Modal Superposition Method

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This technique enables the dynamic response of the structure to be simulated without the disadvantage of storing the transient response for each node or element of the model. Transient FE analysis can be very time consuming and require large disk storage. The subsequent fatigue analysis must then access all this time dependent data for each time step and each location requested which can be time consuming. By using the modal participation factors (generalized coordinates) linearly combined with the stresses from each mode the method is exactly analogous to the quasi-static method in MSC Fatigue, as shown in the table below, but requiring much less disk space, memory and computation time.

	Static Superpositioning	Modal Superpositioning
	Static Analysis	Transient Analysis
Stress Input	Stress for unit load case i	Stress for mode shape i
Loading	Loading function for channel i	Modal Participation factors for Mode i

An advantage of this method is that due to the similarity with the quasi-static method, this technique can be used in S-N, E-N, Spot weld, Seam Weld, Crack Growth and Multi-axial analysis.

Here is an example of how to do modal superposition using MSC Nastran. Analogous methods exist for other solver codes. Some familiarity with each solver code is required to extract the correct information.

1. Run MSC Nastran modal analysis (SOL = 103) for your model and request stress to be written to the .op2 or .xdb file (STRESS = ALL). Use the EIGRL card to select frequency range of interest and / or number of modes.

2. Run MSC Nastran modal transient (SOL = 112) with same EIGRL card. Define the time history loading in the MSC Nastran deck using TABLED1 cards in the normal manner. Request the output to be SDISPLACEMENTS (PUNCH) = ALL. This gives the modal participation time histories for each mode of interest. If six (6) modes are solved for, this will give an ASCII punch file with six (6) time histories.

Note:	In the latest version of NASTRAN steps 1 and 2 can be combined into a single run by specifying the first subcase in the SOL 112 run as the normal modes run.

3. Run MSC Fatigue Pre & Post or MSC Patran and import the .op2 file from the SOL 103 run
(step 1) into the database. Fill the Solution Control and Materials forms as required.

4. Open the Loading information form, enter the number of modes recovered in the number of static conditions data box, and turn the fill down option on. Click on the Load Case ID cell and the Get/Filter Results button to display the stress results from the SOL 103 run. Select the first mode and the associated stress tensor and click on Fill Cell. This should load up the cells in the first column of the spreadsheet with the modal stress IDs corresponding to the number of modes recovered.

5. The creation of the Time histories off the modal participation factors in the punch file is achieved by clicking on the Read Punch button. This button will be displayed on this form when the user clicks on the Time history cell. A local Time history database that contains the time histories from the participation factors in the punch file is created in the local run directory. The local database can now be used to load the cells in the second column by clicking on the first cell in the Time history column and selecting Fill Cell (MSC Fatigue accesses the local database automatically).