linear constraint

Module: core

Category: bc

Type string: "linear constraint"

Parameters

Name	Description	Default	Units
dof	dof	-1	[]
node	node	-1	[]
offset	offset	0	[]
child_dof			[]

Description

A linear constraint can be used to couple nodal degrees of freedom. The linear constraint has one dependent degree of freedom \(u^{*}\), and several independent degrees of freedom \(u_{i}\). The linear constraint is defined as follows:

\[ u^{*}=c_{0}+c_{1}u_{1}+\ldots+c_{n}u_{n} \]

Here, the \(c_{i}\) are user-specified scale factors and \(c_{0}\) can be used to specify an offset.

The dependent degree of freedom \(u^{*}\) will be removed from the linear system of equations. Consequently, this nodal degree of freedom should not be used in any other boundary condition.

To define a linear constraint, set the type attribute to linear constraint. The dependent degree of freedom, i.e. the dof that will be removed, is specified via a node number and a dof identifier. Each child dof is defined via the child_dof tag and similarly requires the corresponding node and dof identifier, as well as the value parameter.

<bc type="linear constraint">
  <node>5</node>
  <dof>x</dof>
  <child_dof>
    <node>8</node>
    <dof>x</dof>
    <value>1.0</value>
  </child_dof>
  <child_dof>
    <node>9</node>
    <dof>x</dof>
    <value>-1.0</value>
  </child_dof>
</bc>