Coupling and
Coupling and
Constraint Equations
in the model, coupling and constraint equations allow you to
relate
the motion of one node to another.
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In this chapter, we will discuss when and how to couple
nodes or write constraint equations among them.
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Topics covered:
A. Coupling
B. Constraint Equations C. Workshop
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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.
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A
coupled set
is a group of nodes coupled in one direction
(i.e, one degree of freedom).
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You can define any number of coupled sets in a model, but
Common applications:
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Enforcing symmetry
•Frictionless interfaces
•Pin joints
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 BC
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 each node pair in UY
Pin joints
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Coupling can be used to simulate pin joints such as hinges
and universal joints.
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This is done by means of a
moment release:
coupling
translational DOF at a joint and leaving the rotational DOF
uncoupled.
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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, shown separated for clarity.
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
• 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.
• 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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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
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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
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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.
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You can define any number of CEs in a model.
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Also, a CE can have any number of nodes and any
combination of DOFs. Its general form is:
Common applications:
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Connecting dissimilar meshes
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Connecting dissimilar element types
•Creating rigid regions
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,
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
Creating rigid regions
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CEs are often used to “lump” together portions of the model
into
rigid regions
.
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Applying the load to one node (the prime node) will transfer
appropriate loads to all other nodes in the rigid region.
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Use the CERIG command (or Preprocessor > Coupling/Ceqn >
Providing Interference fits
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Similar to contact coupling, but allows interference or gap
between 2 surfaces.
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Typical equation:
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This workshop consists of three problems:
W2A. Impeller Blade W2B. Turbine Blade W2C. Swaybar
