cicalengka3

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3. Define Element Types

For this problem, 3 types of elements are used: PIPE16, COMBIN7 (Revolute Joint), COMBIN14(Spring-Damper) . It is therefore required that the types of elements are defined prior to creating theelements. This element has 6 degrees of freedom (translation along the X, Y and Z axis, and rotationabout the X,Y and Z axis).

a. Define PIPE16With 6 degrees of freedom, the PIPE16 element can be used to create the 3D structure.

Preprocessor > Element Type > Add/Edit/Delete... > click 'Add'Select 'Pipe', 'Elast straight 16'Click on 'Apply' You should see 'Type 1 PIPE16' in the 'Element Types' window.

b. Define COMBIN7COMBIN7 (Revolute Joint) will allow the catapult to rotate about nodes 1 and 2.

Select 'Combination', 'Revolute Joint 7'Click 'Apply'.

c. Define COMBIN14 Now we will define the spring elements.

Select 'Combination', 'Spring damper 14'Click on 'OK'

In the 'Element Types' window, there should now be three types of elements defined.

4. Define Real Constants

Real Constants must be defined for each of the 3 element types.

a. PIPE16Preprocessor > Real Constants > Add/Edit/Delete... > click 'Add'Select Type 1 PIPE16 and click 'OK'Enter the following properties, then click 'OK'

OD = 40TKWALL = 10

'Set 1' will now appear in the dialog box

b. COMBIN7 (Joint)

Five of the degrees of freedom (UX, UY, UZ, ROTX, and ROTY) can be constrained with differentlevels of flexibility. These can be defined by the 3 real constants: K1 (UX, UY), K2 (UZ) and K3(ROTX, ROTY). For this example, we will use high values for K1 through K3 since we onlyexpect the model to rotate about the Z axis.

Click 'Add'Select 'Type 2 COMBIN7'. Click 'OK'.In the 'Real Constants for COMBIN7' window, enter the following geometric properties(then click 'OK'):

X-Y transnational stiffness K1: 1e9Z directional stiffness K2: 1e9

University of Alberta ANSYS Tutorials - www.mece.ualberta.ca/tutorials/ansys/AT/Joints/Joints.html

Copyright 2001 University of Alberta


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Rotational stiffness K3: 1e9'Set 2' will now appear in the dialog box.

Note: The constants that we define in this problem refer to the relationship between thecoincident nodes. By having high values for the stiffness in the X-Y plane and along the Zaxis, we are essentially constraining the two coincident nodes to each other.

c. COMBIN14 (Spring)Click 'Add'Select 'Type 3 COMBIN14'. Click 'OK'.Enter the following geometric properties:

Spring constant K: 5

In the 'Element Types' window, there should now be three types of elements defined.

5. Define Element Material Properties 1. Preprocessor > Material Props > Material Models2. In the 'Define Material Model Behavior' Window, ensure that Material Model Number 1 is selected3. Select Structural > Linear > Elastic > Isotropic4. In the window that appears, enter the give the properties of Steel then click 'OK'.

Young's modulus EX: 200000Poisson's Ratio PRXY: 0.33

6. Define Nodes Preprocessor > (-Modeling-) Create > Nodes > In Active CS...N,#,x,y,z

We are going to define 13 Nodes for this structure as given in the following table (as depicted by thecircled numbers in the figure above):

Node Coordinates (x,y,z)

1 (0,0,0)

2 (0,0,1000)

3 (1000,0,1000)

4 (1000,0,0)

5 (0,1000,1000)

6 (0,1000,0)

7 (700,700,500)

8 (400,400,500)

9 (0,0,0)

10 (0,0,1000)

11 (0,0,500)

12 (0,0,1500)




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7. Create PIPE16 elements

a. Define element type

Preprocessor > (-Modeling-) Create > Elements > Elem Attributes ...The following window will appear. Ensure that the 'Element type number' is set to 1 PIPE16,'Material number' is set to 1, and 'Real constant set number' is set to 1. Then click 'OK'.

b. Create elements Preprocessor > (-Modeling-) Create > Elements > (-Auto Numbered-) Thru NodesE, node a, node b

Create the following elements joining Nodes 'a' and Nodes 'b'. Note: because it is difficult to graphically select the nodes you may wish to use the command line(for example, the first entry would be: E,1,6 ).

13 (0,0,-500)

Node a Node b1 6

2 51 4

2 3

3 4

10 8

9 8

7 8

12 5




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You should obtain the following geometry (Oblique view)

8. Create COMBIN7 (Joint) elements

a. Define element type Preprocessor > (-Modeling-) Create > Elements > Elem AttributesEnsure that the 'Element type number' is set to 2 COMBIN7 and that 'Real constant setnumber' is set to 2. Then click 'OK'

b. Create elements When defining a joint, three nodes are required. Two nodes are coincident at the point of rotation.The elements that connect to the joint must reference each of the coincident points. The other nodefor the joint defines the axis of rotation. The axis would be the line from the coincident nodes to theother node.

Preprocessor > (-Modeling-) Create > Elements > (-Auto Numbered-) Thru NodesE,node a, node b, node c

Create the following lines joining Node 'a' and Node 'b'

9. Create COMBIN14 (Spring) elements

13 6

12 13

5 3

6 4

Node a Node b Node c1 9 11

2 10 11




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a. Define element type Preprocessor > (-Modeling-) Create > Elements > Elem AttributesEnsure that the 'Element type number' is set to 3 COMBIN7 and that 'Real constant setnumber' is set to 3. Then click 'OK'

b. Create elements

Preprocessor > (-Modeling-) Create > Elements > (-Auto Numbered-) Thru NodesE,node a, node b

Create the following lines joining Node 'a' and Node 'b'

NOTE: To ensure that the correct nodes were used to make the correct element in the above table, youcan list all the elements defined in the model. To do this, select Utilities Menu > List > Elements >Nodes + Attributes .

10. Meshing

Because we have defined our model using nodes and elements, we do not need to mesh our model. If weinitially defined our model using keypoints and lines, we would have had to create elements in our model

by meshing the lines. It is the elements that ANSYS uses to solve the model.

11. Plot Elements Utility Menu > Plot > Elements

You may also wish to turn on element numbering and turn off keypoint numberingUtility Menu > PlotCtrls > Numbering ...

Node a Node b

5 8

8 6




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5. Solve the System Solution > (-Solve-) Current LSSOLVE

Note: During the solution, you will see a yellow warning window which states that the "Coefficient ratioexceeds 1.0e8". This warning indicates that the solution has relatively large displacements. This is due to

the rotation about the joints.

Postprocessing: Viewing the Results

1. Plot Deformed Shape General Postproc > Plot Results > Deformed ShapePLDISP.2

2. Extracting Information as Parameters

In this problem, we would like to find the vertical displacement of node #7. We will do this using theGET command.

a. Select Utility Menu > Parameters > Get Scalar Data...

b. The following window will appear. Select 'Results data' and 'Nodal results' as shown then click'OK'




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c. Fill in the 'Get Nodal Results Data' window as shown below:

d. To view the defined parameter select Utility Menu > Parameters > Scalar Parameters...




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Therefore the vertical displacement of Node 7 is 323.78 mm. This can be repeated for any of theother nodes you are interested in.

Command File Mode of Solution

The above example was solved using a mixture of the Graphical User Interface (or GUI) and the commandlanguage interface of ANSYS. This problem has also been solved using the ANSYS command languageinterface that you may want to browse. Open the file and save it to your computer. Now go to 'File > Readinput from...' and select the file.




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Design Optimization

Introduction

This tutorial was completed using ANSYS 7.0 The purpose of this tutorial is to introduce a method of solvingdesign optimization problems using ANSYS. This will involve creating the geometry utilizing parameters forall the variables, deciding which variables to use as design, state and objective variables and setting the correcttolerances for the problem to obtain an accurately converged solution in a minimal amount of time. The use ofhardpoints to apply forces/constraints in the middle of lines will also be covered in this tutorial.

A beam has a force of 1000N applied as shown below. The purpose of this optimization problem is to minimizethe weight of the beam without exceeding the allowable stress. It is necessary to find the cross sectionaldimensions of the beam in order to minimize the weight of the beam. However, the width and height of the

beam cannot be smaller than 10mm. The maximum stress anywhere in the beam cannot exceed 200 MPa. The

beam is to be made of steel with a modulus of elasticity of 200 GPa.

Preprocessing: Defining the Problem

1. Give example a Title Utility Menu > File > Change Title ...

/title, Design Optimization

2. Enter initial estimates for variables

To solve an optimization problem in ANSYS, parameters need to be defined for all design variables.

Select: Utility Menu > Parameters > Scalar Parameters... In the window that appears (shown below), type W=20 in the Selection section

University of Alberta ANSYS Tutorials - www.mece.ualberta.ca/tutorials/ansys/AT/Optimization/Optimizati...



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Click Accept. The 'Scalar Parameters' window will stay open. Now type H=20 in the Selection sectionClick Accept'Click Close in the Scalar Parameters window.

NOTE: None of the variables defined in ANSYS are allowed to have negative values.

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

We are going to define 2 Keypoints for this beam as given in the following table:

4. Create Lines Preprocessor > Modeling > Create > Lines > Lines > In Active CoordL,1,2

Create a line joining Keypoints 1 and 2

5. Create Hard Keypoints

Hardpoints are often used when you need to apply a constraint or load at a location where a keypoint doesnot exist. For this case, we want to apply a force 3/4 of the way down the beam. Since there are not anykeypoints here and we can't be certain that one of the nodes will be here we will need to specify ahardpoint

Select Preprocessor > Modeling > Create > Keypoints > Hard PT on line > Hard PT by ratio .This will allow us to create a hardpoint on the line by defining the ratio of the location of the point

Keypoints Coordinates (x,y)

1 (0,0)

2 (1000,0)




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to the size of the line

Select the line when prompted

Enter a ratio of 0.75 in the 'Create HardPT by Ratio window which appears.

You have now created a keypoint labelled 'Keypoint 3' 3/4 of the way down the beam.

6. Define Element Types Preprocessor > Element Type > Add/Edit/Delete...

For this problem we will use the BEAM3 (Beam 2D elastic) element. This element has 3 degrees ofreedom (translation along the X and Y axes, and rotation about the Z axis).

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

In the 'Real Constants for BEAM3' window, enter the following geometric properties: (Note that'**' is used instead '^' for exponents)i. Cross-sectional area AREA: W*H

ii. Area moment of inertia IZZ: (W*H**3)/12iii. Thickness along Y axis: H

NOTE: It is important to use independent variables to define dependent variables such as themoment of inertia. During the optimization, the width and height will change for each iteration. Asa result, the other variables must be defined in relation to the width and height.

8. 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

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

For this example we will specify an element edge length of 100 mm (10 element divisions alongthe line).

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

Solution Phase: Assigning Loads and Solving

1. Define Analysis Type




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Solution > Analysis Type > New Analysis > StaticANTYPE,0

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

Pin Keypoint 1 (ie UX, UY constrained) and constrain Keypoint 2 in the Y direction.

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

Apply a vertical (FY) point load of -2000N at Keypoint 3

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

4. Solve the System Solution > Solve > Current LSSOLVE


Extracting Information as Parameters:

To perform an optimization, we must extract the required information.

In this problem, we would like to find the maximum stress in the beam and the volume as a result of the widthand height variables.




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1. Define the volume

Select General Postproc > Element Table > Define Table... > Add...

The following window will appear. Fill it in as shown to obtain the volume of the beam.

Note that this is the volume of each element. If you were to list the element table you would get avolume for each element. Therefore, you have to sum the element values together to obtain the totalvolume of the beam. Follow the instructions below to do this.

Select General Postproc > Element Table > Sum of Each Item...

A little window will appear notifying you that the tabular sum of each element table will becalculated. Click 'OK'

You will obtain a window notifying you that the EVolume is now 400000 mm 2

2. Store the data (Volume) as a parameter

Select Utility Menu > Parameters > Get Scalar Data...

In the window which appears select 'Results Data' and 'Elem table sums'

the following window will appear. Select the items shown to store the Volume as a parameter.




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Now if you view the parameters (Utility Menu > Parameters > Scalar Parameters...) you will seethat Volume has been added.

3. Define the maximum stress at the i node of each element in the beam


The following window will appear. Fill it in as shown to obtain the maximum stress at the i node ofeach element and store it as 'SMAX_I'.

Note that nmisc,1 is the maximum stress. For further information type Help beam3 into thecommand line

Now we will need to sort the stresses in descending order to find the maximum stress

Select General Postproc > List Results > Sorted Listing > Sort Elems

Complete the window as shown below to sort the data from 'SMAX_I' in descending order




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4. Store the data (Max Stress) as a parameter


In the window which appears select 'Results Data' and 'Other operations'

In the that appears, fill it in as shown to obtain the maximum value.

5. Define maximum stress at the j node of each element for the beam


Fill this table as done previously, however make the following changes:save the data as 'SMAX_J' (instead of 'SMAX_I')

The element table data enter NMISC,3 (instead of NMISC,1). This will give you the maxstress at the j node.

Select General Postproc > List Results > Sorted Listing > Sort Elems to sort the stresses indescending order.

However, select 'SMAX_J' in the Item, Comp selection box

6. Store the data (Max Stress) as a parameter




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In the window which appears select 'Results Data' and 'Other operations'

In the that appears, fill it in as shown previously , however, name the parameter 'SMaxJ'.

7. Select the largest of SMAXJ and SMAXI Type SMAX=SMAXI>SMAXJ into the command line

This will set the largest of the 2 values equal to SMAX. In this case the maximum values for eachare the same. However, this is not always the case.

8. View the parametric data Utility Menu > Parameters > Scalar Parameters

Note that the maximum stress is 281.25 which is much larger than the allowable stress of 200MPa

Design Optimization

Now that we have parametrically set up our problem in ANSYS based on our initial width and heightdimensions, we can now solve the optimization problem.

1. Write the command file

It is necessary to write the outline of our problem to an ANSYS command file. This is so that ANSYScan iteratively run solutions to our problem based on different values for the variables that we will define.

Select Utility Menu > File > Write DB Log File... In the window that appears type a name for the command file such as optimize.txt

Click OK.If you open the command file in a text editor such as Notepad, it should similar to this:

/BATCH! /COM,ANSYS RELEASE 7.0 UP20021010 16:10:03 05/26/2003/input,start70,ans,'C:\Program Files\Ansys Inc\v70\ANSYS\apdl\',,,,,,,,,,,,,,,,1/title, Design Optimization*SET,W , 20*SET,H , 20/PREP7K,1,0,0,,K,2,1000,0,,

L, 1, 2!*HPTCREATE,LINE,1,0,RATI,0.75,!*ET,1,BEAM3!*!*R,1,W*H,(W*H**3)/12,H, , , ,!*!*MPTEMP,,,,,,,,




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MPTEMP,1,0MPDATA,EX,1,,200000MPDATA,PRXY,1,,.3!*LESIZE,ALL,100, , , ,1, , ,1,LMESH, 1FINISH/SOL!*ANTYPE,0FLST,2,1,3,ORDE,1FITEM,2,1!*/GODK,P51X, , , ,0,UX,UY, , , , ,FLST,2,1,3,ORDE,1FITEM,2,2!*/GODK,P51X, , , ,0,UY, , , , , ,FLST,2,1,3,ORDE,1

FITEM,2,3!*/GOFK,P51X,FY,-2000! /STATUS,SOLUSOLVEFINISH/POST1AVPRIN,0,0,ETABLE,EVolume,VOLU,!*SSUM!**GET,Volume,SSUM, ,ITEM,EVOLUMEAVPRIN,0,0,ETABLE,SMax_I,NMISC, 1!*ESORT,ETAB,SMAX_I,0,1, ,!**GET,SMaxI,SORT,,MAXAVPRIN,0,0,ETABLE,SMax_J,NMISC, 3!*ESORT,ETAB,SMAX_J,0,1, ,!**GET,SMaxJ,SORT,,MAX*SET,SMAX,SMAXI>SMAXJ

! LGWRITE,optimization,,C:\Temp\,COMMENT

Several small changes need to be made to this file prior to commencing the optimization. If you createdthe geometry etc. using command line code, most of these changes will already be made. However, if youused GUI to create this file there are several occasions where you used the graphical picking device.Therefore, the actual items that were chosen need to be entered. The code 'P51X' symbolizes thegraphical selection. To modify the file simply open it using notepad and make the required changes. Saveand close the file once you have made all of the required changes. The following is a list of the changeswhich need to be made to this file (which was created using the GUI method)




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Line 32 - DK,P51X, ,0, ,0,UX,UY, , , , , Change this to: DK,1, ,0, ,0,UX,UY, This specifies the constraints at keypoint 1

Line 37 - DK,P51X, ,0, ,0,UY, , , , , ,Change to: DK,2, ,0, ,0,UY,

This specifies the constraints at keypoint 2

Line 42 - FK,P51X,FY,-2000 Change to: FK,3,FY,-2000This specifies the force applied on the beam

There are also several lines which can be removed from this file. If you are comfortable with commandline coding, you should remove the lines which you are certain are not required.

2. Assign the Command File to the Optimization Select Main Menu > Design Opt > Analysis File > Assign

In the file list that appears, select the filename that you created when you wrote the command file.Click OK.

3. Define Variables and Tolerances

ANSYS needs to know which variables are critical to the optimization. To define variables, we need toknow which variables have an effect on the variable to be minimized. In this example our objective is tominimize the volume of a beam which is directly related to the weight of the beam.

ANSYS categorizes three types of variables for design optimization:

Design Variables (DVs) Independent variables that directly effect the design objective. In this example, the width and heightof the beam are the DVs. Changing either variable has a direct effect on the solution of the

problem.State Variables (SVs)

Dependent variables that change as a result of changing the DVs. These variables are necessary toconstrain the design. In this example, the SV is the maximum stress in the beam. Without this SV,our optimization will continue until both the width and height are zero. This would minimize theweight to zero which is not a useful result.

Objective Variable (OV) The objective variable is the one variable in the optimization that needs to be minimized. In our

problem, we will be minimizing the volume of the beam.

NOTE: As previously stated, none of the variables defined in ANSYS are allowed to have negativevalues.

Now that we have decided our design variables, we need to define ranges and tolerances for eachvariable. For the width and height, we will select a range of 10 to 50 mm for each. Because a smallchange in either the width or height has a profound effect on the volume of the beam, we will select atolerance of 0.01mm. Tolerances are necessary in that they tell ANSYS the largest amount of change thata variable can experience before convergence of the problem.




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For the stress variable, we will select a range of 195 to 200 MPa with a tolerance of 0.01MPa.

Because the volume variable is the objective variable, we do not need to define an allowable range. Wewill set the tolerance to 200mm3. This tolerance was chosen because it is significantly smaller than theinitial magnitude of the volume of 400000mm3 (20mm x 20mm x 1000mm).

a. Define the Design Variables (width and height of beam)

Select Main Menu > Design Opt > Design Variables... > Add...

Complete the window as shown below to specify the variable limits and tolerances for theheight of the beam.

Repeat the above steps to specify the variable limits for the width of the beam (identical tospecifications for height)

b. Define the State Variables

Select Main Menu > Design Opt > State Variables... > Add...

In the window fill in the following sectionsSelect 'SMAX' in the Parameter Name section.Enter: Lower Limit (MIN = 195)Upper Limit (MAX = 200)Feasibility Tolerance (TOLER = 0.001)

c. Define the Objective Variable

Select Main Menu > Design Opt > Objective...




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Select VOLUME in the Parameter Name section.Under Convergence Tolerance, enter 200.

4. Define the Optimization Method

There are several different methods that ANSYS can use to solve an optimization problem. To ensure that

you are not finding a solution at a local minimum, it is advisable to use different solution methods. If youhave trouble with getting a particular problem to converge it would be a good idea to try a differentmethod of solution to see what might be wrong.

For this problem we will use a First-Order Solution method.

Select Main Menu > Design Opt > Method / Tool... In the Specify Optimization Method window select First-OrderClick OKEnter: Maximum iterations (NITR = 30), Percent step size SIZE = 100, Percent forward diff.DELTA = 0.2Click OK.

Note: the significance of the above variables is explained below: NITR

Max number of iterations. Defaults to 10.SIZE

% that is applied to the size of each line search step. Defaults to 100%DELTA

forward difference (%) applied to the design variable range that is used to compute the gradient.Defaults to 0.2%

5. Run the Optimization

Select Main Menu > Design Opt > Run... In the Begin Execution of Run window, confirm that the analysis file, method/type and maximumiterations are correct.Click OK.

The solution of an optimization problem can take awhile before convergence. This problem will takeabout 15 minutes and run through 19 iterations.

View the Results

1. View Final Parameters Utility Menu > Parameters > Scalar Parameters...

You will probably see that the width=13.24 mm, height=29.16 mm, and the stress is equal to199.83 MPa with a volume of 386100mm 2.

2. View graphical results of each variable during the solution

Select Main Menu > Design Opt > Design Sets > Graphs / Tables...




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Complete the window as shown to obtain a graph of the height and width of the beam changingwith each iteration

A. For the X-variable parameter select Set number.B. For the Y-variable parameter select H and W.C. Ensure that 'Graph' is selected (as opposed to 'List')

Now you may wish to specify titles for the X and Y axes

Select Utility Menu > Plot Ctrls > Style > Graphs > Modify Axes... In the window, enter Number of Iterations for the X-axis label section.Enter Width and Height (mm) for the Y-axis label.Click 'OK'Select Utility Menu > PlotCtrls

In the graphics window, you will see a graph of width and height throughout the optimization. You can print the plot by selecting Utility Menu > PlotCtrls > Hard Copy...




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You can plot graphs of the other variables in the design by following the above steps. Instead of usingwidth and height for the y-axis label and variables, use whichever variable is necessary to plot.Alternatively, you could list the data by selecting Main Menu > Design Opt > Design Sets > List... . Inaddition, all of the results data (ie stress, displacement, bending moments) are available from the GeneralPostproc menu.


The above example was solved using the Graphical User Interface (or GUI) of ANSYS. This problem hasalso been solved using the ANSYS command language interface that you may want to browse. Open thefile and save it to your computer.

***IMPORTANT*** Before running this code, select Main Menu > Design Opt > Opt Database > Clear & Reset to clearthe optimization database. Then select Utility Menu > File > Clear & Start New . Now go to 'File >Read input from...' and select the file.




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Substructuring

Introduction

This tutorial was completed using ANSYS 7.0 The purpose of the tutorial is to show the how to usesubstructuring in ANSYS. Substructuring is a procedure that condenses a group of finite elements into one super-element . This reduces the required computation time and also allows the solution of very large problems.

A simple example will be demonstrated to explain the steps required, however, please note that this model isnot one which requires the use of substructuring. The example involves a block of wood (E =10 GPa v =0.29)connected to a block of silicone (E = 2.5 MPa, v = 0.41) which is rigidly attached to the ground. A force will beapplied to the structure as shown in the following figure. For this example, substructuring will be used for thewood block.

The use of substructuring in ANSYS is a three stage process:

1. Generation Pass Generate the super-element by condensing several elements together. Select the degrees of freedom tosave (master DOFs) and to discard (slave DOFs). Apply loads to the super-element

2. Use Pass

Create the full model including the super-element created in the generation pass. Apply remaining loadsto the model. The solution will consist of the reduced solution tor the super-element and the completesolution for the non-superelements.

3. Expansion Pass Expand the reduced solution to obtain the solution at all DOFs for the super-element.

Note that a this method is a bottom-up substructuring (each super-element is created separately and thenassembled in the Use Pass). Top-down substructuring is also possible in ANSYS (the entire model is built, then

University of Alberta ANSYS Tutorials - www.mece.ualberta.ca/tutorials/ansys/AT/Substructuring/Substruct...



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super-element are created by selecting the appropriate elements). This method is suitable for smaller models andhas the advantage that the results for multiple super-elements can be assembled in postprocessing.

Expansion Pass: Creating the Super-element


1. Give Generation Pass a Jobname Utility Menu > File > Change Jobname ...

Enter 'GEN' for the jobname

2. Open preprocessor menu ANSYS Main Menu > Preprocessor/PREP7

3. Create geometry of the super-element Preprocessor > Modeling > Create > Areas > Rectangle > By 2 CornersBLC4,XCORNER,YCORNER,WIDTH,HEIGHT

Create a rectangle with the dimensions (all units in mm):

XCORNER (WP X) = 0YCORNER (WP Y) = 40Width = 100Height = 100

4. Define the Type of Element

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

For this problem we will use PLANE42 (2D structural solid). This element has 4 nodes, each with2 degrees of freedom (translation along the X and Y axes).


In the window that appears, enter the following geometric properties for wood:i. Young's modulus EX: 10000 (MPa)


6. Define Mesh Size Preprocessor > Meshing > Size Cntrls > Manual Size > Areas > All Areas ...

For this example we will use an element edge length of 10mm.

7. Mesh the block Preprocessor > Meshing > Mesh > Areas > Free > click 'Pick All'AMESH,1




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1. Define Analysis Type Solution > Analysis Type > New Analysis > SubstructuringANTYPE,SUBST

2. Select Substructuring Analysis Options

It is necessary to define the substructuring analysis options

Select Solution > Analysis Type > Analysis Options

The following window will appear. Ensure that the options are filled in as shown.

Sename (the name of the super-element matrix file) will default to the jobname.In this case, the stiffness matrix is to be generated.With the option SEPR , the stiffness matrix or load matrix can be printed to the outputwindow if desired.

3. Select Master Degrees of Freedom

Master DOFs must be defined at the interface between the super-element and other elements in additionto points where loads/constraints are applied.

Select Solution > Master DOFs > User Selected > Define

Select the Master DOF as shown in the following figure.




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In the window that appears, set the 1st degree of freedom to All DOF

4. Apply Loads

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

Place a load of 5N in the x direction on the top left hand node

The model should now appear as shown in the figure below.




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Now we need to bring the Super-element into the model

4. Define the Super-element Type Preprocessor > Element Type > Add/Edit/Delete...

Select 'Super-element' (MATRIX50)

5. Create geometry of the non-superelement (Silicone) Preprocessor > Modeling > Create > Areas > Rectangle > By 2 CornersBLC4,XCORNER,YCORNER,WIDTH,HEIGHT

Create a rectangle with the dimensions (all units in mm):

XCORNER (WP X) = 0

YCORNER (WP Y) = 0Width = 100Height = 40

6. Define the Non-Superelement Type Preprocessor > Element Type > Add/Edit/Delete...

We will again use PLANE42 (2D structural solid).


In the window that appears, enter the following geometric properties for silicone:i. Young's modulus EX: 2.5 (MPa)


8. Define Mesh Size Preprocessor > Meshing > Size Cntrls > Manual Size > Areas > All Areas ...

For this block we will again use an element edge length of 10mm. Note that is is imperative that thenodes of the non-superelement match up with the super-element MDOFs.

9. Mesh the block Preprocessor > Meshing > Mesh > Areas > Free > click 'Pick All'AMESH,1

10. Offset Node Numbering

Since both the super-element and the non-superelement were created independently, they containsimilarly numbered nodes (ie both objects will have node #1 etc.). If we bring in the super-element withsimilar node numbers, the nodes will overwrite existing nodes from the non-superelements. Therefore, weneed to offset the super-element nodes




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Read in the super-element matrix

Select Preprocessor > Modeling > Create > Elements > Super-elements > From .SUB File... Enter 'GEN2' as the Jobname of the matrix file in the window (shown below)

Utility Menu > Plot > Replot

11. Couple Node Pairs at Interface of Super-element and Non-Superelements

Select the nodes at the interfaceSelect Utility Menu > Select > Entities ...The following window will appear. Select Nodes, By Location, Y coordinates, 40 as shown.

Couple the pair nodes at the interface

Select Preprocessor > Coupling / Ceqn > Coincident Nodes

Re-select all of the nodes




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Select Utility Menu > Select > Entities ...In the window that appears, click 'Nodes > By Num/Pick > From Full > Sele All'


1. Define Analysis Type

Solution > New Analysis > StaticANTYPE,0

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

Fix the bottom line (ie all DOF constrained)

3. Apply super-element load vectors

Determine the element number of the super-element (Select Utility Menu > PlotCtrls >

Numbering...) You should find that the super-element is element 41

Select Solution > Define Loads > Apply > Load Vector > For Super-element

The following window will appear. Fill it in as shown to apply the super-element load vector.

4. Save the database Utility Menu > File > Save as Jobname.dbSAVE

Save the database to be used again in the expansion pass


General Postprocessing: Viewing the Results




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Enter the Solution mode by selecting Main Menu > Solution or by typing /SOLU into thecommand line.

Type 'EXPASS,ON' into the command line to initiate the expansion pass.

2. Enter the Super-element name to be Expanded

Select Solution > Load STEP OPTS > ExpansionPass > Single Expand >Expand Superelem ...

The following window will appear. Fill it in as shown to select the super-element.

3. Enter the Super-element name to be Expanded

Select Solution > Load Step Opts > ExpansionPass > Single Expand > By Load Step...

The following window will appear. Fill it in as shown to expand the solution.


General Postprocessing: Viewing the Results

1. Show the Displacement Contour Plot General Postproc > Plot Results > (-Contour Plot-) Nodal Solution ... > DOF solution, Translation




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USUMPLNSOL,U,SUM,0,1

Note that only the deformation for the super-elements is plotted (and that the contour intervals have been

modified to begin at 0). This results agree with what was found without using substructuring (see figure below).




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The above example was solved using the Graphical User Interface (or GUI) of ANSYS. This problem has also been solved using the ANSYS command language interface that you may want to browse. Open the file andsave it to your computer. Now go to 'File > Read input from...' and select the file.




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Coupled Structural/Thermal Analysis

Introduction

This tutorial was completed using ANSYS 7.0 The purpose of this tutorial is to outline a simple coupledthermal/structural analysis. A steel link, with no internal stresses, is pinned between two solid structures at areference temperature of 0 C (273 K). One of the solid structures is heated to a temperature of 75 C (348 K). Asheat is transferred from the solid structure into the link, the link will attemp to expand. However, since it is

pinned this cannot occur and as such, stress is created in the link. A steady-state solution of the resulting stresswill be found to simplify the analysis.

Loads will not be applied to the link, only a temperature change of 75 degrees Celsius. The link is steel with amodulus of elasticity of 200 GPa, a thermal conductivity of 60.5 W/m*K and a thermal expansion coefficient of12e-6 /K.


According to Chapter 2 of the ANSYS Coupled-Field Guide, "A sequentially coupled physics analysis is thecombination of analyses from different engineering disciplines which interact to solve a global engineering

problem. For convenience, ...the solutions and procedures associated with a particular engineering discipline

[will be referred to as] a physics analysis. When the input of one physics analysis depends on the results fromanother analysis, the analyses are coupled."

Thus, each different physics environment must be constructed seperately so they can be used to determine thecoupled physics solution. However, it is important to note that a single set of nodes will exist for the entiremodel. By creating the geometry in the first physical environment, and using it with any following coupledenvironments, the geometry is kept constant. For our case, we will create the geometry in the ThermalEnvironment, where the thermal effects will be applied.

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Although the geometry must remain constant, the element types can change. For instance, thermal elements arerequired for a thermal analysis while structural elements are required to deterime the stress in the link. It isimportant to note, however that only certain combinations of elements can be used for a coupled physicsanalysis. For a listing, see Chapter 2 of the ANSYS Coupled-Field Guide located in the help file.

The process requires the user to create all the necessary environments, which are basically the preprocessing

portions for each environment, and write them to memory. Then in the solution phase they can be combined tosolve the coupled analysis.

Thermal Environment - Create Geometry and Define Thermal Properties

1. Give example a Title Utility Menu > File > Change Title .../title, Thermal Stress Example


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

We are going to define 2 keypoints for this link as given in the following table:

4. Create Lines Preprocessor > Modeling > Create > Lines > Lines > In Active CoordL,1,2

Create a line joining Keypoints 1 and 2, representing a link 1 meter long.

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

For this problem we will use the LINK33 (Thermal Mass Link 3D conduction) element. This

element is a uniaxial element with the ability to conduct heat between its nodes.


In the 'Real Constants for LINK33' window, enter the following geometric properties:i. Cross-sectional area AREA: 4e-4

This defines a beam with a cross-sectional area of 2 cm X 2 cm.

Keypoint Coordinates (x,y,z)1 (0,0)

2 (1,0)




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7. Define Element Material Properties Preprocessor > Material Props > Material Models > Thermal > Conductivity > Isotropic

In the window that appears, enter the following geometric properties for steel:i. KXX: 60.5

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

For this example we will use an element edge length of 0.1 meters.

9. Mesh the frame Preprocessor > Meshing > Mesh > Lines > click 'Pick All'

10. Write Environment The thermal environment (the geometry and thermal properties) is now fully described and can bewritten to memory to be used at a later time.Preprocessor > Physics > Environment > Write

In the window that appears, enter the TITLE Thermal and click OK.

11. Clear Environment Preprocessor > Physics > Environment > Clear > OK

Doing this clears all the information prescribed for the geometry, such as the element type, material properties, etc. It does not clear the geometry however, so it can be used in the next stage, which isdefining the structural environment.

Structural Environment - Define Physical Properties

Since the geometry of the problem has already been defined in the previous steps, all that is required is to detailthe structural variables.

1. Switch Element Type Preprocessor > Element Type > Switch Elem Type

Choose Thermal to Struc from the scoll down list.




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This will switch to the complimentary structural element automatically. In this case it is LINK 8.For more information on this element, see the help file. A warning saying you should modify thenew element as necessary will pop up. In this case, only the material properties need to be modifiedas the geometry is staying the same.

2. 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: 200e9


Preprocessor > Material Props > Material Models > Structural > Thermal Expansion Coef >Isotropic

i. ALPX: 12e-6

3. Write Environment The structural environment is now fully described.Preprocessor > Physics > Environment > Write

In the window that appears, enter the TITLE Struct


1. Define Analysis Type Solution > Analysis Type > New Analysis > StaticANTYPE,0

2. Read in the Thermal Environment Solution > Physics > Environment > Read

Choose thermal and click OK.




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If the Physics option is not available under Solution, click Unabridged Menu at the bottom of theSolution menu. This should make it visible.

3. Apply Constraints Solution > Define Loads > Apply > Thermal > Temperature > On Keypoints

Set the temperature of Keypoint 1, the left-most point, to 348 Kelvin.


5. Close the Solution Menu Main Menu > Finish

It is very important to click Finish as it closes that environment and allows a new one to be openedwithout contamination. If this is not done, you will get error messages.

The thermal solution has now been obtained. If you plot the steady-state temperature on the link, you willsee it is a uniform 348 K, as expected. This information is saved in a file labelled Jobname.rth , were .rthis the thermal results file. Since the jobname wasn't changed at the beginning of the analysis, this data can

be found as file.rth . We will use these results in determing the structural effects.

6. Read in the Structural Environment Solution > Physics > Environment > Read

Choose struct and click OK.

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

Fix Keypoint 1 for all DOF's and Keypoint 2 in the UX direction.




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8. Include Thermal Effects Solution > Define Loads > Apply > Structural > Temperature > From Therm Analy

As shown below, enter the file name File.rth . This couples the results from the solution of thethermal environment to the information prescribed in the structural environment and uses it duringthe analysis.

9. Define Reference Temperature Preprocessor > Loads > Define Loads > Settings > Reference Temp

For this example set the reference temperature to 273 degrees Kelvin.



1. Hand Calculations Hand calculations were performed to verify the solution found using ANSYS:




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The following list should appear. Note the stress in each element: -0.180e9 Pa, or 180 MPa incompression as expected.


The above example was solved using a mixture of the Graphical User Interface (or GUI) and the commandlanguage interface of ANSYS. This problem has also been solved using the ANSYS command languageinterface that you may want to browse. Open the .HTML version, copy and paste the code into Notepad or asimilar text editor and save it to your computer. Now go to 'File > Read input from...' and select the file.A .PDF version is also available for printing.




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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 modelmeshed with p-elements. The p-method manipulates the polynomial level (p-level) of the finite element shapefunctions which are used to approximate the real solution. Thus, rather than increasing mesh density, the p-levelcan be increased to give a similar result. By keeping mesh density rather coarse, computational time can be keptto 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 modeledas steel with a modulus of elasticity of 200 GPa.


1. Give example a Title Utility Menu > File > Change Title .../title, P-Method Meshing

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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.


For this problem we will use the PLANE145 (p-Elements 2D Quad) element. This element haseight 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.

10 (55,48)

11 (45,48)

12 (20,0)




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

Other types of p-elements exist in the ANSYS library. These include Solid127 and Solid128 whichhave 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 helpfile.


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.


In the window that appears, enter the following geometric properties for steel:i. Young's modulus EX: 200000


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

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

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


1. Define Analysis Type Solution > Analysis Type > New Analysis > Static




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ANTYPE,0

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

The following window will pop up.

A) Set Time at end of loadstep to 1 and Automatic time stepping to ONB) 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

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

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

4. 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.




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1. Read in the Last Data Set 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




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As one can see from the two plots, the mesh density had to be increased by 5 times to get theaccuracy that the p-elements delivered. This is the benefit of using p-elements. You can use a meshthat is relatively coarse, thus computational time will be low, and still get reasonable results.However, care should be taken using p-elements as they can sometimes give poor results or take along time to converge.






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3. Create Rectangle Preprocessor > Modeling > Create > Areas > Rectangle > By 2 Corners

Fill in the window with the following dimensions:WP X = 0WP Y = 0

Width = 0.03Height = 0.03

BLC4,0,0,0.03,0.03


For this example, we will use PLANE55 (Thermal Solid, Quad 4node 55). This element has 4nodes and a single DOF (temperature) at each node. PLANE55 can only be used for 2 dimensionalsteady-state or transient thermal analysis.

5. Define Element Material Properties Preprocessor > Material Props > Material Models > Thermal > Conductivity > IsotropicIn the window that appears, enter the following properties:

i. Thermal Conductivity KXX: 1.8

Preprocessor > Material Props > Material Models > Thermal > Specific HeatIn the window that appears, enter the following properties:

i. Specific Heat C: 2040

Preprocessor > Material Props > Material Models > Thermal > DensityIn the window that appears, enter the following properties:

i. Density DENS: 920

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

For this example we will use an element edge length of 0.0005m.

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


1. Define Analysis Type Solution > Analysis Type > New Analysis > Transient

The window shown below will pop up. We will use the defaults, so click OK.

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ANTYPE,4

2. Turn on Newton-Raphson solver Due to a glitch in the ANSYS software, there is no apparent way to do this with the graphical userinterface. Therefore, you must type NROPT,FULL into the commmand line. This step is necessaryas element killing can only be done when the N-R solver has been used.

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

The following window will pop up.

A) Set Time at end of loadstep to 60 and Automatic time stepping to OFF.




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B) Set Number of substeps to 20.C) Set the Frequency to Write every substep.

Click on the NonLinear tab at the top and fill it in as shown

D) Set Line search to ON .E) Set the Maximum number of iterations to 100.

For a complete description of what these options do, refer to the help file. Basically, the time at theend of the load step is how long the transient analysis will run and the number of substeps defineshow the load is broken up. By writing the data at every step, you can create animations over timeand the other options help the problem converge quickly.

4. Apply Initial Conditions Solution > Define Loads > Apply > Initial Condit'n > Define > Pick All

Fill in the IC window as follows to set the initial temperature of the material to 268 K:

5. Apply Boundary Conditions




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For thermal problems, constraints can be in the form of Temperature, Heat Flow, Convection, Heat Flux,Heat Generation, or Radiation. In this example, all external surfaces of the material will be subject toconvection with a coefficient of 10 W/m^2*K and a surrounding temperature of 368 K.

Solution > Define Loads > Apply > Thermal > Convection > On Lines > Pick All

Fill in the pop-up window as follows, with a film coefficient of 10 and a bulk temperature of 368.

The model should now look as follows:




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Solve the System Solution > Solve > Current LSSOLVE

Postprocessing: Prepare for Element Death 1. Read Results

General Postproc > Read Results > Last SetSET,LAST

2. Create Element Table

Element death can be used in various ways. For instance, the user can manually kill, or turn off, elementsto create the desired effect. Here, we will use data from the analysis to kill the necessary elements tomodel melting. Assume the material melts at 273 K. We must create an element table containing the

temperature of all the elements.

From the General Postprocessor menu select Element Table > Define Table...

Click on 'Add...'

Fill the window in as shown below, with a title Melty and select DOF solution > TemperatureTEMP and click OK.

We can now select elements from this table in the temperature range we desire.

3. Select Elements to Kill

Assume that the melting temperature is 273 K, thus any element with a temperature of 273 or greatermust be killed to simulate melting.

Utility Menu > Select > Entities

Use the scroll down menus to select Elements > By Results > From Full and click OK.




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Ensure the element table Melty is selected and enter a VMIN value of 273 as shown.

Solution Phase: Killing Elements

1. Restart the Analysis Solution > Analysis Type > Restart > OK

You will likely have two messages pop up at this point. Click OK to restart the analysis, and close thewarning message. The reason for the warning is ANSYS defaults to a multi-frame restart, which thisanalysis doesn't call for, thus it is just warning the user.

2. Kill Elements




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The easiest way to do this is to type ekill,all into the command line. Since all elements above meltingtemperature had been selected, this will kill only those elements.

The other option is to use Solution > Load Step Opts > Other > Birth & Death > Kill Elements andgraphically pick all the melted elements. This is much too time consuming in this case.

Postprocessing: Viewing Results

1. Select Live Elements Utility Menu > Select > Entities

Fill in the window as shown with Elements > Live Elem's > Unselect and click Sele All.

With the window still open, select Elements > Live Elem's > From Full and click OK.




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2. View Results General Postproc > Plot Results > Contour Plot > Nodal Solu > DOF solution > TemperatureTEMP

The final melted shape should look as follows:




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This procedure can be programmed in a loop, using command line code, to more accurately modelelement death over time. Rather than running the analysis for a time of 60 and killing any elements abovemelting temperature at the end, a check can be done after each substep to see if any elements are abovethe specified temperature and be killed at that point. That way, the prescribed convection can then act onthe elements below those killed, more accurately modelling the heating process.




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