A gasket element is basically composed of two surfaces (a bottom and a top
surface) separated by the gasket thickness. The element has nodes on its bottom
face and corresponding nodes on its top face.
Two methods are available to define the element geometry.
By Defining the Element's Nodes
You can define the geometry of the gasket element by defining the
coordinates of all the element's nodes. You can define elements with constant
or varying thickness. If the gasket element is very thin in comparison to
dimensions in its surfaces, the thickness of the element calculated from the
nodal coordinates may be inaccurate. In this case you can specify a constant
thickness directly.
By Defining the Bottom Surface of the Element
You can specify a list of only the nodes on the bottom surface of the gasket
element and the positive offset number that will be used to define the
corresponding nodes on the top surface of the gasket element.
Abaqus/Standard
will create the nodes of the top face coincident with those of the bottom face
unless the nodes of the top face have already been assigned coordinates. If the
bottom and top nodes coincide, you must specify the thickness of the gasket
element.
Specifying the Element Thickness
You can specify the gasket element thickness as part of its section property
definition.
Additional Quantities Needed to Specify the Element Geometry
For three-dimensional area elements, the element geometry is defined
entirely by the location of the top and bottom surfaces and the element
thickness. For two- and three-dimensional link elements (elements with two
nodes, one on each face) you should specify the cross-sectional area of the
element. For axisymmetric link elements you should specify the width of the
element. For general two-dimensional elements the out-of-plane thickness is
required. For three-dimensional line elements you should also specify the width
of the element. This additional information is specified as part of the gasket
section property definition; if it is not specified but is needed, it is
assumed to have a value of 1.0.
Default Element Thickness-Direction Definition
Gaskets are usually manufactured to have a desired behavior in their
thickness direction. Therefore, it is important to define the thickness
directions of gasket elements accurately.
Abaqus/Standard
computes these directions by default. The method that
Abaqus/Standard
uses depends on the gasket element type.
Link Elements
Abaqus/Standard
computes the thickness direction for a two-dimensional, three-dimensional, or
axisymmetric link element by subtracting the coordinates of node 1 from those
of node 2, as shown in
Figure 1.
The computed thickness direction is then assigned to each node. If the gasket
element is very thin, the thickness direction may not be predicted accurately.
You can overwrite this direction, as explained below in
Specifying the Thickness Direction Explicitly.
Two-Dimensional and Axisymmetric Elements
To compute the thickness direction for two-dimensional and axisymmetric
elements,
Abaqus/Standard
forms a midsurface by averaging the coordinates of the node pairs forming the
bottom and top surfaces of the element. This midsurface passes through the
integration points of the element, as shown in
Figure 2.
For each integration point
Abaqus/Standard
computes a tangent whose direction is defined by the sequence of nodes given on
the bottom and top surfaces. The thickness direction is then obtained as the
cross product of the out-of-plane and tangent directions. The thickness
direction computed at each integration point is then assigned to the nodes on
either side of the integration point.
Three-Dimensional Area Elements
To compute the thickness direction for three-dimensional area elements,
Abaqus/Standard
forms a midsurface by averaging the coordinates of the node pairs forming the
bottom and top surfaces of the element. This midsurface passes through the
integration points of the element, as shown in
Figure 3.
Abaqus/Standard
computes the thickness direction to the midsurface at each integration point;
the positive direction is obtained with the right-hand rule going around the
nodes of the element on the bottom or top surface. The thickness direction
computed at each integration point is assigned to the nodes on either side of
the integration point.
Three-Dimensional Line Elements
To compute the thickness direction for three-dimensional line elements,
Abaqus/Standard
computes the thickness direction at each integration point of the line element
by differencing the coordinates of the element's surface nodes associated with
the integration point. The thickness direction will point from the node on the
bottom face to the node on the top face of the element. The thickness direction
computed at each integration point is then assigned to the nodes on either side
of the integration point (see
Figure 4).
If the gasket element is very thin, the computation of the thickness
direction may not be accurate. You can overwrite this definition as explained
below in
Specifying the Thickness Direction Explicitly.
Creating a Smooth Gasket
Gasket elements can be used in a single layer or can be stacked in multiple
layers (see
Including Gasket Elements in a Model
for further details). The thickness directions computed at the nodes of gasket
elements on an element-by-element basis are averaged at nodes shared by two or
more gasket elements. This averaging process ensures that, if the gasket is not
planar, it has a thickness direction that varies smoothly even though the
gasket has been discretized by elements. You must ensure that the
connectivities of the elements are such that the thickness direction does not
reverse from one element to the next for this process to work properly. Once
the averaging process is complete, the thickness directions at the nodes of a
given element may vary significantly along the gasket midsurface and through
its thickness, as shown in
Figure 5.
The thickness directions at any of the nodes of an element should not vary in
direction by more than 20°. In addition, the thickness directions of two
associated nodes through the thickness direction should not vary in direction
by more than 5°.
Abaqus/Standard
will require that the gasket be remeshed when such conditions are not met.
Specifying the Thickness Direction Explicitly
For cases when the above averaging process is not satisfactory, two methods
are provided to specify the thickness direction of gasket elements.
Specifying the Thickness Direction as Part of the Gasket Section Definition
You can specify the components of the thickness direction as part of the
gasket section definition. In this case all nodes of the gasket elements using
this section definition are assigned the same thickness direction. The
thickness direction specified at the nodes of the element will be averaged at
nodes shared by two or more elements.
Specifying the Thickness Direction by Specifying a Normal Direction at the Nodes
You can define the thickness direction at a particular integration point
of a gasket element by specifying a normal direction for the node on the bottom
face of the element that is associated with the integration point (see
Normal Definitions at Nodes).
The thickness direction will not be averaged if this node belongs to more than
one element. The thickness direction specified at the bottom node will also be
assigned at the top node associated with the same integration point. This
thickness direction will not be averaged if the top node belongs to more than
one element; however, you can overwrite this thickness direction by specifying
a normal at this node if it is the bottom node of another element. This last
situation can occur only in cases when gasket elements are stacked up through
the thickness direction of the gasket. If this method is used to specify
conflicting thickness directions at the same node,
Abaqus/Standard
will issue an error message. Thickness directions specified using this method
will overwrite any thickness directions specified at a gasket node as part of
the gasket section definition.
Creating Fold Lines
It is possible to introduce a fold line in a gasket by creating gaskets with
coincident nodes and using MPC type TIE or PIN (General Multi-Point Constraints)
to constrain the displacement of these nodes. However, fold lines are rarely
needed in the analysis of gaskets, since almost all gaskets are manufactured
with smoothly varying surfaces.
Verifying the Thickness Direction
Thickness direction definitions can be checked by examining the
analysis input file processor
output. The direction cosines of the thickness directions obtained at the nodes
of gasket elements are listed under GASKET THICKNESS
DIRECTIONS in the data (.dat) file.
Specifying an Initial Gap and an Initial Void in the Thickness Direction of a Gasket Element
The construction of gaskets in their through-thickness direction may be
complex; for example, certain automotive gaskets are usually composed of
several layers of metal and/or elastomeric inserts, and it is likely that the
layers do not all touch until the gasket is compressed. The inter-layer spaces
in a gasket are referred to in
Abaqus
as the initial void. The initial void is used only for calculating thermal
strain and creep strain. It is also possible that the gasket surface geometry
is such that pressure will not start building up until the gasket has been
compressed by a certain amount. The gasket closure that is needed to generate a
pressure is referred to in
Abaqus
as the initial gap.
Figure 6
shows a schematic representation of the initial gap and initial void in a
typical gasket. You can specify both the initial gap and initial void as part
of the gasket section property definition. The initial thickness of the element
should include the initial gap and the initial void.
Stability of Unsupported Gasket Elements
Gasket elements that extend outside neighboring components (unsupported gasket elements) can be
troublesome and should be avoided. If a gasket element is completely or partially
unsupported, incorrect areas can result in an incorrect stiffness, and numerical singularity
problems can occur in the equation solver. Minor extensions (caused by numerical roundoff in
mesh generation) will not usually cause a problem because Abaqus/Standard automatically extends the main surfaces a small amount beyond the edge of the model.
Numerical problems can occur in the direction tangential to the gasket (if general gasket
elements are used and no membrane stiffness is specified) as well as in the direction normal
to the gasket. The numerical singularity problems normal to the gasket can be treated by
stabilizing the elements with a small artificial stiffness. By default, Abaqus/Standard automatically applies a small stabilization stiffness (on the order of 10−9
times the initial compressive stiffness in the thickness direction) to all types of gasket
elements except the link elements. For persistent numerical singularity problems in
unsupported gasket elements the following treatment methods can be considered. First, make
sure that an adequate membrane elasticity is specified. Second, specify a higher value for
the artificial stiffness for the gasket section. If problems still persist, consider
trimming, “skinning,” and using MPCs (see General Multi-Point Constraints).