Turbine Blade (SFEM)

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In the following, performing SFEM analysis with the Turbine Blade structure will be described.

Definition of the probabilistic model

Three different portions of the structure, i.e. the lower, middle and upper parts, are considered individually and hence the Young's modulus of each is modeled using Random Variable with the following descirption:

Summary of the Probabilistic Model

Structural Property

Distribution     Mean Value      CoV Value

Young's Modulus x 3

Normal (truncated) 70 MPa 0.15
Total no of random parameters

3


The corresponding identifiers of the above defined probabilistic model should appear as follows within the NASTRAN input file:

MAT1 ,    1  ,   <cossan name="RV1" format="%10.4e" original="1" />   ,  ,  .3, 8.-6


MAT1  ,   2  ,   <cossan name="RV2" format="%10.4e" original="1" /> ,   ,  .3, 8.-6


MAT1  ,   3  ,   <cossan name="RV3" format="%10.4e" original="1" /> ,  ,  .3, 8.-6


and as follows within the ABAQUS input file:

** ---------------------------------------------------
** ---- *MATERIAL ------------------------------------
** ---------------------------------------------------
**
** material data from MAT1 with MID = 1
**
*MATERIAL, NAME=MAT_MID_1
*ELASTIC
<cossan name="RV1" format="%10.4e" original="1" /> , 0.3
*DENSITY
8e-06,
**
** material data from MAT1 with MID = 2
**
*MATERIAL, NAME=MAT_MID_2
*ELASTIC
<cossan name="RV2" format="%10.4e" original="1" /> , 0.3
*DENSITY
8e-06,
**
** material data from MAT1 with MID = 3
**
*MATERIAL, NAME=MAT_MID_3
*ELASTIC
<cossan name="RV3" format="%10.4e" original="1" /> , 0.3
*DENSITY
8e-06,
**


Performing SFEM Analysis using NASTRAN

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.


TurbineBladeTutorial3.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:


TurbineBladeTutorial2.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:


TurbineBladeTutorial4.jpg


In order to use Perturbation method, 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. rv1 -> young's modulus, etc.


TurbineBladeTutorial1.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.


TurbineBladeTutorial6.jpg


In order to make use of the solverbased implementation, select the corresponding option in the SFEM wizard and enter the IDs of the fixed nodes in the FE model as a vector (values separated by commas).


Remarks:

  • Please note that in order to be able to use the solverbased implementation, the model has to be fully constrained at certain nodes, which have to be entered correctly to the wizard.
  • Also, while using the Neumann method with the solverbased implementation, do not perform more than 100 simulations, since the efficiency might drop significantly for higher number of simulations within this option.


TurbineBladeTutorial5.jpg


If you want to perform Guyan PC analysis, just click on the PC analysis option and select the Guyan method within the "Approach" icon (please note that this method cannot be used together with the componentwise or solverbased implementations). This method is especially developed if the statistics of the response is to be analysed only at few selection locations in the FE model.



TurbineBladeTutorial11.jpg


These location can be entered as Node ID - DOF within the Guyan settings menu. Note that in this case the statistics will be calculated only at these entries of the displacement vector:


TurbineBladeTutorial12.jpg



Performing SFEM Analysis using ABAQUS

If ABAQUS is used as the 3rd party FE solver, there are some additional parameters to be set within the SFEM wizard. The first one of these is the constrained DOFs in the deterministic FE model. These DOFs can be entered using the corresponding section of the SFEM wizard. Enter here the node IDs 616, 1777, 1779, 4120, 4276, 4286 (note that all 6 DOFs for each node are added automatically to the list).


TurbineBladeAbaqus1.jpg


Next, the step definition (defines the boundary conditions to the ABAQUS solver) has to be entered within the wizard. Enter there the following strings line by line as shown below: "**BOUNDARY  ",   "     616, 1,6, 0.",    "     1777, 1,6, 0.",   "     1779, 1,6, 0.",  "     4120, 1,6, 0.",   "     4276, 1,6, 0.", "     4286, 1,6, 0.",    "*DLOAD, OP=NEW",   "ALL_MASSIVE_ELEMENTS, GRAV, 3.5e+08, 0., 1., 0.".


TurbineBladeAbaqus2.jpg


Once these additional parameters are entered, the SFEM analysis can be performed similarly as in the case for NASTRAN solver. Please note that componentwise and solverbased implementations are disabled for this solver (they are only available for NASTRAN).


TurbineBladeAbaqus3.jpg


Results of the SFEM analysis

Once the analysis is completed, the results can be accessed using the GUI. Go to the corresponding directory and double click on the Sfem Output object. You can visualize the calculated mean, std dev and CoV values for the whole displacement vector by clicking on the "open in Table view" option.



TurbineBladeTutorial7.jpg


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

Summary of Statistics (Node 150 - DOF 3)

Response

Neumann (150 samples) Guyan P-C (3.order) Perturbation

Mean Value

9.09 9.07 8.97

CoV

0.11 0.10   0.10


These statistics can be also observed using the table view:

TurbineBladeTutorial8.jpg