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Problem Specificati=
on
In this tutorial, we'll analyze the plane shell with stiffeners shown in=
the figure below.
(Click for enlarged figure.)
All edges are clamped. A constant pressure of 0.05 N/mm2acts =
on the underside of the shell (i.e. the pressure acts in the +z direction).=
Since the geometry and loads are symmetric about both the x and <=
em>y-axes, we need to model only one-quarter of the structure. The dim=
ensions of the plate and stiffeners are shown in the figure below which sho=
ws only one-quarter of the structure.
The Young's modulus E =3D7.3x104 MPa and the Poisson ratio is=
0.33.
Print out this page and have it on hand so that you can easily refer to th=
e geometry and problem specification as you go through the tutorial.
Go to Step 1: Start-up and preliminary set-up
See and rat=
e the complete Learning Module
Go to all ANSYS L=
earning Modules
Step =
1: Start-up and preliminary set-up
Create a folder
Create a folder called shell at a convenient location. We'll us=
e this folder to store files created during the session.
Start ANSYS
On Windows systems, select the appropriate menu path. On my system, the =
path is
Start > Programs > ANSYS 10.0 > ANSYS Product Launcher<=
/strong>
Enter the location of the folder shell that you just created as=
your Working directory by browsing to it.
Enter shell as your I=
nitial jobname. Click on Run.
Resize windows as shown in this snapshot so that you can re=
ad instructions in your browser window and implement them in ANSYS.
Set Preferences
Main Menu > Preferences
In the Preferences for GUI Filtering dialog box, click on the b=
ox next to Structural so that a tick mark appears in the box. From now on, onl=
y the menu options valid for structural problems will be made available.
Units
ANSYS leaves it to us to use a consistent set of units. For convenience,=
we'll use the following set of units: mm for geometric dimensions; N for f=
orces; and N/mm2 for Young's modulus and pressures. The resultin=
g stresses will be in N/mm2 or MPa. Convince yourself that this =
is a consistent unit system; don't take my word for it.
Enter Parameters
We'll play smart and create scalar parameters corresponding to the plate=
and stiffener dimensions_._ This will later allow us to vary these paramet=
ers and perform optimization studies.
Utility Menu > Parameters > Scalar Parameters
Define a parameter for the plate length l1 =
in mm:
L1=3D750
Click Accept. Similarly, define other parameters corresponding to the dimensi=
ons and click Accept after each (parameter names are not case-sensiti=
ve). Before you specify a parameter, refer to the geometry specif=
ication to remind yourself what dimension that parameter represents.
W1=3D250
W2=3D2
W3=
=3D2
H1=3D5
H2=3D15
<=
code>H3=3D20
{{}}
We'll play smarter and also specify the number of stiffeners in each direc=
tion as parameters so that these too can be varied easily in tradeoff studi=
es. We'll employ the labels NSX and NSY for the number of=
stiffeners in the x and y directions, respectively.
NSX=3D2
NSY=3D3
We'll use the above parameters when creating the geometry in Step 4. We'l=
l also define some parameters which we'll use in Step 5 to set the mesh size=
along edges.
NDIV_X=3D3
NDIV_Y=3D6
SIZE_Z=3D5
Close=
span> the Scalar Parameters window.
Go to Step 2: Specify Element Types and Constants
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e the complete Learning Module
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earning Modules
Ste=
p 2: Specify element type and constants
Since thin structures can be modeled efficiently as shells, we'll use sh=
ell elements to build the finite-element model. Shell elements can support =
membrane and bending loads consistent with classical shell theory (sorry, F=
EA doesn't let you off from understanding basic theory). As you can imagine=
, shell elements are appropriate when the thickness of the structure is sma=
ll compared to the other dimensions. The computational savings come about b=
ecause only the mid-surface of the structure is modeled; the thickness and =
other cross-sectional properties are incorporated into the element stiffnes=
s matrix and input as "real constants" in ANSYS. (This is analogous to mode=
ling beams using beam elements where the beams are modeled as lines with th=
ickness and other cross-sectional properties being "real constants"). Secti=
on 2.10 in the ANSYS Element Reference manual gives you a page of =
useful information on shell elements. Be sure to peruse it in the online do=
cumentation since it'll be on the final. :wink:
Specify Element Type<=
/h4>
Let's take a peek at the shell elements available in ANSYS. Bring up the=
ANSYS documentation window, select the Search tab, enter the phrase "pictoria=
l summary" and click on =
List Topics. Then double-click on 3.2 Pictorial Su=
mmary in the left pane. At the top of the pictorial summary of element=
types in the right pane, click on <=
strong>SHELL Elements. This brings up the list of she=
ll elements available in ANSYS including many with specialized capabilities=
. Perusing this list, you'll see thatSHELL63 (4-node elastic shell) is a basic=
shell element and a possible candidate for our problem. A close relative i=
s SHELL93<=
/span>(8-node elastic shell) which has mid-side nodes in addition to the co=
rner nodes. Since the mid-side nodes give greater accuracy, we'll useSHELL93 f=
or our problem. Click on SHELL93in the help and take a few minutes to persue t=
he manual page for this element. What are the "real constants" that we'll n=
eed to enter in the next step? Note that each node has six degrees of freed=
om: three translational and three rotational.
Main Menu > Pre=
processor> Element Type > Add/Edit/Delete > Add...
Pick Shell in the left field and Elastic 8node 93 in the right field. Click OK to=
select this element. The SHELL93 element will now be available in the meshing=
step. Close the Element Types menu.
Specify Element =
Constants
Main Menu > Preprocessor> Real Constants > Add/Edit/Del=
ete > Add
This brings up the Element Type for Real Constants menu. Click =
OK =
to specify the real constants for the SHELL93 element.
When meshing, we'll have to assign three different thickness values: H1 for the plate; W2 and W3 for the stiffeners in t=
he x and ydirections, respectively. This means we'll have=
to create three real constant sets, one for each of these thickness values=
. According to theSHELL93 help page, if the element has a constant=
thickness, only TK(I)=
em>, the shell thickness at the first corner node, needs to=
be input.
Create the first real constant set: make sure Real Constant Set No. is set =
to 1
. For T=
K(I), enter H1
. Leave the other fields bl=
ank since they are not applicable to our problem. Click Apply.
Create the second set: For Real Constant Set No., enter 2
. For=
TK(I), enter {W2}} and click Apply.
Create the last set: For =
Real Constant Set No., enter 3
. For <=
span style=3D"color: rgb(153,0,153);">TK(I), enter W3
and click <=
strong>OK.
Save: Toolbar > SAVE_DB
Go to Step 3: Specify material properties
See and rat=
e the complete Learning Module
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earning Modules
Step 3: =
Specify material properties
Main Menu > Preprocessor >Material Props > Material Mod=
els
In the Define Material Model Behavior menu, double-click on Structural, Linear, Elastic<=
/strong>, and Isotrop=
ic.
Enter Young's modulus EX in MPa: 7.3e4
Enter Poisson's Ratio PRXY:0.33
. Click OK.
Close the Define Material Model Behavior menu.
Save your work: Toolbar > SAVE_DB
Go to Step 4: Specify geometry
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e the complete Learning Module
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earning Modules
Step 4: Specify ge=
ometry
Strategy for=
Geometry Creation
The geometry of the structure has a repetitive pattern as can be seen in=
the schematic below. We'll exploit this feature in creating the finite-ele=
ment mesh for the entire structure. In this step, we'll create the geometry=
for the sub-section AEFG only. In Step 5, we'll mesh this sub-sect=
ion and use it to generate the mesh for the entire structure in two steps:<=
/p>
- We'll copy parts of AEFG to create the sub-section ABCD. (When we copy areas, the associated mesh is also copied.)
- We'll copy sub-section ABCD in both directions to generate the=
mesh for the entire structure. Clever move, eh?
In sub-section AEFG above, the stiffeners cross each other at <=
em>F. Modeling this correctly is tricky, so indulge me while I explain=
how we are going to proceed. At the end of the geometry step, the isometri=
c view of AEFG will look as below, with the keypoint and area numb=
ers turned on (different colors refer to different areas). If the stiffener=
s share keypoints 3,5 and 9, the stiffener crossing is modeled correctly an=
d a load applied to one stiffener will be transferred appropriately to the =
other one. To this end, we will divide the horizontal stiffener into two ar=
eas (A3, A4). This will also yield a regular mesh as we'll see in the meshi=
ng step.
Note that the horizontal stiffener has to be split into two areas A3 and=
A4 because it has a larger width than the vertical stiffener. Instead, if =
the vertical stiffener is the wider one, it'd be the one that you'd have to=
split into two areas. This would change the topology of the model; somethi=
ng to keep in mind when you vary the stiffener dimensions in optimization s=
tudies.
Keypoints Coordinat=
es
Using the figure in the problem specification and the one =
above, create a table of the keypoint coordinates required to create areas =
A1-A4, using the parameters defined in Step 1. Recall that areas correspond =
to the mid-surface of the structure. Are my keypoint coordinates below corr=
ect? || No. || x || y || z ||
1 |
0 |
0 |
0 |
2 |
W1/(2*NSX) |
0 |
0 |
3 |
W1/(2*NSX) |
L1/(2*NSY) |
0 |
4 |
0 |
L1/(2*NSY) |
0 |
5 |
W1/(2*NSX) |
L1/(2*NSY) |
H2 |
6 |
W1/(2*NSX) |
0 |
H2 |
7 |
0 |
L1/(2*NSY) |
H2 |
8 |
0 |
L1/(2*NSY) |
H3 |
9 |
W1/(2*NSX) |
L1/(2*NSY) |
H3 |
Create Keypoints=
and Areas
In previous tutorials, we have defined keypoints (i.e. vertices) using m=
enus. Here, we will instead use the command line to create keypoints. The t=
wo methods are equivalent but the latter is faster for more experienced use=
rs. Let's check the documentation to find the command for creating keypoint=
s. In the ANSYS documentation window, select the Search tab, enter "keypoint" =
as the search term and click on List Topics. Double-click on 5.2 Creating =
Your ..._in the left pane. Section 5.2 has useful information on creating y=
our solid model. Scroll down to section 5.2.1. The table near the beginning=
of this section indicates that the command for creating keypoints is =
K_.=
Note that the corresponding menu path is what we have used in previous tut=
orials to create keypoints. The menu path also indicates that this command =
is part of the Preprocessor module. Click on K to see the format of t=
his command.
Since it is useful to track the keypoint and area numbers as we create t=
he geometry, turn on keypoint and area numbering: Utility Menu >=
PlotCtrls > Numbering
Turn on Keypoint numb=
ers and Area numbers and click OK.
To access the K<=
/strong> command, make sure the preprocessor module is open.
Create keypoint #1 at (0,0,0): at the command prompt, type K,1,0,0=
,0
as below and hit Enter. Note that when you type the comm=
and, the format of the command pops-up as a reminder.
Similarly, create keypoints #2-#4 in the above table by entering the fol=
lowing at the command prompt:
K,2,W1/(2*NSX),0,0
K,3,W1/(2*NSX),L1/(2*NSY),0
K,4,0,L1/(2*NSY),0
ANSYS uses the current value of the parameters W1, L1, NSX and NSY when creating the keypoints. If you=
change the value of any of these parameters after you have create=
d the keypoints, these keypoints will notbe moved accordingly, i.e=
. the keypoint coordinates will still contain the old values of the paramet=
ers. It is important to remember this idiosyncracy of ANSYS; otherwise, it =
could come back to bite you in uncomfortable parts of your anatomy.
Is it safe to presume that you are cheating like I would and cutting-and=
-pasting the command line inputs? That's OK as long as you do them one-by-o=
ne so that you can track the effect of each command. To fit all the keypoin=
ts in your current view, click on the Fit View icon in the rightmo=
st part of the GUI (see snapshot below). You'll have to click on this butto=
n periodically to fit the entire geometry into your view.
To create an area from keypoints #1-#4, enter a,1,2,3,4
at =
the command line. Note that ANSYS automatically assigns the label A1 to this first area. This area corresponds to the plate.
Next create keypoints #5 and #6 followed by the area corresponding to th=
e stiffener in the y-direction. Enter
K,5,W1/(2*NSX),L1/(2*NSY),H2
K,6,W1/(2*NSX),0,H2
A,=
2,3,5,6
To bring up the isometric view, click on the Isometric View ico=
n in the right part of the GUI (see snapshot below). The area is labeled A2. If the area disappears from the view, select Utility Menu > P=
lot > Areas.
Now that we have gotten the hang of this business, we can create the rem=
aining keypoints and areas in our sleep (remember to wipe the drool off the=
keyboard):
K,7,0,L1/(2*NSY),H2
K,8,0,L1/(2*NSY),H3
K,9,W1/(2*NSX),L1/(2*NSY),H3
A,3,4,7,5
A,5,7,8,9
Utility =
Menu > Plot > Areas
The geometry should look like this:
Save your work: Toolbar > SAVE_DB
Go to Step 5: Mesh geometry
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e the complete Learning Module
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earning Modules
Step 5: Mesh geometry=
As discussed in the previous step, we'll first mesh the subsection A=
EFG that we just created.
Set Mesh Size Alon=
g Edges
We'll use the previously-defined parameters NDIV_X, NDIV_Y=
em> and SIZE_Z to set the mesh size along edges. The table below d=
escribes what each parameter is and the value we have assigned to it.
Parameter |
Value |
Description |
NDIV_X |
3 |
No. of divisions for edges along x=
p> |
NDIV_Y |
6 |
No. of divisions for edges along y=
p> |
SIZE_Z |
5 |
Size of divisions for edges along z<=
/p> |
Edges along z are of two different lengths, as should be appare=
nt from the geometry display. For instance, the edge between keypoints #5 an=
d #9 is smaller than that between keypoints #3 and #5. By setting the eleme=
nt size rather than the number of divisions, we can use the same parameter =
for both edge lengths.
Bring up the MeshTool: Main Menu > Preprocessor > MeshTool
We are going to continually use the MeshTool to generate the mesh=
. So resize and rearrange the windows slightly so that you can access the <=
em>MeshTool, ANSYS GUI, and tutorial simultaneously.
If you have trouble selecting the correct lin=
e below, hold down the left mouse button until the line is=
selected and then release the left button. If you want to deselect=
a line, right-click to go into deselect mode, left-click on the l=
ine to be deselected and right-click again to go back into select mode. =
|
Under Size Controls=
and Lin=
es, click Set. Pick all four lines in the x-_direction. and cl=
ick OK in the pick menu. Enter NDIV_X
=
for No. of element =
divisions and click Apply.
Next, pick all three lines in the y-direction and click OK in the pick menu=
. Enter NDIV_Y
for No. of element divisions and click Apply.
Last, pick all five lines in the z-direction and click OK in th=
e pick menu. Enter SIZE_Z
for Element edge length. Make sure No. of element divisions is=
blank. Click OK.
Plot lines to see the element divisions along edges and check that they =
have been set correctly: Utility Menu > Plot > Lines=
. If you made an error, repeat the above steps before saving.
Generate Mesh for P=
late
Recall that the plate and the horizontal and vertical stiffeners have di=
fferent thicknesses which have been assigned to different "real constant" s=
ets. Jog your memory about which thicknesses have been assigned to which "real c=
onstant" sets in Step 2.
We'll first mesh the plate using real constant set #1. Under Element Attributes in MeshTool, click on Set. You will see that the element type and m=
aterial number are already set and the default real constant set is #1. The=
se are the options we need for the plate; so these don't need to be changed=
. Click Cancel.
Plot areas: Utility Menu &=
gt; Plot > Areas
Click on Mesh in MeshTool. Pick area A1 and click OK. The resulting m=
esh for the plate is displayed.
Generat=
e Mesh for Vertical Stiffener
Under Element Attributes=
in MeshTool, click on Set. Set Real constant set number to =
2 a=
nd click OK.
Plot areas: Utility Menu &=
gt; Plot > Areas
Click on Mesh in MeshTool. Pick area A2 and click OK. The resul=
ting mesh for the plate is displayed.
Gener=
ate Mesh for Horizontal Stiffener
Under Element Attribu=
tes, click on <=
strong>Set. Set Real constant set number to 3 and =
click OK.
Plot areas: Utility Menu &=
gt; Plot > Areas
Click on Mesh in MeshTool. Pick areas A3 and A4 and click OK.
Let's change the graphical display so that the geometry is displayed as =
a solid model with the shell thicknesses shown. At the command prompt, type=
/eshape, 1
and then select Utility Menu > Plot > Replot. When the /ESHAPE command in issued, ANSYS uses the real constants associated =
with each element to determine its shape. (Note that commands are not case-=
senstive.)
Do the relative thicknesses of different parts of the shell look correct=
? Feel free to manipulate the graphical display to check this.
You can access different model views such as =
front, right, isometric etc. using the buttons to the right of the graphics=
window. At the bottom of this row of icons is the Dynamic Model Mode=
em> . Clicking =
this icon allows you to manipulate the model using the mouse (alternatively=
, you can hold down the Ctrl key). To see the help page on this mo=
de, right-click on the icon and select Dialog Overview > Pan, Zoom, =
Rotate > Dynamic Mode: Model. |
Save: Toolbar > SAVE_DB=
Copy Mesh in x-Dir=
ection
Turn off the element shapes to make the display less cluttered by enteri=
ng the following commands:
/eshape,0
/replot
Plot areas: Utility Menu &=
gt; Plot > Areas
Copy areas: Main Menu >=
Preprocessor > Modeling > Copy > Areas
Pick A1, A3, and A4 and click OK. (Hold down the left mouse button until the c=
orrect area is selected.)
Copy Areas menu: We want two copies including the original, so =
leave Number of copies=
em> as 2. For X-offset, enter W1/ (2*NSX)
, leave =
Y- =
and Z-offsets blank and click <=
em>OK.
Since the associated keypoints are also copied over, you'll notice that =
there is a collection of two coincident but separate keypoints along shared=
boundaries where the original and copied entities overlap. It's key that w=
e [merge these coincident keypoints|SIMULATION:Semi-monocoque =
shell page 5]; we'll undertake this after we are finished with the copy ste=
p.
Have the elements associated with the areas also been copied? Check this: =
Utility Menu > Plot > Elements
Save: Toolbar > SAVE_DB=
As with keypoints (and lines too), there is a collection of two coincide=
nt but separate nodes along the shared boundaries. Let's convince ourselves=
of this truism:
- Turn on node numbers (in addition to keypoint and area numbers) using <=
span style=3D"color: rgb(51,51,51);">Utility Menu > PlotCtrls &g=
t; Numbering
- Display elements and nodes together: Utility Menu > PlotCtrls > Multi-Plot Ctrls > OK. Leave only N=
odes and Elements turned on and click OK. Select Utility Menu > Plot > Multi-Plots.=
- Zoom into the bottom-center of the model as in the snaphsot below. At t=
he bottom of the symmetry plane, you should notice that there are actually =
two nodes, 2 and 172. Node 2 is associated with the original area and node =
172 with the copy. We'll merge coincident nodes a little later. (Note that =
your node numbers may be different from mine since numbering can vary on di=
fferent computer systems.)
Copy Mesh in y-Dir=
ection
Plot areas: Utility Menu &=
gt; Plot > Areas
Click on the Fit View and Isometric View icons in the =
rightmost part of the GUI.
Copy areas: Main Menu >=
Preprocessor > Modeling > Copy > Areas
Pick A1, A2, and A5 and click OK.
Copy Areas menu: Leave <=
strong>Number of copies as 2. For Y-offset, enter L1/ (2*NSY); delete X-offset; leave Z-offset blank and click OK.
Check the resulting mesh for sub-section ABCD: Utility Menu > Plot &g=
t; Elements
Turn-off node numbers to reduce clutter.
Copy Sub-Section ABC=
D
How many copies of sub-section ABCD do we need to make in the x-=
and y-directions? What are the values of X-Offset and Y-Offset in each case? Jot your answers down so that you can check t=
he values below.
Copy areas: Main Menu > Preprocessor > Modeling > Copy =
> Areas > Pick All
Copy Areas menu: Number of copies =3D NSX
; X-offset =3D =
W1/NSX
; Y-<=
/em> and Z-offsets should be blank or zero. Click Apply.
Repeat copy in y-direction: Select Pick All again in the pick menu=
.
Copy Areas menu: Number of copies =3D NSY
; Y-offset =3D =
L1/NSY
; X-<=
/em> and Z-offsets should be blank or zero. Click OK.
Check the resulting mesh: Utility Menu > Plot > Elements=
strong>
Merge Coincident=
Entities
We saw earlier that the copy operations resulted in coincident nodes, ke=
ypoints, etc. along shared boundaries. We need to merge these coincident it=
ems so that separate portions of the model are combined into one. Otherwise=
, the various portions will live as independent entities and loads applied =
to one portion will not be transferred to its neighbors. The effect of the =
merge operation is shown schematically below.
View documentation about the merge utility: ANSYS Help > Cont=
ents > Modeling and Meshing Guide > Number Control and Element Reorde=
ring > Number Control
This section has useful information about merging entities. It indicates=
that one can either merge keypoints, nodes, etc. individually or merge allcoincident entities at once (with ANSYS ensuring that they are mer=
ged in the proper sequence). Since we'd like to palm off as much work as po=
ssible to ANSYS, we'll use the latter option.
Select Main Menu> Preprocessor> Numbering Ctrls> Merge =
Items
For Type of item to b=
e merged, select All and click OK. This will merge all coinc=
ident entities.
Earlier we saw that nodes 2 and 172 were coincident. Zoom in on this regi=
on again with node numbers turned on. What do you see?
If you performed the merge operation correctly, you'll see that the high=
er numbered node has been deleted and the two coincident nodes have been re=
placed by a single node.
Save: Toolbar > SAVE_DB
Compress Item Number=
s
If you scroll down the help section on numbering that we've been peeking =
at, you'll find a useful spiel on Compressing Item Numbers(section=
11.1.2): "As you build your model, you might, by deleting, clearing, mergi=
ng, or performing other operations, create unused slots in the numbering se=
quence for various items. These slots will remain empty for some items (suc=
h as elements) but will be filled in for other items (such as keypoints) as=
new items are created. To save data storage space (by eliminating otherwis=
e empty numbers) or to preserve desired sequencing (by forcing newly-create=
d items to be assigned numbers greater than those of existing items), you c=
an eliminate these gaps by "compressing" your numbering".
Check the range of node numbers before compressing the numbering: Utility Menu > List > Nodes > OK
Compress numbering for all items (nodes, elements, etc.): Main M=
enu> Preprocessor> Numbering Ctrls> Compress Numbers
For Item to be compre=
ssed , select <=
strong>All and click OK.
Re-check the range of node numbers after compressing. You should find th=
at the range of node numbers is reduced since there are now no gaps in the =
numbering.
Close MeshTool.
Save: Toolbar > SAVE_DB
Go to Step 6: Specify boundary conditions
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e the complete Learning Module
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earning Modules
Step 6: =
Specify boundary conditions
The boundary conditions given in the problem specification=
are summarized in the schematic below. Keep in mind that the edge conditio=
ns need to be applied to the plate as well as the stiffeners.
Apply Symmetry alon=
g AH
We'll apply this BC in two steps:
- Select edges along AH
- Apply symmetry condition to the selected edges
Plot areas: Utility Menu > Plot > Areas
Adjust the display: Click on the Isometric View and Fit Vie=
w icons in the rightmost part of the GUI.
Utility Menu > PlotCtrls > Numbering: Turn of=
f area and node numbering; turn on line numbering.
Select all edges along AH: Utility Menu > Select >=
; Entities
We are going to continually use the Select Entitiesmenu to appl=
y the BC's. So resize and rearrange the windows slightly so that you can ac=
cess this menu, the ANSYS GUI, and the tutorial simultaneously.
Select Entities menu: Select Lines from the pull-down menu at the =
top. Select below that. Choose By LocationY coordinates. Under Min,Max, enter 0. This will select all lines whose centers lie at y=3D0. Make sure From Full is selected so that we are sel=
ecting entities from the full model. Click Apply.
Check which lines have been selected: Select Entities menu >Plot. You should see that the edges along AH have been sel=
ected.
Apply symmetry condition to the selected edges: Main Menu > P=
reprocessor > Loads > Define Loads > Apply > Structural > Di=
splacement > Symmetry B.C. > On Lines > Pick All
This applies the symmetry condition to all the selected lines.
Select the entire model: Click Select All and then Replot in the Select En=
tities menu. You should see the S symbol along the edges wher=
e the symmetry BC has been applied.
Apply Symmetry alon=
g AJ
We'll first select all edges along AJ. Go back to Select Entities menu: Leave Lines and By=
Location in place. Choose X coordinates. Under Min,Max, ret=
ain 0
. This will select all lines whose centers lie at x=
=3D0. Make sure Fro=
m Full is selected. Click Apply.
Check which lines have been selected: Select Entities menu > Replot. You should see that only the edges along AJ are c=
urrently selected.
Let's apply the symmety BC to these edges: Main Menu > Prepro=
cessor > Loads > Define Loads > Apply > Structural > Displac=
ement > Symmetry B.C. > On Lines > Pick All
Select the entire model: Click Select All and then Replot in the Select En=
tities menu.
Apply Clamped BC a=
long HI
Now that we've gotten the hang of this boundary business, let's mop up O=
peration BC's in short order.
Select Entities menu: Leave Lines, By Location and X coordinates selecti=
ons in place. Under Min,=
Max, enter W1
. This will select all lines=
whose centers lie at x=3DW1. Make sure From Full is selected. Cli=
ck Apply=
span>.
Select Entities menu > Replot
Constrain all six nodal degrees of freedom (DOF) for the selected edges:=
Main Menu > Preprocessor > Loads > Define Loads > Apply=
> Structural > Displacement > On Lines > Pick All > All DOF=
> OK
The (cluttered) display will show that all six DOF's have been constrain=
ed.
Select Entities menu: Select All and Replot=
Apply Clamped BC a=
long JI
Select Entities menu: Leave Lines, and By Location in place. Choose <=
span style=3D"color: rgb(102,0,102);">Y coordinates. Under Min,Max=
, enter L1
. This will select all lines wh=
ose centers lie at y=3DL1. Make sure From Full is selected. Click =
Apply.
Select Entities menu > Replot
Constrain all six nodal degrees of freedom (DOF) for selected edges:Main Menu > Preprocessor > Loads > Define Loads > Apply >=
; Structural > Displacement > On Lines > Pick All > All DOF >=
; OK
Select Entities menu: Select All and Replot
Save: Toolbar > SAVE_DB
Apply Pressure on P=
late
Utility Menu > PlotCtrls > Numbering: Turn off line numbering.
Utility Menu > Plot > Areas
Choose areas corresponding to the plate: In the Select Enti=
ties menu, select A=
reas from the pull-down menu at the top. Leave By Location belo=
w that. Choose Z coordin=
ates Under Min,Max, enter 0
. This will selec=
t all areas whose centers lie at z=3D0. Make sure From Full is select=
ed. Click Apply.
Check which areas are currently selected: Select Entities menu =
> Replot
Apply a pressure of 0.05 N/mm2 on the plate in the +z direction: Main Menu > Preprocessor > Loads > Define Loa=
ds > Apply > Structural > Pressure > On Areas > Pick All
For VALUE, enter 0.05
. Click OK.
ANSYS will mark the faces where the pressure is applied. Let's instead p=
lot the applied pressure using arrows to check its direction: Utili=
ty Menu > PlotCtrls > Symbols. For Surface Load Symbols, select Pressures and under Show pres=
and convect as, select Arrows. Click OK. Are the pressures =
acting in the right direction?
Select Entities menu: Select All, Replot and Cancel. You should now s=
ee the entire model. Review that all the BC's have been applied correctly.<=
/p>
Save: Toolbar > SAVE_DB
Create Log File
In parametric studies to be undertaken later, we'll start with the log f=
ile containing the commands from the first six steps that we just went thro=
ugh. To save this log file, select
Utility Menu > File > Write DB log file
Under Write Database =
Log to, enter the filename for the logfile: shell_=
step6.lgw. At the bottom of this menu, select Write Essential Commands on=
ly. Click OK. Review shell_step6.lgw by opening it in a text editor.<=
/p>
Go to Step 7: Solve!
See and rat=
e the complete Learning Module
Go to all ANSYS L=
earning Modules
Step 7: Solve!
Enter Solution Module: Main Menu > Solution
Enter check
in the Inputwindow. If the problem has=
been set up correctly, there will be no errors or warnings reported. You s=
hould see the following message in the Output window: The an=
alysis data was
checked and no warnings or errors were found.<=
/code>
Main Menu > Solution > Solve > Current LS
Review the information in the /STATUS Command window. Close thi=
s window.
Click OK in Solve Current Load Step menu.
ANSYS performs the solution and a window should pop up saying "Solution =
is done!". Close this window.
Save: Toolbar > SAVE_DB
Go to Step 8: Postprocess the results
See and rat=
e the complete Learning Module
Go to all ANSYS L=
earning Modules
Step 8: Post=
process the results
The Results Viewer provides a convenient way to review results.=
Main Menu > General Postproc > Results Viewer
The title bar for the Results Viewer indicates that the results=
are being read from the shell.rst file. Rearrange the windows sli=
ghtly so that you can access the Results Viewer, ANSYS GUI and tut=
orial simultaneously.
Under Choose a result=
item, select Nodal Solution > DOF Solution=
> Displaced structure. Click on the Plot Results icon.
Hold down the Ctrl key and use the mouse to manipulate the model vie=
w;check that the BC's and loads have been imposed correctly. The snapsh=
ot below shows one view that is useful in checking the BC's. Are the symmet=
ry and clamped conditions satisfied at the corresponding edges for the face=
sheet as well as the stiffeners? Is the model deformation as you'd expect f=
or a uniform pressure on the facesheet in the +z direction?
=
p>
The maximum displacement DMX=3D3.88 mm. Where do you think this=
occurs? We'll check this in a minute.
Animate the defromation and obsessively recheck the BC's:
Results Viewer > Animate Results > Deformed Shape > OK =
> Def + undef edge > OK
Select Forward Only=
em> in the Animation Controller.
Plot w Displacement
In the Results Viewer, in place of Displaced structure, choose Nodal Solution > DOF Solution > Z-Component of displacement. Click on the Plot =
Results icon.
The location of maximum deflection wmax is labeled MX. This occurs not at the facesheet center but on the edge x=3D0, =
at approximately y=3DL1/3. As expected, the deflection is=
zero along the clamped edges.
To save a copy of this plot, select Results Viewer > Image Ca=
pture > Capture to file > OK.
For filename, enter w_contours
. This creates the file _w_co=
ntours.png_ in your working directory. Check that you can open this file us=
ing your pet image viewer.
Deflection a=
t Facesheet Center
To query the value of the deflection at the center of the facesheet, sel=
ect the Query Results icon in the Results Viewer.
Pick the node at X=3D0, Y=3D0. The coordinates of the =
picked node and the corresponding value of UZ (i.e. w dis=
placement) are displayed in the Query Subgrid Results menu. The de=
flection at the center of the facesheet is 3.8 mm.
Cancel th=
e Query Subgrid Results menu.
=CF=83xx=
for Facesheet
For clarity, let's first plot =CF=83xx for =
just the facesheet. Select the elements for the facesheet in two steps:
- Select areas corresponding to the facesheet.
- Select elements attached to these previously selected areas. Close the =
Results Viewer.
Utility Menu > Plot > Elements
Utility Menu > Select > Entities
Select Entities menu: Select Areas, By Location and Z coordinates. Under=
Min,Max=
span>, enter 0
. Make sure From Full is selected. Click Apply.
Following this, select Elements, Attached to, Areas and F=
rom Full. Click Apply and then Replot. You should see that o=
nly elements for the facesheet are currently selected.
Main Menu > General Postproc > Results Viewer > Nodal S=
olution > Stress > X-Component of stress
Click Plot Results icon.
Shell theory provides the stresses through the thickness of the shell. T=
his is illustrated in the help page for SHELL93 element. If, like me, you a=
re looking at the top of the facesheet, then the contours values correspond=
to =CF=83xx values for the top face. Check th=
e =CF=83xx value for the top face at the faces=
heet center:
Results Viewer > Query Results
Pick the node at X=3D0, Y=3D0. I get =CF=83xx=3D51 MPa at the center-top of the facesheet.
Hold down the Ctrl key and flip the model over so that you are =
looking at the bottom of the facesheet as in the snapshot below. N=
ow the contours values correspond to =CF=83xx =
values for the facesheet bottom. Use Query Results to determine =
=CF=83xx at the center-bottom of the face=
sheet. I get -56 MPa. What do you get? The negative sign indicates compress=
ion.
(For an enlarged view, click and maximize the browser window=
)
Thus, at the facesheet center, =CF=83xx var=
ies from a tensile stress of 51 MPa at the top to a compressive stress of 5=
6 MPa at the bottom.
Using Query Results=
em>, I get =CF=83xx=3D116 MPa =
at the edge point x=3DW1, y=3D0 for the bottom of the fac=
esheet (see snapshot above). What's the value you finagled out of ANSYS?
Do these values look plausible? We'll investigate this in Step 9 when we =
compare the center and edge stress values to plate theory.
Cancel<=
/span> the Query Subgrid Results menu.
=CF=83yy=
for Facesheet
Results Viewer > Nodal Solution > Stress > Y-Component =
of stress
Click Plot Results icon. The snapshot below shows the =CF=83yy contours.
Using Query Results=
em>, I get the following values for the bottom of the faces=
heet (see snapshot above):
- At the center, =CF=83yy=3D -28 MPa.
- At the clamped edge location (x=3D0, y=3DL1), =CF=
=83yy=3D 77 MPa. What are your corresponding value=
s?
=CF=83xx for Stiffeners
Currently, the facesheet is selected and the stiffeners are unselected. =
To plot stress contours for the stiffeners, we'll unselect the facesheet an=
d select the stiffeners i.e. reverse the selection. This can be done using =
the Invert operation:
Select Entities menu> Invert
Select Entities menu> Replot
(In MS-Windows, you can cycle through windows on the desktop by holding =
down the Alt key and repeatedly pressing the Tab key. In =
case the Select Entities menu has disappeared, exit the Result=
s Viewer, bring up the Select Entities menu and re-enter the =
Results Viewer.)
Results Viewer > Nodal Solution > Stress > X-Component =
of stress
Click Plot Results icon.
Manipulate the view so that you are looking down on the top of the stiff=
eners as in the snapshot below. You might have to flip the model over.
=
p>
The =CF=83xx values for the stiffeners in t=
he y-direction is virtually zero; confirm this using Query Results. This means=
that, as expected, the load in the x-direction is carried by the =
stiffeners in that direction.
Let's determine =CF=83xx values at the =
top of the x-stiffener closest to the center; we'll compare t=
hese values to plate theory in Step 9. Using Query Results<=
/strong>, I get the following values at the top of this stiffener (see snap=
shot above):
- At (x=3D0, y=3DL1/6), =CF=83<=
sub>xx=3D 312 MPa.
- At the clamped edge location (x=3DW1, y=3D=
L1/6), =CF=83xx=3D -653 MPa. What a=
re your corresponding values?
=CF=83yy for Stiffeners
Results Viewer > Nodal Solution > Stress > Y-Component =
of stress
Click Plot Results icon.
=
p>
The =CF=83yy values for the stiffeners in t=
he x-direction is virtually zero; confirm this using Query Results. This means=
that, as expected, the load in the y-direction is carried by the =
stiffeners in that direction.
Let's determine =CF=83yy values at the =
top of the y-stiffener closest to the center which we'll comp=
are to plate theory in Step 9. Using =
Query Results, I get the following values =
at the top of the stiffener (see snapshot above):
- At (x=3DW1/4, y=3D0), =CF=83<=
sub>yy=3D 38 MPa.
- At the clamped edge location (x=3DW1/4, y=
=3DL1), =CF=83yy=3D -300 MPa. What =
are your corresponding values?
Save: Toolbar > SAVE_DB
Go to Step 9:Validate the Results
See and rat=
e the complete Learning Module
Go to all ANSYS L=
earning Modules
Step 9: Validat=
e the results
We checked in the previous step that the BC's have been applied correctl=
y and the deflection looks plausible.
Comparison Wit=
h Plate Theory
An FEA analyst displays his mettle by going head-to-head with theory. Th=
e theoretical solution for a clamped plate subjected to pressure is present=
ed by Timoshenko and Woinowsky-Krieger, page 202. This solution can be modi=
fied to account for the presence of stiffeners using the parallel axis theo=
rem. This calculation and the resulting stress and displacement values have=
been generously provided by Prof. Alan Zehnder and are sumarized in this pdf document. Do take the time to review this document.
The head-to-head comparison of the analytical values with the FEA values=
from Step 8 at the center of the structure is presented in the following ta=
ble.
Entity |
Location |
FEA |
Theory |
w |
|
3.8 mm |
3.6 mm |
=CF=83xx |
Bottom |
-56 MPa |
-50 MPa |
=CF=83xx |
Top |
312 MPa |
350 MPa |
=CF=83yy |
Bottom |
-28 MPa |
-20 MPa |
=CF=83yy |
Top |
38 MPa |
105 MPa |
The deflection at the center is about 8% larger than the theoretical val=
ue due to shear deformation in the FEA model that is not accounted for in t=
he analytical result. Correlation of stresses in the center is reasonably g=
ood. It might improve if solution for anisotropic plate were used. Also, th=
e stiffeners are not at the centerline of the model, while maximum stresses=
in theory are calculated at the center.
The head-to-head comparison of the edge stresses is given in th=
e following table.
Entity |
Location |
FEA |
Theory |
=CF=83xx |
Bottom |
116 MPa |
100 MPa |
=CF=83xx |
Top |
-653 MPa |
-704 MPa |
=CF=83yy |
Bottom |
77 MPa |
78 MPa |
=CF=83yy |
Top |
-300 MPa |
-403 MPa |
There is good correlation of the edge stress on the bottom of facesheet =
but the edge stress at the top of the stiffeners is overestimated by the th=
eory. This is possibly due to the stiffeners not being at the centerline of=
the model while the maximum stresses in theory are calculated at the cente=
r.
Back to Problem Specification
See and rat=
e the complete Learning Module
Go to all ANSYS L=
earning Modules
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