Cyclic symmetry is another type of symmetry about a line. It is best described in terms of a cylindrical coordinate system having its Z axis on the line of symmetry. The structure, loading, and displacements are each said to be cyclically symmetric about a line if they vary with angular position in a repeated (periodic) fashion.
Enforce cyclic symmetry using the Local Constraint as follows:
Model any number of adjacent, representative, cylindrical sectors of the structure; denote the size of a single sector by the angle q.
Assign each joint a local coordinate system such that the local axes 1, 2, and 3 correspond to the coordinate directions +CR, +CA, and +CZ, respectively.
For each cyclically symmetric set of joints (i.e., having the same coordinates CR and CZ, but with coordinate CA differing by multiples of q), define a Local Constraint using all six degrees of freedom: U1, U2, U3, R1, R2, and R3.
Restrain joints that lie on the line of symmetry so that, at most, only axial translations (U3) and rotations (R3) are permitted
For example, suppose a structure is composed of six identical 60° sectors, identically loaded. If two adjacent sectors were modeled, each Local Constraint would apply to a set of two joints, except that three joints would be constrained on the symmetry planes at 0°, 60°, and 120°.
If a single sector is modeled, only joints on the symmetry planes need to be constrained.