Analysis of Stresses in a Long Cylindrical Pressure Vessel

Prepared by Prof. Charlton S. Inao

Answer Key to Exam ansysFrom Srinivas,Sambana,Datti

Problem• A long cylindrical pressure vessel of inside

diameter 10 cm and outside diameter 20 cm is

subjected to an internal pressure P= 10,000 N/cm2

.2D Structural solid element PLANE 82 is used to

perform the analysis. Poisson Ratio =0.3 and the

Young Modulus of elasticity is 2.1 e7 N/cm2. Axis

symmetric option is selected for element behavior.

One material model is defined. Solid modeling

approach is employed and geometric entity model.

The maximum deflection, tangential and radial

stresses induced in the pressure vessel are

determined if stress is taken 10 cm arbitrarily along

the y axis.

Inside diameteer =10 cmOutside diamter=20 cmPressure =10 Kn/cm2

Material element Solid Structural Plane 82(Quad 8 Node 82) Poissons Ratio= 0.3Youngs modulus=2.1e 7 N /cm2

Element Behavior =Axissymmetric

Stress shall be taken 10 cm arbitrarily along y axis

Utility Menu>Change Jobname> type ‘Pressure Vessel’

Utility Menu> File > Change title

Main Menu> preprocessor>>Element Type>Add/Edit/Delete>Add>Structural

Solid>Quad 8 Node 82>Ok

In the Element Type> click Options>element behavior K3, >Axis Symmetric>Ok

Main menu>Preprocessor> Material props> Material Models>Define material Model Behavior>Structural> Linear>Elastic>Isotropic> EX=2.1 E7;>PRXY>0.3> Ok

Preprocessor> Modeling>Create>Keypoints>In Active CS

Keypoint No. X Y Z

1 10 0

2 20 0

3 20 10

4 20 10

Modeling

Utility or Pulldown Menu>List >Keypoints> Coordinates Only (To see the list or tabulation of

keypoints)

Main Menu>Preprocessor> Modeling>Create>Areas>Arbitrary>Through KPs>Pick

keypoints 1,2,3,4 and click OK

MainMenu> Processor> Meshing> Size Controls>Manual Size>Global >Size> Global element sizes> enter 20 for No . Of

Element Divisions>Ok

•

Sizing of elements

Main menu> pre processor>meshing>Mesh> Areas>Free> Pick All

Meshing

Utility Menu> Select EntitiesSelect

1. Nodes from entity Type drop down Box

2. By Location from the Selection Criteria

3. Y coordinates from Location Setting

4. 0 for Min, Max5. From Full for Selection

Function Setting6. Apply followed by

Plot7. Close the Select

Entities by OK

Main menu>Preprocessor> Loads>Define Loads>Apply>Structural>Displacements>On

Nodes>Pick All

Apply Constraints/displacement =0

Apply U,ROT on Nodes dialog box, select Uy for DOF to be constrained and click Ok

After constraints are applied on Y direction for all the nodes, the screen should look like this

In the utility menus> Select>Entities

• Select nodes (Entity Type)

• By Location(Selection Criteria)

• Y coordinates (Location Settings)

• 10 ( for Min , Max)

• From Full(Selection function Setting)

• Apply

• Plot

• Ok

Main Menu>Preprocessor>Coupling/Ceqn>Couple DOFs> Pick All.. Enter 1 for Set Reference Number, Select Uy for Degrees of

Freedom Label and click OK

Utility Menu>Select>EverythingUtility Menu>Plot>Replot

Utility Menu>Select Entities

Nodes (Entity Type)

By location (Selection Criteria)

X Coordinates (Location settings)

10 (Min,Max)

From Full (Selection Function Setting)

Apply

Plot

OK (close the Select Entities Dialog Box)

Main Menu>Preprocessor>loads>Define Loads>Apply> Structural> Pressure> On Nodes>Pick

All

Apply Pressure On Nodes

Apply PRES on Elements dialog box> enter 10000 for Load PRES Value> Click OK

When the pressure of 10000 N/cm2 is applied to all the nodes , the screen should appear like this

Utility Menu>Select>EverythingUtility menu>Plot>Elements>

Save DB in the Ansys Toolbarmain Menu >Finish

SOLUTION PHASE

Main Menu>Solution>Solve>Current LS

Click OK>Solve Current Load Step dialog box

Click Close on the Note quoting Solution is Done

Close the /Status Command Window..

Main Menu>Finish

Utility Menu>Plot Cntrls>Style>Symmetry Expansion>2D Axis Symmetric

On the 2D Axis Symmetric Expansion dialog box>select ¾ Expansion for Selection Expansion Amount ,Ok

Utility Menu> Plot> Replot

Main Menu>General Postproc>Plot Results>Contour Plot>Nodal X Component of Stress>Ok

On the Contour Nodal Solution Data dialog box, select Nodal Solution>Stress>Z –Component of Stress>Click OK

to view the Hoop Stress

In the main menu, select General Postproc>ListResults>Nodal Solution

On the List Nodal solution Data dialog box, select Nodal Solution>Stress>X-Component of Stress>OK

Review and close the PRNSOL Command window.

Utility Menu> File> Exit.Exit from Ansys>Save Everything >OK

Minimum Hoop Stress 16.66 N/mm2 at inner radiusMaximum Radial Stress 9.985 N/mm2 at inner radius

The End

Thank You