## Cyclic Symmetry Analysis with OptiStruct

A component is considered cyclic symmetric if it includes a pattern (the basic segment) which can be repeated X time (X being an integer number) around an axis of symmetry to close the loop. This exists in various parts across different industries such as Aircraft engine turbines, gas turbine compressor wheels, windmill assembly, vehicle rims, flange joints…

The figure below shows an example of such a part with cyclic symmetry:

Figure 1 Full finite element model

The full finite element model consists of 1550000 CHEXA elements

Figure 2 Full finite element model data

The segment model is the one-thirty-sixth of the full model and is cyclic symmetric with respect to the z-axis.

Figure 3 Representative segment

The segment’s finite element model consists of around 43000 CHEXA elements.

Figure 4 Segment’s finite element model data

Cyclic Symmetry Modelling

Here is a snapshot of the entities needed for a cyclic symmetry analysis setup using OptiStruct. Please refer to our online documentation for further details.

Figure 5 Bulk data entries

The cyclic symmetry Analysis setup will be supported soon in HyperWorks.

Meanwhile, one can use the available tcl script (attached to this page) to automatically create the Cyclic Symmetry Boundary Conditions.

Step 1: Define the Cyclic Symmetry Boundary Conditions (CYJOIN)

1. Edit the TCL script and enter the number of segments NSEG

For this example, as the segment is the one-thirty-sixth of the full model we set the number of segments: NSEG=36. This will create the bulk data CYSYM,36 necessary to take in account the 360° of our model.

1. Got to File > Load > Scripts to run the tcl script OptiStructCyclicSymmetry_CYJOIN.tcl.
• Select the components, click Ok
• Select Side 1 (see Figure 6) when required, click proceed
• Select Side 2 (see Figure 6) when required, click proceed

The tcl script will automatically create CYJOIN,1 and CYJOIN,2 bulk data entries in which we define the points of the boundaries that connect to adjacent segments.

Figure 6 Segment’s Sides

Each grid on a CYJOIN entry should be paired with a matching grid on the other CYJOIN entry otherwise the analysis would lose accuracy.

Figure 7 CYJOIN definition

The axis of cyclic symmetry is determined by the geometry and CD fields of the first pair of grids appearing on CYJOIN entries. So, the two CYJOIN entries should have consistent coordinate systems. This requirement can be satisfied by using a cylindrical coordinate system CORD2C placed on the axis of symmetry.

In this example, a cylindrical system can be defined using 3 nodes (0,0,0), (1,0,0), (0,0,1) and use them as the system’s origin, x-axis, and xz plane respectively in the CORD2C card.

Finally a GRDSET entry can be used to select the COORD2C system that we have created in the CD field.

TIP! During the mesh creation process, in order to achieve matching grids on both sides, we can use the periodic Mesh tool. In the Periodic Mesh tool > select the 2D meshed surface as the Source > select the opposite surface as the Target > click on Map Mesh.

Step 2: Define the Cyclic Symmetry Analyses

The supported analysis types include linear static (STATIC) and normal mode analysis (MODES). Please refer to our online documentation for further details on the Cyclic Symmetry analysis guide.

1. Static Analysis Setup

The static analysis can incudes various boundary conditions and loadings such as SPCs, MPCs, Forces, moments, pressures, gravity, centrifugal forces… In the following example we will apply a fixed SPCs in the inner face and pressure loading on the blade.

1. Select the inner face nodes and create a SPC constraints on DOFs 1,2 and 3.

Figure 7 SPC constraints

1. Apply static pressure on the blade’s surface with a PLOAD4 entry.

In this example, use the existing load collector “Pressure”.

Figure 8 Pressure load

To include the static loading in the Cyclic Symmetry Analysis, we need to define them as Cyclic Symmetry loads with LOADCYN or LOADCYH (see Figure 5).

1. Edit the BULK_UNSUPPORTED_CARD that we have created, and add the LOADCYN entry

Set the scale factors S, S1 = 1.0 and reference the id of the pressure load collector L1 = 2.

TIP! For the whole model analysis, we create the same SPC, PLOAD4 entries for the initial segment before we make the rotational transformation. We must check the Transform Loads option box to have loads copied during this process.

d. Create a linear static load step and set:

• Analysis Type = Linear Static
• SPC = SPC load collector that we have created
• SUBACSE OPTIONS > SUBCASE_UNSSUPORTED_CARDS > Comments:

LOAD=555 which is the ID of the cyclic symmetric load entry LOADCYN that we have defined in the BULK_UNSSUPORTED_CARDS (setp c.)

e. Define the Output request on the Cyclic Symmetry Analysis

Create a CASE_UNSUPPORTED_CARDS and type NOUTPOUT=ALL to recover and output results for all the segments.

2. Comparison between the Cyclic Symmetric and the Whole Model Static Analysis

The results from the cyclic symmetry static analysis have been compared with a full model static analysis as a reference. The results show good agreement between the two different analysis approaches.

Figure 9 Displacement comparison between the Cyclic Symmetric and the Whole Model Static Analysis

Figure 10 Element Stresses comparison between the Cyclic Symmetric and the Whole Model Static Analysis

3. Modal Analysis Setup.

We create a modal analysis using the Lanczos method (EIGRL) requesting 20 mode shapes and a max displacement normalization of the eigenvalues.

Below is a section of the .fem file with the modal cyclic symmetry analysis setup

4. Comparison between the Cyclic Symmetric and the Whole Model Modal Analysis

The results from the cyclic symmetry modal analysis have been compared with a full model modal analysis as a reference. The results show good agreement between the two different analysis approaches.

Figure 5 Comparison between the Cyclic Symmetric and the Whole Model Analysis for Mode 7

Figure 6 Comparison between the Cyclic Symmetric and the Whole Model Analysis for Mode 7

5. Preloaded Modal Analysis Setup

In order to create a preloaded modal analysis, we define in the preexisting modal analysis subcase the STATSUB(Preload) entry option, in which we reference the ID of the static load step subcase.

To speed up the solution time, we can request only the results of the initial segment to be recovered and output. This can be achieved by creating a SET of the initial segment and set NOUTPOUT=id of the SET.

6. Comparison between the Cyclic Symmetric and the Whole Model Preloaded Modal Analysis

The results from the cyclic symmetry preloaded modal analysis have been compared with a full model static analysis as a reference. The results show good agreement between the two different analysis approaches.

Figure 11 Comparison between the Cyclic Symmetric and the Whole Model Analysis for Mode 1

Figure 12 Comparison between the Cyclic Symmetric and the Whole Model Analysis for Mode 7

The computational time for cyclic symmetric analysis was significantly improved compared to the full model analysis.

 ANALYSIS TYPE Preloaded Modal Analysis Preloaded Modal Analysis(With 1 segment results output) CYCLIC SYMMETRIC Computational time: 00:44:21 00:35:54 FULL MODEL 02:20:19 -