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Coupling and Constraint Equations
Module 3
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Training Manual3. Coupling & Constraint Equations
• Just as DOF constraints allow you to constrain certain nodes in the model, coupling and constraint equations allow you to relate the motion of one node to another.
• In this chapter, we will discuss when and how to couple nodes or write constraint equations among them.
• Topics covered:
A. Coupling
B. Constraint Equations
C. Workshop
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Coupling & Constraint Equations
A. Coupling
• Coupling is a way to force a set of nodes to have the same DOF value.
– Similar to a constraint, except that the DOF value is usually calculated by the solver rather than user-specified.
– Example: If you couple nodes 1 and 2 in the UX direction, the solver will calculate UX for node 1 and simply assign the same UX value to node 2.
• A coupled set is a group of nodes coupled in one direction (i.e, one degree of freedom).
• You can define any number of coupled sets in a model, but do not include the same DOF in more than one coupled set.
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Coupling & Constraint Equations
...Coupling
Common applications:
• Enforcing symmetry
• Frictionless interfaces
• Pin joints
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...Coupling
Enforcing Symmetry
• Coupled DOF are often used to enforce translational or rotational symmetry. This ensures that plane sections remain plane. For example:
– To model one sector of a disc (cyclic symmetry), couple the node pairs on the two symmetry edges in all DOF.
– To model a half “tooth” of a comb-type model (translational symmetry), couple the nodes on one edge in all DOF.
Symmetry BCon this edge
Couple thesenodes in all DOF
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...Coupling
Frictionless interfaces
• A contact surface can be simulated using coupled DOF if all of the following are true:
– The surfaces are known to remain in contact
– The analysis is geometrically linear (small deflections)
– Friction is to be neglected
– The node pattern is the same on both surfaces
• To do this, couple each pair of coincident nodes in the normal direction.
X
Y
Couple eachnode pair in UY
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...Coupling
Pin joints
• Coupling can be used to simulate pin joints such as hinges and universal joints.
• This is done by means of a moment release: coupling translational DOF at a joint and leaving the rotational DOF uncoupled.
• For example, joint A below will be a hinge if the coincident nodes at A are coupled in UX and UY, leaving ROTZ uncoupled.
Coincident nodes, shownseparated for clarity.
A
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Coupling & Constraint Equations
...Coupling
How to create coupled sets
• There are several ways to do this. The one you choose depends on the application.
• To couple a set of nodes in a direction:
– Select the desired set.
– Then use CP command or Preprocessor > Coupling / Ceqn > Couple DOFs.
– For example, cp,,ux,all couples all selected nodes in the UX direction.
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...Coupling
• To couple coincident pairs of nodes:– First make sure all nodes to be coupled are selected.
– Then use CPINTF command or Preprocessor > Coupling / Ceqn > Coincident Nodes.
– For example,
cpintf,uy
couples all coincident nodes (within a default tolerance of 0.0001, csys dependent) in UY.
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...Coupling
• To couple node pairs that are offset by a distance, such as for cyclic symmetry:
– First make sure all nodes to be coupled are selected.
– Then use CPCYC command or Preprocessor > Coupling / Ceqn > Offset Nodes.
– For example,
cpcyc,all,,1, 0,30,0
couples nodes with a 30º offset in all DOF (Note: Global cylindrical coordinate system in KCN field).
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...Coupling
• Some points to keep in mind:
– The DOF directions (UX, UY, etc.) in a coupled set are in the nodal coordinate system.
– The solver retains the first DOF in the coupled set as the prime DOF and eliminates the rest.
– Forces applied on coupled nodes (in the coupled DOF direction) are summed and applied at the prime node.
– Constraints in the coupled DOF direction should only be applied to the prime node.
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Coupling & Constraint Equations
...Coupling
• Demo:
– Resume sector.db and solve (no coupled DOF)
– Set RSYS=1 and plot SXY. Notice “beam” behavior because of no coupling.
– Show expanded plot (using toolbar button EXPAND12), then turn off expansion
– Switch to PREP7 and couple node pairs using CPCYC (Coupling/Ceqn > Offset Nodes… > KCN = 1, DY = 30)
– Solve
– Set RSYS=1 and plot SXY
– Show expanded plot
– Change DSCALE=1, replot
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Coupling & Constraint Equations
B. Constraint Equations
• A constraint equation (CE) defines a linear relationship between nodal degrees of freedom.
– If you couple two DOFs, their relationship is simply UX1 = UX2.
– CE is a more general form of coupling and allows you to write an equation such as UX1 + 3.5*UX2 = 10.0.
• You can define any number of CEs in a model.
• Also, a CE can have any number of nodes and any combination of DOFs. Its general form is:
Coef1 * DOF1 + Coef2 * DOF2 + Coef3 * DOF3 + ... = Constant
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Coupling & Constraint Equations
...Constraint Equations
Common applications:
• Connecting dissimilar meshes
• Connecting dissimilar element types
• Creating rigid regions
• Providing Interference fits
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...Constraint Equations
Connecting dissimilar meshes
• If two meshed objects meet at a surface but their node patterns are not the same, you can create CEs to connect them.
• Easiest way to do this is with the CEINTF command (Preprocessor > Coupling/Ceqn > Adjacent Regions).
– Requires nodes from one mesh (usually the finer mesh) and elements from the other mesh to be selected first.
– Automatically calculates all necessary coefficients and constants.
– For solid elements to solid elements, 2-D or 3-D.
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...Constraint Equations
Connecting dissimilar element types
• If you need to connect element types with different DOF sets, you may need to write CE’s to transfer loads from one to the other:
– beams to solids or beams perpendicular to shells
– shells to solids
– etc.
• The CE command (Preprocessor > Coupling/Ceqn > Constraint Eqn) is typically used for such cases.
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...Constraint Equations
Creating rigid regions
• CEs are often used to “lump” together portions of the model into rigid regions.
• Applying the load to one node (the prime node) will transfer appropriate loads to all other nodes in the rigid region.
• Use the CERIG command (or Preprocessor > Coupling/Ceqn > Rigid Region).
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...Constraint Equations
Providing Interference fits
• Similar to contact coupling, but allows interference or gap between 2 surfaces.
• Typical equation:
0.01 = UX (node 51) - UX (node 251)
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Coupling & Constraint Equations
C. Workshop
• This workshop consists of three problems:
W2A. Impeller Blade
W2B. Turbine Blade
W2C. Swaybar
Please refer to your Workshop Supplement for instructions.
