symmetry plane

Module: solid

Category: nlconstraint

Type string: "symmetry plane"

Parameters

Name	Description	Default	Units
laugon	laugon	1	[]
tol	tol	0.1	[]
penalty	penalty	1	[]
rhs	rhs	0	[]
minaug	minaug	0	[]
maxaug	maxaug	50	[]

Description

A symmetry plane enforces zero solid displacement normal to a user-selected plane. This constraint is prescribed on a deformable surface of the model and is enforced for every node on that surface. It is the user's responsibility to select only planar surfaces.

<constraint type="symmetry plane" surface="SymmetryPlane01">
    <laugon>1</laugon>
    <penalty>1e6</penalty>
    <tol>1e-6</tol>
    <minaug>0</minaug>
    <maxaug>50</maxaug>
</constraint>

The surface (SymmetryPlane01 in this example), is defined in the Mesh section. Let \(\mathbf{u}\) denote the nodal displacement vector and let \(\mathbf{n}\) denote the unit normal to the plane; the symmetry plane constraint enforces \(u_{n}\equiv\mathbf{u}\cdot\mathbf{n}=0\) using a penalty method, optionally with augmented Lagrangian. The reaction force needed to enforce this constraint is evaluated as \(\varepsilon u_{n}\), where \(\varepsilon\) is the user-specified penalty parameter (with units of force per length). To use the augmented Lagrangian method, set laugon to 1, and the Lagrange multiplier \lambda will be augmented as \(\lambda\leftarrow\lambda+\varepsilon u_{n}\). Augmentations terminate when the relative change in \(\lambda\) is less than the user-specified tolerance tol, or when the number of augmentations exceeds maxaug.