Design Optimization Tutorial

8/11/2019 Design Optimization Tutorial

1/13


www.csa.ru/CSA/CADS/docs/ansys/tut2/optimization.html 1/13

Tutorial Application of Design Optimization

Probl em Description

Two 1000N point loads will be applied perpendicularly in the middle of two different faces of a rectangular solid steel beam. It is necessary to find the cross sectional dimensions of the beam in order to minimize the weight of the beam.

The maximum stress anywhere in the beam cannot exceed 200 MPa. The beam is to be made of steel with a modulusof elasticity = 200 MPa.

Tutorial Goals

The purpose of this tutorial is to introduce a method of solving design optimization problems using ANSYS. This willinvolve creating a command file utilizing parameters for all the variables in the problem, deciding which variables to useas design, state and objective variables and setting the correct tolerances for the problem to obtain an accuratelyconverged solution in a minimal amount of time.

Figure 1: Problem Description

Table of Contents

Preprocessor: Defining the Problem

Entering Initial Guesses for Variables
http://-/?-http://-/?-http://-/?-


2/13



Element TypeElement Geometric PropertiesElement Material Properties

NodesElementsMeshingPlotting ElementsSaving Your Job

Solution

Analysis TypeConstraintsLoadingSolving the System

Postprocessing: Viewing the Results

Extracting Information as Parameters

Design Optimization

Writing the Command FileAssigning the Command File to the OptimizationDefining Variables and TolerancesDefining the Optimization Method

Running the OptimizationViewing the Results of an Optimization Problem

Problem Solution

Preprocessor: Defining the Problem

Entering Initial Guesses for Variables:

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

1. From the Parameters section of the Utility Menu, select the Scalar Parameters option.2. In the window that appears, in the Selection section, type in W=203. Click Accept or press Enter.4. In the Selection section, also type in H=30.5. Click Accept or press Enter.6. Click Close in the Scalar Parameters window.

Element Type:
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


3/13



Within ANSYS there are numerous predefined elements that have constant uniaxial properties. These elements allowthe user to solve even complicated 3D structures using only points to define vertices and lines connecting the points for elements.

Proper care must be taken when selecting element types. Some elements have only enough degrees of freedom(DOFs) at their vertices to only permit 2D structures. Other elements have additional constants to define such

properties as spring constants. Choosing the correct element type will simplify the information that the user will need tosupply but also increase the speed of finding the necessary solution.

For this problem we will use the BEAM4 element. This element has 6 degrees of freedom (translation along the X, Yand Z axiss, and rotation about the X,Y and Z axiss). With 6 degrees of freedom, the BEAM4 element can be usedin 3D analysis.

1. Select 'Element Type' in the 'Preprocessor' menu.2. Select 'Add/Edit/Delete...'3. Click on the 'Add...' button in the 'Element Types' window.4. Under the 'Structural Mass' section, in the middle of the dialog box, Select Beam.5. Then in the next box to the right, select 3D Elastic 4. This specifies an elastic straight beam element.6. Finally click on OK You should see Type 1 BEAM4 in the 'Element Types' window.7. Click on 'Close' in the 'Element Types' dialog box.8. Close the 'Element Type' menu.

Element Geometric Properties:

Each type of element has its own set of constants defining such things as geometry and initial loading of each elementtype.

1. Select 'Real Constants...' in the 'Preprocessor' menu.

2. Click on 'Add...'3. Select 'Type 1 BEAM4' (actually it is already selected). Click on 'OK'.4. In the 'Real Constants for BEAM4 window, enter the following geometric properties:

a. Cross-sectional area AREA: W*H b. Area moment of inertia IZZ: W*H*H*H/12c. Area moment of inertia IYY: H*W*W*W/12d. Thickness along Z axis TKZ: We. Thickness along Y axis TKY: H

5. Click 'OK'6. Click on 'Close' in the 'Real Constants' window.

NOTE: It is important to use independent variables to define dependent variables such as the moment of inertia.During the optimization, the width and height will change for each iteration. As a result, the other variables must bedefined in relation to the width and height in order to be correct for each iteration.

Element Material Properties:

You then need to specify material properties:

1. Select 'Material Props' in the 'Preprocessor' menu.


4/13



2. Select 'Isotropic...' under '-Constant-'3. Click 'OK' in the 'Isotropic Material Properties' window to select material number 1.4. In the window that appears, there are many properties that may be specified. We are going to give the

properties of Steel. Change the following field:a. Young's modulus EX: 200000

5. Click on 'OK'.6. Close the 'Material Props' menu.

Nodes:

The overall geometry is defined in ANSYS using nodes which specify various principal coordinates to define the body.

1. Start the preprocessor by selecting 'Preprocessor' in the 'ANSYS Main Menu'.2. From the 'Preprocessor' menu, select 'Create' (under the '-Modeling-' title).3. Then select 'Nodes' from this 'Create' menu.4. Select 'In Active CS...' on the 'Nodes' menu. This permits you to define nodes in the active Coordinate System.5. We are going to define 3 nodes for this beam as given in the following table (the second node is necessary to

define as the location where the forces act):

Node Coordinates (x,y,z)

1 (0,0,0)

2 (500,0,0)

3 (1000,0,0)

Elements:

1. First close the last menu that was used to create the nodes by double clicking in the upper left-hand corner of the Nodes menu'. This will return you to the 'Create menu'.

2. Select the Elements item.3. We will first define the pipe elements. Click Elem Attributes.4. In the Element Attributes window, ensure that the Element type number, TYPE = 1, the Material number,

MAT = 1 and the Real constant set no., REAL = 1.5. Select Auto Numbered Thru Nodes.6. Enter the numbers from the Node #1 and #2 columns in the following table into the ANSYS Input table. You

must press enter once after Node #1 and twice after Node #2.

Element Node #1 Node#2

1 1 2

2 2 3

1. Click OK in the Elements from Nodes window.

Meshing:

Because we have defined our model using nodes and elements, we do not need to mesh our model. If we initially


5/13



defined our model using keypoints and lines, we would have had to create elements in our model by meshing the lines.ANSYS can only solve models consisting of elements.

Plotting Elements:

1. Select 'Numbering' in the 'PlotCtrls' Menu.2. Turn off Keypoint numbering so that the plot does not become confusing.3. Click on the 'Elem & Attrib numbering' box, and select 'Element numbers'.4. Click on 'OK'.5. From the 'Plot' menu, select 'Elements' and you will then see the elements plotted in multiple colours, with their

element numbers.

Figure 2: Model in ANSYS

Saving Your Job:

Save the model at this time, so if you make some mistakes later on, you will at least be able to come back to this point. To do this, select 'Utility Menu Bar'/'File'/'Save As Jobname.db'. Your model will be saved in a file called'jobname.db', where 'jobname' is the name that you specified in the 'Launcher' when you first started ANSYS.


6/13



It is a good idea to save your job at different times throughout the building and analysis of the model to backup your work in case of a system crash or what have you.

Solution

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

of equations.

Close the 'Preprocessor' menu and open up the 'Solution' menu (from the same 'ANSYS Main Menu').

Analysis Type:

First you must tell ANSYS how you want it to solve this problem:

1. Select 'New Analysis'.2. Ensure that 'Static' is selected; i.e. you are going to do a static analysis on the frame as opposed to a dynamic

analysis, for example.3. Click 'OK'.

Now you must apply some loads and constraints:

Constraints:

It is necessary to apply constraints to the model otherwise the model is not tied down or grounded and a singular solution will result. In mechanical structures, these constraints will typically be fixed, pinned and roller-typeconnections.

1. Select 'Apply >' under '-Loads-' title.2. We will start with constraints, so select 'Displacement >' under the '-Structural-' title.3. Select 'On Nodes' for this example. As you recall, these nodes were defined at the vertices and the midpoint of

the beam.4. Use the mouse to pick the first node defined (just above the x,y,z triad)5. Click on 'Apply' in the 'Apply U,ROT' window.6. Now we select what degrees of freedom are to be constrained. In this example, we will pin this location which

means that all translational DOF's are constrained.7. Select 'UX', 'UY' and 'UZ' by clicking on them.8. Enter '0' in the Value field and click on 'APPLY'.9. You will see some blue triangles in the graphics window indicating the displacement constraints.

10. For the next constraint, we will pick the node at the other end of the beam and constrain that point to only theUY and UZ direction.

11. Follow Steps 4 to 9 but for Step 7 only select UY and UZ.12. Make sure that the value field is still set to '0'.13. Select 'OK'14. Note the blue triangles at these points indicating their fixed directions.15. Close the 'Displacement' menu.

Note: Different element types have different constraints that can be applied to them. Refer to the element manual in


7/13



the ANSYS help file for specific details on any element type.

Loading:

It's time to apply some loads. We will apply a vertical point load of 5000N at node #7.

1. If you still have the 'Apply' menu open, select Force/Moment >. (If you don't have 'Apply' open, its under '-Loads-' in the 'Solution' menu.)

2. Choose On Nodes3. Click node #2 in the Graphics Window.4. Click on OK in the 'Apply F/M' window.5. In the next dialog box to appear:6. Click on the button at the top and select FY. This indicates that we will be applying the load in the 'y' direction.7. Enter a value of "-1000" in the box below.8. Click on 'Apply'. The force will appear in the graphics window as a red arrow.9. Click node #2 in the Graphics Window.

10. Click on OK in the 'Apply F/M' window.11. In the next dialog box to appear:12. Click on the button at the top and select FZ. This indicates that we will be applying a load in the 'z' direction.13. Enter a value of "1000" in the box below.14. Close the 'Force/Moment' menu and the 'Apply' menu.

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

Note: To have the constraints and loads appear each time you select Replot in the Plot section of the UtilityMenu, you must change some settings in Symbols under the PlotCtrls section of the Utility Menu. In thewindow that appears when you select Symbols', click Applied B.C.s in the Boundary Condition Symbol section.


8/13


9/13



height variables. We will do this using element tables and the GET command.

1. Select General Postproc from the ANSYS Main Menu.2. Type the following lines in the ANSYS Input window. Each line is to be followed by Enter.

ETABLE,evol,VOLU,ssum*GET,vsum,SSUM, ,ITEM,EVOLETABLE,stress,nmisc,1ESORT,ETAB,STRESS,0,0, ,*GET,STR,SORT, ,max

To see the values of the parameters that we defined select Scalar Parameters from the Parameters section of theUtility Menu. Based on the initial values of W=20 and H=30 we should see the volume equal 600000 mm^3 andmaximum stress equal 208.3 MPa (much too high).

Design Optimization

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

Writing the Command File:

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

1. From the File section of the Utility Menu select Write DB Log File.2. In the window that appears type a name for the command file such as optimize.txt.3. Click OK.

If you open the command file in a text editor such as Notepad, it should like this:

/PREP7w=20h=30

ET,1,BEAM4

R,1,w*h,w*h*h*h/12,h*w*w*w/12,w,h, ,

UIMP,1,EX, , ,200000

N,1,0,0,0 N,2,500,0,0 N,3,1000,0,0E,1,2E,2,3


10/13



/SOLUD,1,UX,0D,1,UY,0D,1,UZ,0D,3,UY,0D,3,UZ,0F,2,FY,-100000F,2,FZ,1000SOLVE

/POST1ETABLE,evol,VOLUssum*GET,vsum,SSUM, ,ITEM,EVOLETABLE,stress,nmisc,1ESORT,ETAB,STRESS,0,0*GET,STR,SORT,,maxFINISH

Assigning the Command File to the Optimization:

1. From the ANSYS main menu select Design Opt >2. In the Design Opt menu select -Analysis File- Assign.3. In the file list that appears, select the filename that we created when we wrote the command file.4. Click OK.

Defining Variables and Tolerances:

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

beam which is directly related to the weight of the beam.

ANSYS categorizes three types of variables for design optimization:

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

problem.2. State Variables (SVs) Dependent variables that change as a result of changing the DVs. These variables are

necessary to constrain 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 the weight to zerowhich is not a useful result.

3. Objective Variable (OV) The objective variable is the one variable in the optimization that needs to beminimized. In our problem, we will be minimizing the volume of the beam.

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

Now that we have decided our design variables, we need to define ranges and tolerances for each variable. For thewidth and height, we will select a range of 20 to 30 mm for each. Because a small change in either the width or height


11/13



has a profound effect on the volume of the beam, we will select a tolerance of 0.001mm. Tolerances are necessary inthat they tell ANSYS the largest amount of change that a variable can experience before convergence of the problem.

For the stress variable, we will select a range of 190 to 200 MPa with a tolerance of 0.001MPa. Because the volumevariable is the objective variable, we do not need to define an allowable range. We will set the tolerance to 200mm3.This tolerance was chosen because it is significantly smaller than the initial magnitude of the volume of 600000mm3(20mm x 30mm x 1000mm).

To define the design variables in ANSYS:

1. Click Design Variables from the Design Opt menu.2. In the Design Variables window click Add.3. Click on H in the Parameter Name section.4. Enter: Minimum Value (MIN = 20)

Maximum Value (MAX = 30)Convergence Tolerance (TOLER = 0.001)

5. Click Apply6. Click on W in the Parameter Name section.7. Enter: Minimum Value (MIN = 20)

Maximum Value (MAX = 30)Convergence Tolerance (TOLER = 0.001)

8. Click OK9. Click Close on the Design Variables window.

To define the state variables:

1. Click State Variables from the Design Opt menu.

2. In the State Variables window click Add.3. Click on STR in the Parameter Name section.4. Enter: Lower Limit (MIN = 190)

Upper Limit (MAX = 200)Feasibility Tolerance (TOLER = 0.001)

5. Click OK6. Click Close on the State Variables window.

To define the objective variable:

1. Click Objective from the Design Opt menu.2. Click on VSUM in the Parameter Name section.3. For the Convergence Tolerance, enter 200.4. Click OK

Defining the Optimization Method:

There are several different methods that ANSYS can use to solve an optimization problem. To ensure that you are notfinding a solution at a local minimum, it is advisable to use different solution methods. If you have trouble with getting a

particular problem to converge it would be a good idea to try a different method of solution to see what might be


12/13


13/13


Figure 4: Plot of Graph

You can plot graphs of the other variables in the design by following the above steps. Instead of using width and heightfor the y-axis label and variables, use whichever variable is necessary to plot.

Design Optimization Tutorial

Documents

Transcript of Design Optimization Tutorial

Tutorial: Robustness and Optimization

Mathematica Tutorial: Unconstrained Optimization

Optimization of Submodular Functions Tutorial - lecture Ijvondrak/data/submod-tutorial-1.pdf · Optimization of Submodular Functions Tutorial - lecture I Jan Vondrák1 1IBM Almaden

A Tutorial on Bayesian Optimization - arxiv.org · A Tutorial on Bayesian Optimization Peter I. Frazier ... Bayesian optimization (BayesOpt) is a class of machine-learning-based optimization

A Tutorial on Evolutionary Multiobjective Optimization

ANSYS Tutorial Design Optimization

Tutorial on Neural Network Optimization Problems

Tutorial: Topology Optimization and Result Comparison

Mathematica Tutorial: Constrained Optimization - Wolfram Research

Vivado Design Suite Tutorial - xilinx.com€¦ · Locating Tutorial Design Files 1. Download the reference design files from the Xilinx website: ug997-vivado-power-analysis-optimization-tutorial.zip

Vivado Design Suite Tutorial - Xilinx...Using a matrix multiplier example, this tutorial reviews two-design optimization techniques. The first lab explains how design can be pipelined,

CS4234: Optimization Algorithms Tutorial Week 12: Game Day ...gilbert/CS4234/2015/tutorial/Week12… · CS4234: Optimization Algorithms Nov. 5, 2015 Tutorial Week 12: Game Day Slither

Tutorial Composite Optimization MG1

A Tutorial on Adaptive Design Optimization€¦ · A Tutorial on Adaptive Design Optimization Jay I. Myung a, Daniel R. Cavagnarob, and Mark A ... is intended to serve as a practical

Vivado Power Analysis Optimization Tutorial

Connecting Rod Shape Optimization Tutorial (AutoDesign)...Connecting Rod Shape Optimization This tutorials deal with the shape optimization design problem. Design target is a connecting

Vivado Design Suite Tutorial - origin.xilinx.comPower Analysis and Optimization Tutorial Power Analysis and Optimization 6 UG997 (v2017.1) April 5, 2017 Hardware Requirements Supported

Vivado Design Suite Tutorial - Xilinx...Locating Tutorial Design Files 1. Download the reference design files from the Xilinx website: ug997-vivado-power-analysis-optimization-tutorial.zip

SLAS2019 Tutorial: Coupling Assay Design And Process … · 1 © 2019 Artel © 2013 ARTEL SLAS2019 Tutorial: Coupling Assay Design And Process Optimization Toward Minimizing Variability

Vivado Design Suite Tutorial - Xilinx · 2020. 9. 8. · Tutorial Description High-Level Synthesis 7 UG871 (v 2013.4) December 20, 2013 Design Optimization Using a matrix multiplier