김경종
272 lines
26 KiB
Markdown
272 lines
26 KiB
Markdown
<!-- source-page: 301 -->
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# 35.3.1 MESH TIE CONSTRAINTS
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Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE
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# References
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• “Surfaces: overview,” Section 2.3.1
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• \*TIE
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• “Defining tie constraints,” Section 15.15.1 of the Abaqus/CAE User’s Guide, in the HTML version of this guide
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• “Using contact and constraint detection,” Section 15.16 of the Abaqus/CAE User’s Guide, in the HTML version of this guide
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# Overview
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A surface-based tie constraint:
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• ties two surfaces together for the duration of a simulation;
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• can be used only with surface-based constraint definitions;
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• can be used in mechanical, coupled temperature-displacement, coupled thermal-electricalstructural, acoustic pressure, coupled acoustic pressure-displacement, coupled pore pressure–displacement, coupled thermal-electrical, or heat transfer simulations;
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• can also be used to create a constraint on a surface so that it follows the motion of a three-dimensional beam;
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• is useful for mesh refinement purposes, especially for three-dimensional problems;
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• allows for rapid transitions in mesh density within the model;
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• constrains each of the nodes on the slave surface to have the same motion and the same value of temperature, pore pressure, acoustic pressure, or electrical potential as the point on the master surface to which it is closest;
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• will take the initial thickness and offset of shell elements underlying the surface into account by default; and
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• eliminates the degrees of freedom of the slave surface nodes that are constrained, where possible.
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# Defining a tie constraint for a pair of surfaces
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A surface-based tie constraint can be used to make the translational and rotational motion as well as all other active degrees of freedom equal for a pair of surfaces. By default, as discussed below, nodes are tied only where the surfaces are close to one another. One surface in the constraint is designated to be the slave surface; the other surface is the master surface. A name must be assigned to this constraint and may be used in postprocessing with Abaqus/CAE.
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Input File Usage: \*TIE, NAME=name slave\_surface\_name, master\_surface\_name
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Abaqus/CAE Usage: Interaction module: Create Constraint: Tie
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# Defining the surfaces to be constrained
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Either element-based or node-based surfaces can be used as the slave surface. Any surface type (elementbased, node-based, or analytical) can be used as the master surface. You may need to take some surface restrictions into consideration depending on which tie formulation is used and whether the analysis is conducted in Abaqus/Standard or Abaqus/Explicit. Two tie formulations are available: the surface-tosurface formulation, which is used by default in Abaqus/Standard, and the more traditional node-tosurface formulation, which is used by default in Abaqus/Explicit; these formulations are discussed in more detail later in this section. Table 35.3.1–1 and Table 35.3.1–2 provide comparisons of surface restrictions for the different formulations and analysis codes.
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Table 35.3.1–1 Comparison of characteristics for surface-based tie formulations.
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<table><tr><td>Tie formulation</td><td>Optimized stress accuracy</td><td>Node-based surfaces allowed</td><td>Mixture of rigid and deformable subregions allowed</td><td>Treatment of nodes/facets shared between master and slave surfaces</td></tr><tr><td>Surface-to-surface (Abaqus/Standard or Abaqus/Explicit)</td><td>Yes</td><td>Reverts to node-to-surface formulation</td><td>No</td><td>Eliminated from slave</td></tr><tr><td>Node-to-surface in Abaqus/Standard</td><td>No</td><td>Yes</td><td>No</td><td>Eliminated from slave</td></tr><tr><td>Node-to-surface in Abaqus/Explicit</td><td>No</td><td>Yes</td><td>Yes</td><td>Eliminated from master</td></tr></table>
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The surface-to-surface formulation generally avoids stress noise at tied interfaces. As indicated in Table 35.3.1–1 and Table 35.3.1–2, only a few surface restrictions apply to the surface-to-surface formulation: this formulation reverts to the node-to-surface formulation if a node-based or edge-based surface is used. The surface-to-surface formulation does not allow for a mixture of rigid and deformable portions of a surface, and the master surface must not contain T-intersections. Any nodes shared between the slave and master surfaces will not be tied with the surface-to-surface formulation. The same comments apply to both Abaqus/Standard and Abaqus/Explicit in these tables for the surface-to-surface formulation.
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With the more traditional node-to-surface formulation additional surface restrictions apply in Abaqus/Standard but fewer restrictions apply in Abaqus/Explicit in comparison to the surface-to-surface
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Table 35.3.1–2 Comparison of element-based surface characteristics allowed for surface-based tie formulations.
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<table><tr><td rowspan="2">Tie formulation</td><td colspan="4">Surface Characteristics (Yes=allowed, No=not allowed)</td></tr><tr><td>Double-sided</td><td>Discontinuous</td><td>T-intersection</td><td>Edge-based</td></tr><tr><td>Surface-to-surface (Abaqus/Standard or Abaqus/Explicit)</td><td>Master: Yes Slave: Yes</td><td>Master: Yes Slave: Yes</td><td>Master: No Slave: Yes</td><td>Reverts to node-to-surface formulation if either surface is edge-based</td></tr><tr><td>Node-to-surface in Abaqus/Standard</td><td>Master: Yes Slave: Yes</td><td>Master: Yes Slave: Yes</td><td>Master: No Slave: Yes</td><td>Master: Yes Slave: Yes</td></tr><tr><td>Node-to-surface in Abaqus/Explicit</td><td>Master: Yes Slave: Yes</td><td>Master: Yes Slave: Yes</td><td>Master: Yes Slave: Yes</td><td>Master: Yes Slave: Yes</td></tr></table>
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formulation. Relatively stringent restrictions on master surface connectivity for the node-to-surface tie formulation in Abaqus/Standard are indicated in Table 35.3.1–2: the master surface must be simply connected and must not contain complex intersections such as T-intersections (see “Defining contact pairs in Abaqus/Standard,” Section 36.3.1, for examples of surfaces with various connectivity characteristics).
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Differences with the node-to-surface formulation in Abaqus/Explicit are apparent in Table 35.3.1–1: partially rigid surfaces can be used and the treatment of shared portions of slave and master surfaces is unique to this case. Nodes and faces that are shared between the master and slave surfaces are eliminated automatically from the master surface in this case if the paired surfaces are either both element-based or both node-based, enabling the possibility of tying multiple slave surfaces (defined over various regions of the model) to a common master surface defined over the entire model. This is a convenient way to define tie constraints in large models, as it eliminates the need for defining specialized master surfaces for each surface pairing; however, you must still take care that slave surfaces do not include portions of the opposing surface to which they should be tied (for example, no tie constraints will be generated if the master and slave surfaces are identical). In the node-to-surface formulation in Abaqus/Explicit all facets attached to nodes that are common between slave and master surfaces are excluded from being tied to slave nodes. Sometimes when meshes are transitioned from one type of element to another type or from one element size to another element size, common nodes may exist at the interface of the two regions. Typically, a tie constraint is defined at the interface of the two zones to stitch the two meshes together. In a situation like this common nodes may get tied to a neighboring facet on the interface and may cause undesirable mesh distortion due to the tie adjustment. One possible way to avoid the undesirable mesh distortion is to specify a very small position tolerance for the tie pair. Another situation that may arise when common nodes occur between the slave and master surfaces at the interface of mesh transition zones is that slave nodes in the vicinity of the common node may not get tied. This happens due to the exclusion of master facets attached to the common nodes. Therefore, care must be taken to ensure that
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elements in different mesh zones do not share common nodes at the interface. For all such common nodes, duplicate nodes occupying the same physical location should be defined.
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<table><tr><td>Input File Usage:</td><td>Use the *SURFACE option to define the slave and master surfaces used in the constraint (see “Surfaces: overview,” Section 2.3.1):</td></tr><tr><td></td><td>*SURFACE, NAME=slave_surface_name</td></tr><tr><td></td><td>*SURFACE, NAME=master_surface_name</td></tr></table>
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<table><tr><td>Abaqus/CAE Usage:</td><td>In Abaqus/CAE you can select one or more faces directly in the viewport when you are prompted to select a surface. In addition, you can define surfaces as collections of faces and edges using the Surface toolset.</td></tr></table>
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# Specifying the subset of slave nodes to be constrained
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By default, Abaqus uses a position tolerance criterion to determine the constrained nodes based on the distance between the slave nodes and the master surface. Alternatively, you can specify a node set containing the slave nodes to be constrained regardless of their distance to the master surface.
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# Using the position tolerance criterion
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The default position tolerance criterion ensures that nodes are tied only where the slave and master surfaces are close to one another in the initial configuration. For example, consider the case shown in Figure 35.3.1–1. Surfaces Comp1\_surf and Comp2\_surf are defined to cover all exposed faces of Component 1 and Component 2, respectively. These two surfaces can be used as the slave and master surfaces in a tie constraint to tie the two components in the desired region, because only the nodes at the initial interface between the two surfaces are tied.
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<details>
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<summary>text_image</summary>
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desired tie region
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Component 1
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Component 2
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</details>
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Figure 35.3.1–1 Example of two components to be tied together.
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The default value of the position tolerance, $d _ { t o l }$ , typically results in desired tie constraints with little effort. Details regarding the calculation of distances between surfaces and default values of the position tolerances are provided below. You can modify the position tolerance if desired.
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<!-- source-page: 305 -->
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Input File Usage: Use the following option to use the default position tolerance:
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\*TIE
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Use the following option to specify a position tolerance:
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\*TIE, POSITION TOLERANCE=distance
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Abaqus/CAE Usage: Interaction module: Create Constraint: Tie: Position
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Tolerance: Specify distance
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# Calculating the distance between surfaces
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The following factors influence the calculation of the distance between surfaces for a particular slave node:
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• Shell thickness. By default, calculations of distances between surfaces account for shell thickness and offset effects for element-based slave or master surfaces: the distance is measured from the actual top or bottom side of the surface, whichever is closer to the other surface. Alternatively, you can specify that surface thicknesses and offsets should be ignored, which also has implications for nodal position adjustments for resolving initial gaps (discussed later).
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Input File Usage: Use the following option to ignore surface thicknesses and offsets in the distance calculations:
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\*TIE, NO THICKNESS
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# Abaqus/CAE Usage: Interaction module: Create Constraint: Tie: Exclude shell element thickness
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• Whether the surface-to-surface or node-to-surface constraint formulation (discussed below) is used. If a position tolerance is in effect, a constraint is generated at a slave node for either formulation if the distance between the surfaces, as calculated at the slave node, does not exceed $d _ { t o l }$ . Additional slave nodes may be tied if the surface-to-surface constraint formulation is used along with an elementbased slave surface and a master surface that is not node-based, because the following addendum to the position tolerance criterion applies in such cases: if the distance between the surfaces is within $d _ { t o l }$ over a significant portion of a slave face (or segment in two dimensions) that forms an angle of less than $3 0 ^ { \circ }$ with the master surface, all slave nodes attached to such a face (or segment) are considered to satisfy the position tolerance.
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• The types of surfaces involved (element-based, node-based, or analytical).
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# Position tolerance for an element-based master surface
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The default position tolerance for element-based master surfaces is 5% or 10% of the typical master facet diagonal length for the node-to-surface and surface-to-surface tie formulations, respectively. When using an element-based master surface, the distance between surfaces for a particular point on a slave surface is based on the closest point on the master surface (which may be on the edge of the master surface or within a facet). Figure 35.3.1–2 shows an example with no thickness: nodes 2–14 satisfy the position tolerance criterion for the node-to-surface and surface-to-surface constraint formulations. Significant portions of the end slave segments (that is, the segment connecting nodes 1 and 2 and the
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<!-- source-page: 306 -->
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<details>
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<summary>text_image</summary>
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slave surface
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element-based master surface
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position
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tolerance
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</details>
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Figure 35.3.1–2 Tolerance region around an element-based master surface with no thickness.
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segment connecting nodes 14 and 15) are within the position tolerance shown, so nodes 1 and 15 would also satisfy the position tolerance criterion for the surface-to-surface constraint formulation except for the fact that the angle between the slave and master surfaces is slightly greater than 30° at those locations.
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# Position tolerance for a node-based master surface
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The default position tolerance for a node-based master surface is based on the average distance between nodes in the master surface. The distance between the surfaces for a particular slave node is based on the closest master node. If this distance is less than the position tolerance, Abaqus will create a tie constraint between the slave node, the closest master node, and other master nodes in similar proximity to the slave node. For mismatched meshes across a tied interface, the distance between slave and master nodes can be much larger than the “normal” distance between the surfaces, which can lead to confusion when using a position tolerance criterion with a node-based master surface. Figure 35.3.1–3 shows how the tolerance region is defined around a node-based master surface. The surface-to-surface constraint formulation reverts to the node-to-surface constraint formulation for a node-based master surface.
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<details>
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<summary>flowchart</summary>
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```mermaid
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graph TD
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A["1"] --> B["2"]
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B --> C["3"]
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C --> D["4"]
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D --> E["5"]
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E --> F["6"]
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F --> G["7"]
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G --> H["8"]
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H --> I["9"]
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I --> J["10"]
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J --> K["11"]
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K --> L["12"]
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L --> M["13"]
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M --> N["14"]
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N --> O["15"]
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style A fill:#f9f,stroke:#333
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style O fill:#f9f,stroke:#333
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note right of H
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node-based master surface
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end
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```
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</details>
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Figure 35.3.1–3 Tolerance region around a node-based master surface with no thickness.
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# Position tolerance for an analytical rigid master surface
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The default position tolerance for tie constraints between an element-based slave surface and an analytical rigid master surface is 5% or 10% of the typical slave facet diagonal length for the node-to-surface and surface-to-surface tied formulations, respectively. The default position tolerance for tie constraints between a node-based slave surface and an analytical rigid master surface is 5% of the typical distance
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<!-- source-page: 307 -->
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between slave nodes. When using an analytical rigid master surface, the distance between surfaces for a particular point on the slave surface is based on the closest point on the master surface.
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# Specifying the constrained nodes directly
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This method allows you direct control over which slave nodes are tied.
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Input File Usage: \*TIE, TIED NSET=node\_set\_label
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Abaqus/CAE Usage: Specifying the constrained nodes directly is not supported in Abaqus/CAE.
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# Unconstrained nodes in tie constraint pairs
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Abaqus does not constrain slave nodes to the master surface unless they are included in the tied node set or within the tolerance distance from the master surface at the start of the analysis, as discussed above. Any slave nodes not satisfying these criteria will remain unconstrained for the duration of the simulation; they will never interact with the master surface as part of the tie constraint. In mechanical simulations an unconstrained slave node can penetrate the master surface freely unless contact is defined between the slave node and master surface. The general contact algorithm in Abaqus/Explicit will generate contact exclusions automatically for slave node–master surface combinations corresponding to constrained nodes of tie constraint pairs, but no such contact exclusions are generated for nodes outside the position tolerance of the constraints. In a thermal, acoustic, electrical, or pore pressure simulation an unconstrained slave node will not exchange heat, fluid pressure, electrical current, or pore fluid pressure with the master surface.
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Determining which slave nodes have been tied and which slave nodes have not been tied
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For each tie constraint pair, Abaqus creates a node set comprising slave nodes that will be tied and a node set comprising slave nodes that will be left unconstrained. These node sets are available for display during postprocessing in Abaqus/CAE, where they are listed as internal node sets.
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In addition, Abaqus prints a table in the data (.dat) file listing each slave node and the master surface nodes to which it will be tied if model definition data are requested (see “Controlling the amount of analysis input file processor information written to the data file” in “Output,” Section 4.1.1). If a constraint cannot be formed for a given slave node, Abaqus/Standard issues a warning message in the data file.
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In Abaqus/Explicit you can also request two nodal field output variables: TIEDSTATUS will help you identify the constrained and unconstrained slave nodes, and TIEADJUST will help you visualize the adjustment performed at the nodes (see “Abaqus/Explicit output variable identifiers,” Section 4.2.2). A tied node that participates in more than one tie definition as a slave as well as a master is shown as “tied” regardless of whether it got tied as a slave node or as a master node.
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When creating a model with surface-based tie constraints, it is important to use the information provided by Abaqus to identify any unconstrained nodes and to make any necessary modifications to the model to constrain them.
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<!-- source-page: 308 -->
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# Constraining the rotational degrees of freedom
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By default, Abaqus will constrain the rotational degrees of freedom when they exist on both slave and master surfaces (see Figure 35.3.1–4). You can specify that the rotational degrees of freedom should not be tied.
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Input File Usage: \*TIE, NO ROTATION
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Abaqus/CAE Usage: Interaction module: Create Constraint: Tie: toggle off Tie rotational DOFs if applicable
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# Constraining the faces of a cyclic symmetric structure in Abaqus/Standard
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You can enforce proper constraints on the faces bounding a repetitive sector of a cyclic symmetric structure (see “Analysis of models that exhibit cyclic symmetry,” Section 10.4.3). This makes it possible to define a single sector of the cyclic symmetry model together with its axis of cyclic symmetry to define the behavior of the 360° model. Cyclic symmetry models can be used within the following procedures: static; quasi-static; eigenfrequency extraction, based on the Lanczos solver technique; steady-state dynamics, based on modal superposition; and heat transfer. If an eigenfrequency extraction is performed on a cyclic symmetric model, the nodes involved in the cyclic symmetry constraint cannot be used in any other constraint (e.g., multi-point constraints, equations, rigid bodies, couplings, or kinematic couplings).
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Input File Usage: \*TIE, CYCLIC SYMMETRY
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This parameter can be used only with the \*CYCLIC SYMMETRY MODEL option.
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Abaqus/CAE Usage: Interaction module: Interaction→Create: Cyclic symmetry
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# The surface-based tie constraint formulation
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Abaqus uses the criteria discussed above to determine which slave nodes will be tied to the master surface. Abaqus then forms constraints between these slave nodes and the nodes on the master surface. A key aspect in forming the constraint for each slave node is determining the tie coefficients. These coefficients are used to interpolate quantities from the master nodes to the tie point. Abaqus can use one of two approaches to generate the coefficients: the “surface-to-surface” approach or the “node-to-surface” approach.
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If an analysis carried out with Abaqus/Standard is imported into Abaqus/Explicit or vice-versa, the tie constraints are not imported and must be redefined. If the imported analysis is essentially a continuation of the original analysis, it is important that the tie constraints are as similar as possible. Hence, you should make sure that the same constraint type is used. If the default approach was used in the original Abaqus/Standard analysis, the surface-to-surface approach should be specified in the Abaqus/Explicit analysis. Similarly, if the default approach was used in the original Abaqus/Explicit analysis, the node-to-surface approach should be specified in the Abaqus/Standard analysis.
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<!-- source-page: 309 -->
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Figure 35.3.1–4 Surface-based tie algorithm.
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# The “surface-to-surface” approach
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The “surface-to-surface” approach minimizes numerical noise for tied interfaces involving mismatched meshes. The surface-to-surface approach enforces constraints in an average sense over a finite region, rather at discrete points as in the traditional node-to-surface approach. The surface-to-surface formulation for surface-based tie constraints is similar to the surface-to-surface contact formulation (see “Contact formulations in Abaqus/Standard,” Section 38.1.1); however, a fundamental difference is that
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<!-- source-page: 310 -->
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each surface-based tie constraint involves only one slave node (and multiple master nodes), whereas each surface-to-surface contact constraint involves multiple slave nodes.
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The surface-to-surface approach is used by default in Abaqus/Standard with exceptions noted below, and it is optional in Abaqus/Explicit. For the case of infinite acoustic elements tied to shell elements in Abaqus/Standard the added cost of the surface-to-surface approach can be quite significant; therefore, the node-to-surface approach is used by default in this case. If the surface-to-surface approach is “on by default” or explicitly specified, Abaqus automatically reverts to the node-to-surface approach for individual tie constraints in the following circumstances:
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• if either of the surfaces being tied is node-based;
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• if the projection along the slave surface normal direction does not intersect the master surface; or
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• if single-sided slave and master surfaces have surface normals in approximately the same direction.
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Abaqus/Explicit may automatically add a small amount of artificial mass to the model to maintain numerical stability if the surface-to-surface approach is specified.
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The surface-to-surface approach generally involves more master nodes per constraint than the nodeto-surface approach, which tends to increase the solver bandwidth in Abaqus/Standard and, therefore, can increase solution cost. In most applications the extra cost is fairly small, but the cost can become significant in some cases. The following factors (especially in combination) can lead to the surface-tosurface approach being quite costly:
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• A large fraction of tied nodes (degrees of freedom) in the model
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• The master surface being more refined than the slave surface
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• Multiple layers of tied shells, such that the master surface of one tie constraint acts as the slave surface of another tie constraint
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Input File Usage: \*TIE, TYPE=SURFACE TO SURFACE
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Abaqus/CAE Usage: Interaction module: Create Constraint: Tie: Discretization method: Surface to surface
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# The “node-to-surface” approach
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The traditional “node-to-surface” approach (which is used by default in Abaqus/Explicit and is optional in Abaqus/Standard) sets the coefficients equal to the interpolation functions at the point where the slave node projects onto the master surface. This approach is somewhat more efficient and robust for complex surfaces.
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For the node-to-surface method of establishing the tie coefficients with an element-based master surface, the point on the surface closest to each slave node is calculated and used to determine the master nodes that are going to form the constraint (see Figure 35.3.1–5). For example, nodes 202, 203, 302, and 303 are used to constrain node ${ \pmb a } _ { \ast } ^ { \ast }$ nodes 204 and 304 are used to constrain node $b ;$ and node 402 is used to constrain node c.
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Input File Usage: \*TIE, TYPE=NODE TO SURFACE
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Abaqus/CAE Usage: Interaction module: Create Constraint: Tie: Discretization method: Node to surface
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