***mpcs#

Description#

This option is used to add linear relationships (equations) between different degrees of freedom in the problem. This allows the standard set of linear equations to include constraint conditions (MPC = multi-point constraint). Theses MPCs are taken into account using the adjunction of Lagrange multipliers. Theses MPCs are compatible with the solvers FETI and AMFPETI.

Syntax#

***mpcs \(~\,\) **MPC_type \(~\,~\,~\,\) …

The relationship types which are currently defined are summarized in the following table:

CODE

DESCRIPTION

**pair

impose any arbitrary relation between two nodal dofs

**free

impose any arbitrary relation between a group of nodal dofs

**mpc1

sets nodal DOFs of a given type to be equal within a node set

For all mpcs, it is possible to enable Augmented Lagrangian technique and to specify a penalty coefficient and a scaling factor. For the moment, the use of Augmented Lagrangian technique is not taken into account if the MPC is shared accross different subdomains in a parallel computation.

**pair (or free or mpc1) \(~\,\) *augmented_lagrange \(~\,\) *penalty p \(~\,\) *scaling k

**pair#

Description#

This MPC imposes a relation of between two nodal dofs:

\[c_1 \cdot node_1(dof_1) + c_2 \cdot node_2(dof_2) = rhs\]

Syntax#

The command has the following syntax:

**pair \(~\,\) *node1 id1 \(~\,\) *dof1 dof1 \(~\,\) *c1 c1 \(~\,\) *node2 id2 \(~\,\) *dof2 dof2 \(~\,\) *c2 c2 \(~\,\) *rhs rhs

id1, id2

Are valid node ids.

dof1, dof2

Character name for a DOF keyword. The keywords available for different problem types are described in the chapter DOF.

c1, c2

Are floats

rhs

Is a float

**free#

Description#

This MPC imposes any relation of between nodal dofs:

\[c_1 \cdot node_1(dof_1) + \dots + c_n \cdot node_n(dof_n) = rhs\]

Syntax#

The command has the following syntax:

**free \(~\,\) *node id1 dof1 c1 \(~\,\) *node id2 dof2 c2 \(~\,\) *node id3 dof3 c3 \(~\,~\,\) \(\vdots\) \(~\,\) *rhs rhs

id1, …, idn

Are valid node ids.

dof1, …, dofn

Character name for a DOF keyword. The keywords available for different problem types are described in the chapter DOF.

c1, …, cn

Are floats

rhs

Is a float

**mpc1#

Description#

This equation type imposes that a given degree of freedom at all the nodes of a valid node set are equal in value.

Syntax#

**mpc1 \(~\,\) *nset nset_name \(~\,\) *dof dof_name

nset_name

Character name for a valid node set.

dof_name

Character name for a DOF keyword. The keywords available for different problem types are described in the chapter DOF.