Abaqus Coupling

35.3.2 Coupling constraints

Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE

References

Surfaces: overview, Section 2.3.1

*COUPLING

*KINEMATIC

*DISTRIBUTING

Defining coupling constraints, Section 15.15.4 of the Abaqus/CAE User's Guide

Overview

The surface-based coupling constraint:

couples the motion of a collection of nodes on a surface to the motion of a reference node;

is of type kinematic when the group of nodes is coupled to the rigid body motion defined by the referencenode;

is of type distributing when the group of nodes can be constrained to the rigid body motion defined by areference node in an average sense by allowing control over the transmission of forces through weightfactors specified at the coupling nodes;

automatically selects the coupling nodes located on a surface lying within a region of influence;

can be used with two- or three-dimensional stress/displacement elements; and

can be used in geometrically linear and nonlinear analysis.

Surface-based coupling definitions

The surface-based coupling constraint in Abaqus provides coupling between a reference node and a group ofnodes referred to as the coupling nodes. This option provides the same functionality as the kinematic couplingconstraint and the distributing coupling elements (DCOUP2D, DCOUP3D) in Abaqus/Standard with asurface-based user interface. The coupling nodes are selected automatically by specifying a surface and anoptional influence region. The procedure used to define the coupling nodes is discussed below.

For a distributing coupling constraint, the distributing weight factors are calculated automatically if the surface isan element-based surface. In such a case the weight factors are based on the tributary area at each coupling node,except for a surface along a shell edge, where the weight factors are based on the tributary edge length.Furthermore, the distributing weight factors can be modified using one of several weighting methods, whichallow the forces transferred to the coupling nodes to vary inversely with the radial distance from the referencenode.

Typical applications

The coupling constraint is useful when a group of coupling nodes is constrained to the rigid body motion of asingle node. The coupling constraint can be employed effectively in the following applications:

To apply loads or boundary conditions to a model. Figure 35.3.21 illustrates the use of a kinematic

35.3.2 Coupling constraints http://sawse01018:2080/v6.13/books/usb/pt08ch35s03aus133.html#us...

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coupling constraint to prescribe a twisting motion to a model without constraining the radial motion.

Figure 35.3.21 Kinematic coupling constraint.

Figure 35.3.22 illustrates a distributing coupling constraint used to prescribe a displacement and rotationcondition on a boundary where relative motion between the nodes on the boundary is required. In thisexample a twist is prescribed at the end of the structure that is expected to warp and/or deform within theend surface.

Figure 35.3.22 Distributing coupling constraint.

To distribute loads on a model, where the load distribution can be described with a moment-of-inertiaexpression. Examples of such cases include the classic bolt-pattern and weld-pattern distributionexpressions.

To apply dimensionality transitions between continuum and structural elements. For example, adistributing coupling allows flexible coupling between structural and solid elements.


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To model end conditions. For example, modeling a rigid end plate or modeling plane sections of a solid toremain planar can be done easily with a kinematic coupling definition.

To simplify modeling of complex constraints. In a kinematic coupling definition the degrees of freedomthat participate in the constraint may be selected individually in a local coordinate system.

To model interactions with other constraints, such as connector elements. For example, a hinged part maybe modeled more realistically by two distributing coupling definitions, whose reference nodes areconnected by a hinge connector element. The load transfer then occurs between two clouds of nodes,rather than between two single nodes. Substructure analysis of a one-piston engine model, Section4.1.10 of the Abaqus Example Problems Guide, illustrates this use of connector elements in conjunctionwith coupling constraints to model a one-piston engine.

Defining the coupling constraint

Defining a coupling constraint requires the specification of the reference node (also called the constraint controlpoint), the coupling nodes, and the constraint type. The coupling constraint associates the reference node withthe coupling nodes. A name must be assigned to the constraint and may be used in postprocessing withAbaqus/CAE. A node number or node set name may be specified for the reference node. If a node set isspecified, the node set must contain exactly one node. The reference node for a kinematic coupling constraint hasboth translational and rotational degrees of freedom. The surface on which the coupling nodes are located can benode-based; element-based; or, in Abaqus/Explicit, a combination of both surface types. You can specify anoptional radius of influence that limits the coupling nodes to a specific region on the surface. Details on howcoupling nodes are defined by specifying an influence region are discussed below.

The constraint type can be either kinematic or distributing, as discussed below.

Input File Usage: Use the following options:*COUPLING, CONSTRAINT NAME=name, REF NODE=n, SURFACE=surface*KINEMATIC or *DISTRIBUTING

Abaqus/CAE Usage: Interaction module: Create Constraint: Coupling: Coupling type: Kinematic orDistributing

Specifying a region of influence

By default, coupling nodes belonging to the entire surface are selected for the coupling definition. You can limitthe coupling nodes to lie within a spherical region centered about the reference node by defining a radius ofinfluence.

The procedure by which coupling nodes are selected for the constraint definition depends on the surface type:

For a node-based surface, all the nodes defined by the surface definition that fall within the influenceregion are selected for the coupling definitions.

For an element-based surface, the surface facets that are either fully or partially inscribed by the influenceregion are determined. All nodes belonging to these facets, whether or not these nodes fall within theinfluence region, are selected for the coupling nodes. When the influence radius is less than the distance tothe closest coupling node, Abaqus selects all nodes belonging to the closest facet. If the projection of thereference node on the surface falls on an edge or a vertex of multiple facets, all nodes belonging to thesefacets adjoining the edge or vertex are included in the coupling definition. In the case where the influenceradius is less than the distance to the closest coupling node, adjacent surface faces must have consistentnormal directions; otherwise, Abaqus issues an error message.


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A distributing coupling constraint must include at least two coupling nodes. If fewer than two couplingnodes are found, Abaqus issues an error message during input file preprocessing.

Input File Usage: *COUPLING, CONSTRAINT NAME=name, REF NODE=n, SURFACE=surface, INFLUENCE RADIUS=r

Abaqus/CAE Usage: Interaction module: Create Constraint: Coupling: Influence radius: Specify

Kinematic coupling constraints

Kinematic coupling constrains the motion of the coupling nodes to the rigid body motion of the reference node.The constraint can be applied to user-specified degrees of freedom at the coupling nodes with respect to theglobal or a local coordinate system.

Kinematic constraints are imposed by eliminating degrees of freedom at the coupling nodes. In Abaqus/Standardonce any combination of displacement degrees of freedom at a coupling node is constrained, additionaldisplacement constraintssuch as MPCs, boundary conditions, or other kinematic coupling definitionscannotbe applied to any coupling node involved in a kinematic coupling constraint. The same limitation applies forrotational degrees of freedom. This restriction does not apply in Abaqus/Explicit. See Kinematic constraints:overview, Section 35.1.1, for more information.

Input File Usage: Use both of the following options to define a kinematic coupling constraint:*COUPLING*KINEMATICfirst dof, last dof

For example, the following coupling constraint is used to constrain degrees of freedom1, 2, and 6 on surface surfA to reference node 1000:

*COUPLING, CONSTRAINT NAME=C1, REF NODE=1000, SURFACE=surfA*KINEMATIC1, 26,

Abaqus/CAE Usage: Interaction module: Create Constraint: Coupling: Coupling type: Kinematic: toggleon the degrees of freedom

Translational degrees of freedom

Translational degrees of freedom are constrained by eliminating the specified degrees of freedom at the couplingnodes. When all translational degrees of freedom are specified, the coupling nodes follow the rigid body motionof the reference node.

Rotational degrees of freedom

Rotational degrees of freedom are constrained by eliminating the specified degrees of freedom at the couplingnodes.

All combinations of selected rotational degrees of freedom result in rotational behavior identical to existing MPCtypes:

Selection of three rotational degrees of freedom along with three displacement degrees of freedom isequivalent to MPC type BEAM.


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Selection of two rotational degrees of freedom is equivalent to MPC type REVOLUTE inAbaqus/Standard.

Selection of one rotational degree of freedom is equivalent to MPC type UNIVERSAL inAbaqus/Standard.

In Abaqus/Standard internal nodes are created by the kinematic coupling to enforce the constraints that areequivalent to MPC types REVOLUTE and UNIVERSAL. These nodes have the same degrees of freedom as theadditional nodes used in these MPC types and are included in the residual check for nonlinear analysis.

Specifying a local coordinate system

The kinematic coupling constraint can be specified with respect to a local coordinate system instead of the globalcoordinate system (see Orientations, Section 2.2.5). Figure 35.3.21 illustrates the use of a local coordinatesystem to constrain all but the radial translation degrees of freedom of the coupling nodes to the reference node.In this example a local cylindrical coordinate system is defined that has its axis coincident with the structure'saxis. The coupling node constraints are then specified in this local coordinate system.

Input File Usage: *COUPLING, ORIENTATION=local

For example, the following input is used to specify the kinematic coupling constraintshown in Figure 35.3.21:

*ORIENTATION, SYSTEM=CYLINDRICAL, NAME=COUPLEAXIS0.0, -1.0, 0.0, 0.0, 1.0, 0.0*COUPLING, REF NODE=500, SURFACE=Endcap, ORIENTATION=COUPLEAXIS*KINEMATIC2, 3

Abaqus/CAE Usage: Interaction module: Create Constraint: Coupling: Edit: select local coordinate system

Constraint direction and finite rotation

In geometrically nonlinear analysis steps the coordinate system in which the constrained degrees of freedom arespecified will rotate with the reference node regardless of whether the constrained degrees of freedom arespecified in the global coordinate system or in a local coordinate system.

Distributing coupling constraints

Distributing coupling constrains the motion of the coupling nodes to the translation and rotation of the referencenode. This constraint is enforced in an average sense in a way that enables control of the transmission of loadsthrough weight factors at the coupling nodes. Forces and moments at the reference node are distributed either asa coupling node-force distribution only (default) or as a coupling node-force and moment distribution. Theconstraint distributes loads such that the resultants of the forces (and moments) at the coupling nodes areequivalent to the forces and moments at the reference node. For cases of more than a few coupling nodes, thedistribution of forces/moments is not determined by equilibrium alone, and distributing weight factors are usedto define the force distribution.

The moment constraint between the rotation degrees of freedom at the reference node and the average rotation ofthe cloud nodes can be released in one direction in a two-dimensional analysis and one, two, or three directionsin a three-dimensional analysis. In a three-dimensional analysis you can specify the moment constraint directionsin the global coordinate system or in a local coordinate system. All available translational degrees of freedom atthe reference node are always coupled to the average translation of the coupling nodes.


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In a three-dimensional Abaqus/Standard analysis if all three moment constraints are released by specifying onlydegrees of freedom 1 through 3, only translation degrees of freedom will be activated on the reference node. Ifonly one or two rotation degrees of freedom have been released, all three rotation degrees of freedom areactivated at the reference node. In this case you must ensure that proper constraints have been placed on theunconstrained rotation degrees of freedom to avoid numerical singularities. Most often this is accomplished byusing boundary conditions or by attaching the reference node to an element such as a beam or shell that willprovide rotational stiffness to the unconstrained rotation degrees of freedom.

In Abaqus/Explicit releasing one or more of the moment constraints may lead to significant computationalperformance degradation. This is also the case when other constraints intersect the cloud of coupling nodes. Inthese cases, the degradation in performance is particularly noticeable when a large number of such distributedcouplings are present in the model or when the size of the constrained cloud is large. For that matter, when themodeling conditions mentioned above are encountered, the size of the coupling nodes cloud is limited to 1000.To alleviate the released moment constraint issue, the following modeling technique can be used (also availablein Abaqus/Standard): constrain all moments in the distributed coupling and use an appropriate connector elementat the reference node (such as REVOLUTE, HINGE, CARDAN or BUSHING) to model released moments atthe coupling's reference node. This technique has also the advantage of being able to specify finite compliancesuch as elasticity, plasticity or damage in the released rotational component.

Input File Usage: *DISTRIBUTINGfirst dof, last dof

If no degrees of freedom are specified, all available degrees of freedom are coupled. Ifyou specify one or more rotation degrees of freedom but not all available translationdegrees of freedom, Abaqus issues a warning message and adds all available translationdegrees of freedom to the constraint.

For example, the following coupling constraint is used to constrain degrees of freedom15 on the reference node 1000 to the average translation and rotation of surfacesurfA:

*COUPLING, CONSTRAINT NAME=C1, REF NODE=1000, SURFACE=surfA*DISTRIBUTING1, 5

In this example the moment constraint between the reference node and the couplingnodes will be released in the 6-direction but will be enforced in the 4- and 5-directions.This provides a revolute-like rotation connection between the reference node and thecoupling nodes (see General multi-point constraints, Section 35.2.2).

Abaqus/CAE Usage: Interaction module: Create Constraint: Coupling: Coupling type: Distributing: toggleon the rotational degrees of freedom (Abaqus/CAE automatically constrains thetranslational degrees of freedom)

Node-based surface

User-defined weight factors are used for node-based surfaces. The cross-sectional areas specified in the surfacedefinition are used as the weight factors (see Node-based surface definition, Section 2.3.3).

Element-based surface

For element-based surfaces the weight factors are calculated by Abaqus. The default weight distribution is basedon the tributary surface area at each coupling node, except for a surface along a shell edge where the weightdistribution is based on the tributary edge length. The procedure used to calculate the default weight factors isdesigned to ensure that if a radius of influence is prescribed, the default weight distribution varies smoothly with


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the influence radius.

Calculating the default distributing weight factors

The procedure to calculate the distributing weight factors depends on whether or not an influence radius isspecified.

If no influence radius is specified, the entire surface is used in the coupling definition. In this case allnodes located on the surface are included in the coupling definition and the distributing weight factor ateach coupling node is equal to the tributary surface area.

If an influence radius is specified, the default distributing weight factors at the coupling nodes arecalculated as follows:

A participation factor is calculated for each surface facet. The participation factor is definedbelow.

1.

The tributary nodal area (or tributary edge length along a shell edge) at each facet node is computedand is multiplied by the facet participation factor.

2.

The coupling node distributing weight factor is computed as the sum of the corresponding facetnodal areas (calculated above) for all joining facets.

3.

Calculating the facet participation factor

The participation factor defines the proportion of the facet's area that contributes to the distributing weightfactors when an influence radius is specified. The participation factor varies between zero and one.

To define the participation factor, the distance of the facet node closest to the reference node, , and thedistance of the facet node farthest from the reference node, , are calculated.

If , where is the influence radius, all facet nodes lie within the influence region; and aparticipation factor of one is used.

If , none of the facet nodes lie within the influence region; and the participation factor is setto zero.

If , the facet is partially inscribed in the influence region; and the facet is assigned aparticipation factor equal to .

If all coupling nodes fall outside the influence radius (i.e., for all facets), Abaqus selects all nodesbelonging to the closest facets (as outlined under Specifying a region of influence) and uses a participationfactor equal to one.

Weighting methods

You can modify the default weight distribution defined above. Various weighting methods are provided thatmonotonically decrease with radial distance from the reference node. For each case the default weightdistribution that is based on the tributary surface area (or tributary edge length along a shell edge) is scaled bythe weight factor . If the weighting method is not specified, a uniform weighting method is used in which allweight factors are equal to 1.0.

Linearly decreasing weight distribution

A linearly decreasing weighting scheme


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where is the weight factor at coupling node i, is the coupling node radial distance from the reference node,and is the distance to the furthest coupling node.

Input File Usage: *DISTRIBUTING, WEIGHTING METHOD=LINEAR

Abaqus/CAE Usage: Interaction module: Create Constraint: Coupling: Coupling type: Distributing:Weighting method: Linear

Quadratic polynomial weight distribution

A quadratic polynomial weight distribution defined by

Input File Usage: *DISTRIBUTING, WEIGHTING METHOD=QUADRATIC

Abaqus/CAE Usage: Interaction module: Create Constraint: Coupling: Coupling type: Distributing:Weighting method: Quadratic

Monotonically decreasing weight distribution

A monotonically decreasing weight distribution according to the cubic polynomial

Input File Usage: *DISTRIBUTING, WEIGHTING METHOD=CUBIC

Abaqus/CAE Usage: Interaction module: Create Constraint: Coupling: Coupling type: Distributing:Weighting method: Cubic

Specifying a local coordinate system

The distributing coupling constraint can be specified with respect to a local coordinate system instead of theglobal coordinate system (see Orientations, Section 2.2.5). Figure 35.3.22 illustrates the use of a localcoordinate system to release the moment constraints between the reference node and the coupling nodes in thelocal 4- and 6-directions, providing a universal-like rotation connection. In this example a local rectangularcoordinate system is defined that has its local y-axis coincident with the global z-axis. The moment constraint isspecified in this local coordinate system.

Input File Usage: *COUPLING, ORIENTATION=local

For example, the following input is used to specify the distributing coupling constraintshown in Figure 35.3.22:

*ORIENTATION, SYSTEM=RECTANGULAR, NAME=COUPLEAXIS0.0, 1.0, 0.0, 0.0, 0.0, 1.0*COUPLING, REF NODE=500, SURFACE=Endcap, ORIENTATION=COUPLEAXIS


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*DISTRIBUTING1, 35, 5

Abaqus/CAE Usage: Interaction module: Create Constraint: Coupling: Edit: select local coordinate system

Defining the surface coupling method

There are two methods available to couple the motion of the reference node to the average motion of thecoupling nodes: the continuum coupling method and the structural coupling method. The continuum couplingmethod is used by default.

Continuum coupling method

The default continuum coupling method couples the translation and rotation of the reference node to the averagetranslation of the coupling nodes. The constraint distributes the forces and moments at the reference node as acoupling nodes force distribution only. No moments are distributed at the coupling nodes. The force distributionis equivalent to the classic bolt pattern force distribution when the weight factors are interpreted as bolt cross-section areas. The constraint enforces a rigid beam connection between the attachment point and a point locatedat the weighted center of position of the coupling nodes. For further details, see Distributing couplingelements, Section 3.9.8 of the Abaqus Theory Guide.

Input File Usage: *DISTRIBUTING , COUPLING=CONTINUUM

Abaqus/CAE Usage: Coupling the motion of the reference node to the average motion of the coupling nodes isnot supported in Abaqus/CAE.

Structural coupling method

The structural coupling method couples the translation and rotation of the reference node to the translation andthe rotation motion of the coupling nodes. The method is particularly suited for bending-like applications ofshells when the coupling constraint spans small patches of nodes and the reference node is chosen to be on orvery close to the constrained surface. The constraint distributes forces and moments at the reference node as acoupling node-force and moment distribution. For this coupling method to be active, all rotation degrees offreedom at all coupling nodes must be active (as would be the case when the constraint is applied to a shellsurface) and the constraints must be specified in all degrees of freedom (default). In addition, for the constraintto be meaningful, the local (or global) z-axis used in the constraint should be such that it is parallel to the averagenormal direction of the constrained surface.

With respect to translations, the constraint enforces a rigid beam connection between the reference node and amoving point that remains at all times in the vicinity of the constrained surface. The location of this movingpoint is determined by the approximate current curvature of the surface, the current location of the weightedcenter of position of the coupling nodes (see Distributing coupling elements, Section 3.9.8 of the AbaqusTheory Guide), and the z-axis used in the constraint. This choice avoids unrealistic contact interactions ifmultiple pairs of distributed coupling constraints are used to fasten shell surfaces (see Breakable bonds,Section 37.1.9, for more details).

With respect to rotations, the constraint is different along different local directions. Along the z-axis (twistdirection), the constraint is identical to the one enforced via the continuum coupling method (see Distributingcoupling elements, Section 3.9.8 of the Abaqus Theory Guide). By contrast, the rotational constraint in theplane perpendicular to the z-axis relates the in-plane reference node rotations to the in-plane rotations of thecoupling nodes in the immediate vicinity of the reference node. This choice provides a more realistic (compliant)response when the constrained surface is small and deforms primarily in a bending mode.


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Input File Usage: *DISTRIBUTING, COUPLING=STRUCTURAL

Abaqus/CAE Usage: Coupling the motion of the reference node to the average motion of the coupling nodes isnot supported in Abaqus/CAE.

Moment release and finite rotation

In geometrically nonlinear analysis steps the coordinate system of the degrees of freedom that define the momentrelease rotates with the reference node regardless of whether the global coordinate system or a local coordinatesystem is used.

Colinear coupling node arrangements

The distributing coupling constraint transmits moments at the reference node as a force distribution among thecoupling nodes, even if these nodes have rotational degrees of freedom. Thus, when the coupling nodearrangement is colinear, the constraint is not capable of transmitting all components of a moment at the referencenode. Specifically, the moment component that is parallel to the colinear coupling node arrangement will not betransmitted. When this case arises, a warning message is issued that identifies the axis about which the elementwill not transmit a moment.

Limitations

A distributing coupling constraint cannot be used with axisymmetric elements with asymmetricdeformation. This element type is not compatible with the distributing coupling constraint.

If a distributing coupling constraint is used with axisymmetric elements with twist, the constraint will notinclude the twist degree of freedom 5 in those elements. It will involve only the displacement degrees offreedom 1 and 2.

A distributing coupling definition with a large number of coupling nodes produces a large wavefront inAbaqus/Standard. This may result in significant memory usage and a long solution time to solve the finiteelement equilibrium equations.

A distributing coupling constraint cannot involve more than 46,000 degrees of freedom inAbaqus/Standard, which implies an upper limit of 23,000 nodes per constraint for two-dimensional andaxisymmetric cases and an upper limit of 15,333 nodes per constraint for three-dimensional cases.


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