The distributing coupling element constrains the motion of the coupling
nodes to the translation and rotation of the element node. This constraint is
enforced in an average sense and in a way that enables control of the
transmission of loads. These characteristics make the distributing coupling
element useful in a number of applications:
The element can be used to prescribe a displacement and rotation
condition on a boundary in cases where relative motion among the nodes on the
boundary is required. An example of such a case is prescribing a twist on the
end of a structure that is expected to warp and/or deform within the end
surface (see
Figure 1).
DCOUP3D element used to impart a rotation on the surface of a structure
without constraining motion within the surface.
The element can be used to provide, through the motion of the reference
node, a weighted average of the motion of the coupling nodes.
The element can be used to distribute loads, where the load distribution
can be described with moment-of-inertia expressions. Examples of such cases
include the classic bolt-pattern and weld-pattern load distribution
expressions.
The element can be used as a coupling between two parts
(structural-solid) to transfer forces and moments. In comparison to
MPCs and the kinematic coupling constraint,
the distributing coupling element can be considered a more “flexible”
connection.
Choosing an Appropriate Element
Two- and three-dimensional distributing coupling elements are available.
Element DCOUP2D describes behavior only in the global
X–Y plane. Element DCOUP2D can be used in an axisymmetric analysis; however, its use
requires care in selecting the load distributing weight factors. For example, a
uniform axial load distribution to a structure would require specification of
load distribution weight factors in proportion to the radius of the coupling
nodes. Since the radius of these nodes will change with deformation, this use
of DCOUP2D would only approximate the correct load distribution behavior in
a large-displacement analysis.
Defining the Distributing Coupling
To define a distributing coupling, you specify the coupling nodes to which
loads are to be distributed, along with the corresponding weighting of the
distribution. A minimum of two coupling nodes is required.
Example
This example (see
Figure 1)
illustrates the use of the DCOUP3D element to impart a rotation to the surface of a structure that
is expected to deform in a general way. In this case warping and motion within
the plane of the end surface are expected to occur.
The element distributes loads such that the resultants of the forces on the
coupling nodes are equal to the forces and moments on the element node. For
cases of more than a few coupling nodes, the distribution of the forces is not
determined by equilibrium alone, and the user-specified weight factors are used
to define the distribution. The weight factors are dimensionless and are
normalized within each element so that the sum of all weight factors is one. As
a consequence, the normalized weight factors describe the proportion of the
total element force and moment that is transmitted through the particular
coupling node. In the case of transmission of forces alone, the proportion of
force transmitted through the node is simply the normalized weight factor. In
the general case of transmission of forces and moments, the force distribution
follows that of a classic bolt-pattern analysis, where the weight factors could
be considered the areas of particular bolt cross-sections. Refer to
Distributing coupling constraints
for specific details of the load distribution.
In the example shown in
Figure 1
the weight factor distribution chosen is homogeneous, with a value of 1.0. For
the rotation depicted, a more accurate load distribution would reflect the fact
that the shear forces on nodes near the edge of the slot will diminish to zero,
which could be described by choosing individual weight factors for nodes near
the slot edge. If the loading on the element were along the axis of the
structure, the homogeneous distribution shown would be appropriate. For cases
where different loading modes require different descriptions of the weight
factor distribution, multiple distributing coupling elements with different
element nodes and different weight factors can be used.
Colinear Coupling Node Arrangements
The distributing coupling element transmits moments at the element 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 element is not capable of transmitting all components of a moment
at the element 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.
Use with Nonuniform Meshes
When the distributing coupling element is used with coupling nodes attached
to elements of varying size, care should be taken in selecting the weight
factors. The weight factor selected for a node should generally scale with the
size of the elements attached to that node.
Processing of Unattached Nodes
Cloud nodes that have no stiffness cause numerical singularities in Abaqus/Standard analyses. You can guide Abaqus/Standard to provide proper management of such nodes. By default, Abaqus/Standard issues an error message. You can direct Abaqus/Standard to remove or allow nodes that are not attached to any user elements. You should keep
unattached nodes if they derive their stiffness by being main nodes to other nodes that have
stiffness.
Output
Element nodal forces (the force the element places on the element and
coupling nodes) are available through element variable NFORC. Element kinetic energy is available in dynamic procedures
through the whole element variable ELKE.
