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    INTRODUCTION TO FINITE ELEMENT ANALYSIS

    Finite Element Analysis

    FEA consists of a computer model of a mathematical or design that is stressed and

    analyzed for specific results. It is used in new product design and existing product refinement. Acompany is able to verify a proposed design will be able to perform to the client specifications

    prior to manufacturing. Modifying an existing product or structure is used to qualify the product.

    In case of structure failure FEA is used to help determine the design modifications to melt the

    new condition.

    There are generally two types of analysis that are used in industry. 2D modeling

    and 3D modeling while 2D modeling conserves simplicity and allows the analysis to be run on a

    relatively normal computer it tends to yield less accurate results. 3D modeling however produces

    more accurate results while scarifying the ability to run on all fastest computer effectively within

    each of these modeling schemes the programmer can insert numerous algorithms which may takethe system behave linearly or non-linearly.

    FEA Working Principle

    FEA uses a complex system of points called nodes which make a grid called a

    mesh. This mesh is programmed to contain the material and structural properties which define

    how the structure will react to certain loading conditions nodes are assigned at a certain density

    throughout the material depending on the anticipated stress levels. Usually have a higher node

    density than these which experience little or no stress points of interest may consists of fracture

    point of previously tested material. The mesh acts as a spider mesh is that from each node these

    extend a mesh element to each adjustment nodes.

    Each FEA program may come with an element library or one is constructed

    overtime. Some sample elements are

    i. Rod elements

    ii. Beam elements

    iii. Plate, shell, composite elements

    iv. Solid element

    v. Spring and Mass element

    vi. Rigid element

    vii. Viscous damping element.

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    Main steps of FEA Process.

    (i).Model Creation.

    A detailed model of the component is drawn is 2D or 3D space according to the

    requirement. The model can also be made in preprocessor or some different CAD package and

    data can be then transferred to make a new model according to the analysis being carried out.

    (ii). Applying Mesh.

    Mesh generation is a process of dividing the analysis process into finite element

    to set better results. The finer the mesh more accurate the results and longer the time taken.

    Aim of mesh generation is to create a minimum number of elements is order to

    reduce the processing time.

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    (iii). Assigning Properties.

    Material properties such as density, thermal conductivity coefficient of heat etc

    are defined and their effects are analyzed under different operating conditions. Optimization goal

    such as addition of material and removal and design modifications are also defined. Areas where

    in weight can be reduced are indicated along with design suggestions to minimize the chances ofpart failure.

    May FEA programs also equipped with the capability to use multiple materials

    within structure such as

    i. Isotropic.

    ii. Orthotropic.

    iii. Anisotropic.

    Types of Analysis

    (i).Structural Analysis:

    Consists of linear and non-linear models. Linear models use simple parameters

    and assume that the material is not plastically deformed non linear models consists of stressing

    the material part its elastic capabilities.

    (ii). Vibration Analysis.

    It is used to test the material against random vibrations. Shock and impact each of

    these incidents may act upon natural frequency of the incidents may act upon natural frequency

    of the material which is turn may cause resonance and subsequent failure.

    (iii).Fatigue Analysis.

    Fatigue analysis helps designers to predict the life of material or structure by

    showing the effects of cyclic loading.

    (iv).Heat Transfer analysis.

    Heat transfer analysis models the conductivity or thermal fluid dynamic of the

    material or structure. This may consists of a steady state or transient transfer.

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    Results of finite element analysis

    FEA has become a solution to the task of predicting failure due to

    unknown stresses by showing problems is a material and allowing designers to see all the

    theoretical stresses within. This method of product design and testing is far superior to the

    manufacturing costs which would be accurate if each sample was actually built and tested.

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    EX.NO:01 SPACE TRUSS ANALYSIS

    Date:00.02.13

    AIM:

    To determine displacement and reaction forces at joints and supports of space

    truss and compare results with ANSYS results.

    PROBLEM DESCRIPTION:

    A 3D space truss is made of steel (E=200Gpa) and is to support the load. All

    dimensions are is centimeters. Cross sectional area of each member is 20cm2. As it is a space

    truss 3D spar element link and is used for analysis one real constant set and are material model

    are defined. The joint displacements reactions at supports are determined.

    PROCEDURE:

    PREPROCESSOR:

    1. In main menu select preprocessor element type Add/Edit/delete.

    2. On the element type dialog box click add. On element type library select structural link in

    the left list box and then select 3D finit stn 180 in the right list box. Click ok to accept theelement.

    3. In main menu select preprocessor Real constant Add/edit/delete.

    4. On real constant dialog box, Click add. On the element types for real constants dialog

    box. Select link8 under choose element type and click ok.

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    5. On the real constant set number1 for link8 dialog box enter 20 for cross sectional area.

    Click ok.

    6. In main menu select preprocessor Material properties Material models. On the

    define material model behavior dialog box. Double click structural linear elastic

    isotropic in the material models available box.

    7. On the linear isotropic properties for material number dialog box. Enter 20E6 for Ex and

    click ok. Set PRXY to 0.0

    8. In the main menu select preprocessor modeling create nodes In active CS.

    On create nodes in active CS system enter 1 for node number & (120,0,0) for X,Y,Z

    location Click ok. Create elements 2,3,4 and 5 using data from below table.

    In the main menu select preprocessor modeling create elements auto

    numbered Thru nodes. Pick node 1 and node 2 using left mouse button. Repeated again

    create elements 2,3,4,5,6,7,8 and 9 using the below table.

    Element No

    Coordinates in Global Cartesian System

    Local Node 1 Local Node 2

    1 1 4

    2 1 2

    3 1 34 1 5

    5 2 4

    6 2 5

    7 3 4

    8 3 5

    9 4 5

    Node NoCoordinates in Global Cartesian System

    X (cm) Y (cm) Z (cm)

    1 120 0 0

    2 0 0 -60

    3 0 0 60

    4 0 120 0

    5 0 0 0

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    9. In the main menu select solution define loads apply structural displacement

    on nodes. Pick nodes 2, 3, 4 and click apply on the apply U ROT on nodes picking menu.

    10. On the apply U ROT on nodes dialog box select all DOF from the DOFs to be

    constrained list box. Click ok.

    11. In the main menu select solution define loads apply structural force/moment

    value on nodes pick nodes 1, 5 and click apply.

    12. On the apply F/M on nodes dialog box select FY from direction of Force/moment drop

    down box and enter -2000 for value click apply.

    13. Again pick nodes 1, 5 and click apply. Select FZ from the direction of force/moment drop

    down box and enter -1000 for force/moment value and click ok.

    SOLUTION:

    14. In the main menu select solution solve current LS click ok. On the Solve current

    load step dialog box. Close solution done. Close the dialogue box.

    GENERAL POST PROCESSOR:

    15. In the main menu select general post processor plot result contour plot

    nodal solution DOF Solution X component of displacement.

    16. Nodal Solution DOF solution Y component of displacement.

    17. Select nodal solution DOF solution Z component of displacement.

    18. In the main menu select general post processor list results nodal solution. Select

    nodal solution DOF solution displacement vector sum and click ok.

    19. Review the results and close command window.

    20. From utility menu select file exit save all and Click ok.

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    RESULT:

    Thus the nodal deflection and reaction forces of the truss are determined using ANSYS.

    (a). Nodal displacement

    Node NoDisplacement in "cm" along

    X axis Y axis Z axis

    1 -2.116 X 10-3

    -2.116 X 10-3 -0.838 X 10-3

    5 -0.419 X 10-3 6 X 10-3 -0.75 X 10-3

    (b). Reaction forces at supports

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    Node NoReaction forces in "N" along

    X axis Y axis Z axis

    2 2000 0 1500

    3 0 0 500

    4 -2000 4000 0

    EX.NO: 02 ANALYSIS OF A LONG CYLINDER PRESSURE VESSEL

    Date: 00.02.13

    AIM:

    To analyze a long cylinder pressure vessel and to determine the maximum deflection,

    tangential and radial stresses.

    PROBLEM DESCRIPTION:

    A long cylinder pressure vessel of inside diameter 10cm and outside diameter 20cm is

    subjected to an internal pressure 10kN/cm2. 20 structural solid element plane 82 is used to

    perform analysis.

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    PROCEDURE:

    PREPROCESSOR:

    1. In the main menu select preprocessor Element type Add/Edit/Delete on the library

    of element dialog box select structural solid in the left list box and then select Quad 8 node 82 in

    the right list box. Select axis symmetric from element behavior drop down box and click Ok.

    2. In main menu preprocessor materials properties material models double click

    structural linear elastic isotropic in right list box.

    3. Enter 2.1E7 for EX & 0.3 for PRXY.

    4. Select preprocessor modeling create key points Inactive CS on the create key

    points in active co-ordinate system dialog box enter 1 for key point number and (10,0,0) for XYZ

    location in active cs.

    5. Select preprocessor modeling create Areas Arbitrary Through KPS

    6. Pick key points 1,2,3,4 click ok on the picking menu.

    7. Select preprocessor Meshing Size Controls Manual Size Global Size on theglobal element sizes dialog box enter 20 for number of element divisions and click Ok.

    8. Select Preprocessor Meshing Mesh Areas Free Boundary Loading

    Conditions.

    9. Select Preprocessor Loads Define loads apply structural displacements On

    modes on the apply u, ROT to be constrained and click Ok.

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    10. In the utility menu select entities, select plot Replot, Select Entities

    11. Select Preprocessor Loads Define Loads Apply Structural Pressure On

    nodes on the apply press on elements dialog box enter 10,000 for load press value.

    12. Select everything

    13. Plot elements click save DB in ansys tool bar.

    SOLUTION:

    14. In the main menu select solution solve current LS click ok. On the Solve

    current load step dialog box. Close solution done. Close the dialogue box.

    GENERAL POST PROCESSOR:

    15. Select general post processor plot results contour plot nodal solutions.

    16. Select nodal solutions stress X component stress contour nodal solution dialog

    box select nodal solution stress Z component of stress Clock Ok.

    17. In the main menu select general post processor list results Nodal solution on the list

    nodal solution data dialog box.

    18. Select nodal solution stress X component of stress Click Ok.

    19. Review and close the PRNSOL command window. In the utility menu select File

    Exit on the exit from ansys select save everything and click Ok.

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    RESULT:

    Thus the maximum deflection, tangential and radial stress induced in long cylindrical pressure

    vessel in determined using ANSYS.

    Maximum hoop stress = 6665.58N/ cm2

    Maximum radial stress=-99984.51N/cm2

    EX.NO: 03 AXIAL DEFLECTION OF OPEN COILED HELICAL SPRING

    Date: 00.02.13

    AIM:

    To determine the deflection of an open coil helical spring.

    PROBLEM DESCRIPTION:

    An open coiled helical spring consist of 10 coils of mean diameter 5cm the wire forming thecoils bring 6mm diameter and making a constant angle of 300 with planes perpendicular to the

    axis of spring. The spring is attached to a tensile load of 125N E=2.1E7N/cm2, G=8.4E6 N/cm2.

    The spring is analyzed for maximum deflection 3D-10 node tetrahedral structural solid element

    solid 92 is used to perform the analysis.

    PROCEDURE:

    PREPROCESSOR:

    1. Initially click the preferences and select the structural preferences structural Ok

    2. In the main menu select preprocessor Element Type Add/Edit/Delete on the library

    of element types dialog box select structural solid in the box and select Tet 10 node 92 in

    the right list box.

    3. Select preprocessor Material Props Material models Double click structural

    Linear Elastic Orthotropic Enter 2.1E7 for Ex, EY,EZ and 8.4E6 for Gxy, Gyz, Gzx.

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    4. Select preprocessor Modeling Create Key points inactive CS Enter (0,0,0) for

    x,y,z location.

    5. Select work plane select and change active CS to global co-ordinates.

    6. Select preprocessor Modeling Create Lines In Active CS co-ordinates pick keypoints 21 and 22 in the same order and close the picking menu.

    7. In the utility menu select work plane off set wp by increments enter(0,0,90) for

    xy,yz,zx angles and Click Ok.

    8. Select preprocessor Modeling Create Areas Circle Solid Circle enter 0.3 for

    radius and click Ok.

    9. Select Preprocessor Modeling Operate Extrude Areas Along lines Pick

    area 1 and click Ok.

    10. Select preprocessor Meshing Mash tool on the mesh tool dialog box click mesh and

    click pick all from mesh volumes picking menu.

    11. Select preprocessor Loads define Loads Apply Structural Displacement On

    Areas Pick Area and click Ok . Select all DOF and click Ok.

    12. Select Preprocessor Loads Define loads Apply Structural Force/Moment

    On key points Pick key points and click Ok.

    13. On the apply Force/Moment on key points dialog box select Fz from direction of

    Force/Moment drop down box and enter 125 for Force/Moment value.

    SOLUTION:

    14. In the main menu select Finish and select solution Solve Current Ls.

    15. In the main menu select finish.

    GENERAL POST PROCESSOR:

    16. Select general post processor Plot results Counter Plot Nodal solution Select

    Nodal Solution DOF solution Z component of displacement Click Ok.

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    RESULT:

    Thus the axial deflection of an open coil is determined of an open coil helical spring is

    determined using ANSYS.

    Minimum axial deflection =-0.003329cm

    Maximum axial deflection=1.229cm

    EX.NO:6 MODAL ANALYSIS ON CANTILEVER BEAM

    Date: 00.02.13

    AIM:

    To determine displacement at modal points of cantilever beam using ANSYS and

    analysis the modal results.

    PROBLEM DESCRIPTION:

    NOMENCLATURE:

    L =5m, Length of beam

    b =0.5m, Cross Section Base

    h =0.5m Cross Section Height

    E=7*1010N/m^2, Youngs Modulus of Aluminum

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    =0.35, Poissons Ratio of Aluminum

    =2700kg/m^3, Density of Aluminum

    =1/192 m^4, Moment of Inertia

    In this module, we will introduce the ANSYS MechanicalAPDL Vibration AnalysisType. This uses the Modal solution method. This tutorial will explore the free vibration of a

    cantilever beam modeled with 1D BEAM elements and we will extract the natural frequencies

    and mode shapes at these frequencies.

    PROCEDURE

    PREFERENCES

    1. Go to Main Menu Preferences

    2. Check the box that says Structural

    3. Click OK

    KEY POINTS

    Since we will be using 1D Elements, our goal is to model the length of the beam.

    1. Go to Main Menu Preprocessor Modeling Create Keypoints On Working

    Plane

    2. Click Global Cartesian

    3. In the box underneath, write: 0,0,0. This will create a key point at the origin.

    4. Click Apply

    5. Repeat Steps 3 and 4 for 5,0,06. Click Ok

    7. The Triad in the top left corner is blocking keypoint 1.

    To get rid of the triad, type /triad,offin Utility Menu Command Prompt8. Go to Utility Menu Plot Replot

    LINE

    1. Go to Main Menu Preprocessor Modeling Create Lines Lines Straight

    Line

    2. Select Pick

    3. Select List of Items4. Type 1,2 for points previously generated.

    5. Click Ok

    PREPROCESSOR

    1. Go to Main Menu Preprocessor Element Type Add/Edit/Delete Add

    2. Click Beam 2D Elastic 3 .Click OK

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    REAL CONSTANTS AND MATERIAL PROPERTIES.

    Now we will dimension our beam.

    1. Go to Main Menu Preprocessor Real Constants Add/Edit/Delete

    2. Click Add

    3. Choose Type 1 Beam3 Click OK

    4. Under Cross-sectional area AREA enter 1/4

    5. Under Area moment of inertia IZZ Enter 1/192

    6. Under Total beam height HEIGHT enter 0.5 Click OK

    7. Click Close

    Now we must specify Youngs Modulus, Poissons Ratio and Density

    1. Go to Main Menu Preprocessor Material Props Material Models

    2. Go to Material Model Number 1 Structural Linear Elastic Isotropic

    3. Input 7E10 for the Youngs Modulus in EX.

    4. Input 0.35 for Poissons Ratio in PRXY .Click OK5. Go to Material Model Number 1 Structural Density

    6. Input 2700 for the Density in DENS .Click OK

    7. close Of Define Material Model Behavior window

    MESHING

    1. Go to Main Menu Preprocessor Meshing Mesh Tool

    2. Go to Size Controls: Global Set

    3. Under NDIV No. of element divisions put 10. This will create a mesh of a total 10

    elements .Click OK

    4. Click Mesh5. Click Pick All

    6. Go to Utility Menu Plot Nodes

    7. Go to Utility Menu Plot Controls Numbering

    8. Check NODE Node Numbers to ON .Click OK

    DISPLACEMENT

    1. Go to Main Menu Preprocessor Loads Define Loads Apply Structural

    Displacement On Nodes

    2. Select Pick Single and click node 1.Click OK

    3. Under Lab2 DOFs to be constrained select All DOF

    4. Under Value Displacement value enter 0 .Click OK

    SOLUTION

    Analysis Type

    1. Go to Main Menu Solution Analysis Type New Analysis

    2. Choose Modal .Click OK

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    PREPROCESSOR:

    1. Create geometry.

    Modelling create areas rectangle by 2 corners x=0 y=0 width = 1

    height = 1

    2. Element type.

    Preprocessor element type Add/Edit/Delete Select thermal mass

    solid Quad4node 55.

    3. Material properties.

    Preprocessor material props material model Thermal conductivity

    Isotropic kxx=1v

    4. Mesh size.

    Preprocessor meshing size control manual Size areas all areas.

    5. Mesh.

    Preprocessor meshing mesh areas free pick all.

    6. Define load.

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    Solution define load apply thermal temperature on lines.

    7. Apply convection boundary convection.

    Solution define loads apply thermal convection on lines.

    8. Apply insulated boundary condition.

    Solution define loads apply thermal Convection on lines.

    9. Solve.

    Solution solve current LS Solution is done.

    10. Read Results.

    General post processor plot results contour plot Nodal solution DOF

    solution temperature.

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    RESULT:

    The mixed boundary [conduction/convection/insulation] for given example were

    determined using ANSYS.

    EX.NO:08 BRIDGE STRUCTURE ANALYSES

    Date:00.02.13

    AIM:

    To determine stresses and the vertical displacements at joints and supports of bridge structurewith ABAQUS results.

    PROBLEM DESCRIPTION:

    The two dimensional bridge structure, which consists of steel Tsections, is simply

    supported at its lower corners. A uniform distributed load of 1000 N/m is applied to the lower

    horizontal members in the vertical downward direction.

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    Determine the stresses and the vertical displacements.

    PROCEDURE:

    1. Start Abaqus and choose to create a new model database2. In the model tree double click on the Parts node (or right click on parts and select

    Create)

    3. In the Create Part dialog box (shown above) name the part and

    a. Select 2D Planar

    b. Select Deformable

    c. Select Wire

    d. Set approximate size = 20

    e. Click Continue

    4. Create the geometry shown below (not discussed here)

    5. Double click on the Materials node in the model tree

    a. Name the new material and give it a description

    b. Click on the Mechanical tabElasticityElastic

    c. Define Youngs Modulus and Poissons Ratio (use SI units)

    WARNING: There are no predefined system of units within Abaqus, so the user is responsible

    for ensuring that the correct values are specified

    d. Click OK

    6. Double click on the Profiles node in the model tree

    a. Name the profile and select T for the shape

    i. Note that the T shape is one of several predefined crosssections

    b. C lick Continue

    c. Enter the values for the profile shown below

    d. Click OK

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    7. Double click on the Sections node in the model tree

    a. Name the section Beam Properties and select Beam for both the category and

    the type

    b. Click Continue

    c. Leave the section integration set to During Analysis

    d. Select the profile created above (TSection)

    e. Select the material created above (Steel)

    f. Click OK

    8. Expand the Parts node in the model tree, expand the node of the part just created, and

    double click on

    Section Assignments

    a. Select the entire geometry in the viewport and press Enter

    b. Select the section created above (Beam Properties)

    c. Click OK

    9. Expand the Assembly node in the model tree and then double click on Instances

    a. Select Dependent for the instance type

    b. Click OK

    10. Double click on the Steps node in the model tree

    a. Name the step, set the procedure to General, and select Static, General

    b. Click Continue

    c. Give the step a description

    d. Click OK

    11. Expand the Field Output Requests node in the model tree, and then double click

    on FOutput1 (FOutput1 was automatically generated when creating the step)

    a. Uncheck the variables Strains and Contact

    b. Click OK

    12. Expand the History Output Requests node in the model tree, and then right click

    on HOutput1 (HOutput1 was automatically generated when creating the step) and

    select Delete

    13. Double click on the BCs node in the model tree

    a. Name the boundary conditioned Pinned and select Displacement/Rotation forthe type

    b. Click Continue

    c. Select the lowerleft vertex of the geometry and press Done in the prompt area

    d. Check the U1 and U2 displacements and set them to 0

    e. Click OK

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    f. Repeat for the lowerright vertex, but model a roller restraint (only U2 fixed)

    instead

    14. Double click on the Loads node in the model tree

    a. Name the load Distributed load and select Line load as the type

    b. Click Continuec. Select the lower horizontal edges of the geometry press Done in the prompt

    area

    d. Specify component 2 = 1000

    i. Note that because we have been using standard SI units the load applied is

    1000 N/m, which is a total of 10,000 N distributed across the lower

    horizontal members

    e. Click OK

    15. In the model tree double click on Mesh for the Bridge part, and in the toolbox area

    click on the Assign Element Type icona. Highlight all members in the viewport and select Done

    b. Select Standard for element type

    c. Select Linear for geometric order

    d. Select Beam for family

    e. Note that the name of the element (B21) and its description are given below the

    element controls

    f. Click OK

    16. In the toolbox area click on the Seed Edge: By Number icon (hold down icon to bring

    up the other options)

    a. Select the entire geometry, except the lower horizontal lines, and click Done in

    the prompt area

    b. Define the number of elements along the edges as 5

    c. Repeat for the lower horizontal lines, except specify 10 elements along the edges

    17. In the toolbox area click on the Mesh Part icon

    a. Click Yes in the prompt area

    18. In the menu bar select ViewPart Display Options

    a. Check the Render beam profiles option on the General tabb. Click OK

    19. Change the Module to Property

    a. Click on the Assign Beam Orientation icon

    b. Select the entire geometry from the viewport

    c. Click Done in the prompt area

    d. Accept the default value of the approximate n1 direction

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    20. Note that the preview shows that the beam cross sections are not all orientated as desired

    (see Problem Description)

    21. In the toolbox area click on the Assign Beam/Truss Tangent icon

    a. Click on the sections of the geometry that are off by 180 degrees

    22. In the model tree double click on the Job nodea. Name the job Bridge

    b. Click Continue

    c. Give the job a description

    d. Click OK

    23. In the model tree right click on the job just created (Bridge) and select Submit

    a. While Abaqus is solving the problem right click on the job submitted (Bridge),

    and select Monitor

    b. In the Monitor window check that there are no errors or warningsi. If there are errors, investigate the cause(s) before resolving

    ii. If there are warnings, determine if the warnings are relevant, some

    warnings can be safely ignored

    24. In the model tree right click on the submitted and successfully completed job (Bridge),

    and select Results

    25. In the menu bar click on ViewportViewport Annotations Options

    a. Uncheck the Show compass option

    b. The locations of viewport items can be specified on the corresponding tab in the

    Viewport Annotations Optionsc. Click OK

    26. Display the deformed contour of the (Von) Misses stress overlaid with the undeformed

    geometry

    a. In the toolbox area click on the following icons

    i. Plot Contours on Deformed Shape

    ii. Allow Multiple Plot States

    iii. Plot Undeformed Shape

    27. In the toolbox area click on the Common Plot Options icon

    a. Note that the Deformation Scale Factor can be set on the Basic tabb. On the Labels tab check the show node symbols icon

    c. Click OK

    28. To determine the stress values, from the menu bar click ToolsQuery

    a. Check the boxes labeled Nodes and S, Misses

    b. In the viewport mouse over the element of interest

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    c. Note that Abaqus reports stress values from the integration points, which may

    differ slightly from the values determined by projecting values from the

    surrounding integration points to the nodes

    i. The minimum and maximum stress values contained in the legend are

    from the stresses projected to the nodes

    d. Click on an element to store it in the Selected Probe Values portion of the

    dialogue box

    e. Click Cancel

    29. To change the output being displayed, in the menu bar click on ResultsField

    Output

    a. Select Spatial displacement at nodes

    i. Component = U2

    b. Click OK

    30. To create a text file containing the stresses, vertical displacements, and reactionforces (including the total), in the menu bar click on ReportField Output

    a. For the output variable select (Von) Misses

    b. On the Setup tab specify the name and the location for the text file

    c. Uncheck the Column totals option

    d. Click Apply

    e. Back on the Variable tab change the position to Unique Nodal

    f. Uncheck the stress variable, and select the U2 spatial displacement

    g. Click Apply

    h. On the Variable tab, uncheck Spatial displacement and select the RF2 reactionforce

    i. On the Setup tab, check the Column totals option

    j. Click OK

    31. Open the .rpt file with any text editor

    a. One thing to check is that the total reaction force is equal to the applied load (

    10,000 N)

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    RESULT:

    Thus the stresses and the vertical displacements of the bridge structure are determined using

    ABAQUS.

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    The various functions within ABAQUS are organized into modules and we are going to use

    these modules to define the steps in our procedure.

    1. >module load abaqus/6.9-2

    2. >abaqus cae

    3. Once you start ABAQUS CAE select Create Model Database to create a new model.

    4. The default module that opens up is the Part Module.

    PART MODULE:

    This module allows you to create the geometry required for the problem. To create a 3-D

    geometry you first create a 2-D profile and then manipulate it to obtain the solid geometry.

    1. From the Part Toolbox on the left of the viewport select Create Part.

    2. You can name the part as cylinder or anything else you like. We are going to create adeformable solid shape in the 3-D modeling space through extrusion so we do not change

    the default selections.

    3. Enter 1 as the approximate size and click Continue.

    4. Click Create Circle Center and Perimeter on the drawing toolbox and enter 0, 0 as the

    center point in field below the viewport and press Enter. Enter the perimeter point as

    0.21, 0 and press Enter to complete the circle. Similarly make another circle with the

    same center and the perimeter point as 0.2, 0. Press Esc to exit the circle definition andthen press Done.

    5. Enter the extrusion depth as 1 and press OK.

    6. Click Auto-Fit View in the toolbar above to zoom out and view all the points.

    This finishes our work in the Part module. Select Module: Property from the toolbar above

    the viewport.

    PROPERTY MODULE:

    In this module you define the material properties for your analysis and assign thoseproperties to the available parts.

    1. Select Create Material from the Property Toolbox.

    2. Enter material name as Aluminum. Click on the General tab and select Density from thedrop-down menu. Type in the mass density as 2700. Click on the Mechanical tab and

    select Elasticity>Elastic from the drop-down menu. Enter the Youngs Modulus as 70E9

    and the Poissons Ratio as 0.33. Click on the Mechanical tab and select Expansion. Editthe reference temperature to 273.15 and the expansion coefficient to 23e-6. Click on the

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    Thermal tab and select Conductivity. Enter the thermal conductivity as 160. Click on the

    Thermal tab and select Specific Heat. Enter the value as 900 and click OK.

    3. Select Create Section from the property toolbox. Name the section as you like. We need a

    solid homogeneous section for our problem. Click Continue. Select the material as

    Aluminum and click OK.

    4. Click Assign Section on the property toolbox and select the part from the viewport. Click

    Done below. Select the section you had created and click OK.

    Our work in the Property module is done and we select the Assembly Module from the

    toolbar above the viewport.

    ASSEMBLY MODULE:

    This module allows you to assemble together parts that you have created. Even if you have a

    single part you need to include it in your assembly.

    1. Select Instance Part from the Assembly Toolbox.

    2. Select the part you have created from the parts list and then select Instance type:Independent. Click OK.

    Select Module: Step from the toolbar above.

    STEP MODULE:

    This module allows you to select the kind of analysis you want to perform on your model

    and define the parameters associated with it. You can also select which variables you want to

    included in the output files in this modules. You apply loads over a step. To apply a sequence ofloads create several steps and define the loads for each of them.

    1. Select Create Step from the Step Toolbox.

    2. Name the step as you want and select Coupled temp-displacement as the procedure. ClickContinue.

    3. The edit step dialog box lets you choose the solution technique, the solver type and definethe time stepping strategy.

    4. Under Basic change the Response to Steady-state and click OK.

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    The Interaction Module allows you to set up interactions (contact, film), constraints,

    connectors, fasteners and wire feature between parts. Our problem does not involve any of these

    features but it will be a good idea to explore this module on your own at a later time.

    Select Module: Load from the toolbar above.

    LOAD MODULE:

    The Load Module is where you define the loads and boundary conditions for your modelfor a particular step (indicated in the toolbar above). You can even define loads and boundary

    conditions as fields like electric potential, acoustic pressure, etc.

    1. Select Create Load from the Load Toolbox. Select Surface Traction and click Continue.Select the top face of the cylinder (z=1) (it gets highlighted in red) and click Done.

    2. Change the Traction type to General. Click on the Edit tab under Direction in the dialog

    box. Enter the starting point of the direction vector as (0, 0, 0) and the end point as (0,0,1). Enter the Magnitude as 2e5 and click OK.

    3. Select Create Boundary Condition from the Load Toolbox. Select Symmetry /

    Antisymmetry / Encastre and click Continue. Select the bottom face (z=0) of the cylinder

    and click Done. Select Pinned (U1=0, U2=0, U3=0) and click OK.

    4. Again select Create Boundary Condition from the Load Toolbox. Switch Category to

    Other and select Temperature and click Continue. Select the bottom face of the cylinder

    and press Done. Enter the magnitude as 273.15 and click OK. Similarly put the top faceat 274.15.

    Now that we have defined the loads and the boundary conditions we move on to mesh thegeometry.

    Select Module: Mesh from the toolbar above the viewport.

    MESH MODULE:

    The mesh model controls how you mesh your model the type of element, their size etc.

    1. Select Seed Part Instance from the mesh toolbox. Enter the approximate global size as

    0.025.

    2. Click on Mesh Part Instance and then on Yes to mesh the model.

    3. Select Assign Element Type from the mesh toolbox. Under Family select Coupled

    Temperature-Displacement and switch Geometric Order to Quadratic. Click OK.

    When finished

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    select Module: Job from the toolbar above.

    JOB MODULE:

    This module allows you to submit your model for analysis.

    1. Select Create Job from the Job Toolbox. Name the job as you like. Select your model andclick Continue.

    2. You can add a description to the job, allocate memory, allot multiple processors and

    select precision. Use the default values and click OK.

    3. Select the Job Manager from the toolbox and click on the Write Input tab.

    4. If you are running the job for the first time it is advisable to run Data Check to check the

    input file for errors. Click OK to overwrite the job files.

    5. Once the data check is completed Submit the job for analysis. Click OK to overwrite the

    job files. You can click Monitor to observe the progress of the solution process. You cansee the errors, warnings, data and message file.

    6. Once the job is completed click on the Results tab on the job manager. This opens theVisualization Module for post processing.

    VISUALIZATION MODULE:

    This model allows you to look at your model after deformation. You can also plot values

    of stress, displacement, reaction forces, etc. as contours on your model surface or as vectors or

    tensors.

    1. Select Plot Deformed Shape from the Visualization toolbox.

    2. Select Plot Contours on Deformed Shape to plot stress contours on the model surface.

    3. You can see the location of the maximum & minimum stresses by selecting Contour

    Options>Limits>Show Location.

    4. Select Results>Field Output from the main menu. This opens a dialog box that allows

    you to select the variable you want to plot in the viewport.

    5. Select U (Spatial Displacement at nodes)>Magnitude>OK to plot the displacement

    contours on the model.

    6. To plot displacement vectors click on Plot Symbols on Deformed Shape on the toolbox.

    7. You can now animate this plot by selecting Animate Harmonic.

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    RESULT:

    Thus the temperature distribution on the inside the cylinder determined using ABAQUS.