WORKSHOP 13- BAR TRUSS OPTIMIZATION SUBJECT TO STATIC LOADINGSubcase 1X: -16,000 lbsY: -12,000 lbsSubcase 2X: 16,000 lbsY: -12,000 lbsnDesign Model DescriptionuObjective Function: Weight minimizationuDesign Variables: Cross-sectional area A1 and A2uConstraints:Stress Allowable: 20 ksi tension15 ksi compressionDisplacement at grid 4:X direction 0.2 inY direction 0.2 innSuggested Exercise Steps1.Open a new database and call it wkshp1.db.2.Turn on all the labels and select front view.3.Create new nodes for the model.4.Create bar elements from the previous nodes5.Make a new material called alum and sets its properties.6.Create a 1-D rod with property set named prop_1 and sets its material property to alum with area of 1.7.Create another 1-D rod with property set named prop_2 and sets its material property to alum with area of 2.8.Under Loads/BCs, create a new nodal displacement called disp_1 and sets its translation and rotation parameters.9.Create another nodal displacement called disp_2 and sets its parameters.10.Create a nodal force called force_1 and sets its force property and application region.11.Create another force called force_2 and sets its force properties and application region.12.Create a load case called case_1 and sets its properties.13.Create another load case called case_2 and sets its displacement and force properties.14.Create design variables using 1-D rod with prop_1 and prop_2 and associated areas.15.Create design objective from the design study pre-processing tools.16.Create design constraints on X displacement, Y displacement, and axial stress.nSuggested Exercise Steps17.Create a design study called opt_1 by including design variables, objectives and constraints.18.Review the design study contents using the Design Study Summary option.19.Create an input file for optimization Set necessary parameters.20.Select the existing design study and global objective.21.Create the subcases by including desired constraints. Select subcase for the job. Generate the analysis Bulk Data file: wkshp1.bdf22.Compare wkshp1.bdf with the sample input file.23.Compare wkshp1.bdf with the sample input file (contd).24.Compare wkshp1.bdf with the sample intput file (contd).25.Submit the wkshp1.bdf for Nastran analysis and check for errors.26.Compare the results with the sample output. 27.In Patran, read the result file using Nastrans generated file, wkshp1.op2.28.Plot the Design Variable History on the XY plot.29.Plot the Objective Function History on the XY plot.30.Plot the Maximum Constraint History on the XY plot.31.Quit MSC.Patran.Figure 1.2 Constraints and Applied Forces (Case 1)Figure 1.3 Constraints and Applied Forces (Case 2)1231234XYZFigure 1.1 Geometry and Finite ElementsTable 1.1 Material PropertiesStep 1. Create a New DatabaseOpen database.a.File / New.b.Enter wkshp1 for File Name.c.Click OK.d.Under New Model Preferences, select Based on Model Tolerance.e.Select MSC.NASTRAN for Analysis Code.f.Select Structural for Analysis Type.g.OK.agfedbcStep 2. Show All LabelsShow labels and change the view to front view.a.Show all entity labelsb.Front viewWhenever possible, deselect Auto Execute option.baStep 3. Create New NodesCreate new nodesa.Elementsb.Create/Node/Editc.Deselect Associate with Geometryd.Enter -10 0 0 for Node Location Liste.ApplyRepeat the same steps a c with 0 0 0 for Node Location Listand click ApplyRepeat the same steps a c with 10 0 0 for Node Location List and click ApplyRepeat the same steps a c with 0 -10 0 for Node Location List and click Apply bcdezaStep 4. Create barsCreate barsa.Elementsb.Create/Element/Editc.Select Bar for Shaped.Select Node 1 from the viewport for Node 1 =e.Enter Node 4 from the viewport for Node 2 =f.ApplyRepeat steps a c with: Node 2 for Node 1 =Node 4 for Node 2 = and click Apply.Repeat steps a c with:Node 3 for Node 1 =Node 4 for Node 2 = and click Apply. zbcedfaStep 5. Create and Define the Materials propertiesDefine a material using the specified modulus of elasticity and allowable stresses.a.Materialsb.Create/Isotropic/Manual Inputc.Enter alum for Material Named.Input Propertiese.Enter 10e6 for Elastic Modulus =f.Enter 0.3 for Poisson Ratio =g.Enter 0.1 for Density =h.OKi.ApplybcdefghiaStep 6. Create a 1-D Rod and Set its PropertiesCreate a 1D rod with aluminum properties.a.Propertiesb.Create/1D/Rodc.Enter prop_1 for Property Set Named.Input Propertiese.Select alum in the Select Material databox for Material Name.f.Enter 1 for Areag.OKh.For Select Members, click on Beam Element iconand select rod elements 1 and 3 from the view port.i.Addj.ApplyefgbcdhijaStep 7. Create another Rod and Set its PropertiesCreate another property with the new input properties.a.Propertiesb.Create/1D/Rodc.Enter prop_2 for Property Set Named.Input Propertiese.Select alum in the Select Material databox for Material Name.f.Enter 2 for the Area g.OKh.For Select Members, click on Beam Element iconand select Elm 2 for Select Membersi.Addj.ApplybcdhijefgaStep 8. Create a Load/BC Create a nodal displacement called disp_1.a.Loads/BCsb.Create / Displacement / Nodal.c.Enter disp_1 for New Set Named.Input Datae.Enter for Translations f.Enter for Rotations g.OKh.Select Application Regionsi.Select FEM under Geometry Filterj.Drag the mouse to select Node 1, Node 2, and Node 3 from the viewport for Select Nodesk.Addl.OKm.ApplymlkjihgfedcbaStep 9. Create a Load/BC (Cont.)Create another nodal displacement called disp_2.a.Loads/BCsb.Create / Displacement / Nodal.c.Enter disp_2 for New Set Named.Input Datae.Enter for Translations f.Enter for Rotations g.OKh.Select Application Regionsi.Select FEM under Geometry Filterj.Select Node 4 from the viewport for Select Nodesk.Addl.OKm.ApplymlkjihgfedcbaStep 10. Apply Forces on X and YCreate a new nodal force called force_1.a.Loads/BCsb.Create/Force/Nodalc.Enter force_1 for New Set Named.Input Datae.Enter for Force f.OKg.Select Application Regionh.Select FEM under Geometry Filteri.Select Node 4 from the viewport for Select Nodesj.Addk.OKl.ApplykjihgfedcblaStep 11. Apply Forces on X and Y (Cont.)Create another nodal force called force_2.a.Loads/BCsb.Create/Force/Nodalc.Enter force_2 for New Set Named.Input Datae.Enter for Force f.OKg.Select Application Regionh.Select FEM under Geometry Filteri.Select Node 4 from the viewport for Select Nodesj.Addk.OKl.ApplykjihgfedcblaStep 12. Create Load CasesCreate a new Load Case called case_1.a.Load Cases.b.Createc.Enter case_1 as Load Case Named.Input Datae.Under Select Individual Loads/BCs databox, select Displ_disp_1Displ_disp_2Force_force_1f.OKg.ApplygfedcbaStep 13. Create Load Cases (Cont.) Create another Load Case called case_2.a.Load Cases.b.Createc.Enter case_2 as Load Case Named.Input Datae.Under Select Individual Loads/BCs databox, select Displ_disp_1Displ_disp_2Force_force_2f.OKg.ApplyNote: The viewport stays the same.gfedcbaStep 14. Create Design Variable from ToolsUse Tools to create the Design Variables for the model.a.Tools/Design Study/Pre-Processb.Create/Design Variable/Propertyc.Select 1D for Dimensionsd.Select Rod for Typee.Select prop_1 from Select Property Set databoxf.Select Area from Select Property Name databoxg.ApplyagfedcbStep 14a. Create Design Variable from Tools (Cont.)gfedcbUse Tools to create the Design Variables for the model.a.Tools/Design Study/Pre-Processb.Create/Design Variable/Propertyc.Select 1D for Dimensionsd.Select Rod for Typee.Select prop_2 from Select Property Set databoxf.Select Area from Select Property Name databoxg.Applyh.ClosehaStep 15. Create Design Objective from ToolsCreate Objective for the Design Study.a.Tools/Design Study/Pre-Processb.Create / Objectivec.Select Global as the Solution.d.Select Weight as the Response.e.Enter Total_Weight as the Objective Namef.Select minimize under Min/Max selection box.g.ApplyedcbfgaStep 16. Create Design Constraints from Tools (Cont.)Create Design Constraints for the Design Studya.Tools/Design Study/Pre-Processb.Create /Constraintc.DISP_1 for Constraint Named.Select Node 4 for Select Node e.Select TX option under Displacement Componentf.Enter 0.2 for Lower Boundg.Enter 0.2 for Upper Boundh.Applyi.DISP_2 for Constraint Namej.Select Node 4 for Select Node k.Select TY option under Displacement Componentl.Enter 0.2 for Lower Boundm.Enter 0.2 for Upper Boundn.ApplyahfdcbigjklmenStep 16a. Create Design Constraints from Tools (Cont.)Create Stress Constraints for the Design Studya.Tools/Design Study/Pre-Processb.Create/Constraintc.Select Stress for the Response.d.STRESS_1 for Constraint Namee.Select FEM under Constraint Regionf.Select 1Dg.Select Rod h.Under Select Finite Element, drag your mouse to select Element 1, Element 2, and Element 3 from the viewporti.For Select Component, select Axialj.Enter 15000 for Lower Bound input box.k.Enter 20000 for Upper Bound input boxl.ApplyagfedcbihjklStep 17. Create Design Study from ToolsCreate Design Study and set its properties.a.Tools/Design Study/Pre-Processb.Create / Design Studyc.Enter opt_1 for Design Study Named.Select Design Variablese.For prop_1_Area, enter 0.1 under Lower Bound and press Enter, and 100 under Upper Bound and press Enter forf.For prop_2_Area, enter 0.1 under Lower Bound and press Enter, and 100 under Upper Bound and press Enter forg.OKh.Select Objectivei.Select Total_Weight for the studyj.Closek.Select Constraintsl.Select desired constraints (all of them for this study).m.Closen.ApplyfedcbagijlnmhkStep 18. Design Study Summary From ToolsReview contents in a Design Study.a.Tools/Design Study/Pre-Processb.Summary / Design Studyc.Select opt_1 from Design Study Listboxd.Review various contents of the design study.e.ClosedcbaeStep 19a. Create an Input File for Analysis Translation ParametersGenerate an input file and sets its parameters for analysis.a.Analysisb.Optimize/Entire Model/Analysis Deckc.Enter wkshp1 for Job Named.Translation Parameterse.For Data Output, select OP2 and Printf.For MSC.Nastran Version, enter 2005g.OKagfedcbStep 19b. Create an Input File for Analysis Optimization Parameters Generate an input file and set its parameters for analysis (Cont.)a.Optimization Parametersb.Enter 10 for Maximum Number of Standard Design Cycles (DESMAX) =c.Enter 1 for Print Design Data (P1) every n-th cycle where n=d.Enter 1 for Print Analysis Results(NASPRT) every n-th cycle where n =e.OKaedcbStep 20a. Create an Input File for Analysis Design Study SelectabSelect the Design Studya.Design Study Selectb.Select opt_1Step 20b. Create an Input File for Analysis Global Objective SelectacbSelect a Global Objective a.Global Objective Selectb.Select Total_WeightStep 21a. Create an Input File for Analysis Subcase CreateSelect constraintsa.Subcasesb.Select case_1 from the Available Subcasesc.Select Constraints/Objectived.Select Constraintse.Select all of the existing constraints. f.OKg.Applyh.Select case_2 from the Available Subcasesi.Repeat steps c.-g. for case_2.j.Cancel adcbfeghijStep 21b. Create an Input File for Analysis Subcase SelectGenerate an input file and sets its parameters for analysisa.Subcase Selectb.Select 101 LINEAR STATIC for Solution Typec.Under Subcases Available, select case_1 and case_2d.OKe.ApplyAn MSC.Nastran input file called wkshp1.bdf will be generated. This process of translating your model into an input file is called the Forward Translation. The Forward Translation is complete when the Heartbeat turns green. MSC.Nastran users should proceed to the next step. aedcbeStep 22. Generated Input FileLook for the generated input file named wkshp1.bdf. It should be similar to the output below.SOL 200TIME 600$ Direct Text Input for Executive ControlCENDTITLE = MSC.Nastran job created on 25-Apr-05 at 13:06:35ECHO = NONEMAXLINES = 999999999DESOBJ(MIN) = 1ANALYSIS = STATICS$ Direct Text Input for Global Case Control DataSUBCASE 1$ Subcase name : case_1 SUBTITLE=case_1 SPC = 2 LOAD = 2 DISPLACEMENT(SORT1,REAL)=ALL SPCFORCES(SORT1,REAL)=ALL STRESS(SORT1,REAL,VONMISES,BILIN)=ALL DESSUB = 21$ Direct Text Input for this SubcaseSUBCASE 2$ Subcase name : case_2 SUBTITLE=case_2 SPC = 2 LOAD = 4 DISPLACEMENT(SORT1,REAL)=ALL SPCFORCES(SORT1,REAL)=ALL STRESS(SORT1,REAL,VONMISES,BILIN)=ALL DESSUB = 22$ Direct Text Input for this SubcaseBEGIN BULKPARAM POST -1PARAM PRTMAXIM YESPARAM NASPRT 1$ Direct Text Input for Bulk Data$ Elements and Element Properties for region : prop_1PROD 1 1 1.Step 23. Generated Input File (Cont.)$ Pset: prop_1 will be imported as: prod.1CROD 1 1 1 4CROD 3 1 3 4$ Elements and Element Properties for region : prop_2PROD 2 1 2.$ Pset: prop_2 will be imported as: prod.2CROD 2 2 2 4$ Referenced Material Records$ Material Record : alum$ Description of Material : Date: 25-Apr-05 Time: 08:32:04MAT1 1 1.+7 .3 .101$ Nodes of the Entire ModelGRID 1 -10. 0. 0.GRID 2 0. 0. 0.GRID 3 10. 0. 0.GRID 4 0. -10. 0.$ Loads for Load Case : case_1SPCADD 2 4 6LOAD 2 1. 1. 1$ Displacement Constraints of Load Set : disp_1SPC1 4 123456 1 2 3$ Displacement Constraints of Load Set : disp_2SPC1 6 3456 4$ Loads for Load Case : case_2LOAD 4 1. 1. 3$ Nodal Forces of Load Set : force_1FORCE 1 4 0 20000. -.8 -.6 0.$ Nodal Forces of Load Set : force_2FORCE 3 4 0 20000. .8 -.6 0.$ Referenced Coordinate Frames$ .DESIGN VARIABLE DEFINITION$ prop_1_AreaDESVAR 1 prop_1:11. .1 100. 1.$ prop_2_AreaDESVAR 2 prop_2:22. .1 100. 1.$ .DEFINITION OF DESIGN VARIABLE TO ANALYSIS MODEL PARAMETER RELATIONSDVPREL1 1 PROD 1 A 1 1.DVPREL1 2 PROD 2 A 2 1.Step 24. Generated Input File (Cont.)$ .STRUCTURAL RESPONSE IDENTIFICATIONDRESP1 1 W WEIGHT$ DCONADD21DCONADD 21 1 2 3$ DCONADD22DCONADD 22 1 2 3$ DISP_1DRESP1 2 DIS2 DISP 1 4$ DISP_2DRESP1 3 DIS3 DISP 2 4$ STRESS_1DRESP1 4 STR4 STRESS ELEM 2 1 2 3$ .CONSTRAINTSDCONSTR 1 2 -.2 .2DCONSTR 2 3 -.2 .2DCONSTR 3 4 -15000. 20000.$ .OPTIMIZATION CONTROLDOPTPRM DESMAX 10 FSDMAX 0 P1 1 P2 1 CONV1 .001 CONV2 1.-20 CONVDV .001 CONVPR .01 DELP .2 DELX 1. DPMIN .01 DXMIN .05ENDDATA 3951b41dStep 25. Submit the Model to Nastran for AnalysisIf you have MSC.NASTRAN on your Network, you can submit the wkshp1.bdf for analysis. Open MSC.NASTRAN.a.Find and Open wkshp1.bdf .b.Open.c.Run.d.Check for fatal errors by opening up wkshp1.f06 file as a text document and searching for the word FATAL. If no fatal errors exist, then the analysis completed successfully. If no matches exist, search for the word WARNING. Determine whether existing WARNING messages indicate modeling errors.acbStep 26. View Results in the f06 File (Cont.) * S U M M A R Y O F D E S I G N C Y C L E H I S T O R Y * (HARD CONVERGENCE ACHIEVED) NUMBER OF FINITE ELEMENT ANALYSES COMPLETED 7 NUMBER OF OPTIMIZATIONS W.R.T. APPROXIMATE MODELS 6 OBJECTIVE AND MAXIMUM CONSTRAINT HISTORY - OBJECTIVE FROM OBJECTIVE FROM FRACTIONAL ERROR MAXIMUM VALUE CYCLE APPROXIMATE EXACT OF OF NUMBER OPTIMIZATION ANALYSIS APPROXIMATION CONSTRAINT - INITIAL 4.828427E+00 -3.234952E-01 1 2.887955E+00 2.888277E+00 -1.114384E-04 -2.479180E-02 2 2.754460E+00 2.754398E+00 2.250540E-05 -4.326953E-03 3 2.717907E+00 2.717877E+00 1.105302E-05 6.591797E-05 4 2.705185E+00 2.705179E+00 2.203353E-06 1.682617E-04 5 2.697357E+00 2.697340E+00 6.098927E-06 1.448145E-03 6 2.695266E+00 2.695282E+00 -6.015127E-06 1.754883E-03 -1 MSC.NASTRAN JOB CREATED ON 27-APR-05 AT 09:58:58 APRIL 27, 2005 MSC.NASTRAN 9/23/04 PAGE 137 0 SUBCASE 1 DESIGN VARIABLE HISTORY - INTERNAL | EXTERNAL | | DV. ID. | DV. ID. | LABEL | INITIAL : 1 : 2 : 3 : 4 : 5 : - 1 | 1 | PROP_1:1 | 1.0000E+00 : 7.6733E-01 : 7.8602E-01 : 8.0348E-01 : 8.2228E-01 : 8.3472E-01 : 2 | 2 | PROP_2:2 | 2.0000E+00 : 7.1794E-01 : 5.3120E-01 : 4.4529E-01 : 3.7943E-01 : 3.3640E-01 : - INTERNAL | EXTERNAL | | DV. ID. | DV. ID. | LABEL | 6 : 7 : 8 : 9 : 10 : 11 : - 1 | 1 | PROP_1:1 | 8.4580E-01 : 2 | 2 | PROP_2:2 | 3.0301E-01 :Compare the results obtained in the .f06 file with the following:Step 27. View Results using PatranContinue to view results in PATRAN.a.Analysis.b.Access Results/Read Output2/Result Entities.c.Select Results Filed.Select wkshp1.op2.e.OK.f.Apply.aedcbfStep 28. Post Design Variable History XYWINDOW Post DesignVariableHistory Plota.XY Plotb.Post / XYWindowc.For Select Current XY Window, select DesignVariableHistory d.For Post/Unpost XY Windows, select DesignVariableHistorye.ApplyaedcbStep 29. Post Objective Function XYWINDOW adcbPost ObjectiveFunction Plota.XY Plotb.Post / XYWindowc.For Select Current XY Window, select ObjectiveFunction d.For Post/Unpost XY Windows, select ObjectiveFunction e.ApplyeStep 30. Post Maximum Constraint CurveadcbPost Maximum Constraint History Plota.XY Plotb.Post / XYWindowc.For Select Current XY Window, select MaximumConstraintHistory d.For Post/Unpost XY Windows, select MaximumConstraintHistorye. ApplyeStep 31. Quit MSC.Patran Quit MSC.PATRAN.a.File / Quit.This ends this exercise.a