UBLow represents the duplicate sector low side edge

UBHigh represents the duplicate sector high side edge

The equation is a function of harmonic index k generating different sets of constraint equations for each harmonic index. Therefore, for each harmonic index solution requested, the program creates the appropriate constraint equations automatically, connects the edge-component nodes on basic sector A and duplicate sector B, and solves.

Constraint equations that tie together the low and high edges of your model are generated from the lowand high-edge components, and nowhere else. You should verify that automatically detected components are in the correct locations and that you are able to account for all components; to do so, you can list (CMLIST) or plot (CMPLOT) the components.

7.3.1.3. Non-Cyclically Symmetric Loading

A load is non-cyclic when it varies between sectors and involves at least one harmonic index greater than zero. Support is available for cyclic analyses that have some combination of cyclic and non-cyclic loading.

For non-cyclic loading, applicable to static and full harmonic cyclic solutions, the program considers

the arbitrary forces acting on the full system as the sum of a finite number of spatial Fourier harmonics. The program analyzes the structure for each spatial harmonic index by applying constraint equations between the basic sector and duplicate sector. For each spatial Fourier harmonic, the program solves

a corresponding equation, then expands and sums the calculated harmonics of the response to give the response for each substructure. For more information, see Cyclic Symmetry Transformations in the

Mechanical APDL Theory Reference.

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7.3.1.3.1. Specifying Non-Cyclic Loading

This section is applicable to static and full harmonic cyclic analyses only. For cyclic mode-superposition harmonic analyses, non-cyclic loading is applied in a different manner. For more information, see Solving a Mode-Superposition Harmonic Cyclic Symmetry Analysis (p. 186).

Specify non-cyclically symmetric loading via the CYCOPT command' s LDSECT (load-on-sector) value. A value greater than 0 (the default, indicating that the loads are identical on all sectors) restricts sub-

sequently defined force loads and surface loads to the specified sector. The restriction remains in effect until you change or reset it.

When non-cyclic loading applies, the program creates or modifies the required SECTOR tabular boundary condition (BC) data to apply on the appropriate sector. Therefore, it is not necessary to manipulate tables for situations where the applied BC is not a function of other tabular BC variables such as TIME, X, Y, Z, and so on.

If a SECTOR-varying table exists on an entity-BC combination (for example, node 17 FZ) and you enter another value for the same entity-BC combination (perhaps specifying a different sector on which to apply the load), the following conditions occur:

•The program modifies the existing table to accommodate the new specification.

•The table cannot reference any other independent variable (for example, TEMP). You must manually define any BC table requiring more than one independent variable.

If a table exists for an entity-BC combination and you enter another table for the same entity-BC combination, but the table does not reference SECTOR, the new table reference replaces the existing one.

During preprocessing, all tabular BC listings referencing SECTOR will list the table names only. During solution or postprocessing, all tabular BC listings referencing SECTOR will list the values per sector as they would be applied when solving (SOLVE).

Any tabular data X, Y, or Z variation applied to a cyclic model may not be applied in the same manner in which such a variation would occur for an equivalent full model (the exception being a variation in the axial direction). For example, if a tabular value of a nodal force is applied as function of the tabular variable Y, the program applies it to the designated cyclic sectors using values based upon the Y values of the basic sector only.

A given high-edge node is usually the same location in the structure as the corresponding low-edge node of the adjacent sector; therefore, it is necessary to apply constraints consistently. Note that inconsistent constraints are impossible to satisfy if the solution remains cyclic. The results can be unpredictable.

If a high (or low)-edge DOF has a constant (non-tabular) constraint, and the corresponding low (or high)-edge DOF is unconstrained, the program copies the constraint to the opposite edge. If a high (or low)-edge DOF has a tabular constraint, and the corresponding low (or high)-edge DOF is unconstrained, the program stops the solution with an error message. If a high-low corresponding pair of DOF are both constrained in any manner, the program assumes that you have specified constraints in a consistent manner.

One warning is issued the first time this is done for a given SOLVE operation.

Because edge nodes are rotated into the cyclic coordinate system during solution, any applied displacements or forces on sector edges will be in the cyclic coordinate system.

Example 7.1: Non-Cyclic Loading via Automatically-Defined Tabular Load

CYCOPT,LDSECT,1 ! LOADS ON SECTOR 1 ONLY

SFL,ALL,PRES,10000

For DOF constraints, force loads, and body forces, any non-tabular load is cyclic. Any tabular load that does not reference the variable SECTOR is cyclic. The program assumes any tabular load referencing SECTOR to be non-cyclic (although it could be identical on all sectors).

Example 7.2: Non-Cyclic Loading via User-Defined Tabular Load

*DIM,S1PRES,TABLE,5,1,1,SECTOR

*SET,S1PRES(1,0,1),1,2,3,4,5

*SET,S1PRES(1,1,1),10000,0,0,0,0 ! PRESSURE ON SECTOR 1 ONLY

SFL,ALL,PRES,%S1PRES%

When combined with other independent variables, SECTOR can be in positions 1, 2, or 3 only. Other independent variables operate as they do for non-cyclic data. (Think of X, Y, and Z as “ghost” coordinates, behaving as though all sectors have been modeled with actual nodes and elements.)

Example 7.3: Deleting a Sector Load

To delete a previously applied load on a specified sector, issue an FDELE command.