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  • 1. OpenSees Interpreters
  • 2. Installation
  • 3. Command Manual
    • 3.1. Model Commands
      • 3.1.1. model Command
      • 3.1.2. node Command
      • 3.1.3. SP_Constraint Commands
      • 3.1.4. MP_Constraint Commands
        • 3.1.4.1. EqualDOF Constraints
        • 3.1.4.2. Rigid Diaphragm
        • 3.1.4.3. Rigid Link
      • 3.1.5. uniaxialMaterial Command
      • 3.1.6. nDMaterial Command
      • 3.1.7. section Command
      • 3.1.8. Geometric Transformation Command
      • 3.1.9. Element Command
      • 3.1.10. Time Series Command
      • 3.1.11. Pattern Command
      • 3.1.12. Damping Commands
    • 3.2. Analysis Commands
    • 3.3. Output Commands
    • 3.4. Misc. Commands
  • 4. Examples
  • 5. Questions, Bugs & Feature Requests
  • 6. Copyright and License

Framework for Developer

  • 1. Source Code
  • 2. Building Application
  • 3. References
  • 4. Extending Application
  • 5. Contributing Code & Documentation
  • 6. Issues
OpenSees Documentation
  • 3. Command Manual
  • 3.1. Model Commands
  • 3.1.4. MP_Constraint Commands
  • 3.1.4.3. Rigid Link
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3.1.4.3. Rigid Link

This command is used to construct a single MP_Constraint object.

rigidLink $type $retainedNodeTag $constrainedNodeTag

Argument

Type

Description

$type

string

string-based argument for rigid-link type:
bar only the translational degree-of-freedom will be constrained to be exactly the same as those at the master node
beam both the translational and rotational degrees of freedom are constrained.

$retainedNodeTag

integer

integer tag identifying the retained node

$constrainedNodeTag

integer

integer tag identifying the constrained node

Note

  1. By retained node, we mean the node who’s degrees-of-freedom are retained in the system of equations. The constrained nodes degrees-of-freedom need not appear in the system (depending on the constraint handler).

  2. For 2d and 3d problems with a beam type link, the constraint matrix (that matrix relating the responses at constrained node, \(U_c\), to responses at retained node, \(U_r\), i.e. \(U_c = C_{cr} U_r\), is constructed assuming small rotations. For 3d problems this results in the following constraint matrix:

    (3.1.4.5)\[\begin{split}\begin{bmatrix} 1 & 0 & 0 & 0 & \Delta Z & -\Delta Y \\ 0 & 1 & 0 & -\Delta Z & 0 & \Delta X \\ 0 & 0 & 1 & \Delta Y & -\Delta X & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \end{bmatrix}\end{split}\]

    For 2d problems, the constraint matrix is the following:

    (3.1.4.5)\[\begin{split}\begin{bmatrix} 1 & 0 & -\Delta Y \\ 0 & 1 & \Delta X \\ 0 & 0 & 1 \end{bmatrix}\end{split}\]

    where \(\Delta X\) is x coordinate of constrained node minus the x coordinate of the retained node. \(\Delta Y\) and \(\Delta Z\) being similarily defined for y and z coordinates of the nodes.

  3. For 2d and 3d problems with a rod type link the constraint matrix, that which matrix relates the responses at translational degrees-of-freedom at the constrained node to corresponding responses at retained node, is the identity matrix. For 3d problems this results in the following constraint matrix:

(3.1.4.5)\[\begin{split}\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\end{split}\]

For 2d problems, the constraint matrix is the following:

(3.1.4.5)\[\begin{split}\begin{bmatrix} 1 & 0 \\ 0 & 1 \\ \end{bmatrix}\end{split}\]
  1. The rod constraint can also be generated using the equalDOF command.

Example:

The following command will constrain node 3 to move rigidly following rules for small rotations to displacements and rotations at node 2 is

  1. Tcl Code

rigidLink beam 2 3
  1. Python Code

rigidLink('beam',2,3)

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