then defined by the standard Abaqus convention for such directions (see “Conventions,” Section 1.2.2). In Figure 35.2.2–18 this MPC is applied to nodes d, e, and f in the same manner.
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MPC type V LOCAL can be useful for defining a complex motion within a model. For example, the MPC can be used to model the steering of an automobile in a dynamic analysis for which the resulting inertial effects are of interest. See “Local velocity constraint,” Section 6.6.5 of the Abaqus Theory Guide, for more details on the local velocity constraint.
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<details>
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<summary>text_image</summary>
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+
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θ
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a,b
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f
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d,e
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θ
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</details>
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Figure 35.2.2–18 Local velocity constraint.
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<!-- source-page: 290 -->
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# Input data
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Give the node whose velocity components are constrained (node a or d in Figure 35.2.2–18), the node whose rotation defines the rotation of the local directions (node b or e in Figure 35.2.2–18), and the node whose velocity components are in these local directions (node c or f in Figure 35.2.2–18). Nodes a and b (or d and e) can be the same.
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<table><tr><td>Input File Usage:</td><td>*MPC</td></tr><tr><td></td><td>V LOCAL, a, b, c</td></tr><tr><td></td><td>V LOCAL, d, e, f</td></tr></table>
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Abaqus/CAE Usage: Local velocity component multi-point constraints are not supported in Abaqus/CAE.
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