WORKSHOP 17 ANNULAR PLATE NAS120, Workshop 17, November 2003 WS17-1
WORKSHOP 17
ANNULAR PLATE
NAS120, Workshop 17, November 2003 WS17-1
WS17-2NAS120, Workshop 17, November 2003
WS17-3NAS120, Workshop 17, November 2003
Problem DescriptionShown below is a 2-D representation of the annular plate shown on the title page. The outer edge of the plate is simply supported and a uniform line load of 85 lb/in is applied a distance ro from the center of the plate.
w
b
a
row
simply supportedsimply supported
WS17-4NAS120, Workshop 17, November 2003
Problem Description (Cont.)The annular plate dimensions, material properties, and element properties are specified below:
Outer Radius, a 1.5 in
Inner Radius, b 0.375 in
Annular Line Load Radius, ro 0.75 in
Line Load, w 85 lb/in
Elastic Modulus, E 10E6 psi
Poisson’s Ratio, ν 0.3
Thickness, t 0.125 in
WS17-5NAS120, Workshop 17, November 2003
Theoretical Results (R. J. Roark, “Formulas for stress and strain”, Table 24, case 1a ):
Displacement:
Plate constant:
Plate constants dependent on the ratio a/b:
Loading constants dependent upon the ratio a/ro:
⎟⎟⎠
⎞⎜⎜⎝
⎛−
−= 3
7
913
LC
LCDway
( )2
3
112 vEtD−
=
( ) ⎟⎠⎞
⎜⎝⎛ −−=
⎟⎠⎞
⎜⎝⎛ −
−+
+=
ab
bavC
ab
bav
ba
abvC
27
1
121
41ln
21
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠⎞
⎜⎝⎛−
−+
+=
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
−⎟⎠⎞
⎜⎝⎛+
⎥⎥⎦
⎤
⎢⎢⎣
⎡+⎟
⎠⎞
⎜⎝⎛=
20
0
09
20
0
200
3
14
1ln2
1
1ln14
arv
rav
arL
ar
ra
ar
arL
WS17-6NAS120, Workshop 17, November 2003
Theoretical Results (cont.):
Plate constant:
D = 1788.576
Plate constants dependent on the ratio a/b:
Loading constants dependent upon the ratio a/ro:
Maximum displacement:
y = -0.0218
C1 = 0.8815 C7 = 1.7063
L3 = 0.01455 L9 = 0.2909
WS17-7NAS120, Workshop 17, November 2003
Suggested Exercise Steps:
1. Create a geometry model of the annular plate. Build the model in sections to facilitate application of the line load.
2. Use Mesh Seeds to define the mesh density.
3. Create a finite element mesh. (GRID and CQUAD4)
4. Define material properties. (MAT1)
5. Define element properties and apply them to the model. (PSHELL)
6. Apply loads and boundary conditions to the model.
7. Submit the model to MSC.Nastran for analysis.
8. Post Process results using MSC.Patran.
WS17-8NAS120, Workshop 17, November 2003
Create New Database
Create a new database called annular_plate.db
a. File / New.
b. Enter annular_plate as the file name.
c. Click OK.
d. Choose Default Tolerance.
e. Select MSC.Nastran as the Analysis Code.
f. Select Structural as the Analysis Type.
g. Click OK.
WS17-9NAS120, Workshop 17, November 2003
Step 1. Geometry: Create/Curve/XYZ
Create the first curve
a. Geometry: Create / Curve / XYZ.
b. Enter <0.375 0 0> for the Vector Coordinate List.
c. Enter [0.375 0 0] for the Origin Coordinate List.
d. Click Apply.
e. Click the Show Labelsicon.
a
b
c
d
e
WS17-10NAS120, Workshop 17, November 2003
Step 1.(Cont.) Geometry: Create/Curve/XYZ
a
b
c
Create the second curve.
a. Enter the second Vector Coordinate List: <0.75 0 0>.
b. Enter [0.75 0 0] as the new Origin Coordinate List.
c. Click Apply.
WS17-11NAS120, Workshop 17, November 2003
Step 1. (Cont.) Create/Surface/Revolve
Create the surfaces by revolving the two curves 360 degrees.
a. Create / Surface / Revolve.
b. Set the Total Angle to 360.
c. Screen pick curve 1
d. Screen pick curve 2
a
b
c d
WS17-12NAS120, Workshop 17, November 2003
Step 2. Finite Elements: Create/Mesh Seed/Uniform
Create mesh seeds that will be used to guide the mesh.
a. Finite Element: Create / Mesh Seed / Uniform.
b. Enter 40 as the Number of Elements.
c. Screen pick the inner edge of the plate for the Curve List.
a
b
c
d
WS17-13NAS120, Workshop 17, November 2003
Step 2 (cont). Finite Elements: Create/Mesh Seed/Uniform
Repeat the previous procedure to create 2 more sets of mesh seeds.
a. Enter 5 as the Number of Elements.
b. Screen pick Curve 1 for the Curve List.
c. Enter 10 as the Number of Elements.
d. Screen pick Curve 2 for the Curve List.
WS17-14NAS120, Workshop 17, November 2003
Step 3. Finite Elements: Create /Mesh/Surface
a
bc
d
e
fCreate surface mesh based on mesh
seeds created in previous steps.a. Create / Mesh / Surface.b. Select IsoMesh as the
Mesher.c. Select Quad4 for element
topologyd. Screen pick both surfaces for
the Surface List.e. Click Apply.f. Click the Hide Labels icon to
hide the labels.
WS17-15NAS120, Workshop 17, November 2003
Step 3. Finite Element: Equivalence /All/Tolerance Cube
Merge all coincident nodes by Equivalencing the model.
a. Equivalence / All / Tolerance Cube.
b. Click Apply.a
b
WS17-16NAS120, Workshop 17, November 2003
Step 3. Finite Element: Verify /Element/ Boundaries
Use Free Edge plot to inspect the model for any disconnected elements.
a. Verify / Element / Boundaries.b. Select Free Edges as the
Display Type.c. Click Apply.
a
b
c
WS17-17NAS120, Workshop 17, November 2003
Step 4. Material: Create /Isotropic/ Manual Input
Create a material property for the model.a. Material: Create / Isotropic /
Manual Input.b. Type in alum for the Material
Name.c. Click on the Input Properties
button to bring up the Input Option window.
d. Enter 10E6 for the Elastic Modulus and 0.3 for Poisson Ratio.
e. Click OK to return to the main material menu.
f. Click Apply.
a
b
c
d
e f
WS17-18NAS120, Workshop 17, November 2003
Step 5. Element Properties: Create /2D/ Shell
Create element properties.a. Properties: Create / 2D /
Shell.b. Enter plate as the Property
Set Name.c. Click on the Input Properties
button.d. Click on the Select Material
icon.e. Click on alum in the Select
Existing Material Window.f. Enter 0.125 as the thickness.g. Click OK.h. Screen pick both surfaces for
the Application Region.i. Click Add.j. Click Apply.
a
b
c
d
f
e
g
hi
j
WS17-19NAS120, Workshop 17, November 2003
Step 6. Loads/BCs: Create/ Displacement/Nodal
Create the boundary condition for the model.
a. Loads/BCs: Create / Displacement / Nodal.
b. Enter constraint as the New Set Name.
c. Click on the Input Databutton.
d. Enter <0 0 0> for the Translations.
e. Click OK.f. Click on Select
Application Region.g. Select Geometry as the
geometry filter.h. Set the picking filter to
Curve or Edge.i. Select the outer edge of
the plate for the Application Region.
j. Click Add.k. Click OK.l. Click Apply.
a
b
c
d
ef
g
hi
j
k
l
WS17-20NAS120, Workshop 17, November 2003
Step 6.(cont.) Loads/BCs: Create Boundary Conditions
Annular plate with outer edge simply supported.
WS17-21NAS120, Workshop 17, November 2003
Step 6. Loads/BCs: Create/Distributed Load/Element Uniform
Apply distributed load to the model.a. Create / Distributed Load /
Element Uniform.b. Enter load as the New Set
Name.c. Select 2D as the Target
Element Type.d. Click on the Input Data
button.e. Enter <0 0 –85> in the Edge
Distr Load field.f. Click OK.g. Click on Select Application
Region button.h. Select Geometry as the
Geometry Filter.i. Select Surface 1.3 (the
edge between the two surfaces) for the Application Region.
j. Click Add, and OK.k. Click Apply.
a
b
c
d
e
f g
h
i
j
jk
WS17-22NAS120, Workshop 17, November 2003
Step 6(cont.) Loads/BCs: Create Distributed Load
The distributed load is applied to the annular plate as shown.
Rotate the model using the middle mouse button to get a better view.
WS17-23NAS120, Workshop 17, November 2003
Step 7. Analysis: Analyze/ Entire Model/Full Run
Submit the model for analysis.a. Analysis: Analyze / Entire Model
/ Full Run.b. Click on the Solution Type.c. Select LINEAR STATIC as the
Solution Type.d. Click OK.e. Click Apply.
a
b
c
de
WS17-24NAS120, Workshop 17, November 2003
Step 8. Analysis: Access Results / Attach XDB/ Result Entities
After the job is completed, attach the XDB result file.
a. Access Results / Attach XDB / Result Entities.
b. Click on Select Result File.c. Select the file called
annular_plate.xdb.d. Click OK.e. Click Apply.
a
b
c d
e
WS17-25NAS120, Workshop 17, November 2003
Step 8 (cont.) Results: Create/Quick Plot
Plot stress fringe and deformed shape on the same plot.
a. Results: Create / Quick Plot.b. Select the Default result case.c. Select Stress Tensor for the
Fringe Result.d. Select Displacement,
Translational for the Deformation Result.
e. Click Apply.
The Maximum Von Mises Stress is 2.98E4 psi
The Maximum Deformation is 2.19E-2 in
a
b
c
d
e
WS17-26NAS120, Workshop 17, November 2003