Small Satellite (SFEM - Modal)

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Performing the SFEM analysis

In this analysis, the combined effect of the uncertainties within the young's modulus and density on the second natural frequency will be investigated. Since only Perturbation method implementation can be used with the Modal analysis, the uncertainties in the thicknesses are omitted for this case (the rest of the probabilist model definition is the same, i.e. 8 random variables are used in total).


Summary of the Probabilistic Model

Structural Property

Distribution     Mean Value      CoV Value

Young's Modulus x 4

Normal (truncated) 70 GPa 0.15

Density x 4

Normal (truncated) 2700 kg/m3
0.10
Total no of random parameters

8


After defining the input, the connector is created by right-clicking on the connector icon in the tree view and selecting the "add connector" option. The connector to NASTRAN is defined as follows for this example. Please note that the connector type should be chosen as NASTRAN within the configuration of the connector.


SatelliteModal1.jpg


Also, another important step within the definition of the connector is the creation of the injector. The definition of the identifiers (please note the formatting) for this tutorial is shown in the screenshot below:


SatelliteModal2.jpg


Important Note: Although an extractor is not used within the SFEM analysis, it has to be defined within the connector for the completeness.


Once the connector is defined properly, a physical model has to be defined accordingly, which is depicted in the following screenshot:

SatelliteModal3.jpg


Please note that only Perturbation method can be applied for the modal analysis case, hence simply click on the Perturbation option. No other input parameters are required for this method. Please also make sure that the association of the random variables to the structural properties are set correctly, i.e. all RVs starting with the name "E" correspond to Young's modulus and with "D" correspond to the density.


SatelliteModal4.jpg


Once you select the method, click on the next button. Before proceeding to the analysis, you will be asked to set the High Performance Computing settings. First select the Oracle Grid Engine and wait until all the queues are retrieved from the system. Once this step is completed click on the Queue column in the Analysis selection menu and select the NASTRAN queue. Click on finish to start the analysis.


SatelliteModal5.jpg


The matlab code required for the COSSAN engine for this example is shown below:


%% Create the input

% define the RVs
Evert   = RandomVariable('Sdistribution','normal', 'mean',7e6,'cov',0.15);    
Ehor    = RandomVariable('Sdistribution','normal', 'mean',7e6,'cov',0.15);
Ecyl    = RandomVariable('Sdistribution','normal', 'mean',7e6,'cov',0.15); 
Enozzle = RandomVariable('Sdistribution','normal', 'mean',7e6,'cov',0.15);

Dvert   = RandomVariable('Sdistribution','normal', 'mean',2700e-6,'cov',0.1); 
Dhor    = RandomVariable('Sdistribution','normal', 'mean',2700e-6,'cov',0.1); 
Dcyl    = RandomVariable('Sdistribution','normal', 'mean',2700e-6,'cov',0.1);    
Dnozzle = RandomVariable('Sdistribution','normal', 'mean',2700e-6,'cov',0.1);   

Xrvs = RandomVariableSet('Cmembers',{'Evert','Ehor','Ecyl','Enozzle',...
                                     'Dvert','Dhor','Dcyl','Dnozzle'}); 
Xinp = Input('Sdescription','Xinput object');       
Xinp = add(Xinp,Xrvs);

%% Construct the Model

Sdirectory = fullfile(CossanX.getCossanRoot,'examples','Tutorials','SmallSatellite','FEinputFiles');
Xinj       = Injector('Sscanfilepath',Sdirectory,'Sscanfilename','Modal.cossan',...
                      'Sfile','Modal.inp');
Xcon       = Connector('Stype','nastran_x86_64',...
                     'SmaininputPath',Sdirectory,...
                     'Smaininputfile','Modal.dat',...
                     'Lkeepsimfiles',false);
Xcon       = add(Xcon,Xinj);
Xeval      = Evaluator('Xconnector',Xcon,'CSmembers',{'Xcon'});
Xmodel     = Model('Xevaluator',Xeval,'Xinput',Xinp);

%% Perform SFEM Analysis

Xsfem = Perturbation('Xmodel',Xmodel,'Sanalysis','Modal',...
                     'CdensityRVs',{'Dvert','Dhor','Dcyl','Dnozzle',},...
                     'CyoungsmodulusRVs',{'Evert','Ehor','Ecyl','Enozzle',});

Xout = Xsfem.performAnalysis;

Xout = getResponse(Xout,'Sresponse','specific','Nmode',2);
display(Xout);


Results of the SFEM analysis


The estimated statistics of the response obtained using various methods are summarized in the following table:

Summary of Statistics (2. Natural Frequency)

Response

   Perturbation Method   

Mean Value

3.22 Hz

CoV

0.16


See Also