Symmetry Conditions (CHECK_LINK)

This section gives information on how to link nodes with other nodes.

Important:

This kind of design variable constraint is available with bead sensitivity optimization only when TYPE = SURF_PLANE_SYM is used, while it is available with bead controller optimization only with all other TYPEs.

The model must be symmetric to use these constraint types.

This page discusses:

See Also
In Other Guides
DVCON_BEAD
LINK_BEAD
Applicable for BEAD_CONTROLLER BEAD_SENSITIVITY
POINT_SYM OK -
PLANE_SYM OK -
SURF_PLANE_SYM - OK
ROTATION_SYM OK -

Symmetry conditions can also be applied in Tosca Structure.bead. A LINK-condition is needed to create a symmetry condition.

The types of symmetry supported by Tosca Structure.bead are point, plane, and rotational symmetry:

bead controller optimization


LINK_BEAD
  ID_NAME = <link_name>
  TYPE    = POINT_SYM
            PLANE_SYM, AXIS_*
            ROTATIONAL_SYM, AXIS_*
  CS      = <cs_name>
END_

bead sensitivity optimization


LINK_BEAD
  ID_NAME    = <link_name>
  TYPE       = PLANE_SYM
  CLIENT_DIR = <X_1>, <X_2>, <X_3>
  CS         = <cs_name>
END_

The origin of the coordinate system referenced by the <cs_name> is the symmetry point or a point on the symmetry plane, where AXIS_* is the normal to this plane. For rotational symmetry, the origin of the coordinate system is a point on the symmetry axis, where AXIS_* gives the direction.

The following figure shows an asymmetric load case without (left) and with (right) symmetry condition:

Important:
  1. AXIS_* can be AXIS_1, AXIS_2, or AXIS_3 of the chosen coordinate system.
  2. Only cartesian coordinate systems can be used for symmetry conditions.
  3. The name of the link is referenced in a DVCON_BEAD command using CHECK_LINK=<link_name>.
  4. The LINK conditions cannot be used together with TEST_SHAPE. TEST_SHAPE will not fail, but the LINK conditions are not executed.

Point Symmetry (POINT_SYM)

Note:

Couple displacements that are symmetric with respect to a point.

This kind of constraint is available only for controller-based optimizations. To couple displacements symmetric to a point, the position of the point must be exactly specified. The following parameters are necessary for the definition of the link condition: 


LINK_BEAD
 ID_NAME = <link_name>
 TYPE    = POINT_SYM, AXIS_*
 CS      = <cs_name>
END_

The origin of the coordinate system referenced by CS defines the symmetry point. The symmetry of the nodes (assigned by ND_GROUP in the DVCON_BEAD command) is checked against the symmetry point. Symmetric nodes are assembled into a symmetry group (normally two symmetric nodes per symmetry group). Then the main node of the symmetry group is determined and the displacements of the client nodes are calculated in such a way that they move symmetric to the point of the main node (see the following figure).

Important:

  • The coordinate system referenced by CS must be a Cartesian coordinate system.

Plane Symmetry (CONTROLLER)

Note:

Couple design nodes that are symmetric to a plane - for arbitrary meshes.

This kind of constraint is available only for controller-based optimizations. To couple displacements symmetric to a plane, the position and the orientation of the plane must be specified exactly. Therefore, the plane is created using the coordinate system and an axis normal to the plane. A possible link definition could look like the following: 


LINK_BEAD
 ID_NAME    = <link_name>
 TYPE       = PLANE_SYM
 CLIENT_DIR = <X_1>, <X_2>, <X_3>
 CS         = <cs_name>
END_

The symmetry of the nodes (assigned by ND_GROUP in the DVCON_BEAD command) is checked against the symmetry plane. Symmetric nodes are assembled into a symmetry group (normally two symmetric nodes per symmetry group). Then the main node of the symmetry group is determined and the displacements of the client nodes are calculated in such a way that they move symmetrically to the plane of the main node (see the following figure).

Important:

  • The coordinate system referenced by CS must be a Cartesian coordinate system.

Plane Symmetry (SENSITIVITY)

Note:

Couple design nodes that are symmetric to a plane - for arbitrary meshes.

This kind of constraint is only available for sensitivity-based optimizations. To be able to couple displacements symmetrically to a plane, the position and the orientation of the plane must be specified. This is supported for symmetric and unsymmetric meshed geometries. The following parameters are necessary for the definition of the link condition: 


LINK_BEAD
 ID_NAME    = <link_name>
 TYPE       = PLANE_SYM
 CLIENT_DIR = <X_1>, <X_2>, <X_3>
 CS         = <cs_name>
END_

The origin of the coordinate system referenced by CS defines a point on the symmetry plane. The direction specified by the PLANE_NORMAL parameter defines the normal of the plane.

The symmetry of the nodes (assigned by ND_GROUP in the DVCON_BEAD command) is checked against the symmetry plane. For each node, a reference displacement is calculated for its symmetric "counterpart." This counterpart is obtained by reflecting the node at the symmetry plane; that is, by intersecting a line through the node in the plane normal direction with the surface defined by all selected nodes. The reference displacement is obtained by interpolation of the optimization displacements of the adjacent nodes.

The symmetry is built up by using the maximum (default) or the minimum of the displacement of the selected node (d1 in the following figure) and the interpolated displacement of its plane symmetric counter part (reference displacement d2 in the following figure).

Rotational Symmetry (ROTATION_SYM)

Note:

Couple displacements that are rotational symmetric around an axis.

This kind of constraint is available only for controller-based optimizations. To couple displacements rotationally symmetric about an axis, the position and the orientation of the axis must be specified exactly. The mesh of the coupled node group should be rotational symmetric. These parameters are specified as follows: 


LINK_BEAD
  ID_NAME = <link_name>
  TYPE    = POINT_SYM, AXIS_*
  CS      = <cs_name>
  ANGLE   = <value>
END_

The origin of the coordinate system referenced by CS defines a point on the axis. The direction specified by the AXIS* parameter defines the axis direction. The symmetry of the nodes assigned by ND_GROUP in the DVCON_BEAD command is checked against the symmetry axis. Symmetric nodes are assembled into a symmetry group, a simplification of the GROUP_AUTO_DEF command, where these symmetry groups can be build according to cylindrical coordinate systems. Then the main node of the symmetry group is determined and the displacements of the client nodes are calculated in such a way that they move rotational symmetric to the axis (see the following figure).

In addition, an angle can be defined to divide the search area into discrete sections.