workshop 17 annular plate - unizg.hr · nas120, workshop 17, november 2003 ws17-3 problem...

WORKSHOP 17

ANNULAR PLATE

NAS120, Workshop 17, November 2003 WS17-1

WS17-2NAS120, 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


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


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


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


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.


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.


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


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.


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


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


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.


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.


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


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


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


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


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


Step 6.(cont.) Loads/BCs: Create Boundary Conditions

Annular plate with outer edge simply supported.


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


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.


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


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


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

workshop 17 annular plate - unizg.hr · nas120, workshop 17, november 2003 ws17-3 problem...

Documents