# MPC

Bulk Data Entry The MPC Bulk Data Entry defines a multipoint constraint equation of the form.

(1)
$\sum _{j}{A}_{j}{u}_{j}=0$

Where,

${A}_{j}$ is the coefficient that can be used to define the relationship between the degrees-of-freedom associated with grid points (or a scalar point) in the model.

${u}_{j}$ is the degree-of-freedom associated with a grid point (or a scalar point).

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MPC SID G C A G C A blank
blank G C A etc.     blank

## Example

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MPC 3 28 3 6.2 2 2 4.29
1 4 -2.91

## Definitions

Field Contents SI Unit Example
SID Set identification number.

(Integer > 0)

G Grid point or a scalar point identification number.

(Integer > 0 or <PartName.number>) 4

C Component number. The component refers to the coordinate system referenced by the grid point.

(Integer zero or blank for scalar points, or any one of the digits 1-6 for grid points)

A Coefficient that can be used to define the relationship between the degrees-of-freedom associated with grid points (or a scalar point).

(Real; the first A must be non-zero)

1. The first coordinate in the sequence is assumed to be the dependent coordinate. A dependent degree-of-freedom assigned by one MPC entry cannot be assigned dependent by another MPC entry or by a rigid element.
2. When the SPSYNTAX setting on the SYSSETTING I/O Option is set to CHECK (default) or STRICT, it is required for grid/component pairs (G#/C#) that the component be 0 or blank when the grid reference is a scalar point ( SPOINT), and that the component be ≥ 1 when the grid reference is a structural grid point (GRID). When SPSYNTAX is set to MIXED, it is allowed for grid/component pairs (G#/C#) that the grid reference be either a scalar point (SPOINT) or a structural grid point (GRID) when the component is 0, 1 or blank; interpreting all of these as 0 for scalar points and as 1 for structural grids. When the component is greater than 1, the grid reference must always be a structural grid (GRID).
3. Figure 1 can be used to illustrate an MPC application. Independent grid points G1 and G2 of a 2D quad element are connected with the help of an MPC; where Gd is the dependent grid point. The objective of this example is to force the displacement of Gd to be equal to the sum of the displacements of grid points G1 and G2 in the X (1) direction using an MPC.
Rewriting the MPC equation for three grid points:(2)
${A}_{1}{u}_{1}+{A}_{2}{u}_{2}+{A}_{3}{u}_{3}=0$
Substituting A1 = 1.0, A2 = -1.0 and A3 = -1.0 in the equation above:(3)
$\left(1.0\right){u}_{d}+\left(-1.0\right){u}_{1}+\left(-1.0\right){u}_{2}=0$
Rearranging equation terms:(4)
${u}_{d}={u}_{1}+{u}_{2}$
Where,
ud
Displacement of grid point Gd in X direction
u1
Displacement of grid point G1 in X direction
u2
Displacement of grid point G2 in X direction
4. Supported local entries in specific parts can be referenced by the use of "fully-qualified references" on MPC entries in the model. A fully-qualified reference ("PartName.number") is similar to the format of a numeric reference. "PartName" is the name of the part that contains the referenced local entry (part names are defined on the BEGIN Bulk Data Entry in the model). "number" is the identification number of a referenced local entry in the part "PartName". See Parts and Instances in the User Guide for detailed information on the use of fully-qualified references.
5. This card is represented as an equation in HyperMesh.