Airplane wing analysis

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Vibration #3: Vibration in an Airplane WingIntroduction: In this example you will execute modal analysis of an airplane wing and find its naturalfrequencies.

Physical Problem: The wing is uniform along its length with cross sectional area as defined below.It is firmly attached to the body of the airplane at one end.

Problem Description:The chord of the airfoil has dimensions and orientation as shown in the figure.y The wing is made of low density polyethylene with a Young's modulus of 38e3 psi, Poisson's ration of

0.3, and a density of 8.3E-5 lbf-sec2/in4.Assume the side of the wing connected to the plane is completely fixed in all degrees of freedom. The wing issolid and material properties are constant and isotropic.y The flow velocity of air is 2m/s.y Objective:

To determine the natural frequencies of vibrationTo generate animations of these vibrations.

Figure:

IMPORTANT: Convert all dimensions and forces into SI units.

Starting ANSYS:y Click on ANSYS 6.1in the programs menu.y SelectInteractive.y The following menu comes up. Enter the working directory. All your files will be stored in this directory.

Also under Use Default Memory Modelmake sure the values 64 for Total Workspace, and 32 forDatabase are entered. To change these values unclick Use Default Memory Model.


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y Click RUNMODELING THE STRUCTURE

y Go to the ANSYS Utility Menuy Click Workplane>WP Settingsy The following window will appear:


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y Check the Cartesian and Grid Only buttonsEnter the values shown in the figure above.y Go to the ANSYS Main Menu.y Choose Utility Menu>PlotCtrls>Pan Zoom Rotate and click on the enlarge button (the big black

circle) five times. This will zoom in on the center of the area, and it will be easier to select theappropriate points below.

y Go to Main Menu>Preprocessor>Modeling>Create>Keypoints>On Working Plane.Create the keypoints as shown in the figure below:


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Note that I have only plotted lines before to make it easier to see the keypoints.y Go to Main Menu>Preprocessor>Modeling>Create>Lines>Splines thru KeypointsCreate two splines through the top three and the bottom three splines. The figure should look like the onebelow:


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y Now create an area enclosed by the two splines. Go to Modeling>Create>Areas>Arbitrary>By

Lines.y Pick the two splines and click OK. The model should look like the one below.

The modeling of the problem is done for now.

MATERIAL PROPERTIES

Setting preferences that are relevant to this problem:Main Menu>PreferencesTurn on Structural filtering.


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Hit OK.

MATERIAL PROPERTIESy Choose Preprocessor>Material Props>Material Models


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Double click Structural>Linear>Elastic>Isotropic

y Enter 38000 for Youngs Modulus. Enter 0.3 for Poissons Ratioy

Also, double click Density and input8.3e-5


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Exit Define Behavior

MESHING:

y As opposed to the standard method we have generated, of choosing element types in the previous stage,we will do so in this meshing section, because it is more intuitive. In this tutorial, we are going to first meshthe cross sectional area, using a 2D mesh.. with 2D element constraints. Then we will extrude thiselement into a 3D object, and generate a 3D mesh as well, obviously with 3D element constraints. So, weneed to define two types of elements:

y Click Preprocessor>Element Type>Add/Edit/Delete... In the 'ElementTypes' window that opensclick on Add... The following window opens:

y Click on Structural Mass>Solid and selectQuad 4node 42. Click APPLY. Next, choose Brick8node 45 and hitOK. Close the 'Element types' window.

y So now we have created the appropriate material model and the element types. Meshing will produce an


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appropriate model.

DIVIDINGTHE AREA INTO ELEMENTS:Go to Preprocessor>Meshing>MeshtoolClick Set on the line with Global under Size Controls


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y The following window appears. Enter 0.25 for element edge length. HitOK.

y Click Mesh, and in the Picking Dialog, choose Pick All. Note that you will likely see a warning. Dontworry about it. The problem is designed taking into consideration a limit on the number of nodes that

the educational version of ANSYS we have. If we make the mesh more fine, then when we extrude theshape, the limit will likely be exceeded. Continue.

y So far, the mesh should appear as follows:

y Now, choose Main Menu>Preprocessor>Modeling>Operate>Extrude>Elem Ext Optsy Choose 2 (Solid45) for the Element type number and enter 10 for the number of element divisions. Hit

OK.


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y Now choose Main Menu>Preprocessor>Modeling>Operate>Extrude>Areas>By XYZ Offsety Select Pick All in the selection dialog.

y Dont mind the warning. If we were using a full version of ANSYS, we would be able to choose SOLID95instead.

y Choose Utility Menu>PlotCtrls>Pan Zoom Rotate. Click on ISO and also on Fit. Hit close.


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BOUNDARY CONDITIONS AND CONSTRAINTS

The firs thing to do is to unselect the Plane42 elements used in the 2D area mesh since they wont beneeded/used for the analysis. Choose Utility Menu>Select>Entities.Choose Elements, By Attributes, Elem Type num, Enter 1 for the number, choose Unselect and hitApply

y Next, constraints will be applied to all nodes located where the wing is fixed to the body. Select allnodes at z = 0, then apply displacement constraints:

y Choose Nodes, By Location, Z Coordinates, enter 0 for the value, choose From Full and hitApply.


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Go to Preprocessor>Loads>Define Loads>Apply>Structural>Displacement>On Nodes. PickAll in the picking dialog. This will pick all Selected Nodes (we just decided that already)Choose All DOF and hit ok (by leaving the displacement value blank, we assign zero displacement)


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y The model should appear as follows, with new constraints on the end.

y Finally, we reselect all the nodes. Return to the Select dialog that is still open somewhere.y Choose By Num/Pick, click Sele All (Select All)and then click Cancel to close the box.SOLUTION

Go to ANSYS Main Menu>Solution>Analysis Type>New AnalysisChoose Modaly Choose Main Menu>Solution>Analysis Type>Analysis Options


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y Choose Block Lanczos and then enter 5 for the modes to extract and 5 for the modes to expand.HitOK.


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y Click OK again.Go to Solution>Solve>Current LS.

Click OK for the warnings. We already addressed the fact that these warnings are accepted. It is also okthat we did not use the Plane42 element in the analysis, since it was only developed to create the 2Dmesh we eventually build off of.Wait for ANSYS to solve the problem.Click on OKand close the 'Information' window.

POST-PROCESSING

Go to GeneralPostproc>Results Summary


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It is ok if your results are slightly different due to mesh uniqueness.

y Also, we want to animate the separate modal shapes.y First, select the first mode. Main Menu>General PostProc>Read Results>First Sety Utility Menu>Plot Ctrls>Animate>Mode Shape You can pick Linear or Sinusoidal Below.


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y Choose 30 frames and .25 seconds per frame. Then select Def+undef edge. Hit OK. Watch the firstshape:

y Play with settings if you want. For instance, in that animate dialog that opens, decrease the delay to5 or so for the animation to be more smooth.

y To see other modes of vibration, return to General PostProc and this time choose ReadResults>Next Set

y Animate again with Utility Menu>Plot Ctrls>Animate>Mode Shapey OK

Here are files for all 5 modes: (click on the image to see/download the file)Note, I tried to use a view that showed the deformations best. Try ISO for all the animations first if you want.Also, I plotted all the deformed shapes individually using General PostProc>Plot Results>Deformed Shape

First


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ISO

Second

TOP

Third


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RIGHT

Fourth

FRONT

Fifth


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TOP

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Airplane wing analysis