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Equation

*Equation [, <type>] [, option] 
<subsequent lines>

With this option, a linear equation constraint between arbitrary degrees of freedoms (see the remark) at any nodes where these are active can be imposed. The equation is assumed to be homogeneous (all variables are to be written on the left hand side of the equation). The entries of the <subsequent lines> depend on the chosen [<type>]

  • No type given (default). This command is used to construct a multi-point constraint between nodes forcing them to share the same value for different DOFs. The <subsequent line> takes the following form:

    <master node set name>, <degree of freedom constrained for the master node>, <slave node set name>, <degree of freedom constrained for the slave node>

    where <master node set name> and <slave node set name> are the node set labels containing the nodes to be constrained.

    Both sets must not have the same number of nodes, but at least one per set. The nodes will be paired according to their shortest distance to each other. If the master set has fewer nodes than the slave node set, then the master nodes with the next shortest distance to the slave node will be paired.

    The <degree of freedom> tag specifies the DOF to be constrained. Possible DOF are summarized in the Table below.

  • <type> = EqualDOF. This command is used to construct a multi-point constraint between nodes forcing them to share the same value for one specific DOF. The <subsequent line> takes the following form:

    <master node set name>, <slave node set name>, <degree of freedom>

    where <master node set name> and <slave node set name> are the node set labels containing the nodes to be constrained. The node sets must have the same number of nodes. The nodes will be paired according to their shortest distance to each other.

    The <degree of freedom> tag specifies the DOF to be constrained. Possible DOF are summarized in the Table below.

In addition numgeo offers the possibility to prescribe the penalty parameter \(\alpha_0\) , the default value of \(\alpha_0=10^8\) is based on the heuristic square root rule. The heuristic square root rule states, that the penalty factor \(\alpha_0\) should not exceed \(\sqrt{10^p}\), where \(p\) is the working machine precision 1. To change the value of \(\alpha_0\) the following statement in the line following the *Equation command:

*penalty=<user value>

Degrees of freedom that can be constrained using the *Equation keyword:

Degree of freedom numgeo key
Solid displacements in \(x_1\), \(x_2\) and \(x_3\) direction u1, u2, u3
Water displacements in \(x_1\), \(x_2\) and \(x_3\) direction w1, w2, w3
Pore water pressure pw
Pore air pressure pa

  1. Robert D. Cook and others. Concepts and applications of finite element analysis. John Wiley & Sons, 2007. ↩