Aim: To Analyze the Analysis of Cantilever Beam I Sem FEA Lab... · Web viewAnalysis of cantilever beam using ANSYS Workbench Figure 01 shows an overview of the beam problem for load

SRI VENKATESWARA COLLEGE OF ENGINEERING & TECHNOLOGY(AUTONOMOUS)

Experiment No. Date:

SRI VENKATESWARA COLLEGE OF ENGINEERING AND TECH

(AUTONOMOUS)

RVS NAGAR, CHITTOOR-517127

DEPATMENT OF MECHANICAL ENGINEERING

I M.Tech I Sem

FEA-I LAB (2015-16)

COMMON TO CAD/CAM &MACHINE DESIGNLABORATORY MANUAL

Prepared by

DEPATMENT OF MECHANICAL ENGINEERING

SRI VENKATESWARA COLLEGE OF ENGINEERING AND TECHNOLOGY

RVS NAGAR, CHITTOOR-51712

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1. Analysis of cantilever beam using ANSYS Workbench

Figure 01 shows an overview of the beam problem for load case 1 (point load) and figure 02 shows a representative finite element model for this load case.

Figure 01: Overview of Simple Beam Problem with Vertical Point Load (Case 1)

The beam is 2 metres long with the left hand edge built into a thick wall and the centre of the beam is simply supported.The beam is made from steel with E = 200 GPa.

. We will use SI system units for this tutorial: length = m, mass = kg, time = sec, force = N, stress/pressure = Pa.

Step 1: Launch ANSYS Work benchStep 2: Define Material PropertiesStep 3: Define the Beam Cross Section

Unfortunately the problem definition doesn't actually specify which type of cross section the beam has. That isn't a problem and we can work around it. We know that the beam cross section has a second moment of area of I = ?

type of cross section to fit this second moment of area value. We will assume that the beam has a I section:

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Figure 03: Calculating the beam second moment of Inertia

The Aluminium used for the beam has the following material properties.Density 2,700 kg/m^3 Youngs Modulus 70x10^9 Pa Poisson Ratio 0.35.

Start ANSYS Workbench & Load Files

In this section we will launch ANSYS Workbench and then load the project file, "cantilever.wbpj" that was created in the "Cantilever Beam" tutorial.

Start > All Programs > ANSYS 12.1 > Workbench

File > OpenThen choose the "cantilever.wbpj" file that you created in the "Cantilever Beam" tutorial.

Management of Screen Real Estate

This tutorial is specially configured, so the user can have both the tutorial and ANSYS open at the same time as shown below. It will be beneficial to have both ANSYS and your internet browser displayed on your monitor simultaneously. Your internet browser should consume approximately one third of the screen width while ANSYS should take the other two thirds as shown below.

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Modal (ANSYS) Project Selection

Left, click on Modal ANSYS, and drag it to the right of the "Cantilever" project. You should then see a red box to the right of the "Cantilever" project that says "Create standalone system" as shown below.

Next, enter "Aluminium" and press enter. You should now have Aluminum listed as one of the materials in table called "Outline of Schematic B2: Engineering Data", as shown below.

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Then, (expand) Linear Elastic, as shown below.

Now, (Double Click) Isotropic Elasticity. Then set Young's Modulus to 70e9 Pa and set Poisson's Ratio to 0.35 , as shown below

Next, (expand) Physical Properties, as shown below

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Now, (Double Click) Density. Then, set Density to 2,700 kg / m^3 , as shown below

Now, the material properties for Aluminum have been specified. Lastly, (Click) Return To

Project,

Save

Save your project now and periodically, as you work. ANSYS does not have an auto-save feature.

Step 2 Geometry: Attach Geometry from Cantilever to Cantilever ModalThe geometry for the "Cantilever Beam Modal Analysis" tutorial is the same as the geometry for the "Cantilever Beam" tutorial. Instead of recreating the geometry, we will simple attach the geometry from the Static Structural Analysis System (Cantilever) to the Modal Analysis System (Cantilever Modal). In order to attach the geometry, (left click) Geometry in the "Cantilever" project and drag it to Geometry in the "Cantilever Modal" project, as shown below.

Then release the left mouse button. You should now see that the geometries are shared as shown in the following image.

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Save

Step 3:

Mesh

Launch Mechanical

Generate Default Mesh

First, (click) Mesh in the tree outline. Next, (click) Mesh > Generate Mesh as shown below

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Size Mesh

In this section we will size the mesh, such that it has ten uniform elements. In order to size the mesh, first expand Sizing located within theDetails of "Mesh" table. Next, set Element Size to 0.40 m, as shown below.

Now, (click) Mesh > Generate Mesh in order to generate the new mesh. You should obtain the mesh, that is shown in the following image.

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Note that in this simulation we are working with beam elements, which are simply line segments. As a visualization tool ANSYS displays a beam with width and height. In order to display the actual mesh (click) View > (deselect) Thick Shells and Beams. You will then see the mesh displayed in its native form. SAVE.

Step 4:

Physics SetupMaterial AssignmentAt this point, we will tell ANSYS to assign the Aluminum material properties that we specified earlier to the geometry. First, (expand) Geometry then (click) Line Body, as shown below.

Then, (expand) Material in the "Details of Line Body" table and set Assignment to Aluminum, as shown below.

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Fixed Support

First, (right click) Modal > Insert > Fixed Support, as shown below.

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Next, click the vertex selection filter button,. Then, click on the left end of the beam and apply it as the Geometry in the "Details of Fixed Support" table.

First, (right click) Modal > Insert > force, as shown below.

Numerical Solution

Specify Results (Deformation)

Here, we will tell ANSYS to find the deformation for the first six modes. Then, we will be able to see the shapes of the six modes. Additionally, we will be able to watch nice animations of the six modes.

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In order to request the deformation results (right click) Solution > Insert > Deformation > Total as shown below.

Save.

Run Calculation

In order to run the simulation and calculate the specified outputs, click the Solve button,

Results:

Calculate Deformation and stresses, factor of safety

Maximum principle stress: 1.0367e7 Pa

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2.Two dimensional truss using ANSYS

Determine the displacement distribution and stress distribution in the framework due to the applied loading and boundary conditions. A two-dimensional structural truss element (often also called a "spar", "spring" or "link" element) will be used for this analysis. The Figure below shows an overview of the truss problem on the left hand side and a representative finite element model on the right hand side.

Figure 01 : Overview of Truss Framework Problem and Representative FE Model

The relevant node and element data are given in the tables below. We will use SI system units for this tutorial: length = m, mass = kg, time = sec, force = N, stress/pressure = Pa.

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We can use the information in the tables above to define our nodes and elements. In order to define the boundary conditions and loads on the finite element model we can reference figure 01 in order to generate a list of constraints and loads on each node, as shown in the table below.

Figure 02 shows an overview of the expected results from the Practical Stress Analysis with Finite Elements book. We are going to attempt to recreate these results here.

Figure 02: Expected Results from the Finite Element Analysis

Step 1: Launch ANSYS

We have already covered how to launch ANSYS properly in tutorials 1 and 2. Please go back and re-read these tutorials if you cannot remember how to do it.

Step 2: Define Element Type

1. In the Main Menu select Preprocessor > Element Type > Add/Edit/Delete2. Click on Add in the dialog box that appears.

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3. Select Link in the left hand menu and 3Dfinit stn 180 in the right hand menu and then click Ok

4. This will define element type 1 as a LINK 180 element. LINK 180 is actually a 3D truss element but we are going to use it as a 2D truss by later suppressing some of it's degrees of freedom.

5. Click Close to close the Element Type dialog box.

Step 3: Define Element Cross Sectional Area (Real Constant)

1. In the Main Menu select Preprocessor > Real Constants > Add/Edit/Delete2. Click on Add in the dialog box that appears.3. Click on OK to define a real constant for element type 1 LINK 180

4. Enter the value for cross sectional area for element 1: 0.05m2 and then click OK

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5. Click on Close to close the real constants dialog box.

Step 4: Define the Material Behaviour

1. In the Main Menu click on Preprocessor > Material Props > Material Models, the Define Material Model Behaviour dialog box will now appear.

2. Expand the options in the right hand pane of the dialog box: Structural > Linear > Isotropic

3. In the dialog box that pops up, enter suitable material parameters for steel ( E = 210 x 109 Pa, Poissons ratio = 0.3):

4. Click on Ok to close the dialog box in which you entered the material parameters.5. Close the Define Material Model Behaviour dialog box by clicking on the X in the upper

right corner.

Step 5: Define Nodes and Elements

1. In the Main Menu click on Preprocessor > Modeling > Create > Nodes > In Active CS

2. In the dialog box that appears: enter the x and y coordinates for node 1 (i.e. 0,0) and click on Apply (note that Apply issues the command to create the node but keeps the dialog box open, clicking OK would also issue the command to create the node but would close the dialog box).

3. Now enter the x and y coordinates for node 2 (i.e. 2,1.5) and click Apply

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=

4. Enter the x and y coordinates for node 3 (i.e. 0,1.5) and click OK to dismiss the dialog box

5. You may have notice nodes appearing on the main window when you clicked apply. You should now be able to see 3 nodes in the main window (note that node 1 is at the origin so you may not be able to see it due to the display of the triad at the origin, this is OK):

6. We must now create the elements that join the nodes together: click on Preprocessor > Modeling > Create > Elements > Auto Numbered > Thru Nodes

7. In the main window click on node 1 and then node 2. Then click Apply in the dialog box. You should see a line element appear joining nodes 1 and 2.

8. Now click on node 2 and then node 3 and click OK. A line element should appear joining nodes 2 and 3.

9. Your display should now look like this:

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Step 6: Define Boundary Conditions

1. In this case we are using a 3D truss to model a 2D truss problem so we must prevent the nodes from moving in the Z direction (i.e. only allow movement in the X and Y directions). In order to do this we constrain all nodes in the finite element model in the Z direction.

2. Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Nodes

3. Select Pick All in the dialog box that appears.4. Select UZ in the next dialog box that appears and enter a value of 0 for displacement

value5. Click Ok to close the dialog box. You should notice blue crosses appearing at each of the

nodes. 6. Now we can apply the problem boundary conditions.7. Using the table above: we must constrain node 1 and 3 in both the X and Y directions.8. Again, select: Preprocessor > Loads > Define Loads > Apply > Structural >

Displacement > On Nodes9. Click on Nodes 1 and 3 and then click Ok10. Select UX, UY and UZ and enter a value of 0 for displacement value11. Click Ok to close the dialog box. Your should have noticed extra constraints appearing at

nodes 1 and 3 (blue triangles pointing in the horizontal and vertical directions)

Step 7: Define Loads

1. Select Preprocessor > Loads > Define Loads > Apply > Structural > Force/ Moment > On Nodes

2. Pick node 2 and click on Ok3. In the dialog box that appears make sure that the direction of force is set to FY and that

the Force/ Moment value is 100000

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4. Click on Ok to close the dialog box.5. You should see a red arrow appear on node 2 pointing to upwards.

Step 8: Solve the Problem

1. In the Main Menu select Solution > Analysis Type > New Analysis2. Make sure that Static is selected in the dialog box that pops up and then click on OK to

dismiss the dialog.3. Select Solution > Solve > Current LS to solve the problem4. A new window and a dialog box will pop up. Take a quick look at the infromation in the

window ( /STATUS Command) before closing it.5. Click on OK in the dialog box to solve the problem.6. Once the problem has been solved you will get a message to say that the solution is done,

close this window when you are ready.

Step 9: Examine the Results

1. In the Main Menu select General Postproc > Plot Results > Deformed Shape

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In the dialog box that appears make sure that Def + undef edge is selected. This shows the deformed shaped overlaid on the original shape of the finite element model. Click on OK to plot the deformed shape:

2. Now, select General Postproc > List Results > Nodal Solution > DOF solution > Displacement Vector Sum and click OK

3. You should get a screen similar to this:

4. This gives us the displacement results for each node in the finite element model.

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5. The truss element that we have used is quite basic and it is difficult to get stress results directly from it. In order to access stress results we have to define an element table.

6. Select General Postproc > Element Table > Define Table > Add7. Edit the options in the dialog box so that they look like this:

8. It is very important to add the "1" after "LS, " !9. Click on Ok to define the element table.10. Click on Close to close the other dialog box.11. Now select General Postproc > Element Table > List Elem Table you should get a

listing like this:

12. This listing gives the stress in each element, for example element 1 has an axial stress of 0.3333 x 106 Pa or 0.333 MPa

13. Finally, we need to obtain the reaction forces for each node in the finite element model: select General Postproc > List Results > Reaction Solu and click on OK in the dialog box that appears, you should see a listing like this:

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14. This listing gives the reaction force at each node, for example node 3 has a x direction reaction force of 13,333 N.

Step 10: Validate the Results

Result Quantity Ansys Result Result in book % Accuracy

X Displacement of Node 2 -0.25397e-5 m -0.2539e-5 m 100% Y Displacement of Node 2 0.1e-4 m 1e-5 m 100% Stress in Element 1 0.33333e6 Pa 0.33 x 106 Pa 100% Stress in Element 2 -0.26667e6 Pa -0.266 x 106 Pa 100% RX of Node 1 -13,333 N -13,333 N 100% RY of Node 1 -10,000 N -10,000 N 100% RX of Node 3 13,333 N 13,333 N 100% RY of Node 3 0 N 0 N 100%

As the table above clearly shows, our finite element results are consistent with those given in the book.

Summary

This tutorial has given you the following skills:

1. The ability to model 2-D truss problems in ANSYS.2. The ability to generate finite element models using the direct method (i.e. defining nodes

and then defining elements linking those nodes, as opposed to taking a solid model and dividing it up into elements which we will do in subsequent tutorials).

3. The ability to define element types, real constants and material parameters for a finite element model.

4. The ability to apply boundary conditions and loads to specific nodes in a finite element model.

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5. The ability to run a simple linear static analysis.6. The ability to plot the deformed shape of a model and overlay it on the original shape7. The ability to list displacement results for each node in the finite element model.8. The ability to create an element table to obtain additional results from a finite element

model and to list these results.

Experience in comparing the results obtained from your finite element model with other results

and validating your results against the other results

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3. 3D Plane stress rectangular block with hole using ANSYS Workbench

Problem Specification

Consider the classic example of a small circular hole in a rectangular plate of constant thickness subjected to an in-plane tensile load. The material is structural steel with a Young's Modulus of 29E6 psi and a Poisson ratio of 0.3. The geometric dimensions and applied tensile load are shown below.

P =6.89GPaa = 12.7 mmW = 127 mmL = 254 mmt = 5 mm

This Exercise will show you how to use ANSYS Workbench to find the displacement and the stresses in the plate.

Analytical vs. Numerical Approaches

We can either assume the geometry as an infinite plate and solve the problem analytically, or approximate the geometry as a collection of "finite elements", and solve the problem numerically. The following flow chart compares the two approaches.

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Open ANSYS Workbench

Now that we have the pre-calculations, we are ready to do a simulation in ANSYS Workbench! Open ANSYS Workbench by going to Start > ANSYS > Workbench. Similar to first exercise.

To begin, we need to tell ANSYS what kind of simulation we are doing. The plate with a hole is a static structural simulation. Load the static structural tool box by dragging and dropping it into the Project Schematic.

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Name the Project "Plate with a Hole" by double clicking the text Static Structural and typing in Plate with a Hole.

Material Selection

Now we need to specify what type of material we are working with. Double click Engineering Data and it will take you to the Engineering Data Menus.

Engineering Data Window, you will see that the default material is Structural Steel. The Problem Specification specifies the material's Modulus of Elasticity and Poisson's ratio. To add a new material, click in an empty box labeled Click here to add a new material and give it a name.

On the left hand side of the screen in the Toolbox window, expand Linear Elastic and double click Isotropic Elasticity to specify the Elastic Modulus and Poisson's Ratio.

Now that the material has been specified, we are ready to make the geometry in ANSYS.

Step2 Geometry creation:

Create in solid works modeling software and convert to .IGS or STEP.

That file import to ANSYS Workbench.

Step 3 Mesh Generation:

Go to Units > U.S. Customary (in. lbm, lbf, F, s, V, A) to make sure the proper units are selected.

To begin the Mesh process, click Mesh in the outline window. This will bring up the Mesh Menu bar in the Menu bar.

We want to control the size of the elements in the mesh for this problem; to accomplish this, click Mesh Control > Sizing. We now need to pick the geometry we are going to mesh. Make sure the Face Selection Filter is selected then click the face of the geometry to select it. In the Details window click Geometry > Apply. Now, we can set some of the details of our mesh. Select Element Size > Default, this will allow you to change the size of the element. Choose the size of the elements to be .05 mm.

Turn off the Advanced Size Function in the details window of "Mesh". If we leave the Advanced Size Function on, ANSYS will override the face sizing we applied.

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In the details window, change the Refinement parameter from 1 to 3, this will give us the finest mesh at the hole which will improve accuracy of the simulation.

Now that we have our mesh setup, click Mesh > Generate Mesh. This will create the mesh to our specifications. Click to display it. It should look something like this:

Now that the mesh has been created, we are ready to specify the boundary conditions of the problem.

Step4.Physics define:

Boundary conditions:

Click Loads > Pressure to specify a traction. Select the right edge of the geometry and apply it in the details view window. The pressure's magnitude from the problem specification is -1e6 psi (pressure in ANSYS defaults to compression, and we need tension, hence the negative sign). Now that the forces have been set, we need to set up the solution before we solve.

Click Fixed other two sides.

Step 5 Results:

Calculate deformation ,stress for above exercise.

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4. Buckling analysis on linear materials using ANSYS APDL

Problem Description:Determine the critical buckling load of an axially loaded long slender bar of length l with hinged ends. The bar has a cross-sectional height h, and area A. Only the upper half of the bar is modeled because of symmetry.The boundary conditions become free-fixed for the half-symmetry model. The moment of inertia of the bar is calculated as I =Ah^2/12After you enter the ANSYS program, follow these steps to set the title.1. Choose menu path Utility Menu> File> Change Title.

2. Enter the text "Buckling of a Bar with Hinged Ends" and click on OK.

Problem Specifications:

The model is assumed to act only in the X-Y plane.

The following material properties are used: E =200E5 N/mm^2

The following geometric properties are used:

L= 100mm

A=0.25 mm^2

H= 0.5 mm^2

F= 1 Kg.

Problem Sketch:

Bar with Hinged Ends:

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Set the Analysis Title:

After you enter the ANSYS program, follow these steps to set the title.1. Choose menu path Utility Menu> File> Change Title.

2. Enter the text "Buckling of a Bar with Hinged Ends" and click on OK.

Define the Element Type

In this step, you define BEAM188 as the element type.1. Choose menu path Main Menu> Preprocessor> Element Type> Add/Edit/Delete. The Element Typesdialog box appears.2. Click on Add. The Library of Element Types dialog box appears.3. In the scroll box on the left, click on "Structural Beam" to select it.4. In the scroll box on the right, click on "2 Node 188" to select it.5. Click on OK. The Library of Element Types dialog box closes.6. Click on Options in the Element Types dialog box.7. Choose Element Behavior K3 : Cubic Form. Click on OK.

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

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Define the Real Constants and Material Properties1. Choose menu path Main Menu> Preprocessor> Sections> Beam> Common Sections. The BeamTooldialog box appears.2. Enter .5 for B and .5 for H.3. Click on OK.4. Choose menu path Main Menu> Preprocessor> Material Props> Material Models. The Define Ma-terial Model Behavior dialog box appears.5. In the Material Models Available window, double-click on the following options: Structural, Linear,Elastic, Isotropic. A dialog box appears.6. Enter 30e6 for EX (Young's modulus), and click on OK. Material Model Number 1 appears in the Mater-ial Models Defined window on the left.

7. Choose menu path Material> Exit to remove the Define Material Model Behavior dialog box.

Define Nodes and Elements1. Choose menu path Main Menu> Preprocessor> Modeling> Create> Nodes> In Active CS. The CreateNodes in Active Coordinate System dialog box appears.2. Enter 1 for node number.3. Click on Apply. Node location defaults to 0,0,0.4. Enter 11 for node number.5. Enter 0,100,0 for the X, Y, Z coordinates.

6. Click on OK. The two nodes appear in the ANSYS Graphics window.

NoteThe triad, by default, hides the node number for node 1. To turn the triad off, choose menupath Utility Menu> PlotCtrls> Window Controls> Window Options and select the "NotShown" option for Location of triad. Then click OK to close the dialog box.7. Choose menu path Main Menu> Preprocessor> Modeling> Create> Nodes> Fill between Nds. TheFill between Nds picking menu appears.8. Click on node 1, then 11, and click on OK. The Create Nodes Between 2 Nodes dialog box appears.9. Click on OK to accept the settings (fill between nodes 1 and 11, and number of nodes to fill 9).

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10. Choose menu path Main Menu> Preprocessor> Modeling> Create> Elements> Auto Numbered>Thru Nodes. The Elements from Nodes picking menu appears.11. Click on nodes 1 and 2, then click on OK.12. Choose menu path Main Menu> Preprocessor> Modeling> Copy> Elements> Auto Numbered. TheCopy Elems Auto-Num picking menu appears.13. Click on Pick All. The Copy Elements (Automatically-Numbered) dialog box appears.14. Enter 10 for total number of copies and enter 1 for node number increment.

15. Click on OK. The remaining elements appear in the ANSYS Graphics window.

Define the Boundary Conditions1. Choose menu path Main Menu> Solution> Unabridged Menu> Analysis Type> New Analysis. TheNew Analysis dialog box appears.2. Click OK to accept the default of "Static."3. Choose menu path Main Menu> Solution> Analysis Type> Analysis Options. The Static or Steady-State Analysis dialog box appears.4. In the scroll box for stress stiffness or prestress, scroll to "Prestress ON" to select it.5. Click on OK.6. Choose menu path Main Menu> Solution> Define Loads> Apply> Structural> Displacement> OnNodes. The Apply U,ROT on Nodes picking menu appears.7. Click on node 1 in the ANSYS Graphics window, then click on OK in the picking menu. The Apply U,ROT on Nodes dialog box appears.8. Click on "UY" and “ROTZ” to select them, and click on OK.9. Choose menu path Main Menu> Solution> Define Loads> Apply> Structural> Displacements> OnNodes. The Apply U,ROT on Nodes picking menu appears.10. Click on node 11 in the ANSYS Graphics window, then click on OK in the picking menu. The ApplyU,ROT on Nodes dialog box appears.11. Click on "UX" to select it, and click on OK.12. Choose menu path Main Menu> Solution> Define Loads> Apply> Structural> Force/Moment> OnNodes. The Apply F/M on Nodes picking menu appears.13. Click on node 11, then click OK. The Apply F/M on Nodes dialog box appears.14. In the scroll box for Direction of force/mom, scroll to "FY" to select it.15. Enter -1 for the force/moment value, and click on OK. The force symbol appears in the ANSYS Graphics window.16. Choose menu path Main Menu> Solution> Define Loads> Apply> Structural> Displacement>

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Symmetry B.C.> On Nodes. The Apply SYMM on Nodes box dialog appears.

17. In the scroll box for Norml symm surface is normal to, scroll to “z-axis” and click on OK.

Solve the Static Analysis1. Choose menu path Main Menu> Solution> Solve> Current LS.2. Carefully review the information in the status window, and click on Close.3. Click on OK in the Solve Current Load Step dialog box to begin the solution.

4. Click on Close in the Information window when the solution is finished.

Solve the Buckling Analysis

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

NoteClick on Close in the Warning window if the following warning appears: Changing theanalysis type is only valid within the first load step. Pressing OK will cause you to exit andreenter SOLUTION. This will reset the load step count to 1.2. In the New Analysis dialog box, click the "Eigen Buckling" option on, then click on OK.3. Choose menu path Main Menu> Solution> Analysis Type> Analysis Options. The Eigenvalue BucklingOptions dialog box appears.4. Enter 1 for number of modes to extract.5. Click on OK.6. Choose menu path Main Menu> Solution> Load Step Opts> ExpansionPass> Single Expand> Expand Modes.7. Enter 1 for number of modes to expand, and click on OK.8. Choose menu path Main Menu> Solution> Solve> Current LS.9. Carefully review the information in the status window, and click on Close.10. Click on OK in the Solve Current Load Step dialog box to begin the solution.

11. Click on Close in the Information window when the solution is finished.

Review the Results1. Choose menu path Main Menu> General Postproc> Read Results> First Set.2. Choose menu path Main Menu> General Postproc> Plot Results> Deformed Shape. The Plot De-formed Shape dialog box appears.3. Click the "Def + undeformed" option on. Click on OK. The deformed and undeformed shapes appear

in the ANSYS graphics window.

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Exit ANSYS1. In the ANSYS Toolbar, click on Quit.

2. Choose the save option you want and click on OK.

Log Files / Input Files

The log file for this tutorial may also be used as an input file to automatically run the analysis in ANSYS. In order to use this file as an input file save it to your working directory and then select Utility Menu > File > Read input from... and select the file. You should notice ANSYS automatically building the finite element model and issuing all the commands detailed above.

Quitting ANSYS

To quit ANSYS select Utility Menu > File > Exit.... In the dialog box that appears click on Save Everything (assuming that you want to) and then click on Ok

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5.Analysis of bracket using ANSYS APDL

The problem to be modeled in this example is a simple bracket shown in the following figure. This bracket is to be built from a 20 mm thick steel plate. A figure of the plate is shown below.

This plate will be fixed at the two small holes on the left and have a load applied to the larger hole on the right.

Preprocessing: Defining the Problem

1. Give the Bracket example a Title

Utility Menu > File > Change Title

2. Import geometry to ANSYS

Utility Menu > File >Import>IGS

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3. Define the Type of Element

As in the verification model, PLANE183 will be used for this example

o Preprocessor > Element Type > Add/Edit/Delete

o Use the 'Options...' button to get a plane stress element with thickness o Under the Extra Element Output K3 select nodal stress.

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2. Define Geometric Contantso Preprocessor > Real Constants > Add/Edit/Delete o Enter a thickness of 20mm.

3. Element Material Propertieso Preprocessor > Material Props > Material Library > Structural > Linear >

Elastic > Isotropic

We are going to give the properties of Steel. Enter the following when prompted:

EX 200000PRXY 0.3

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4. Mesh Sizeo Preprocessor > Meshing > Size Cntrls > Manual Size > Areas > All Areas o Select an element edge length of 5. Again, we will need to make sure the model

has converged.

5. Mesho Preprocessor > Meshing > Mesh > Areas > Free and select the area when

prompted

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Saving Your JobUtility Menu > File > Save as...

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Solution Phase: Assigning Loads and Solving

You have now defined your model. It is now time to apply the load(s) and constraint(s) and solve the the resulting system of equations.

1. Define Analysis Typeo 'Solution' > 'New Analysis' and select 'Static'.

2. Apply Constraints

As illustrated, the plate is fixed at both of the smaller holes on the left hand side.

o Solution > Define Loads > Apply > Structural > Displacement > On Nodes o Instead of selecting one node at a time, you have the option of creating a box,

polygon, or circle of which all the nodes in that area will be selected. For this case, select 'circle' as shown in the window below. (You may want to zoom in to select the points Utilty Menu / PlotCtrls / Pan, Zoom, Rotate...) Click at the center of the bolt hole and drag the circle out so that it touches all of the nodes on the border of the hole.

o

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o Click on 'Apply' in the 'Apply U,ROT on Lines' window and constrain all DOF's in the 'Apply U,ROT on Nodes' window.

o Repeat for the second bolt hole. 3. Apply Loads

As shown in the diagram, there is a single vertical load of 1000N, at the bottom of the large bolt hole. Apply this force to the respective keypoint ( Solution > Define Loads > Apply > Structural > Force/Moment > On Keypoints Select a force in the y direction of -1000)

The applied loads and constraints should now appear as shown below.

4. Solving the System

Solution > Solve > Current LS

Post-Processing: Viewing the Results

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We are now ready to view the results. We will take a look at the deflected shape and the stress contours once we determine convergence has occured.

1. Convergence using ANSYS

As shown previously, it is necessary to prove that the solution has converged. Reduce the mesh size until there is no longer a sizeable change in your convergence criteria.

2. Deformationo General Postproc > Plot Results > Def + undeformed to view both the

deformed and the undeformed object.

The graphic should be similar to the following

o Observe the locations of deflection. Ensure that the deflection at the bolt hole is indeed 0.

3. Deflectiono To plot the nodal deflections use General Postproc > Plot Results > Contour

Plot > Nodal Solution then select DOF Solution - USUM in the window.

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Alternatively, obtain these results as a list. (General Postproc > List Results > Nodal Solution...) Are these results what you expected? Note that all translational degrees of freedom were constrained to zero at the bolt holes. StressesGeneral Postproc > Plot Results > Nodal Solution... Then select von Mises Stress in the window.

You can list the von Mises stresses to verify the results at certain nodes General Postproc > List Results. Select Stress, Principals SPRINLog Files / Input FilesThe log file for this tutorial may also be used as an input file to automatically run the analysis in ANSYS. In order to use this file as an input file save it to your working directory and then select Utility Menu > File > Read input from... and select the file. You should notice ANSYS automatically building the finite element model and issuing all the commands detailed above.

Quitting ANSYS


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6.Creation and analysis of solid model – I Using ANSYS APDL

The loading, material, and the boundary conditions are planar symmetric about XY plane. So create the bottom half of the clamp using Top down approach.A.Define PrimitivesCreate a solid cylinder of radius 50 and depth 20,with centre at centre at 0,0.1.Choose pre-processor> Modelling>Create>Volumes>Cylinder>Solid cylinder. In the solid cylinder dialog box, enter the following

Parameter ValueX Value 0Y Value 0Radius 50Depth 20

Create a volumetric block of 68 X 46 X 20. 2.Choose pre-processor>Modelling>Create>Volumes>Block>By Dimensions dialog box, specify the two diagonal corners of cuboids as -34,-75,0 and 34,0,20 respectively.Create clamp Beam with Dimension 100 X 46 X 20.3.Choose pre-processor>Modelling>Create>Volumes>Block>By Dimensions. Specify two diagonal corners as 0,-23,0 and 100,23,20.Create a partial cylinder to complete the round for the clamp beam.4. Choose pre-processor>Modelling>Create>Volumes>Cylinder>partial Cylinder. Enter the following parameters in the Partial Cylinder dialog box.

Parameter ValueX Value 100Y Value 0Radius-1 23Theta-1 -90Radius-2 0Theta-2 90Depth 20

Now you get results, as shown in below.

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B. Add volumes:5.Select Pre-processor>Modelling>Operate>Booleans>Add>Volumes. Choose Pick All in the Add Volumes picker menu to select volumes. The geometry is now converted into a single block.6.Refresh the geometry. From the utility Menu choose plot>Replot.C. Create volumes:Create cylinders to generate holes in the clamp.7. Choose pre-processor>Modelling>Create>Volumes>Cylinder>Solid Cylinder. Enter X,Y coordinate value as 0,0.Specify radius value as 32 and depth as 20.8.Similarly create another solid cylinder with X,Y value 100,0 with radius and height as 12.5 and 20 respectively.D. Subtract Volumes:9.Select Pre-processor>Modelling>Operate>Booleans>Substract>Volumes.Select the main Block and choose OK .Next select the cylinders to be subtract from main model.

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Create an opening(jaw) in the clamp by subtracting a block.10. Choose pre-processor>Modelling>Create>Volumes>Block>By 2 Corners & Z and input the following values.

Parameter ValueX Value -6Y Value -75Width 12Height 75Depth 20

11.Substract the block from the main block, as illustrated below.

E. Change View:Change the view to isometric for better visualization.12.From the slandered Toolbar, select icon (or) from the utility Menu, choose Plot Ctrls>Pan Zoom Rotate....In the Pan-Zoom-Rotate dialog box, click Iso button. View changes to isometric.

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ANSYS provides option to rotate the view dynamically (using CTRL+ Right mouse button).CTRL+Left button is used to pan the view.CTRL+Middle button is used to rotate and magnify the view.F. Align Work plane:To create bolt holes for the geometry the work plane has to be positioned normal to the cylinder's height.13.From the utility Menu, choose work plane>Align WP with>Keypoints+.Click 1,2 and 3 points as illustrated below to align the wok plane.

G. Create Bolt Holes:14.Construct a solid cylinder with centre at 0,20 with radius and depth value as 6 and -68 respectively.15.Substract the cylinder from the main block.The completed model looks as shown below.

16.Save the geometry as clamp.db in your directory.

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17.Quit ANSYS Session.


3. Select solid in the left hand menu and 2 node 186 in the right hand menu and then click on OK.

4. This will define element type 1 as a SOLID 186 element. SOLID 188 is actually a 3D clamp element but we are going to use it as a 1D truss by later suppressing some of it's degrees of freedom Click Close to close the Element Type dialog box.

3.Define the Material Behaviour



3. In the dialog box that pops up, enter suitable material parameters for steel ( E = 67500 Pa, Poissons ratio = 0.34)


right corner.6. Density= 2.7e-6 kg/m^3

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4.: Mesh the Geometry

1. In the Main Menu click on Preprocessor > Meshing > Mesh Tool2. This will open the Mesh Tool window.3. We are now going to use the Mesh Tool to set the size of the elements to all be a constant

size before we begin the meshing process. In the Mesh Tool click on Volumes > Set as shown in the figure below:

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In the dialog box, check smart size and set the value to 4.Choose Tetragonal shape and free mesh type. Pick Mesh button and when prompted to select volumes, Select Pick All Button in the picker. Ignore any warning. The meshed model looks as shown below.

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5.Apply Loads and find Solution:Apply Displacement ConstraintsSet all degree of freedom to zero on the inner face of the clamp.1.Choose Solution>Define Loads>Apply>Structural>Displacement>On Areas. Select the inner cylindrical faces and set ALL DOF to zero.

Apply Pressure:Apply a bolt pressure of 70 N/mm^2 on the washer area.2. Define Loads>Apply>Structural> Force/Moment>On nodes. Click Pick All in the picker menu.Choose FY as direction of a force and -25 as force value in the negative direction.

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6.Solution:Run the analysis choosing Solution>Solve>Current LS from the main Menu. Ignore waning.7.Postpocessing:1.Display stress contoursChoose General Postprocc>Element Table>Define Table. Click add..In the Define Additional Element Table Items dialog box, enter user label as stress. Choose item. Comp Results data item as stress, vonMises and press OK. Close the dialog box.

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2.Choose General Postproc>Element Table>Plot Elem Table. Choose Stress under item to be plotted. The element table is plotted on the screen as shown below.

3.Choose General post proc>Plot Results>Deformed Shape. In the plot Deformed Shape dialog box choose Def+undeformed.

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The deflection is plotted on the screen as shown below.8.Concusion:According to Von Mises theroy (suitable for ductile materials) the maximum stress should be less than the permissible yield stress. The max stress values and deflection value indicate it is far safe and hence can be optimized.Redesign the clamp lessening the thickness of clamp beam as shown and find the value.Stress--------------------------------Strain----------------------------------This design should be safe and weight reduction should be considerable.

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7. Creation and analysis of solid model – II Using ANSYS APDL

Axisymmetric Solid Tutorial: Pressure Vessel

In this tutorial you will examine the expansion of a pressure vessel due to an internal pressure using ANSYS. The problem is adapted from case study E on page 327 of the textbook Practical Stress Analysis with Finite Elements (2nd Ed) by Bryan J. Mac Donald. You will determine the principal stresses in the pressure vessel due to the applied loading and boundary conditions. An axisymmetric solid element will be used for this analysis. We will use SI system units for this tutorial: length = m, mass = kg, time = sec, force = N, stress/pressure = Pa. In this case the vessel is made from steel (E = 207 Gpa, v = 0.27) and the internal pressure is 10,000 Pa.

There are standard theories available for the behaviour of thin and thick walled cylinders subjected to internal pressure. These equations can be found in any text book on mechanics of solids or in any reference book. We can use these theories to predict the expected stresses in the pressure vessel due to the applied loading. The calculations for the various stresses is shown on pages 328 to 329 of Practical Stress Analysis with Finite Elements (2nd Ed) by Bryan J. Mac Donald and is summarised in the table below.

An axisymmetric analysis assumes that the geometry and all loads and boundary conditions can be expressed in the XY plane and this plane is then swept 360 degrees around the Y-axis to form the full model. An axisymmetric model is appropriate in this case as the geometry of the pressure vessel is axisymmetric and the loading is also axisymmetric. Figure 2 shows an overview of the axisymmetric model we will build:

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1. In the Main Menu select Preprocessor > Element Type > Add/Edit/Delete 2. Click on Add in the dialog box that appears:

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3. Select Solid in the left hand menu and Quad 8 node 183 in the right hand menu and then click OK

4. This defines element type 1 as a 2D quadratic 8-node quadrilateral element (i.e. a rectangle with curved edges) 5. Now we must define how this element behaves. Click on Options in the Element Types dialog box:.

5. Now we must define how this element behaves. Click on Options in the Element Types dialog box:

6. In the element type options dialog box that appears, make sure that the Element behavior is set to "Axisymmetric" as shown in the figure below:

7. Click on OK and then click close to close the Element Type dialog box.

Step 3: Define the Material Model



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4. Click on Ok to close the dialog box in which you entered the material parameters.

5. Close the Define Material Model Behaviour dialog box by clicking on the X in the upper right corner.

Step 5: Create the Model Geometry

1. In the Main Menu click on Preprocessor > Modelling > Create > Areas > Rectangle > By 2 Corners

2. Enter the values shown below to create the bottom rectangle of the pressure vessel:

3. Repeat the above process and enter these values to create the side wall of the pressure vessel:

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4. Finally, repeat the process again to create the top rectangle of the pressure vessel:

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5. Your screen should now look like this:

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6. Note: if the background of your screen is black then that is not a problem. In the image above reverse video has been used. If you want to use reverse video (i.e. have a white background) then simply go to: Utility Menu > PlotCtrls > Style > Colors > Reverse Video

7. Now we must add the three areas together to form one area that defines the pressure vessel geometry. Main Menu > Modelling > Operate > Booleans > Add > Areas

8. Click on "Pick All" in the picker dialog box:

9. You should notice that all the areas merged into one area.

Step 6: Mesh the Geometry

1. In the Main Menu click on Preprocessor > Meshing > Mesh Tool

2. This will open the Mesh Tool window.

3. We are now going to use the Mesh Tool to set the size of the elements to all be a constant size before we begin the meshing process. In the Mesh Tool click on Areas > Set as shown in the figure below:

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4. Use your mouse to click on the plate geometry. Once you have clicked on it, the Element Size at Picked Areas dialog box will appear. Enter 0.002 m for the Element Edge Length to define the size of each element, as shown below:

5. Click on OK to close the dialog box.

6. In the MeshTool make sure that Quad and Free are selected and then click on Mesh. Click on the geometry in order to mesh it.

7. Your model should now look like this:

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Step 7: Apply the Boundary Conditions

1. Although the solver already knows that we are performing an axisymmetric analysis due to an axisymmetric element being used, we still need to place a symmetry constraint on the edges of the model that touch the Y-axis.

2. Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > Symmetry B.C. > On Lines pick the lines on the axis of symmetry (i.e. the two vertical lines on the left hand edge of the model) then click OK in the picker dialog box.

3. You should notice small "S" symbols appear near the lines to indicate that a symmetry boundary condition has been applied.

4. In order to prevent any unwanted movement of the entire model in the vertical direction (rigid body motion) we must constrain at least one node in the vertical direction:

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6. Click on any node in the centre of the side wall of the vessel and then click on OK

7. In the dialog box that appears make sure the DOFs to be constrained is set to UY only and then click on OK.


1. Although the solver already knows that we are performing an axisymmetric analysis due to an axisymmetric element being used, we still need to place a symmetry constraint on the edges of the model that touch the Y-axis.

2. Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > Symmetry B.C. > On Lines pick the lines on the axis of symmetry (i.e. the two vertical lines on the left hand edge of the model) then click OK in the picker dialog box.

3. You should notice small "S" symbols appear near the lines to indicate that a symmetry boundary condition has been applied.

4. In order to prevent any unwanted movement of the entire model in the vertical direction (rigid body motion) we must constrain at least one node in the vertical direction:


6. Click on any node in the centre of the side wall of the vessel and then click on OK 7. In the dialog box that appears make sure the DOFs to be constrained is set to UY only and then click on OK.

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8. You will probably get a warning saying that "Both solid model and finite element boundary conditions have been applied to this model. As solid loads are transferred to the nodes or elements, they can overwrite directly applied loads". This is OK just click on Close to dismiss this dialog.

Step 8: Apply the Internal Pressure Load

1. In the Main Menu click on Preprocessor > Loads > Define Loads > Apply > Structural > Pressure > On Lines

2. Click on all the lines representing the internal wall of the pressure vessel and then click on OK in the picker dialog box.

3. The "Apply Pres on a Line" dialog box will now appear. Enter 10000 as the pressure value as shown below:

4. Click on OK to close the dialog box.

5. You should notice a red arrows appearing on your model to indicate the pressure load as shown below:

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1. In the Main Menu select Solution > Analysis Type > New Analysis

2. Make sure that Static is selected in the dialog box that pops up and then click on OK to dismiss the dialog.

3. Select Solution > Solve > Current LS to solve the problem

4. A new window and a dialog box will pop up. Take a quick look at the infromation in the window ( /STATUS Command) before closing it.

5. Click on OK in the dialog box to solve the problem.

6. Once the problem has been solved you will get a message to say that the solution is done, close this window when you are ready.


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1. In the Main Menu select General Postproc > Plot Results > Deformed Shape

2. Select Def + undef edge in order to show both the deformed and undeformed shapes.

3. Your screen should look something like this:

4. It is clear that the side wall of the pressure vessel has slightly "bowed" out due to the internal pressure. The end caps have significantly deformed in comparison to the side wall. The maximum displacement is, however, approximately 2 x 10-6 m which is well below the yield stress for steel meaning our assumption of a linear elastic material is valid. Note that ANSYS, by default, will exaggerate any deformation by scaling it up in order to make it obvious.

5. Now let's examine the principal stresses: General Postproc > Plot Results > Contour Plot > Nodal Solu > Stress > 1st Principal Stress, click on OK to display the plot, which should look like this:

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6. The first principal stress is the Hoop Stress and we are expecting a value of approximately 55,000 Pa based on our analytical calculations. Clearly something is wrong with this plot. We are seeing very large stress concentrations at the sharp corner where the end caps join the side wall. It is likely that the stress in the side wall itself is quite close to the predicted analytical value. Let's investigate this by only displaying results for the elements at the middle of the vessel side wall:

7. Utility Menu > Select > Entities

8. In the "Select Entities" dialog box that appears make sure that "Elements" is selected in the top box and then click on OK

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9. The "Select Elements" picker dialog box will appear. Change the picking type to "Box" as

10. Now draw a box around the central elements in the side wall, as shown below:

11. Click on OK in the "Select Elements" picker dialog to select all the elements inside the box.

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12. Now, only the selected elements will be displayed in any stress contour plots and the rest of the model will be ignored.

13. Your screen should now look something like this:

14. Now, let's replot the 1st principal stress: General Postproc > Plot Results > Contour Plot > Nodal Solu > Stress > 1st Principal Stress, click on OK to display the plot, which should look like this:

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15. Notice that the maximum value is 56,680 Pa which is reasonably close to our predicted value of 55,455 Pa

16. Let's check the Axial Stress: General Postproc > Plot Results > Contour Plot > Nodal Solu > Stress > 2nd Principal Stress, click on OK to display the plot, which should look like this:

17. Notice that the axial stress varies between 22,158 Pa and 23,340 Pa which is, again, reasonably close to our predicted value of 22,727 Pa.

18. Let's now check the radial stress: General Postproc > Plot Results > Contour Plot > Nodal Solu > Stress > 3rd Principal Stress, click on OK to display the plot, which should look like this:

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19. In this case the maximum radial stress is -9,993 Pa which is very close to our predicted value of 10,000 Pa.

20. When you are finished looking at the results for this subset of elements, you can re-select the entire model by issuing the command: Utility Menu > Select > Everything. Now if you replot a stress contour you will see the entire model again.

This Exercise has given the following skills:

1. The ability to model axisymmetric problems in ANSYS.

2. The ability to select a subset of a finite element model and only examine the result for that subset.

3. Experience in comparing the results obtained from your finite element model with other results and validating your results against the other results.

Log Files / Input Files

The log file for this tutorial may also be used as an input file to automatically run the analysis in ANSYS. In order to use this file as an input file save it to your working directory and then select Utility Menu > File > Read input from... and select the file. You should notice ANSYS automatically building the finite element model and issuing all the commands detailed above.

Quitting ANSYS


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8. Application of distributed loads Using ANSYS APDL

Figure 01: Overview of Simple Beam Problem with Applied Bending Moment

Figure 02: Representative Finite Element Model of the Simple Beam Problem with Applied Bending Moment

The beam is 2 metres long with the left hand edge built into a thick wall and the centre of the beam is simply supported.

UDL beam load of 12 kN/m is 1m remaining 1m free load. The beam is made from steel with E = 200 GPa and I = 4 x 10-6 m4 .


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We can use the information in the tables above to define our nodes, elements and boundary conditions.




7.8. Select Beam in the left hand menu and 2 node 188 in the right hand menu and then click

on OK.9. This will define element type 1 as a BEAM 188 element. BEAM 188 is actually a 3D

beam element but we are going to use it as a 1D truss by later suppressing some of it's degrees of freedom


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Step 3: Define the Beam Cross Section

Unfortunately the problem definition doesn't actually specify which type of cross section the beam has. That isn't a problem and we

can work around it. We know that the beam cross section has a second moment of area of I = 4 x 10-6 m4 so let's choose the simplest

type of cross section to fit this second moment of area value. We will assume that the beam has a rectangular cross section:

Figure 03: Calculating the beam height from the given second moment of area

1. In the Main Menu select Preprocessor > Sections > Beam > Common Sections2. The beam tool should appear as shown below. Enter a value of 0.0832358 for B and for

H.

3.

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4. Click on OK to close the Beam Tool.




11. In the dialog box that pops up, enter suitable material parameters for steel ( E = 200 x 109 Pa, Poissons ratio = 0.3)


right corner.



2. In the dialog box that appears: enter the x and y coordinates for node 1 (i.e. 0,0) and click on Apply

(note that Apply issues the command to create the node but keeps the dialog box open, clicking OK

would also issue the command to create the node but would close the dialog box).

3. Now enter the x and y coordinates for node 2 (i.e. 1,0) and click Apply4. Finally, enter the x and y coordinate for node 3 (i.e. 2,0) and click OK.5. We must now create the elements that join the nodes together: click on Preprocessor >

Modeling > Create > Elements > Auto Numbered >

Thru Nodes In the main window click on node 1 and then node 2. Then click Apply in the dialog box.

You should see a line element appear joining nodes 1 and 2. (Note: node 1 is probably hidden behind the x-y symbol ar the origin -

this is know as "the triad" - if you can't see node 1 then just click on the triad and it should automatically be selected.)


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1. In this case we are using a 3D beam to model a 1D beam problem so we must prevent the nodes from moving in the X and Z direction

(i.e. only allow movement in the Y direction for bending). Since beam elements also have rotational degrees of freedom at each

node we must also constrain rotations about the X and Y axis (i.e. only allow rotations about the Z axis - for bending moments in the X-Y plane).

In order to do this we constrain all nodes in the finite element model in the UX, UZ, ROTX and ROTY directions.

Step 7: Apply a Distributed Load to Element 1

1. Preprocessor > Loads > Define Loads > Apply > Structrual > Pressure > On Beams2. Click on element 1 and then click on OK to close the picker dialog box3. Make sure the Load Key is changed to 2 and enter 12000 for the Pressure Value at Node

I

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4. The default Load Key is 1 and this makes the distributed load act in the Y-Z plane, which is the default for beam elements. Putting a value of 2 here makes the load act in the X-Y plane, which is what we want. If we wanted a non-constant distributed load in the beam then we could enter another value for node J, but because we want a constant load, we simply leave this blank.

5. Now, click on OK to close the dialog box.6. Your screen should now look something like this:

7. Notice the red line indicating the distributed load.



dismiss the dialog.3. Select Solution > Solve > Current LS to solve the problem

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4. A new window and a dialog box will pop up. Take a quick look at the infromation in the window ( /STATUS Command) before closing it.

5. Click on OK in the dialog box to solve the problem.6. Once the problem has been solved you will get a message to say that the solution is done,



1. In the Main Menu select General Postproc > Plot Results > Deformed Shape 2. You screen should look something like this:

3. Now we must examine the displacement and rotation (i.e. slope) at each node, as before. Follow the instructions given above for case 1 to get printouts of the displacement and rotation of each node in the finite element model. You should obtain results similar to these:

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4.

Notice that the dispalcement of node 1 is 0.002 m and the displacement of node 2 is 0.0057 m. The slope at both nodes is 0.00375 radians.

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9.Non–linear analysis of a cantilever beam Using ANSYS APDLStep 1: Launch ANSYS












right corner.

If you are wondering why a 'Linear' model was chosen when this is a non-linear example, it is because this example is for non-linear geometry, not non-linear material properties.

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If we were considering a block of wood, for example, we would have to consider non-linear material properties.





1. In the Main Menu select Preprocessor > Sections > Beam > Common Sections2. The beam tool should appear as shown below. Enter a value of 0.125 for B and for H for

0.25.

Step 5: Define Keypoints

1. In the Main Menu click on Preprocessor > Modeling > Create > Keypoints > In Active CS




3. Now enter the x and y coordinates for node 2 (i.e. 5,0) and click OK.4. In the Main Menu click on Preprocessor > Modeling > Create > Lines > Create lines

Select 1 and 2 Key points and create line.

Step 6: Define Meshing

1.Preprocessor > Meshing > Size Cntrls > ManualSize > Lines > All Lines...

For this example we will specify an element edge length of 0.1 " (50 element divisions along the line).

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Mesh the frame

Preprocessor > Meshing > Mesh > Lines > click 'Pick All'LMESH,ALL.

Solution: Assigning Loads and Solving

1. Define Analysis Type

Solution > New Analysis > StaticANTYPE,0

2. Set Solution Controls

Select Solution > Analysis Type > Sol'n Control...

The following image will appear:

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Ensure the following selections are made (as shown above)

A. Ensure Large Static Displacements are permitted (this will include the effects of large deflection in the results)

B. Ensure Automatic time stepping is on. Automatic time stepping allows ANSYS to determine appropriate sizes to break the load steps into. Decreasing the step size usually ensures better accuracy, however, this takes time. The Automatic Time Step feature will determine an appropriate balance. This feature also activates the ANSYS bisection feature which will allow recovery if convergence fails.

C. Enter 5 as the number of substeps. This will set the initial substep to 1/5 th of the total load.

The following example explains this: Assume that the applied load is 100 kg*m. If the Automatic Time Stepping was off, there would be 5 load steps (each increasing by 1/5 th of the total load):

20 kg*m 40 kg*m 60 kg*m 80 kg*m 100 kg*m

Now, with the Automatic Time Stepping is on, the first step size will still be 20 kg*m. However, the remaining substeps will be determined based on the response of the material due to the previous load increment.

D. Enter a maximum number of substeps of 1000. This stops the program if the solution does not converge after 1000 steps.

E. Enter a minimum number of substeps of 1. F. Ensure all solution items are writen to a results file.

NOTEThere are several options which have not been changed from their default values. For more information about these commands, type help followed by the command into the command line.

Function Command Comments

Load Step KBC Loads are either linearly interpolated (ramped) from

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the one substep to another (ie - the load will increase from 10 kgs to 20 kgs in a linear fashion) or they are step functions (ie. the load steps directly from 10 kgs to 20 kgs). By default, the load is ramped. You may wish to use the stepped loading for rate-dependent behaviour or transient load steps.

Output OUTRES This command controls the solution data written to the database. By default, all of the solution items are written at the end of each load step. You may select only a specific iten (ie Nodal DOF solution) to decrease processing time.

Stress Stiffness SSTIF This command activates stress stiffness effects in nonlinear analyses. When large static deformations are permitted (as they are in this case), stress stiffening is automatically included. For some special nonlinear cases, this can cause divergence because some elements do not provide a complete consistent tangent.

Newton Raphson NROPT By default, the program will automatically choose the Newton-Raphson options. Options include the full Newton-Raphson, the modified Newton-Raphson, the previously computed matrix, and the full Newton-Raphson with unsymmetric matrices of elements.

Convergence Values CNVTOL By default, the program checks the out-of-balance load for any active DOF.

Apply Constraints Solution > Define Loads > Apply > Structural > Displacement > On Keypoints

Fix Keypoint 1 (ie all DOFs constrained).

Apply Loads Solution > Define Loads > Apply > Structural > Force/Moment > On Keypoints

Place a -100 kg*m moment in the MZ direction at the right end of the beam (Keypoint 2)

Solve the System Solution > Solve > Current LSSOLVE

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The following will appear on your screan for NonLinear Analyses

General Postprocessing: Viewing the Results

1. View the deformed shape

General Postproc > Plot Results > Deformed Shape... > Def + undeformed

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2. View the deflection contour plot

General Postproc > Plot Results > Contour Plot > Nodal Solu... > DOF solution, UY

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If this example is performed as a linear model there will be no nodal deflection in the horizontal direction due to the small deflections assumptions. However, this is not realistic for large deflections. Modeling the system non-linearly, these horizontal deflections are calculated by ANSYS.General Postproc > List Results > Nodal Solution...> DOF solution, UX

Other results can be obtained as shown in previous linear static analyses

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EXTRA EXERCISES

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Using P-Elements

Introduction

This tutorial was completed using ANSYS 7.0. This tutorial outlines the steps necessary for solving a model meshed with p-elements. The p-method manipulates the polynomial level (p-level) of the finite element shape functions which are used to approximate the real solution. Thus, rather than increasing mesh density, the p-level can be increased to give a similar result. By keeping mesh density rather coarse, computational time can be kept to a minimum. This is the greatest advantage of using p-elements over h-elements.

A uniform load will be applied to the right hand side of the geometry shown below. The specimen was modeled as steel with a modulus of elasticity of 200 GPa.


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1. Give example a Title

Utility Menu > File > Change Title .../title, P-Method Meshing

2. Activate the p-Method Solution Options

ANSYS Main Menu > Preferences/PMETH,ON

Select p-Method Struct. as shown below

3. Open preprocessor menu

ANSYS Main Menu > Preprocessor/PREP7

4. Define Keypoints

Preprocessor > Modeling > Create > Keypoints > In Active CS...K,#,x,y,z

We are going to define 12 keypoints for this geometry as given in the following table:

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Keypoint Coordinates (x,y,z)1 (0,0)2 (0,100)3 (20,100)4 (45,52)5 (55,52)6 (80,100)7 (100,100)8 (100,0)9 (80,0)10 (55,48)11 (45,48)12 (20,0)

5. Create Area

Preprocessor > Modeling > Create > Areas > Arbitrary > Through KPsA,1,2,3,4,5,6,7,8,9,10,11,12

Click each of the keypoints in numerical order to create the area shown below.

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6. Define the Type of Element

Preprocessor > Element Type > Add/Edit/Delete...

For this problem we will use the PLANE145 (p-Elements 2D Quad) element. This element has eight nodes with 2 degrees of freedom each (translation along the X and Y axes). It can support a polynomial with maximum order of eight.

After clicking OK to select the element, click Options... to open the keyoptions window, shown below. Choose Plane stress + TK for Analysis Type.

Keyopts 1 and 2 can be used to set the starting and maximum p-level for this element type. For now we will leave them as default.

Other types of p-elements exist in the ANSYS library. These include Solid127 and Solid128 which have electrostatic DOF's, and Plane145, Plane146, Solid147, Solid148 and Shell150 which have structural DOF's. For more information on these elements, go to the Element Library in the help file.

Define Real Constants Preprocessor > Real Constants... > Add...

In the 'Real Constants for PLANE145' window, enter the following geometric properties:

i. Thickness THK: 10

This defines an element with a thickness of 10 mm.

Define Element Material Properties Preprocessor > Material Props > Material Models > Structural > Linear > Elastic > Isotropic

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In the window that appears, enter the following geometric properties for steel:

i. Young's modulus EX: 200000 ii. Poisson's Ratio PRXY: 0.3

Define Mesh Size Preprocessor > Meshing > Size Cntrls > ManualSize > Areas > All Areas...

For this example we will use an element edge length of 5mm.

Mesh the frame Preprocessor > Meshing > Mesh > Areas > Free > click 'Pick All'



Solution > Analysis Type > New Analysis > StaticANTYPE,0

Set Solution Controls Solution > Analysis Type > Sol'n Controls

The following window will pop up.

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A) Set Time at end of loadstep to 1 and Automatic time stepping to ON B) Set Number of substeps to 20, Max no. of substeps to 100, Min no. of substeps to 20. C) Set the Frequency to Write every substep

Apply Constraints Solution > Define Loads > Apply > Structural > Displacement > On Lines

Fix the left side of the area (ie all DOF constrained)

Apply Loads Solution > Define Loads > Apply > Pressure > On Lines

Apply a pressure of -100 N/mm^2

The applied loads and constraints should now appear as shown in the figure below.


Postprocessing: Viewing the Results

1. Read in the Last Data Set Page 96



General Postproc > Read Results > Last Set

2. Plot Equivalent Stress

General Postproc > Plot Results > Contour Plot > Element Solu

In the window that pops up, select Stress > von Mises SEQV

The following stress distribution should appear.

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Plot p-Levels General Postproc > Plot Results > p-Method > p-Levels

The following distribution should appear.

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Note how the order of the polynomial increased in the area with the greatest range in stress. This allowed the elements to more accurately model the stress distribution through that area. For more complex geometries, these orders may go as high as 8. As a comparison, a plot of the stress distribution for a normal h-element (PLANE2) model using the same mesh, and one with a mesh 5 times finer are shown below.

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As one can see from the two plots, the mesh density had to be increased by 5 times to get the accuracy that the p-elements delivered. This is the benefit of using p-elements. You can use a mesh that is relatively coarse, thus computational time will be low, and still get

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reasonable results. However, care should be taken using p-elements as they can sometimes give poor results or take a long time to converge.

Contact Elements

Introduction

This tutorial was completed using ANSYS 7.0 The purpose of the tutorial is to describe how to utilize contact elements to simulate how two beams react when they come into contact with each other.

The beams, as shown below, are 100mm long, 10mm x 10mm in cross-section, have a Young's modulus of 200 GPa, and are rigidly constrained at the outer ends. A 10KN load is applied to the center of the upper, causing it to bend and contact the lower.


1. Give example a Title

Utility Menu > File > Change Title .../title, Contact Elements

2. Open preprocessor menu

ANSYS Main Menu > Preprocessor/PREP7

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3. Define Areas

Preprocessor > Modeling > Create > Area > Rectangle > By 2 CornersBLC4,WP X, WP Y, Width, Height

We are going to define 2 rectangles as described in the following table:

Rectangle Variables (WP X,WP Y,Width,Height)1 (0, 15, 100, 10)2 (50, 0, 100, 10)

4. Define the Type of Elemento Preprocessor > Element Type > Add/Edit/Delete...

For this problem we will use the PLANE42 (Solid, Quad 4node 42) element. This element has 2 degrees of freedom at each node (translation along the X and Y).

o While the Element Types window is still open, click Options.... Change Element behavior K3 to Plane strs w/thk as shown below. This allows a thickness to be input for the elements.

5. Define Real Constants

Preprocessor > Real Constants... > Add...

In the 'Real Constants for PLANE42' window, enter the following geometric properties:

i. Thickness THK: 10

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This defines a beam with a thickness of 10 mm.

Define Element Material Properties Preprocessor > Material Props > Material Models > Structural > Linear > Elastic > Isotropic

In the window that appears, enter the following geometric properties for steel:

i. Young's modulus EX: 200000 ii. Poisson's Ratio PRXY: 0.3

Define Mesh Size Preprocessor > Meshing > Size Cntrls > ManualSize > Areas > All Lines...

For this example we will use an element edge length of 2mm.

Mesh the frame Preprocessor > Meshing > Mesh > Areas > Free > click 'Pick All'

Define the Type of Contact Element Preprocessor > Element Type > Add/Edit/Delete...

For this problem we will use the CONTAC48 (Contact, pt-to-surf 48) element. CONTAC48 may be used to represent contact and sliding between two surfaces (or between a node and a surface) in 2-D. The element has two degrees of freedom at each node: translations in the nodal x and y directions. Contact occurs when the contact node penetrates the target line.

While the Element Types window is still open, click Options.... Change Contact time/load prediction K7 to Reasonabl T/L inc. This is an important step. It initiates a process during the solution calculations where the time step or load step, depending on what the user has specified in the solution controls, incremements slowly when contact is immenent. This way, one surface won't penetrate too far into the other and cause the solution to fail.

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It is important to note, CONTAC48 elements are created in the space between two surfaces prescribed by the user. This will be covered below. As the surfaces approach each other, the contact element is slowly "crushed" until it's upper node(s) lie along the same line as the lower node(s). Thus, ANSYS can calculate when the two prescribed surfaces have made contact. Other contact elements, such as CONTA175, require a target element, such as TARGE169, to function. When using contact elements in your own analyses, be sure to understand how the elements work. The ANSYS help file has plenty of useful information regarding contact elements and is worth reading.

Define Real Constants for the Contact Elements Preprocessor > Real Constants... > Add...

In the 'Real Constants for CONTAC48' window, enter the following properties:

i. Normal contact stiffness KN: 200000 CONTAC48 elements basically use a penalty approach to model contact. When one surface comes into "contact" with the other, ANSYS numerically puts a spring of stiffness KN between the two. ANSYS recommends a value between 0.01 and 100 times Young's modulus for the material. Since this "spring" is so stiff, the behaviour of the model is like the two surfaces have made contact. This KN value can greatly affect your solution, so be sure to read the help file on contact so you can recognize when your solution is not converging and why. A good rule of thumb is to start with a low value of KN and see how the solution converges (start watching the ANSYS Output Window). If there is too much penetration, you should increase KN. If it takes a lot of iterations to converge for a single substep, you should decrease KN.

ii. Target length tolerance TOLS: 10 Real constant TOLS is used to add a small tolerance that will internally increase the length of the target. This is useful for problems when node to node contact is likely to occur, rather than node to element edge. In this situation, the contact node may repeatedly "slip" off one of the target nodes, resulting in convergence

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difficulties. A small value of TOLS, given in %, is usually enough to prevent such difficulties.

The other real constants can be used to model sliding friction, tolerances, etc. Information about these other constants can be found in the help file.

Define Nodes for Creating Contact Elements Unlike the normal meshing sequence used for most elements, contact elements must be defined in a slightly different manner. Sets of nodes that are likely to come into contact must be defined and used to generate the necessary elements. ANSYS has many recommendations about which nodes to select and whether they should act as target nodes or source nodes. In this simple case, source nodes are those that will move into contact with the other surface, where as target nodes are those that are contacted. These terms are important when using the automatic contact element mesher to ensure the elements will correctly model contact between the surfaces. A strong understanding of how the elements work is important when using contact elements for your own analysis.

First, the source nodes will be selected.

Utility Menu > Select > Entities... Select Areas and By Num/Pick from the pull down menus, select From Full from the radio buttons and click OK. Select the top beam and click OK. This will ensure any nodes that are selected in the next few steps will be from the upper beam. In this case, it is not too hard to ensure you select the correct nodes. However, when the geometry is complex, you may inadvertantly select a node from the wrong surface and it could cause problems during element generation.

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Utility Menu > Select > Entities... Select Nodes and By Location from the pull down menus, Y coordinates and Reselect from the radio buttons and enter a value of 15 and click OK. This will select all nodes along the bottom of the upper beam.

Utility Menu > Select > Entities... Select Nodes and By Location from the pull down menus, X coordinates and Reselect from the radio buttons and enter values of 50,100. This will select the nodes above the lower beam.

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Now if you list the selected nodes, Utility Menu > List > Nodes... you should only have the following nodes remaining.

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It is important to try and limit the number of nodes you use to create contact elements. If you have a lot of contact elements, it takes a great deal of computational time to reach a solution. In this case, the only nodes that could make contact with the lower beam are those directly above it, thus those are the only nodes we will use to create the contact elements.

Utility Menu > Select > Comp/Assembly > Create Component Enter the component name Source as shown below, and click OK. Now we can use this component, Source, as a list of nodes to be used in other functions. This can be very useful in other applications as well.

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Now select the target nodes. Using the same procedure as above, select the nodes on the lower beam directly under the upper beam. Be sure to reselect all nodes before starting to select others. This is done by opening the entity select menu, Utility Menu > Select > Entities..., clicking the Also Select radio button, and click the Sele All button. These values will be the ones you'll use.

Click the lower area for the area select. The Y coordinate is 10 The X coordinates vary from 50 to 100.

When creating the component this time, enter the name Target.

IMPORTANT: Be sure to reselect all the nodes before continuing. This is done by opening the entity select menu, Utility Menu > Select > Entities..., clicking the Also Select radio button, and click the Sele All button.

Generate Contact Elements Main Menu > Preprocessor > Modeling > Create > Elements > Elem Attributes

Fill the window in as shown below. This ensures ANSYS knows that you are dealing with the contact elements and the associated real constants.

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Main Menu > Preprocessor > Modeling> Create > Elements > Surf / Contact > Node to Surf

The following window will pop up. Select the node set SOURCE from the first drop down menu (Ccomp) and TARGET from the second drop down menu (Tcomp). The rest of the selections remain unchanged.

At this point, your model should look like the following.

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Unfortunately, the contact elements don't get plotted on the screen so it is sometimes difficult to tell they are there. If you wish, you can plot the elements (Utility Menu > Plot > Elements) and turn on element numbering (Utility Menu > PlotCtrls > Numbering > Elem/Attrib numbering > Element Type Numbers). If you zoom in on the contact areas, you can see little purple stars (Contact Nodes) and thin purple lines (Target Elements) numbered "2" which correspond to the contact elements, shown below.

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The preprocessor stage is now complete.



Solution > Analysis Type > New Analysis > StaticANTYPE,0

Set Solution Controls Select Solution > Analysis Type > Sol'n Control...

The following image will appear:

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Ensure the following selections are made under the 'Basic' tab (as shown above)

A. Ensure Automatic time stepping is on. Automatic time stepping allows ANSYS to determine appropriate sizes to break the load steps into. Decreasing the step size usually ensures better accuracy, however, this takes time. The Automatic Time Step feature will determine an appropriate balance. This feature also activates the ANSYS bisection feature which will allow recovery if convergence fails.

B. Enter 100 as the number of substeps. This will set the initial substep to 1/100 th of the total load.

C. Enter a maximum number of substeps of 1000. This stops the program if the solution does not converge after 1000 steps.

D. Enter a minimum number of substeps of 20. E. Ensure all solution items are writen to a results file.

Ensure the following selection is made under the 'Nonlinear' tab (as shown below)

F. Ensure Maximum Number of Iterations is set to 100

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NOTEThere are several options which have not been changed from their default values. For more information about these commands, type help followed by the command into the command line.

These solution control values are extremely important in determining if your analysis will succeed or fail. If you have too few substeps, the contact nodes may be driven through the target elements before ANSYS "realizes" it has happened. In this case the solution will resemble that of an analysis that didn't have contact elements defined at all. Therefore it is important to choose a relatively large number of substeps initially to ensure the model is defined properly. Once everything is working, you can reduce the number of substeps to optimize the computational time. Also, if the maximum number of substeps or iterations is left too low, ANSYS may stop the analysis before it has a chance to converge to a solution. Again, leave these relatively high at first.

Apply Constraints Solution > Define Loads > Apply > Structural > Displacement > On Lines

Fix the left end of the upper beam and the right end of the lower beam (ie all DOF constrained)

Apply Loads Solution > Define Loads > Apply > Structural > Force/Moment > On Nodes

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Apply a load of -10000 in the FY direction to the center of the top surface of the upper beam. Note, this is a point load on a 2D surface. This type of loading should be avoided since it will cause a singularity. However, the displacement or stress near the load is not of interest in this analyis, thus we will use a point load for simplicity.

The applied loads and constraints should now appear as shown in the figure below.


Postprocessing: Viewing the Results

1. Open postprocessor menu

ANSYS Main Menu > General Postproc/POST1

2. Adjust Graphical Scaling

Utility Menu > PlotCtrls > Style > Displacement Scaling

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Click the 1.0 (true scale) radio button, then click ok. This is of huge importance! I lost many hours trying to figure out why the contact elements weren't working, when in fact it was just due to the displacement scaling to which ANSYS defaulted. If you leave the scaling as default, many times it will look like your contact nodes have gone through the target elements.

Show the Stress Distribution in the Beams General Postproc > Plot Results > Contour Plot > Nodal Solu > Stress > von Mises

Adjust Contour Scale Utility Menu > PlotCtrls > Style > Contours > Non-Uniform Contours

Fill in the window as follows:

This should produce the following stress distribution plot:

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As seen in the figure, the load on the upper beam caused it to deflect and come in contact with the lower beam, producing a stress distribution in both

1. ANALYSIS OF CANTILEVER BEAM

Figure 01 shows an overview of the beam problem for load case 1 (point load) and figure 02 shows a representative finite element model for this load case.

Figure 01: Overview of Simple Beam Problem with Vertical Point Load (Case 1)

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Figure 02: Representative Finite Element Model of the Simple Beam Problem (Case 1)

The beam is 2 metres long with the left hand edge built into a thick wall and the centre of the beam is simply supported.

The free end of the beam supports a shear load of 40 kN and a bending moment of 20 kNm. The beam is made from steel with E = 200 GPa and I = 4 x 10-6 m4 .


We can use the information in the tables above to define our nodes, elements and boundary conditions.




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Figure 03: Calculating the beam height from the given second moment of area

5. In the Main Menu select Preprocessor > Sections > Beam > Common Sections

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6. The beam tool should appear as shown below. Enter a value of 0.0832358 for B and for H.

7.

8. Click on OK to close the Beam Tool.






right corner.

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10. Now enter the x and y coordinates for node 2 (i.e. 1,0) and click Apply11. Finally, enter the x and y coordinate for node 3 (i.e. 2,0) and click OK.12. We must now create the elements that join the nodes together: click on Preprocessor >

Modeling > Create > Elements > Auto Numbered >

Thru Nodes In the main window click on node 1 and then node 2. Then click Apply in the dialog box.

You should see a line element appear joining nodes 1 and 2. (Note: node 1 is probably hidden behind the x-y symbol ar the origin -

this is know as "the triad" - if you can't see node 1 then just click on the triad and it should automatically be selected.)



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2. In this case we are using a 3D beam to model a 1D beam problem so we must prevent the nodes from moving in the X and Z direction

(i.e. only allow movement in the Y direction for bending). Since beam elements also have rotational degrees of freedom at each

node we must also constrain rotations about the X and Y axis (i.e. only allow rotations about the Z axis - for bending moments in the X-Y plane).

In order to do this we constrain all nodes in the finite element model in the UX, UZ, ROTX and ROTY directions.


4. Select Pick All in the dialog box that appears.5. Select UX, UZ, ROTX and ROTY in the next dialog box that appears and enter a value

of 0 for displacement value - your screen

should look like this:

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6. Click Ok to close the dialog box. You should notice constraints appearing at each of the nodes.

The blue triangles represent a node constrained from displacing in a particular direction and the orange double arrows show

that the node is prevented from rotating about that axis.

7. Now we can apply the problem boundary conditions.8. Using the table above: we must constrain node 1 in all degrees of freedom:

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9. Again, select: Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Nodes

10. Click on Node 1 then click Ok. 11. Select All DOF and enter a value of 0 for displacement value12. Click Ok to close the dialog box. Your should have noticed extra constraints appearing at

node 1.

Step 7: Define Point Loads

1. Select Preprocessor > Loads > Define Loads > Apply > Structural > Force/ Moment > On Nodes

2. Pick node 2 and click on Ok3. In the dialog box that appears make sure that the direction of force is set to FY and that

the Force/ Moment value is -40000.

The minus ensures that the load acts downwards.

4. You should notice a red arrow appearing at node 2 pointing downwards.



dismiss the dialog.3. Select Solution > Solve > Current LS to solve the problem4. A new window and a dialog box will pop up. Take a quick look at the infromation in the

window ( /STATUS Command) before closing it.5. Click on OK in the dialog box to solve the problem.6. Once the problem has been solved you will get a message to say that the solution is done,



1. In the Main Menu select General Postproc > Plot Results > Deformed Shape 2. You screen should look something like this:

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3. Now we must examine the displacement of each node: General Postproc > List Results > Nodal Solution > DOF Solution >

Displacement Vector Sum

4. You should get a printout of the displacement of the beam at each node:

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5. Notice that Node 2 has moved downwards by 0.0133 m and Node 3 has moved 0.03839 m.

6. Now, we must check the slope of the beam: General Postproc > List Results > Nodal Solution > DOF Solution > Rotation Vector Sum

7. You should get a printout of the slope of the beam (i.e. rotation) at each node:

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8. Notice that the slope at nodes 2 and 3 is 0.025 radians.

Summary

This exercise has given you the following skills:

1. The ability to model beam problems in ANSYS.2. The ability to generate finite element models using the direct method (i.e. defining nodes

and then defining elements linking those nodes, as opposed to taking a solid model and dividing it up into elements which we will do in subsequent tutorials).

3. The ability to define element types, real constants and material parameters for a finite element model.

4. The ability to apply boundary conditions and loads to specific nodes in a finite element model.

5. The ability to apply distributed loads to beam elements and to specify which face of the beam they act upon.

6. The ability to run a simple linear static analysis.7. The ability to list displacement and rotation results for each node in the finite element

model.8. Experience in comparing the results obtained from your finite element model with other

results and validating your results against the other results.

4. 2-D DISTRIBUTION OF STRESS IN A FLAT PLATE WITH A HOLE

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Overview

2-D distribution of stress in a flat plate with a hole loaded in simple tension using ANSYS. The "plate with a hole" problem is one of the fundamental learning steps in any study of finite element analysis as it illustrates a number of key points fundamental to correct application of the finite element method to stress analysis. If you pick up pretty much any book on FEA you will find that it covers the "plate with a hole" problem once 2D plane elements have been introduced.

Figure 01: Overview of the "Plate with a Hole Problem"

Figure 01 shows an overview of the problem we are going to model in this tutorial. We have a square plate 0.1m wide and 0.1m high. It has a thickness of 0.001m and is subjected to a tensile load of 1000 N. It has a circular hole located in the centre of the plate with a diameter of 0.01m. We are going to make two different models of this problem, as shown in figure 02. First we will model the entire problem unsing plane stress elements then we will exploit symmetry and create another model that only requires 1/4 of the plate to be modelled but will still give the same solution!

Figure 02: The two modelling approaches we are going to use to model the "plate with a hole" problem. The Full Model (left) and the 1/4 Model (Right).

In both cases we are seeking to find the maximum horizontal stress in the plate which we will validate against analytical theory with the help of a stress concentration factor.

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Analytical Theory

Simple stress theory tells us that stress is load divided by area, so for the above plate (ignoring the hole) the nominal stress would be:

Now, we can find a "stress concentration factor" for a plate with a hole in tension. There are tables available which list these for various ratios of r/D where r is the radius of the hole and D is the height of the plate. In our case r/D = 0.005/0.1 = 0.05. Now, checking the graph of stress concentration factor vs r/D ratio:

we can easily see that, in our case, the stress concentration factor, K is going to be more or less equal to 3. So, K = 3.

The means that the maximum stress in the plate, due to the presence of the hole is going to be three times the nominal stress in the plate, or in other words:

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https://sites.google.com/site/onlinefiniteelement/ansys-tutorials/2d-plane-stress-analysis-of-a-plate-with-a-hole/tut08_fig04.png?attredirects=0



So, the maxmimum stress in the horizontal direction that we expect see in our finite element resultsisaround30MPa.Let'sgoaheadandstartthefiniteelementanalysis.




1. In the Main Menu select Preprocessor > Element Type > Add/Edit/Delete2. Click on Add in the dialog box that appears:

3. Select Solid in the left hand menu and Quad 8 node 183 in the right hand menu and then click OK

4. This defines element type 1 as a 2D quadratic 8-node quadrilateral element (i.e. a rectangle with curved edges)

5. Now we must define how this element behaves. Click on Options in the Element Types dialog box:

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6. In the element type options dialog box that appears, make sure that the Element behavior is set to "Plane Stress with thickness" as shown in the figure below:


Step 3: Define The Plate Thickness (Real Constant)

1. In the Main Menu select Preprocessor > Real Constants > Add/Edit/Delete2. Click on Add in the dialog box that appears.3. Click on OK to define a real constant for element type 1 PLANE 183.

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4.5. Enter the value for the plate thickness: 0.001 m and then click OK6. Click on Close to close the real constants dialog box.






right corner.

Step 5: Create the Plate Geometry

1. In the Main Menu click on Preprocessor > Modelling > Create > Areas > Rectangle > By 2 Corners

2. The WP X and WP Y boxes are used to define the coordinates for the lower left coordinates of the rectangle and the width and height are entered in the other boxes. Set the lower left corner at the coordinates (0,0) and make the width and height equal to 0.1 m, as show below:

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3. You should see a blue square appear on your screen.4. We will now create the hole: Preprocessor > Modelling > Create > Areas > Circle >

Solid Circle5. We must place the centre of the circle at the centre of the square so enter 0.05 for WP X

and WP Y. The radius of the circle is 0.005 m :

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6. You should notice the outline of a circle appearing in the centre of the plate.7. Now, we are going to subtract the circle area from the rectangular area to give the correct

plate with a hole geometry: Preprocessor > Modelling > Operate > Booleans > Subtract > Areas

8. The Subtract Areas pick box will appear. If you look at the bottom of the main menu you will see a prompt asking you to "Pick or enter base areas from which to subtract". This means we need to pick the square first. Click on the square with your mouse.

9. You will probably find a dialog box like this appearing:

10. This means that ANSYS is not entirely sure which area you meant to pick (either the circle or the rectangle). Take a look at the screen and if the entire rectangle has changed colour (to indicate that it is picked) then you can just click on OK in this dialog box. If things don't look ok then click on Next or Prev to toggle between selecting the two areas.

11. Now click on OK in the Subtract Areas pick box.12. A new Subtract Areas pick box will immediatly appear and the message at the bottom of

the main window will change to "Pick or enter areas to be subtracted". This means we need to pick the circle. Click on the circle with your mouse. Use the "multiple entities"

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13. dialog box if required to ensure it is only the circle that is selected and then click on OK to close the Subtract Areas dialog box.

14. Your geometry should now look like this:

Step 6: Mesh the Geometry

4. In the Main Menu click on Preprocessor > Meshing > Mesh Tool5. This will open the Mesh Tool window.6. We are now going to use the Mesh Tool to set the size of the elements to all be a constant

size before we begin the meshing process. In the Mesh Tool click onAreas > Set as shown in the figure below:

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7.

Use your mouse to click on the plate geometry. Once you have clicked on it, the Element Size at Picked Areas dialog box will appear. Enter 0.001 m for the Element Edge Length to define the size of each element, as shown below:

8. Click on OK to close the dialog box.9. Now we must divide the plate up into elements. In the Mesh Tool window click on Mesh.10. You should see the plate divided up into quadrilateral finite elements:

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1. In the Main Menu click on Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Lines

2. Pick the vertical line on the left hand side of the plate and the click OK in the picker dialog box.

3. In the dialog box that appears make sure that only UX is selected as we only want to constrain this line in the X (i.e. horizontal) direction.

4. You should notice some blue triangles appearing on the line indicating that it has been constrained.

If we only applied this displacement then there would be nothing to stop the entire model from moving in the

vertical direction even though we will not be applying any loads in the vertical direction. This could occur due

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to imbablances in the mesh as internal forces work their way through the mesh etc. In order to prevent this from

happening we need to constrain at least one more node in the vertical direction also. We are going to constrain

a node at the centre of the left hand vertical line in the Y direction:5. Preprocessor > Loads > Define Loads > Apply > Structural > Displacement > On Nodes6. Click on the node at the centreline of the plate on the left hand edge and then click on OK7. In the dialog box that appears make sure the DOFs to be constrained is set to UY only and then

click on OK.

8. You will probably get a warning saying that "Both solid model and finite element boundary

conditions have been applied to this model. As solid loads are transferred to the nodes or elements,

they can overwrite directly applied loads". This is OK just click on Close to dismiss this dialog.

Step 8: Couple the Nodes on the Right Hand Edge and Apply the Force

1. In the Main Menu click on Preprocessor > Coupling/ Ceqn > Couple DOF2. Make sure that the box option is selected in the Define Coupled DOFs pick box, as shown below:

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3.4. Draw a box around the nodes on the right hand edge of the plate finite element model by

clicking your left mouse button and holding it down to draw the box. Release the left mouse

button when the box is the size you require.

5. Now, click on OK to close the picker dialog box.6. The next dialog box asks you for a Set Reference Number - enter any number you wish

(I have used 99 in the image below). The dialog box also asks you which degree of freedom you

wish to couple: make sure that this is set to UX, as shown below.

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7. You should notice green arrows appearing on all the nodes on the right hand edge of the plate,

indicating that their UX degree of freedom has been coupled.

8. We can now apply the required force to any one of the coupled nodes: Preprocessor > Loads >

Define Loads > Apply > Structural > Force/Moment > On Nodes

9. Click on any of the nodes on the right hand edge of the plate and then click on OK to

close the picker dialog.

10. Change the force direction to FX and enter a Force/Moment value of 1000 in order to apply 1000 N.

11.12. You should notice a read arrow appearing on your screen pointing to the right.

Your screen should now look like this:

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13.


1. In the Main Menu select Solution > Analysis Type > New Analysis2. Make sure that Static is selected in the dialog box that pops up and then click on OK to dismiss the dialog.3. Select Solution > Solve > Current LS to solve the problem4. A new window and a dialog box will pop up. Take a quick look at the infromation in the window

( /STATUS Command) before closing it.

5. Click on OK in the dialog box to solve the problem.6. Once the problem has been solved you will get a message to say that the solution is done,



1. In the Main Menu select General Postproc > Plot Results > Deformed Shape 2. Select Def + undef edge in order to show both the deformed and undeformed shapes.3. Your screen should look something like this:

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4. Notice that the plate has reduced height and elongated in the horizontal direction. The hole

has changed shape from a perfect circle to an ovoid shape. This is all as we would expect.

5. In the Main Menu select General Postproc > Plot Results > Contour Plot > Nodal Solu >

Stress > X-Component of Stress

6. You should see a plot similar to this:

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7. Notice that the maximum stress is approximately 30 MPa and is at the top and bottom of the hole.

This is the result that was predicted by our analytical theory.

Step 12: Change the Model to take advantage of Symmetry

1. We are now going to remove 3/4 of the model and use a 1/4 symmetry model of the plate to

obtain the same result as above.

2. We must first clear the mesh: Main Menu select Preprocessor > Meshing > Clear > Areas and

click on Pick All in the picker dialog box.

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3. You will get a message telling you that the coupled set has been deleted - this is ok, just click on

close to get rid of this message.

4. In order to display the geometry again: Utility Menu > Plot > Areas5. We are going to use the workplane to cut the existing model into four quarters.

Turn on the workplane by selecting: Utility Menu > WorkPlane > Display Working Plane

6. By default, the workplane is located and aligned with the global origin. We must now move

it to the centre of the plate: Utility Menu > WorkPlane > Offset WP to > XYZ Locations

7. Enter the coordinates 0.05,0.05 in the pick dialog box that appears:

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8. You should notice the workplane move to the centre of the hole in the centre of the plate.9. By default ANSYS uses the XY plane of workplane to cut through an object.

We must now rotate the workplane so that it's XY plane cuts through the plate.

Utility Menu > WorkPlane > Offset WP by increments....

10. In the dialog box that appears change the number of degrees to 90 and then rotate the

workplane in the positive X - direction, as shown below:

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11. Click on OK to close the Offset WP dialog box.12. Now let's start cutting up the plate: Main Menu > Preprocessor > Modelling > Operate >

Booleans > Divide > Area by Workplane

13. Click on the plate and then click on OK. 14. The plate is now divided vertically into two halves. Let's now delete the lower half:

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Main Menu > Preprocessor > Modelling > Delete > Area and Below

15. Click on the lower half of the plate and click on OK. Your screen should now look like this:

16. We will now repeat a lot of the above process to remove the left hand 1/4 of the plate:

Utility Menu > WorkPlane > Offset WP by increments....

17. Click on the +Y rotation button to rotate the workplane so the XY plane is in the vertical direction on

the screen then click on OK to close the dialog box.

18. Now let's cut the plate again: Main Menu > Preprocessor > Modelling > Operate > Booleans >

Divide > Area by Workplane

19. Click on the plate and then click on OK.

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20. The plate is now divided horizontally into two halves. Let's now delete the left hand half:

Main Menu > Preprocessor > Modelling > Delete > Area and Below

21. Click on the left hand side of the plate and click on OK. 22. It is good practice to put the workplane back in its original position when you are finished using it:

Your screen should now look like this: Utility Menu > WorkPlane > Align WP with > Global Cartesian

23. You can also turn off the workplane again: Utility Menu > WorkPlane > Display Working Plane24. Now, let's do a replot to tidy up our display: Utility Menu > Plot > Areas25. Your screen should now look like this:

26. We want to ensure that we get a nice regular mesh when we mesh this 1/4 of the plate.

A very regular mapped mesh would be desireable here but a mapped mesh is only possible with a four sided area and our area has five sides. In order to overcome this we are going to concatanate the lines on the top and the right (i.e. merge them into one line). This way we can "trick" the mesher into thinking it is a four sided object and obtain a nice mapped mesh.

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27. Main Menu > Preprocessor > Modelling > Operate > Booleans > Add > Lines28. Pick the lines at the top and right of the 1/4 plate and then click on OK29. A dialog box will appear asking you if you want to keep or delete the existing lines: make sure

"Deleted" is selected and then click on OK You will get a warning message telling you

that the lines do not share a common slope at the upper right hand corner and this will

cause problems if you try to sweep the new line to form another object. This doesn't apply

here, as we won't be doing this, so we can just ignore this warning and close the warning.

30. We can now begin to mesh our 1/4 plate: Main Menu > Preprocessor > Meshing > Meshtool

In the MeshTool, under "Size Controls" click on Lines > Set Click on the line at the bottom

of the plate and click on OK. In the dialog box that appears enter 20 for the number of

divisions and 5 for the spacing ratio. This will ensure that this line is divided into 20

elements and that the elements at one end of the line will be 5 times bigger than

the elements at the other end.

31. Make sure that the small elements are near the hole: Utility Menu > Plot > Lines If they are not in the right place then use the Flip button on the meshtool to flip the spacing over.

32. Repeat steps 33-35 with the line at the left hand edge of the 1/4 plate.

Now, we will set the number of divisions on the curved line that defines the hole:

this time enter 20 for the number of divisions and set the spacing ratio to 1 as we don't want

the elements to change size over the length of this line.

33. We can now mesh the 1/4 plate: In the Meshtool make sure that the Shape is set to

"Quad" and that "Mapped" meshing is selected, then click on Mesh.

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34. Pick the 1/4 area and then click on OK. Your screen should look like this:

35. Now, apply a symmetry boundary condition to the lines on the left and the bottom of the 1/4 plate:

Main Menu > Preprocessor > Loads > Define Loads > Apply > Structural > Displacement >

Symmetry BC > On Lines

36. Pick the lines on the left and the bottom of the 1/4 plate and then click on OK.

You should see small "s" symbols appear along these lines to show that a symmetry constraint

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has been applied.Now, we must couple the nodes on the right hand line together and apply

the load as we did above. Repeat the steps detailed above to do this, but this time, take care

to only apply a load of 500 N, as due to the symmetry boundary conditions, any load

we applied will be effectively doubled.

37. Now, solve the problem as usual and then check the deformed shape and the stress in the X-direction.38. The deformed shape:

39. This is as expected40. The stress in the41. Again, as expected and with a magnitude of 29.7 MPa. This is slightly below what we

expected 30 MPa but is still 99% accurate. We could possibly improve the accuracy by

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changing the mesh.

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Documents

Aim: To Analyze the Analysis of Cantilever Beam I Sem FEA Lab... · Web viewAnalysis of cantilever beam using ANSYS Workbench Figure 01 shows an overview of the beam problem for load