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Multi-Point Constraints and Gap Elements

*MPC cards and *GAP cards may be defined by using the command:

PROPERTY BOUNDARY GENERAL part1 idof1 part2 [idof2] [real]

'*MPC' cards are generated if 'real' is set to zero, '*GAP' cards if 'real' is non-zero. 'part1' and 'part2' must be points, lines, or surfaces only. The orientations of 'part1' and 'part2' must be identical (e.g. two lines must be defined in the same direction, two surfaces must have the same orientation and start lines etc).

The FEMGV commands 'PROPERTY BOUNDARY MPC RBEAM' and 'PROPERTY BOUNDARY MPC RCONNECT' are now supported, see Paragraph 5.2.2.

Multi-point Constraints

When using the command 'PROPERTY BOUNDARY GENERAL' to generate '*MPC' cards, 'idof2' and 'real' are not needed and should not be defined. Parameters 'part1' and 'part2' are used to define the parts to be 'joined' by the '*MPC' card. The distance between the two parts, parameter 'idof1', and the ratio of divisions between the parts govern the type of '*MPC' card which the interface will produce. Note that 'part1' cannot be a set and 'part2' can only be a set if 'part1' is a point.

The interface will produce three types of MPC; Rigid Links/joints, Mesh Refinements, and Shell-Solid connections.

Mesh Refinement MPC's are defined thus:

'Part1' must have twice the number of divisions as 'Part2' on the first side, the element types must be the same on both parts, 'idof' must be defined but is not used, and ...

Where the elements are type QU4, '*MPC 1' cards will be produced corresponding to figure 5.1

**Figure 5.1:** Example MPC1: PROPERTY BOUNDARY GENERAL L1 0 L2
$\begin{figure} \centerline{ \psfig {figure=mpc1.ps,width=3.5in} }\end{figure}$

Where the elements are type QU8, '*MPC 2' cards will be produced corresponding to figure 5.2

**Figure 5.2:** Example MPC2: PROPERTY BOUNDARY GENERAL L1 0 L2
$\begin{figure} \centerline{ \psfig {figure=mpc2.ps,width=3.5in} }\end{figure}$

Where the elements are type HE8, '*MPC 3' cards will be produced corresponding to figure 5.3

**Figure 5.3:** Example MPC3: PROPERTY BOUNDARY GENERAL S1 0 S2
$\begin{figure} \centerline{ \psfig {figure=mpc3.ps,width=3.5in} }\end{figure}$

Where the elements are type HE20, '*MPC 4' cards will be produced corresponding to figure 5.4

**Figure 5.4:** Example MPC4: PROPERTY BOUNDARY GENERAL S1 0 S2
$\begin{figure} \centerline{ \psfig {figure=mpc4.ps,width=3.5in} }\end{figure}$

Rigid Link/Joint MPC's are defined thus:

Each part must have the same number of nodes, and ... Where 'idof1' = 9, and the two parts are touching, '*MPC 5' cards will be produced corresponding to figure 5.5

**Figure 5.5:** Example MPC5: PROPERTY BOUNDARY GENERAL L1 9 L2
$\begin{figure} \centerline{ \psfig {figure=mpc5.ps,width=3.5in} }\end{figure}$

Where 'idof1' = 123, and the two parts are not touching, '*MPC 6' cards will be produced corresponding to figure 5.6

**Figure 5.6:** Example MPC6: PROPERTY BOUNDARY GENERAL L1 123 L2
$\begin{figure} \centerline{ \psfig {figure=mpc6.ps,width=3.5in} }\end{figure}$

Where 'idof1' = 9, and the two parts are not touching, '*MPC 7' cards will be produced corresponding to figure 5.7

**Figure 5.7:** Example MPC7: PROPERTY BOUNDARY GENERAL L1 9 L2
$\begin{figure} \centerline{ \psfig {figure=mpc7.ps,width=3.4in} }\end{figure}$

Where 'idof1' = 123, and the two parts are touching, '*MPC 9' cards will be produced corresponding to figure 5.8

**Figure 5.8:** Example MPC9: PROPERTY BOUNDARY GENERAL L1 123 L2
$\begin{figure} \centerline{ \psfig {figure=mpc9.ps,width=3.5in} }\end{figure}$

Shell-Solid Connections are defined thus

'Part2' must have the same number of divisions as 'Part1' on the first side, and ... Where 'part1' is element type QU8, and 'part2' is element type HE20, *MPC 14' cards will be produced corresponding to figure 5.9

**Figure 5.9:** Example MPC14: PROPERTY BOUNDARY GENERAL L1 0 S2
$\begin{figure} \centerline{ \psfig {figure=mpc14.ps,width=4.0in} }\end{figure}$

Where 'part1' is a point the interface will associate the node at that point with all nodes on 'part2' using '*MPC 6' cards if 'idof1' = 123, or '*MPC 7' cards if 'idof1' = 9, otherwise '*EQUATION' cards will be produced. corresponding to figure 5.10

**Figure 5.10:** Example Point MPC: PROPERTY BOUNDARY GENERAL P1 9 S1
$\begin{figure} \centerline{ \psfig {figure=mpcp.ps,width=3.0in} }\end{figure}$

MPC RBEAM and RCONNECT Constraints

Two of the FEMGV MPC commands are supported via the following commands:

PROPERTY BOUNDARY MPC RBEAM [name] part point dof

PROPERTY BOUNDARY MPC RCONNECT [name] part1 part2 dof

where the RBEAM command is used to connect a single master point to any number of other slave parts and the RCONNECT command is used to connect part1 to part2 either as a series of one to one master-slave relationships or as a series of many to one relationships for mesh refinement. A 'part' refers, here, to either a point, a line, a surface, a body or a set. The user is referred to the FEMGV User Manual for more details on these commands.

Where the degree(s) of freedom specified are available as an ABAQUS *MPC definition this type of card is generated in the input file (MPC types BEAM and LINK are produced). Where the degree(s) of freedom is not supported as a *MPC definition a group of *EQUATION cards is generated.

When *EQUATION cards are generated, the interface will attempt to sort the constraint definitions prior to writing them to the ABAQUS input file. This is done to ensure that degrees of freedom are eliminated in the correct order, in accordance with ABAQUS rule. This sorting process can potentially be very slow (especially if many such MPCs were defined) and a printout of the current state of the sort is displayed at regular intervals. It is possible to interrupt the sort at any time using the Ctrl-C key on Unix machines or ALT-C key on PCs. When the sort is aborted the program will continue as normal outputting the constraints in the current sorted order.

ABAQUS 5.2 Named MPC's

ABAQUS 5.2 supports both numbered and named MPC's. The interface will produce numbered MPC's when the ABAQUS 4.9 environment is active, and named MPC's when the ABAQUS 5.2 environment is active. There is a direct correspondence between the MPC numbers and names which is illustrated below (for the MPC types which the interface supports).

**Table 5.2:** MPC Number-Name Mappings
ABAQUS 4.9	ABAQUS 5.2
1	LINEAR
2	QUADRATIC
3	BILINEAR
4	C BIQUAD
5	TIE
6	LINK
7	BEAM
9	PIN
12	SLIDER
13	SS LINEAR
14	SS BILINEAR
15	SSF BILINEAR

Gap Elements

When using the command 'PROPERTY BOUNDARY GENERAL' to generate '*GAP' cards, all of the command parameters are needed, but 'idof2' is disregarded by the interface. Parameters 'part1', and 'part2' are used to define the location of the gap(s) in the model, 'idof1' is used to define the gap type, and 'real' to define the gap dimension. The following gap types are supported:

Set 'idof1' = 1 for GAPUNI
Set 'idof1' = 2 for GAPCYL
Set 'idof1' = 3 for GAPSPHER

For 'GAPUNI' and 'GAPCYL', this information must be supplemented by a local axis system to define the gap closure direction; this is done by using the following commands:

CONSTRUCT COORDSYS type GAPn
PROPERTY ATTACH part1 COORDSYS GAPn

For 'GAPUNI', a local rectangular system must be defined. For 'GAPCYL' a local cylindrical system must be defined. For 'GAPUNI' the local x-axis is mapped to the closure direction, for 'GAPCYL' the cylinder axis definition is used directly. The following conditions apply:

The first three letters of the local system must be 'GAP'
The local system and gap type must be compatible
The local system must be attached to 'part1' only

An example of a gap definition follows:

*ELEMENT, TYPE=GAPUNI, ELSET=CO4 
   20   30   20
   21   29   19
*GAP, ELSET=CO4 
0.002, 1.0 , 0.0 , 0.0

Next: Distributing Coupling Up: Kinematic Constraints Previous: Rigid Constraints

Femsys Limited
9/9/1999