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ABAQUS的接触问题中，Tie、MPC和Coupling的区别和使用原则
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作者：梵音静思　　出处：技术邻　　阅读：1899　　推荐：0
依个人经验和理解，针对ABAQUS的接触问题中，Tie、MPC和Coupling的区别和使用原则在此做个总结。不足之处，希望多多评改...
依个人经验和理解，针对ABAQUS的接触问题中，Tie、MPC和Coupling的区别和使用原则在此做个总结。不足之处，希望多多评改。TKS!
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Tie：在刚度数据传递上相当于两个面刚性连接，绑定区域不发生相对运动和变形，刚度较大； 在约束形式上tie约束为面对面的约束，主要是用于点（一个或多个，但不能是RP） 和面以及面与面之间的绑定约束，用悬臂梁算模态的方法，测试RP和面之间用tie绑定完全没效果。
Coupling：可以理解为对接触问题的一种简化方式。Coupling可用于建立参考点（只测试过RP点）和关注对象之间（耦合点）的约束，关注对象和参考点之间有相同的刚体运动，可以在参考点上施加约束载荷。在约束形式上coupling为点对面的一中约束。
其中，coupling分为两种：运动耦合和分布耦合
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版权所有：中国CAE联盟 Copyright
　All Rights Reservedcoupling分为两种：运动耦合和分布耦合
coupling分为两种：运动耦合和分布耦合；是对接触问题的一种简化方式，一般来讲，分布耦合处的刚度小于运动耦合处的刚度；
【1】运动耦合：即在此区域的各节点与参考点之间建立一种运动上的约束关系。
【2】分布耦合：
在此区域的各节点与参考点之间建立一种约束关系，但是对此区域上各节点的运动进行了加权处理，使在此区域上受到的合力和合力距与施加在参考点上的力和力矩相等效。换言之，分布耦合允许面上的各部分之间发生相对变形，比运动耦合中的面更柔软。
31.3.2 Coupling constraints
Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE
References
The surface-based coupling constraint:
couples the motion of a collection of nodes on a surface to the
is of type kinematic when the group of nodes is coupled to the
rigid body motion defined b
is of type distributing when the group of nodes can be
constrained to the rigid body motion defined by a reference node in
an average sense by allowing control over the transmission of
forces through weight factors specified a
automatically selects the coupling nodes located on a surface
lying within a
can be used with two- or three-dimensional stress/displacement
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 of nodes referred to
as the “coupling nodes.” This option provides the same
functionality as the kinematic coupling constraint and the
distributing coupling elements (DCOUP2D, DCOUP3D) in
Abaqus/Standard with a surface-based user interface. The coupling
nodes are selected automatically by specifying a surface and an
optional 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 is an
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, which allow
the forces transferred to the coupling nodes to vary inversely with
the radial distance from the reference node.
Typical applications
The coupling constraint is useful when a group of coupling nodes
is constrained to the rigid body motion of a single node. The
coupling constraint can be employed effectively in the following
applications:
To apply loads or boundary conditions to a model.
illustrates the use of a kinematic coupling
constraint to prescribe a twisting motion to a model without
constraining the radial motion.
31.3.2&1 Kinematic coupling constraint.
illustrates a distributing coupling constraint used to
prescribe a displacement and rotation condition on a boundary where
relative motion between the nodes on the boundary is required. In
this example a twist is prescribed at the end of the structure that
is expected to warp and/or deform within the end surface.
31.3.2&2 Distributing coupling constraint.
To distribute loads on a model, where the load distribution can
be described with a moment-of-inertia expression. Examples of such
cases include the classic bolt-pattern and weld-pattern
distribution expressions.
To apply dimensionality transitions between continuum and
structural elements. For example, a distributing coupling allows
flexible coupling between structural and solid elements.
To model end conditions. For example, modeling a rigid end plate
or modeling plane sections of a solid to remain planar can be done
easily with a kinematic coupling definition.
To simplify modeling of complex constraints. In a kinematic
coupling definition the degrees of freedom that participate in the
constraint may be selected individually in a local coordinate
To model interactions with other constraints, such as connector
elements. For example, a hinged part may be modeled more
realistically by two distributing coupling definitions, whose
reference nodes are connected by a hinge connector element. The
load transfer then occurs between two “clouds” of nodes, rather
than between two single nodes. , illustrates this use of
connector elements in conjunction with 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 control point), the
coupling nodes, and the constraint type. The coupling constraint
associates the reference node with the coupling nodes. A name must
be assigned to the constraint and may be used in postprocessing
with Abaqus/CAE. A node number or node set name may be specified
for the reference node. If a node set is specified, the node set
must contain exactly one node. The reference node for a kinematic
coupling constraint has both translational and rotational degrees
of freedom. The surface on which the coupling nodes are located can
be node- element- or, in Abaqus/Explicit, a combination
of both surface types. You can specify an optional radius of
influence that limits the coupling nodes to a specific region on
the surface. Details on how coupling 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
, CONSTRAINT NAME=name, REF NODE=n,
SURFACE=surface
Abaqus/CAE Usage:
Interaction module: Create Constraint: Coupling: Coupling type:
Kinematic or
Distributing
Specifying a region of influence
By default, coupling nodes belonging to the entire surface are
selected for the coupling definition. You can limit the coupling
nodes to lie within a spherical region centered about the reference
node by defining a radius of influence.
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 influence region are selected for
the coupling definitions.
For an element-based surface, the surface facets that are either
fully or partially inscribed by the influence region are
determined. All nodes belonging to these facets, whether or not
these nodes fall within the influence region, are selected for the
coupling nodes. When the influence radius is less than the distance
to the closest coupling node, Abaqus selects all nodes belonging to
the closest facet. If the projection of the reference node on the
surface falls on an edge or a vertex of multiple facets, all nodes
belonging to these facets adjoining the edge or vertex are included
in the coupling definition.
A distributing coupling constraint must include at least two
coupling nodes. If fewer than two coupling nodes are found, Abaqus
issues an error message during input file preprocessing.
Input File Usage:
, CONSTRAINT NAME=name, REF NODE=n,
SURFACE=surface, INFLUENCE RADIUS=r
Abaqus/CAE Usage:
Interaction module: Create Constraint: Coupling: Influence radius:
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 the global or a local coordinate system.
Kinematic constraints are imposed by eliminating degrees of
freedom at the coupling nodes. In Abaqus/Standard once any
combination of displacement degrees of freedom at a coupling node
is constrained, additional displacement constraints—such as MPCs,
boundary conditions, or other kinematic coupling definitions—cannot
be applied to any coupling node involved in a kinematic coupling
constraint. The same limitation applies for rotational degrees of
freedom. This restriction does not apply in Abaqus/Explicit. See
more information.
Input File Usage:
Use both of the
following options to define a kinematic coupling
constraint:
first dof, last dof
For example, the following coupling constraint is used to
constrain degrees of freedom 1, 2, and 6 on surface surfA to reference node 1000:
, CONSTRAINT NAME=C1, REF NODE=1000, SURFACE=surfA
Abaqus/CAE Usage:
Interaction module: Create Constraint: Coupling: Coupling type:
Kinematic:
toggle on the degrees of freedom
Translational degrees of freedom
Translational degrees of freedom are constrained by eliminating
the specified degrees of freedom at the coupling nodes. When all
translational degrees of freedom are specified, the coupling nodes
follow the rigid body motion of the reference node.
Rotational degrees of freedom
Rotational degrees of freedom are constrained by eliminating the
specified degrees of freedom at the coupling nodes.
All combinations of selected rotational degrees of freedom
result in rotational behavior identical to existing MPC types:
Selection of three rotational degrees of freedom along with
three displacement degrees of freedom is equivalent to MPC type
Selection of two rotational degrees of freedom is equivalent to
MPC type REVOLUTE in
Abaqus/Standard.
Selection of one rotational degree of freedom is equivalent to
MPC type UNIVERSAL in
Abaqus/Standard.
In Abaqus/Standard internal nodes are created by the kinematic
coupling to enforce the constraints that are equivalent to MPC
types REVOLUTE and UNIVERSAL. These nodes have the same degrees of
freedom as the additional 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 global coordinate
system (see ).
illustrates the use of a local coordinate
system 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's axis. The coupling node
constraints are then specified in this local coordinate system.
Input File Usage:
, ORIENTATION=local
For example, the following input is used to specify the kinematic
coupling constraint shown in :
, SYSTEM=CYLINDRICAL, NAME=COUPLEAXIS
0.0, -1.0, 0.0, 0.0, 1.0, 0.0
, REF NODE=500, SURFACE=Endcap,
ORIENTATION=COUPLEAXIS
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 are specified will
rotate with the reference node regardless of whether the
constrained degrees of freedom are specified 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 reference node. This
constraint is enforced in an average sense in a way that enables
control of the transmission of loads through weight factors at the
coupling nodes. Forces and moments at the reference node are
distributed either as a coupling node-force distribution only
(default) or as a coupling node-force and moment distribution. The
constraint distributes loads such that the resultants of the forces
(and moments) at the coupling nodes are equivalent to the forces
and moments at the reference node. For cases of more than a few
coupling nodes, the distribution of forces/moments is not
determined by equilibrium alone, and distributing weight factors
are used to define the force distribution.
The moment constraint between the rotation degrees of freedom at
the reference node and the average rotation of the cloud nodes can
be released in one direction in a two-dimensional analysis and one,
two, or three directions in a three-dimensional analysis. In a
three-dimensional analysis you can specify the moment constraint
directions in the global coordinate system or in a local coordinate
system. All available translational degrees of freedom at the
reference node are always coupled to the average translation of the
coupling nodes.
In a three-dimensional Abaqus/Standard analysis if all three
moment constraints are released by specifying only degrees of
freedom 1 through 3, only translation degrees of freedom will be
activated on the reference node. If only one or two rotation
degrees of freedom have been released, all three rotation degrees
of freedom are activated at the reference node. In this case you
must ensure that proper constraints have been placed on the
unconstrained rotation degrees of freedom to avoid numerical
singularities. Most often this is accomplished by using boundary
conditions or by attaching the reference node to an element such as
a beam or shell that will provide rotational stiffness to the
unconstrained rotation degrees of freedom.
In Abaqus/Explicit releasing one or more of the moment
constraints may lead to significant computational performance
degradation. This is also the case when other constraints intersect
the cloud of coupling nodes. In these cases, the degradation in
performance is particularly noticeable when a large number of such
distributed couplings are present in the model or when the size of
the constrained “cloud” is large. For that matter, when the
modeling 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 available in Abaqus/Standard): constrain all
moments in the distributed coupling and use an appropriate
connector element at the reference node (such as REVOLUTE, HINGE, CARDAN or BUSHING) to model released moments at the
coupling's reference node. This technique has also the advantage of
being able to specify finite compliance such as elasticity,
plasticity or damage in the “released” rotational component.
Input File Usage:
first dof, last dof
If no degrees of freedom are specified, all available degrees of
freedom are coupled. If you specify one or more rotation degrees of
freedom but not all available translation degrees of freedom,
Abaqus issues a warning message and adds all available translation
degrees of freedom to the constraint.
For example, the following coupling constraint is used to
constrain degrees of freedom 1&5 on the reference node 1000 to the
average translation and rotation of surface surfA:
, CONSTRAINT NAME=C1, REF NODE=1000, SURFACE=surfA
In this example the moment constraint between the reference node
and the coupling nodes 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
the coupling nodes (see ).
Abaqus/CAE Usage:
Interaction module: Create Constraint: Coupling: Coupling type:
Distributing:
toggle on the rotational degrees of freedom (Abaqus/CAE
automatically constrains the translational degrees of freedom)
Node-based surface
User-defined weight factors are used for node-based surfaces.
The cross-sectional areas specified in the surface definition are
used as the weight factors (see ).
Element-based surface
For element-based surfaces the weight factors are calculated by
Abaqus. The default weight distribution is based on the tributary
surface area at each coupling node, except for a surface along a
shell edge where the weight distribution is based on the tributary
edge length. The procedure used to calculate the default weight
factors is designed to ensure that if a radius of influence is
prescribed, the default weight distribution varies smoothly with
the influence radius.
Calculating the default distributing weight
The procedure to calculate the distributing weight factors
depends on whether or not an influence radius is specified.
If no influence radius is specified, the entire surface is used
in the coupling definition. In this case all nodes located on the
surface are included in the coupling definition and the
distributing weight factor at each coupling node is equal to the
tributary surface area.
If an influence radius is specified, the default distributing
weight factors at the coupling nodes are calculated as follows:
A “participation factor” is calculated for each surface facet.
The participation factor is defined below.
The tributary nodal area (or tributary edge length along a shell
edge) at each facet node is computed and is multiplied by the facet
participation factor.
The coupling node distributing weight factor is computed as the
sum of the corresponding facet nodal areas (calculated above) for
all joining facets.
Calculating the facet participation factor
The participation factor defines the proportion of the facet's
area that contributes to the distributing weight factors 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 the distance of the facet node
farthest from the reference node, , are calculated.
If , where
is the influence radius, all facet nodes
lie within
and a participation factor of one
If , none of the facet nodes lie within the
and the participation factor is set to zero.
If , the facet is partially inscribed in the
and the facet is assigned a participation factor
equal to .
If all coupling nodes fall outside the influence radius (i.e.,
for all facets), Abaqus selects all nodes
belonging to the closest facets (as outlined under “Specifying a
region of influence”) and uses a participation factor equal to one.
Weighting methods
You can modify the default weight distribution defined above.
Various weighting methods are provided that monotonically decrease
with radial distance from the reference node. For each case the
default weight distribution that is based on the tributary surface
area (or tributary edge length along a shell edge) is scaled by the
weight factor . If the weighting method is not
specified, a uniform weighting method is used in which all weight
factors are equal to 1.0.
Linearly decreasing weight distribution
A linearly decreasing weighting scheme
is the weight factor at coupling node
is the coupling node radial distance from
the reference node, and
is the distance to the furthest coupling
Input File Usage:
, WEIGHTING METHOD=LINEAR
Abaqus/CAE Usage:
Interaction module: Create Constraint: Coupling: Coupling type:
Distributing:
method: Linear
Quadratic polynomial weight distribution
A quadratic polynomial weight distribution defined by
Input File Usage:
, WEIGHTING METHOD=QUADRATIC
Abaqus/CAE Usage:
Interaction module: Create Constraint: Coupling: Coupling type:
Distributing:
method: Quadratic
Monotonically decreasing weight distribution
A monotonically decreasing weight distribution according to the
cubic polynomial
Input File Usage:
, WEIGHTING METHOD=CUBIC
Abaqus/CAE Usage:
Interaction module: Create Constraint: Coupling: Coupling type:
Distributing:
method: Cubic
Specifying a local coordinate system
The distributing coupling constraint can be specified with
respect to a local coordinate system instead of the global
coordinate system (see ).
illustrates the use of a local coordinate
system to release the moment constraints between the reference node
and the coupling nodes in the local 4- and 6-directions, providing
a “universal-like” rotation connection. In this example a local
rectangular coordinate system is defined that has its local
y-axis coincident with the
global z-axis. The moment
constraint is specified in this local coordinate system.
Input File Usage:
, ORIENTATION=local
For example, the following input is used to specify the
distributing coupling constraint shown in :
, SYSTEM=RECTANGULAR, NAME=COUPLEAXIS
0.0, 1.0, 0.0, 0.0, 0.0, 1.0
, REF NODE=500, SURFACE=Endcap,
ORIENTATION=COUPLEAXIS
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 the coupling nodes: the
continuum coupling method and the structural coupling method. The
continuum coupling method is used by default.
Continuum coupling method
The default continuum coupling method couples the translation
and rotation of the reference node to the average translation of
the coupling nodes. The constraint distributes the forces and
moments at the reference node as a coupling nodes force
distribution only. No moments are distributed at the coupling
nodes. The force distribution is 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 located at the
weighted center of position of the coupling nodes. For further
details, see .
Input File Usage:
, COUPLING=CONTINUUM
Abaqus/CAE Usage:
Coupling the motion of the reference node to the
average motion of the coupling nodes is not supported in
Abaqus/CAE.
Structural coupling method
The structural coupling method couples the translation and
rotation of the reference node to the translation and the rotation
motion of the coupling nodes. The method is particularly suited for
bending-like applications of shells when the coupling constraint
spans small patches of nodes and the reference node is chosen to be
on or very close to the constrained surface. The constraint
distributes forces and moments at the reference node as a coupling
node-force and moment distribution. For this coupling method to be
active, all rotation degrees of freedom at all coupling nodes must
be active (as would be the case when the constraint is applied to a
shell surface) and the constraints must be specified in all degrees
of freedom (default). In addition, for the constraint to be
meaningful, the local (or global) z-axis used in the constraint should be
such that it is parallel to the average normal direction of the
constrained surface.
With respect to translations, the constraint enforces a rigid
beam connection between the reference node and a moving point that
remains at all times in the vicinity of the constrained surface.
The location of this moving point is determined by the approximate
current curvature of the surface, the current location of the
weighted center of position of the coupling nodes (see ), and the z-axis
used in the constraint. This choice avoids unrealistic contact
interactions if multiple pairs of distributed coupling constraints
are used to fasten shell surfaces (see , for more details).
With respect to rotations, the constraint is different along
different local directions. Along the z-axis (twist direction), the
constraint is identical to the one enforced via the continuum
coupling method (see ). By contrast, the rotational constraint in the plane
perpendicular to the z-axis
relates the in-plane reference node rotations to the in-plane
rotations of the coupling 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.
Input File Usage:
, COUPLING=STRUCTURAL
Abaqus/CAE Usage:
Coupling the motion of the reference node to the
average motion of the coupling nodes is not 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 moment release rotates
with the reference node regardless of whether the global coordinate
system or a local coordinate system is used.
Colinear coupling node arrangements
The distributing coupling constraint transmits moments at the
reference node as a force distribution among the coupling nodes,
even if these nodes have rotational degrees of freedom. Thus, when
the coupling node arrangement is colinear, the constraint is not
capable of transmitting all components of a moment at the reference
node. Specifically, the moment component that is parallel to the
colinear coupling node arrangement will not be transmitted. When
this case arises, a warning message is issued that identifies the
axis about which the element will not transmit a moment.
Limitations
A distributing coupling constraint cannot be used with
axisymmetric elements with asymmetric deformation. This element
type is not compatible with the distributing coupling
constraint.
A distributing coupling definition with a large number of
coupling nodes produces a large wavefront in Abaqus/Standard. This
may result in significant memory usage and a long solution time to
solve the finite element equilibrium equations.
A distributing coupling constraint cannot involve more than
46,000 degrees of freedom in Abaqus/Standard, which implies an
upper limit of 23,000 nodes per constraint for two-dimensional and
axisymmetric cases and an upper limit of 15,333 nodes per
constraint for three-dimensional cases.
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