Cyclic Symmetry¶

The cyclic symmetry constraint enables to model only a sector of a 360° cyclic periodic structure and reduces the computation time and memory consumption considerably. The user defines the center and axis of the cyclic symmetry as well as the sector angle. The master and slave surfaces define the cyclic periodicity boundaries.

Selection of master and slave faces¶

Generally the more refined of the two periodic boundary surfaces should be chosen to be the slave. In the case of a cyclic symmetry this will in the most cases not matter since both faces should be meshed with nearly the same element sizes.

Definition of the cyclic symmetry axis and sector angle¶

The user has to define the axis of revolution and the sector angle explicitly. The sector angle has to be given in degrees. Available ranges for the angle are from 0° to 180° and only values that divide 360° to an integer number are valid. The axis is defined by the axis origin and the axis direction. The Definition of Axis and Angle has to be in accordance with the right hand rule such that it defines a rotation that maps the slave to the master surface.

For an example see the picture below:

The Slave surface is highlighted red, revolution axis is chosen as the negative y-Axis (0,-1,0) and the sector angle is 36°

Resulting displacement on sector (left) and transformed on the full 360° model (right)

Important remarks:

• All DOFs of the slave nodes will be constrained, adding an additional constraint on those nodes could lead to an overconstrained system.
• This is a linear constraint, so no large rotations or large deformations are allowed in the proximity of cyclic symmetry boundaries.
• A cyclic symmetry condition is only valid if geometry and loading conditions are symmetric.