analysis & simulation lab manual

AAMEC- Mechanical Engineering DepartmentComputer aided simulation and analysis laboratory manual

Ex. No: 1

Date:Stress Analysis of a Plate with a Circular hole

Problem: A rectangular plate of size 0.5 x 0.25 m with negligible thickness with a circular hole of diameter 0.125 located at the centre is propped at its end. A force of 500 N and 250 N is applied on the plate as shown in the figure below. The plate is made of C 35 steel having young’s modulus 2.060E5, specific weight of 0.0784 N/cc and Poisson’s ratio 0.3. Determine the maximum deflection and stress created in the plate and plot the results.

STEPS1. Specify title for the analysis.2. Set preferencePreprocessor3. Select the unit system4. Select the element type5. Specify the material properties6. Create a rectangle and circle for the given dimensions7. Subtract the circle from the rectangle8. Mesh the geometry 9. Save the databaseSolution10. Specify the boundary conditions11. Solve Postprocessor12. Plot the deflection and stress diagram 13. Determine the maximum deflection and stress values

Step1: Title specification

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File → Change title → Specify the title name → OK.

Step 2: Set preference

ANSYS Main menu → Preference → Check the structural type →OK

Step 3: Unit system selection

ANSYS Main menu → Preprocessor → Material props → Material library

→ Select units → Check the SI system of units → OK

Step 4: Element selection

ANSYS Main menu → Preprocessor→ Element type →Add/Edit/Delete

Add →Select the Plane 82 element→ OK →Close the element type window.

Step 5: Material property specification

ANSYS Main menu →Preprocessor →Material props →Isotropic

→Specify the material number →Specify the young’s modulus, density and

Poisson’s ratio in the isotropic material property window →OK

Step 6: Creation of Geometry

Rectangle creation:a. Create key pointsb. Connect with linesc. Create the rectangular plane

a. Key point creation

ANSYS Main menu →Preprocessor →Create →Key points→ In active CS → In the key point coordinate window specify the key point number, and x, y & z coordinates value for one corner of the rectangle.

Similarly create the other three key points.

b. Connect with lines

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ANSYS Main menu →Preprocessor →Create → Lines →Straight

lines→ Pick the key point 1 & 2 , 2 & 3, 3 &4 and 4& 1 →OK

c. Rectangle creation

ANSYS Main menu →Preprocessor →Create →Areas → Arbitrary

→By lines →Select the four lines created in the previous step.

Circle creation

ANSYS Main menu →Preprocessor →Create →Circle →Solid circle

→Specify the circle centre and its radius →OK.

Step 7: Subtraction of circle from rectangle:

ANSYS Main menu →Preprocessor →Operate →Subtract →Areas

→Select the rectangle →OK →Select the circle →OK.

Step 8: Meshing of Geometry.

ANSYS Main menu →Preprocessor →Mesh tool →In the mesh tool click

the Global set →Specify the element edge length →OK →Mesh →Select

the area to be meshed →OK

Step 9: Save the database as .db

Step 10: Boundary conditions specification:

a. Applying constraints

ANSYS Main menu →Solution →Apply →Displacement →On Nodes

→Select the nodes →OK →Specify All DOF →OK.

b. Applying forces

ANSYS Main menu →Solution →Apply →Force/Moment →On Key

point →Select the topmost right corner key point →OK →Specify the

direction of force and magnitude of force →OK

Similarly apply another force at the lowermost right corner with the given force value.

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Step 11 Solve the domain:

ANSYS Main menu →Solution →Solve →Current LS.

Save the data base

Step 12: Retrieval of Stress and Deflection plots

ANSYS Main menu →General postprocessor→Last set →Plot results

→Select the vonmisses stress →OK → capture the stress plot image

Similarly capture the Deflection plot

RESULT:Deflection and stress determined in the Plate with a hole for the given

boundary conditions are ______________________.

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Ex. No: 2

Date:Stress Analysis of Rectangular L Bracket

Problem: Analyze the stress in the rectangular L bracket shown in the figure. The L bracket is made of Cast Iron having young’s modulus 1.000E5 N/mm2, poisson’s ratio 0.23 and specific weight 0.072N/cc. A pressure load of 500 N/m2 is applied as shown.

STEPS1. Specify title for the analysis.2. Set preferencePreprocessor3. Select the unit system4. Select the element type5. Specify the material properties6. Create the geometry.7. Subtract the circle from the L shaped bracket8. Mesh the geometry 9. Save the databaseSolution10. Specify the boundary conditions11. Solve Postprocessor12. Plot the deflection and stress diagram 13. Determine the maximum deflection and stress values

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RESULT:Deflection and stress determined in the Plate with a hole for the given

boundary conditions are ______________________.

Ex. No: 3 Stress Analysis of a Axis-symmetric component

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Date:

Problem: A long thick-walled pipe is rigidly supported at its ends between two walls. Determine the maximum deflection in the pipe due to gravity loading. Determine the maximum tensile stress at the outer surface of the pipe at Y = 4.1666 in.

STEPS1. Specify title for the analysis.2. Set preferencePreprocessor3. Select the unit system4. Select the element type5. Specify the material properties6. Create the geometry.7. Divide the lines8. Mesh the geometry 9. Save the databaseSolution10. Specify the boundary conditions11. Solve Postprocessor12. Plot the deflection and stress diagram 13. Determine the maximum deflection and stress values

Step 1 and 2 follow the same procedure as in the exercise 1 and 2.Step 3:

Specify the unit system as BIN.Step 4: Select axis symmetric harmonic element as PLANE 25.Step 5: Follow the same procedure to specify the material property as in the exercise 1.Step 6: Creation of Geometry:

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Since the geometry given in the problem is axis symmetry, the model shown below is enough to draw.

Creation of key pointsKey point 1 at x = 0.5 and y = 0.Key point 2 at x = 0.5 and y = 100Generate two additional key points in the x direction.

Preprocessor →Copy →Key points →Pick the KP 1 and 2

→OK →specify the number of copies as 2 and x offset as 1.

Step 7 : Divide the lines:

Create a line joining the key point 1 and 2.Divide the line in to 12 divisions.

Preprocessor →Meshing →Size cntrls →Lines →Picked lines

→Select the line →OK →Specify the number of divisions as 12 and spacing ratio as 1.

Similarly create lines L2 between KP 2 and 3 and divide the line in to 1 division. Line L3 between KP 3 and 4 and divide in to 12 divisions and finally create L4 between 3 and 4 and divide in to 1 division.

Create the area with in the four lines.

Step 8: Mesh the geometry as mapped quadrilateral mesh.Step 9: Save the database.

Step 10: Applying boundary conditions

Analysis assumption:

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The loading g, which is constant in magnitude and direction around the circumference of the pipe, is applied as the sum of two harmonically varying loads. Each load has one wave around the circumference and is 90 out of phase with the other.

Ansys →Main menu →Solution →Load →Apply

→structural→inertia→Gravity →Specify gravity value as 386 and -386 in x and z coordinate respectively.

Ansys Main menu →Solution → load step opts→ Other →For Harmonic

Ele →specify the number of harmonic wave as 1 and check the symmetric condition.

Constraint the nodes at y = 0 in all DOFConstraint the nodes at y=100 in Y DOF.

Step 11: Solve the problem

Save the Database.

PostprocessorPlot the deflection and stress diagram Determine the maximum deflection and stress values

RESULT:Deflection and stress determined in the given axis symmetric component

are ______________________.

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Ex.No: 4

Date:

Deflection Analysis on T shaped Cantilever beam

Problem: Find the maximum deflection in an un symmetric T beam subjected to uniform bending Mz, with dimensions and geometric properties as shown below.

STEPS1. Specify title for the analysis.2. Set preferencePreprocessor3. Select the unit system4. Select the element type as BEAM 545. Specify the real constant:

Main menu Preprocessor Real constant Add Select the element OK Specify the following in the Real constant window:

Cross sectional area AREA 1Moment of Inertial about Z IZ1Distance from CG to top Y surf HYT1Distance from CG to bottom surf HYB1

6. Specify the material properties7. Create the geometry.

Node creation:

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Main menu →Preprocessor →Create →Node →In active CS

→Specify the coordinate value for the node 1 and 2.

Element creation:

Main menu →Preprocessor →Create →Elements →Through

nodes→ Pick the node 1 and 2 →OK.

Note: In the geometry is created with node and filled with elements, then there is no need to mesh the geometry.

8. Save the databaseSolution9. Specify the boundary conditions

a. Constraint all the DOF at the Node 1b. Specify the moment about z at the node 2 as 100,000 in- lb

10. Solve Postprocessor11. Plot the deflection contour.

RESULT:The maximum deflection determined in the T cantilever beam is

___________.

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Ex.No: 5

Date:Natural Frequency of a Spring mass system

Problem: An instrument of weight W is set on a rubber mount system having a stiffness k. Determine its natural frequency of vibration f.

Analysis assumptions and Modeling notes

The spring length is arbitrarily selected. One master degree of freedom is chosen at the mass in the spring length direction. The weight of the lumped mass element is divided by gravity in order to obtain the mass.

Mass = W/g = 2.5/386 = 0.006477 lb-sec2/in.

Steps:

1. Specify title for the analysis.2. Set preference

Preprocessor

3. Select the unit system as BIN4. Select the element type as a. COMBIN 14 and b. MASS 21.

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COMBIN14 Element is used for spring and MASS 21 is used as load acting on the spring.For the COMBIN 14 element choose the option and specify “Use 2/3D DOF opt” for K2 and 2-D longitudinal for K3.Similarly for the MASS 21 element specify “parallel to global” for K2 and “2-D w/o rot iner” for K3.

5. Main menu →Preprocessor →Real constant →Add →Select the

element →OK →Specify the following in the Real constant window:Real constant specification

Specify the real constant as 48 (spring stiffness) for element 1 and 0.006477(load) as mass for element 2.

6. Specify the material properties7. Create the geometry8. Node creation:

9. Main menu →Preprocessor →Create →Node →In active CS

→Specify the coordinate value for the node 1 and 2.

10. Element creation

Create spring element

11. Main menu →Preprocessor →Create →Elements → Element attributes choose the element and real constant number →Element through

nodes→ Pick the node 1 and 2 →OK. Create mass element:

12. Main menu →Preprocessor →Create →Elements → Element attributes choose the element and real constant number →Element through

nodes→ Pick the node 2 →OK.

13. Save the database

Solution

14. Select the analysis type

Main menu →Solution →Analysis type →New analysis →Modal

→OK

15. Main menu →Solution →Analysis type →Analysis option →check

the “reduced” option →specify “1” for the number of modes to extract

→check the “Expand mode shapes” → OK →OK.

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Master Degree of Freedom specification

16. Main menu →solution →Master DOFs →Define →Pick the node

→OK →Choose the Uy →OK.

Apply constraints:

Apply constraints at node 1 in both directions and at node 2 in x direction only.

17. Solve.

Postprocessor

18. Main menu →General postprocessor →Result summary.

Result: Natural frequency determined for the above spring mass system is ______.

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Ex.No: 6

Date:

Eigen Frequency modes of a Spring mass system

Compute the Eigen frequency modes of a spring mass system given below:

E=1N/m2

V=0

F=None applied for modal analysis

X1=5

X2=11

Result: The Eigen modes values are______________

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Ex.No: 7

Date:

Harmonic response of a Two mass spring system

Problem: Determine the response amplitude and phase angle for each mass of the system shown below when excited by a harmonic force (F1sint) acting on mass m1.

Step 1:

1. Choose menu path Utility Menu →File →Change Title.2. Type the text "Harmonic Response of Two-Mass-Spring System" and

click on OK.

3. Select the preference as structural.

Step 2: Define the Element Types

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1. Choose menu path Main Menu →Preprocessor→ Element Type

→Add/Edit/Delete.2. Click on Add. The Library of Element Types dialog box appears.

3. Scroll down the list on the left to "Combination" and select it.

4. Click once on "Spring-damper 14" in the list on the right.

5. Click on Apply.

6. Scroll up the list on the left to "Structural Mass" and select it.

7. Click once on "3D mass 21" in the list on the right.

8. Click on OK. The Library of Element Types dialog box closes.

9. Click on Close in the Element Types dialog box.

Step 3: Define the Real Constants

1. Choose menu path Main Menu →Preprocessor →Real Constants.2. Click on Add. The Element Type for Real Constants dialog box appears.

3. Click once on Type 1 to highlight it.

4. Click on OK. The Real Constants for COMBIN14 dialog box appears.

5. Enter 200 for the spring constant (K) and 0.1 for the damping coefficient (CV1). Click on OK.

6. Repeat steps 2-4 for Type 2, MASS21.

7. Enter .5 for mass in X direction and click on OK.

8. Click on Close to close the Real Constants dialog box.

Step 4: Create the Nodes

1. Choose menu path Main Menu →Preprocessor

→Modeling→Create → Nodes →In Active CS.2. Enter 1 for node number.

3. Enter 0, 0, 0 for the X, Y, and Z coordinates, respectively.

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4. Click on Apply.

5. Enter 4 for node number.

6. Enter 1, 0, 0 for the X, Y, and Z coordinates, respectively.

7. Click on OK.

8. Choose menu path Utility Menu →PlotCtrls →Numbering. The Plot Numbering Controls dialog box appears.

9. Click once on "Node numbers" to turn node numbers on.

10. Click on OK.

11. Choose menu path Main Menu →Preprocessor→

Modeling→Create→ Nodes→ Fill between Nds. A picking menu appears.

12. In the ANSYS Graphics window, click once on nodes 1 and 4 (on the left and right sides of the screen). A small box appears around each node.

13. Click on OK on the picking menu. The Create Nodes Between 2 Nodes dialog box appears.

14. Click on OK to accept the default of 2 nodes to fill. Nodes 2 and 3 appear in the graphics window.

Step 5: Create the Spring Elements

1. Choose menu path Main Menu→ Preprocessor →Modeling→

Create → Elements→ Auto Numbered- Thru Nodes. A picking menu appears.

2. In the graphics window, click once on nodes 1 and 2.

3. Click on Apply. A line appears between the selected nodes.

4. Click once on nodes 2 and 3.

5. Click on Apply. A line appears between the selected nodes.

6. Click once on nodes 3 and 4.

7. Click on OK. A line appears between the selected nodes.

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Step 6: Create the Mass Elements

1. Choose menu path Main Menu →Preprocessor→ Modeling→

Create→ Elements→ Elem Attributes.2. Enter 2 for element type number.

3. Enter 2 for real constant set number and click on OK.

4. Choose menu path Main Menu →Preprocessor →Modeling→

Create→ Elements →Auto Numbered→ Thru Nodes. A picking menu appears.

5. In the graphics window, click once on node 2.

6. Click on Apply.

7. Click once on node 3 and click on OK.

Step 7: Specify the Analysis Type, MDOF, and Load Step Specifications:

1. Choose menu path Main Menu →Solution →Analysis Type→ New Analysis.

2. Click once on "Harmonic" and click on OK.

3. Choose menu path Main Menu→ Solution →Analysis Options.

4. Click once on "Full" to select the solution method.

5. Click once on "Amplitud + phase" to select the DOF printout format and click on OK.

6. Click OK in the Full Harmonic Analysis dialog box.

7. Choose menu path Main Menu →Solution →Load Step Opts→

Output Ctrls →Solu Printout.

8. Click on "Last substep" to set the print frequency and click on OK.

9. Choose menu path Main Menu→ Solution →Load Step Opts→

Time/Frequenc →Freq & Substeps.

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10. Enter 0 and 7.5 for the harmonic frequency range.

11. Enter 30 for the number of substeps.

12. Click once on "Stepped" to specify stepped boundary conditions.

13. Click on OK.

Step 8: Define Loads and Boundary Conditions

1. Choose menu path Main Menu →Solution →Loads→Apply

→Structural→Displacement→On Nodes. A picking menu appears.2. Click on Pick All. The Apply U, ROT on Nodes dialog box appears.

3. In the scroll box for DOFs to be constrained, click once on "UY" to highlight it (make sure no other selections are highlighted).

4. Click on OK.

5. Choose menu path Main Menu →Solution →Loads→Apply

→Structural→Displacement →On Nodes. A picking menu appears.

6. In the graphics window, click once on nodes 1 and 4.

7. Click on OK. The Apply U, ROT on Nodes dialog box appears.

8. In the scroll box for DOFs to be constrained, click once on "UX" to highlight it and click once on "UY" to de-select it.

9. Click on OK.

10. Choose menu path Main Menu→ Solution →Loads→Apply

→Structural →Force/ Moment→ On Nodes. A picking menu appears.

11. In the graphics window, click once on node 2.

12. Click on OK. The Apply F/M on Nodes dialog box appears.

13. In the scroll box for direction of force/moment, click once on "FX."

14. Enter 200 for the real part of force/moment and click on OK.

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Step 9: Solve the Model

1. Choose menu path Main Menu →Solution→ Solve→Current LS.2. Review the information in the status window and click on Close.

3. Click on OK on the Solve Current Load Step dialog box to begin the solution.

4. When the solution is finished, a dialog box stating "Solution is done!" appears. Click on Close.

Step 10: Review the Results

For this sample, you will review the time-history results of nodes 2 and 3.

1. Choose menu path Main Menu →TimeHist Postpro→ Define Variables. The Defined Time-History Variables dialog box appears.

2. Click on Add. The Add Time-History Variable dialog box appears.

3. Click on OK to accept the default of Nodal DOF result. The Define Nodal Data dialog box appears.

4. Enter 2 for reference number of variable.


6. Enter 2UX for the user-specified label.

7. In the scroll box on the right, click once on "Translation UX" to highlight it.

8. Click on OK.

9. Click on Add in the Defined Time-History Variables dialog box. The Add Time-History Variable dialog box appears.

10. Click on OK to accept the default of Nodal DOF result. The Define Nodal Data dialog box appears.

11. Enter 3 for reference number of variable.


13. Enter 3UX for the user-specified label.

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14. In the scroll box on the right, click once on "Translation UX" to highlight it.

15. Click on OK and click close.

16. Choose menu path Utility Menu →PlotCtrls→ Style→ Graphs. The Graph Controls dialog box appears.

17. In the scroll box for type of grid, scroll to "X and Y lines" to select it.

18. Click on OK.

19. Choose menu path Main Menu →TimeHist Postpro →Graph Variables. The Graph Time-History Variables dialog box appears. Your graph should look like this:

20. Enter 2 for 1st variable to graph.

21. Enter 3 for 2nd variable to graph.

22. Click on OK. A graph appears in the graphic window.

Step 11: Exit ANSYS

1. In the ANSYS Toolbar, click on Quit.2. Choose the save option you want and click on OK.

Result: The maximum amplitude is obtained in the frequencies ___________

Ex.No:8

Date:

Temperature Distribution in a short cylinder (Conductive heat transfer)

Problem: A short solid cylinder is subjected to the surface temperatures shown. Determine the temperature distribution with in the cylinder.

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STEPS14. Specify title for the analysis.15. Set preference as ThermalPreprocessor16. Select the unit system as BFT17. Select the element type SOLID 8718. Specify the material properties19. Creation of geometry (partial cylinder)

Main menu →Preprocessor →Create →Volumes →Cylinder

→Partial cylinder →Specify the following values:Wx = 0Wy = 0Rad1 = 0.5Theta1 = 45 (assumption)Depth = 0.5

20. Mesh the geometry 21. Save the databaseSolution22. Specify the boundary conditions

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23. Solve Postprocessor24. Plot the Temperature distribution.25. Determine the temperature at the centre line.

Result: The temperature at the centre line is determined as __________

Ex.No: 9

Date:

Heat conduction across a chimney (conductive and convective heat transfer)

Problem: Determine the temperature distribution and the rate of heat flow q per foot of height for a tall chimney whose cross section is shown below. Assume that

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the inside gas temperature is Tg, the inside convective coefficient is hi, the surrounding air temperature is Ta and the outside convective coefficient is ho.

STEPS1. Specify title for the analysis.2. Set preference as ThermalPreprocessor3. Select the unit system as BFT4. Select the element type PLANE555. Specify the material properties6. Creation of geometry

a. Create a square of size a.b. Create a square of size bc. Subtract the square of size b from the square of size a.

7. Mesh the geometry 8. Save the databaseSolution9. Specify the boundary conditions10. Solve Postprocessor

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11. Plot the Temperature distribution.12. Determine the temperature at the centre line.

Result: The temperature at the centre line is determined as __________

Ex.No: 10

Date:Heat conduction across the Fin

Problem: Determine the temperature distribution and the rate of heat flow if the fine base temperature is 1500c and the fins are exposed to the atmospheric air at

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30 degree C having transfer coefficient of 50 W/m2K. The base material is copper and fin material is aluminum.

Steps:

1. Specify title for the analysis 2. Set preference as Thermal Preprocessor3.Select the unit system as SI4.Select the element type SOLID 87 for base material 5.Specify the material properties for base material6.Select the same element type SOLID 87 for fin material7. Specify the material properties for fin material8. Create volumes by dimensions for base of 3X5.9X1 m

9. Create volumes by dimensions for single fin of width 3m, length 4 m and thickness 0.3m

10. Preprocessor – Modeling-copy –volumes select the volume to be copied next the following window appears

11. Enter number of copies as 3 and offset value as 2

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12. Next glue the new completed fin assembly to the base by using Preprocessor – Modeling –Operate – Booleans – Glue – Volumes. Choose the base and click once on the fin assembly and click OK.

13. Mesh the areas by picking all the areas with smart size option with value 1.14. Apply thermal load of convection boundary of 50 W/m2K and 283 K on

the fin surfaces by clicking on loop apply CONVEC on AREAS window and select one by one fin surfaces and click ok. Apply the values.

15. Similarly apply the temperature on base as 1773K.16. Solve17. Postprocessor-Plot the Temperature distribution.

Result: The temperature distribution plot is attached.

Ex.No: 11

Date:Thermal stress in a Long cylinder

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A long thick walled cylinder is maintained at a temperature Ti on the inner surface and To on the outer surface. Determine the temperature distribution through the wall thickness. Also determine the axial stress and the tangential stress at the inner and outer surfaces.

Note: This problem is a coupled field analysis. First the thermal analysis is performed and later structural analysis is carried out.

Thermal analysis1. Specify title for the analysis.2. Set preference as Thermal and structuralPreprocessor3. Select the unit system as BIN4. Select the element type PLANE555. Specify the material properties6. Create the geometry as represented in the above figure7. Mesh the geometry 8. Save the database

Solution9. Specify the boundary conditions10. Solve Postprocessor

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11. Plot the Temperature distribution.

Structural analysis12. Switch the element type:

Main menu →Preprocessor →Element →Switch element type

→Structural to Thermal →OK

13. Apply structural boundary conditions. (Constraint the DOF at the suitable nodes)

SolvePostprocessor14. Plot the stress and deflection plot.

Result: 1.Temperature distribution plot in long cylinder is attached 2.Deformed shape is attached

Ex.No: 12

Date:

Laminar flow analysis in a 2-D duct by CFD analysis

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Model the air flow inside the 2-D duct by CFD analysis. The geometric properties and fluid properties are given the table.

Dimensions & Properties

Inlet length 4 in

Inlet height 1 in

Transition length 2 in

Outlet height 2.5 in

Initial outlet length 4 in

Inlet velocity 1 in/sec*

Outlet pressure 0 psi

Result: The velocity distribution plot over entire length of duct is attached

LAB - Viva Questions

1. Define element and node?

2. List the steps in FEA?

3. What are the different types of elements used in FEA?

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4. What are the different types of stresses and strain in an object?

5. Write the equilibrium equation?

6. Write the [L] Matrix for a 3D problem?

7. Define Minimum potential energy approach?

8. List different software uses FEA as tool?

9. What are the different weighted residual methods?

10. List the advantages of FEA?

11. How is minimum number of degrees of freedom per node determined in an

element? Give am example.

12. Distinguish between essential and non-essential boundary conditions.

13. Express the constitutive matrix for a plane strain condition.

14. Give the compact representation of shape function for a four-node

quadrilateral element.

15. How are in an isoparametric element the constant strain and rigid body

conditions met?

16. What is static condensation? State any of its applications.

17. Name different types of dynamic analysis. Give one application for each.

18. Distinguish between consistent mass matrix and lumped mass matrix.

19. Express the governing equation for heat conduction in a solid body in

cylindrical coordinate system.

20. State two applications where fluid structure interaction is involved.

21. List four advantages of finite element analysis.

22. Explain the following terms clearly: Nodes, Primary nodes, Secondary

nodes and internal nodes.

23. Define shape function and write its properties.

24. What are the higher order elements? Where are they preferred?

25. State the isoparametric concept in finite element analysis.

26. What is Gaussian quadrature integration technique?

27. Write lumped and consistent mass matrices for an axial element.

28. Write one example for explicit and implicit methods for numerical

integration.

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29. Write the governing differential equation for a two dimensional heat

transfer problem.

30. The definitions for translation and rotation of fluids are not quite the same

as for rigid bodies. Justify the statement.

31. What is a boundary value problem? Give an example.

32. State the properties of shape functions.

33. What are higher order elements?

34. List few dimensional field problems.

35. What is an isoparametric element?

36. What is meant by plane strain problem?

37. How do axisymmetric problems differ from two dimensional problems?

38. What are h and p elements?

39. Write down the governing differential equation for longitudinal vibration.

40. What are the properties of stiffiness matrices?

41. What is the basic difference between bar and beam elements?

42. State the use of shape functions.

43. How is a quadratic triangular element different from linear triangular

element?

44. Define the term “static condensation”.

45. What is lumped mass matrix?

46. Give the advantage and limitation of ritz vectors

47. State any two non-linear problems in finite element analysis

48. Explain the analogies between structural, heat transfer and fluid

mechanics.

49. What are the limitations of ID elements?

50. What is the need for adopting penalty approach?

51. Distinguish between CST and LST elements.

52. What are serendipity elements?

53. Give the compact representation of shape functions of a four-node

quadrilateral element.

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54. Sketch a quadratic strain brick element.

55. Specify the mass matrix for a truss element having four degreed of

freedom.

56. State the required condition for solving dynamic problems as specified by

characteristic polynomial method.

57. Sketch a differential element depicting two dimensional conduction with

surface convection.

58. Define the stream function for a one dimensional incompressible flow.

59. define aspect ratio. State its significance

60. Classify boundary conditions. Give examples.

61. State the conditions to be satisfied in order to use axisymmetric elements.

62. Sketch a quadratic strain tetrahedran element.

63. What is meant by isoparametric formulation?

64. What is meant by static condensation? State its significance.

65. What is called finite element semidiscretization? Give an example.

66. What are some differences between implicit and explicit methods of

numerical integration?

67. Define element capacitance matrix for unsteady state heat transfer

problems.

68. Define the stream function for a two – dimensional incompressible flow.

69. What are the situations that demand the use of finite element method for

engineering analysis?

70. State the characteristics of stiffness matri.

71. What is CST element? Why is it called so?

72. Why are super parametric elements not much used in engineering element?

73. Express the interpolation function corresponding to node 4 of a cubic

triangular element.

74. What is static condensation?

75. What is mean by coordinate transformation?

76. What are the properties of axis symmetry elements?

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77. Compare the principle of virtual force and the principle of virtual

displacement.

78. Specify any two applications of FEA in fluid mechanics.

79. What do you understand by discretization of domain?

80. What role did the computer play in the use of the finite element method?

81. Distinguish between local global coordinate system.

82. Define transformation mapping.

83. Write down the consistent mass matrix for a bar element.

84. Clearly explain about the classification of direct integration techniques.

85. A burner is heating a spot on a two dimensional body. How do you attempt

to model this?

86. What is the effect of mesh size on the accuracy of solution?

87. Explain variational methods of formulation of boundary value problem.

88. What is area co-ordinate used in FEM?

89. What are gauss propositions to derive the gauss qudrature?

90. What are the plane stress and strain conditions represented in solid

mechanics?

91. With an example explain the element and global stiffness matrix.

92. Write strain displacement relations for 3D strain conditions.

93. Write the displacement functions for a second order triangular element.

94. What are the salient features of a shape function?

95. Compare the beam and bar elements used in FEM.

96. Explain the principle of stationery potential energy.

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analysis & simulation lab manual

Documents

circle ok

rectangle ok

radius ok

dof ok

element ok close

structural type ok step

preference preprocessor

key point number