Prescribed Displacement/Rotation

Prescribed Displacement/Rotation

The node adds an edge (3D), boundary (2D), or point (2D and 3D) condition where the displacements and rotations are prescribed in one or more directions. It is also possible set maximum and minimum limits for the displacements, so that for example a one-sided support can be modeled.

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If a prescribed displacement or rotation is not activated in any direction, this is the same as a constraint.

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If zero displacements and rotations are prescribed, this is the same as a .

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If only zero displacements are prescribed, this is the same as a constraint.

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If only zero rotations are prescribed, this is the same as a constraint.

Coordinate System Selection

Specify the coordinate system to use for specifying the prescribed displacement/rotation. See the section for Edge Load.

Prescribed Displacement

For the displacement in each direction, select a setting from the list — , , or . Select:

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(the default) to leave the displacement component unconstrained

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to constrain the displacement component to a given value. Enter a scalar value for the component of the prescribed displacement u0.

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to set a maximum and a minimum limit for the displacement component. Enter a scalar value for the component of the maximum displacement u0,max and the minimum displacement u0,min. By default, they are set to Inf and -Inf, which corresponds to no active constraint.

If any displacement component is set to , an additional section is visible. Select the used to implement the weak inequality constraint — or . For both methods, enter a kp.

By default, the method is suggested, which in principle enforces the maximum and minimum limits for the displacement by adding nonlinear springs with a stiffness equal to kp when the limits are exceeded. This method is usually robust, but the accuracy is directly dependent on the chosen penalty factor.

The method adds extra degrees of freedom to improve the accuracy of the constraint. Here, the penalty factor is a numerical parameter, and has less impact on the accuracy of the constraint compared to when using the penalty method. The implementation of the augmented Lagrangian method puts no restrictions on the solver sequence, but for good convergence, proper scaling of the extra degrees of freedom can be important.

The default value for the kp depends on what type of entity the node is added to.

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For points, the default expression is 100*beam.Eequ*beam.area*beam.re^2/beam.<tag>.charLen^4

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For edges, the default expression is 100*beam.Eequ*beam.area*beam.re^2/beam.<tag>.charLen^3

In these expressions, beam is the tag of the Beam interface and <tag> is the tag of the Prescribed Displacement/Rotation node. The expressions are given as an estimation to the bending stiffness of the beam, where beam.Eequ is the equivalent Young’s modulus, beam.re is the equivalent radius of gyration, and beam.area is the cross-section area. The variable beam.<tag>.charLen is by default equal to the length of the mesh element. To improve the estimate of the penalty factor, replace beam.<tag>.charLen with the free length of the beam. The penalty factor can also be tuned by changing the multiplier at the beginning of each expression.


	For details about setting maximum and minimum limits for the displacements, see Limited Displacement

Prescribed Rotation


	For 2D models, to define a prescribed rotation select the Prescribed in out of plane direction check box and enter a value or expression for θ0z.

For 3D models, select a prescribed rotation from the list — or . Select:

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(the default) to leave the rotations unconstrained.

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to activate a prescribed rotation. Enter values or expressions for the prescribed rotation vector θ. When the study is geometrically linear, you directly prescribe the individual components of the rotation vector. Under , select one or several of the , , and check boxes to remove the constraint for the corresponding rotation component. If unchecked, the rotations are constrained to either the input value or to the default zero rotation. The status of the check boxes has no effect when geometric nonlinearity is activated under the study settings. This is because the constraints put on different rotation components are not independent of each other in the case of finite rotations. Here, θ should be interpreted as a rotation vector in the given coordinate system. The norm of the vector is the angle of rotation, and the orientation of the axis of rotation is given by the vector components.


	In a geometrically nonlinear analysis in 3D, you should prescribe all three components of the rotation vector. Prescribing only one or two components may not give unique results, since finite rotations are not commutative.

Constraint Settings

To display this section, click the button (

) and select in the dialog box.

In the COMSOL Multiphysics Reference Manual:

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Constraint Reaction Terms

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Weak Constraints

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Constraint Settings

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You can add a Harmonic Perturbation subnode for specifying a harmonic variation of the values of the prescribed displacements in a frequency domain analysis of perturbation type.

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You can activate and deactivate this boundary condition by assigning it to a constraint group. See Load Cases in the Structural Mechanics Modeling chapter.

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You can assign the value of the prescribed displacement to a load group. See Load Cases in the Structural Mechanics Modeling chapter.

Location in User Interface

Physics tab with or elected: