Coupling and Constraint EquationsModule 3

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October 30, 2001Inventory #0015713-*3. Coupling & Constraint EquationsJust 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. CouplingB. Constraint EquationsC. Workshop

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October 30, 2001Inventory #0015713-*Coupling & Constraint EquationsA. CouplingCoupling 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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October 30, 2001Inventory #0015713-*Coupling & Constraint Equations...CouplingCommon applications:Enforcing symmetryFrictionless interfacesPin joints

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October 30, 2001Inventory #0015713-*Coupling & Constraint Equations...CouplingEnforcing SymmetryCoupled 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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October 30, 2001Inventory #0015713-*Coupling & Constraint Equations...CouplingFrictionless interfacesA contact surface can be simulated using coupled DOF if all of the following are true:The surfaces are known to remain in contactThe analysis is geometrically linear (small deflections)Friction is to be neglectedThe node pattern is the same on both surfacesTo do this, couple each pair of coincident nodes in the normal direction.

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October 30, 2001Inventory #0015713-*Coupling & Constraint Equations...CouplingPin jointsCoupling 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.

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October 30, 2001Inventory #0015713-*Coupling & Constraint Equations...CouplingHow to create coupled setsThere 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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October 30, 2001Inventory #0015713-*Coupling & Constraint Equations...CouplingTo 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,uycouples all coincident nodes (within a default tolerance of 0.0001, csys dependent) in UY.

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October 30, 2001Inventory #0015713-*Coupling & Constraint Equations...CouplingTo 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, 0,30,0couples nodes with a 30 offset in all DOF (Note: Global cylindrical coordinate system in KCN field).

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October 30, 2001Inventory #0015713-*Coupling & Constraint Equations...CouplingSome 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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October 30, 2001Inventory #0015713-*Coupling & Constraint Equations...CouplingDemo: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 expansionSwitch to PREP7 and couple node pairs using CPCYC (Coupling/Ceqn > Offset Nodes > KCN = 1, DY = 30)SolveSet RSYS=1 and plot SXYShow expanded plotChange DSCALE=1, replot

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October 30, 2001Inventory #0015713-*Coupling & Constraint EquationsB. Constraint EquationsA 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

*Abaqus use constraints>equation

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October 30, 2001Inventory #0015713-*Coupling & Constraint Equations...Constraint EquationsCommon applications:Connecting dissimilar meshesConnecting dissimilar element typesCreating rigid regionsProviding Interference fits

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October 30, 2001Inventory #0015713-*Coupling & Constraint Equations...Constraint EquationsConnecting dissimilar meshesIf 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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October 30, 2001Inventory #0015713-*Coupling & Constraint Equations...Constraint EquationsConnecting dissimilar element typesIf you need to connect element types with different DOF sets, you may need to write CEs to transfer loads from one to the other:beams to solids or beams perpendicular to shellsshells to solidsetc.The CE command (Preprocessor > Coupling/Ceqn > Constraint Eqn) is typically used for such cases.

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October 30, 2001Inventory #0015713-*Coupling & Constraint Equations...Constraint EquationsCreating rigid regionsCEs 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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October 30, 2001Inventory #0015713-*Coupling & Constraint Equations...Constraint EquationsProviding Interference fitsSimilar 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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October 30, 2001Inventory #0015713-*Coupling & Constraint EquationsC. WorkshopThis workshop consists of three problems:W2A. Impeller BladeW2B. Turbine BladeW2C. SwaybarPlease refer to your Workshop Supplement for instructions.

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