WORKSHOP PROBLEM 2Unrestricted and restrictedTopology Optimization of aPlateObjectivess Generation of the FE-models Unrestricted topology optimizations Restricted topology optimization- exclude elements- frozen elements- initial elements (nucleus for material removal)s Global stiffness / ComplianceMSC/CONSTRUCT Exercise Workbook2-12-2MSC/CONSTRUCT Exercise WorkbookWorkshop 2Topology optimization of a plateMSC/CONSTRUCT Exercise Workbook2-3Model Description:The goal of this exercise is to find the optimized topology for a plate subject to a single force with different options.Figure 2.1 below shows the geometry and boundary conditions of the plate.Figure 2.1 Geometry and boundary conditions of the plateYoung’s Modulus: 2.1 * 105 N/mm 2 Poisson Ration:0.3Length: 480mm Width: 320mm Thickness: 20mm Loading:600N480320xF=600NyIntroductionWithin MSC/CONSTRUCT various restrictions can be specified toinfluence the topology optimization process in order to meet functional orproduction requirements.E. g. you cana)- exclude elements from the optimization group(see workshop example No. 1)b)- freeze elements (frozen elements)c)- mark areas where to start the optimization (initial elements)d)- limit the maximum displacement of the structure (global stiffness)Items a) - d) shall be applied in this example but first of all an unrestrictedtopology optimization shall be carried out.2-4MSC/CONSTRUCT Exercise WorkbookWorkshop 2Topology optimization of a plateMSC/CONSTRUCT Exercise Workbook2-5Exercise Procedure:1. Unrestricted topology optimization1.1Prepare the FE-Model with MSC/PATRANIn comparison to workshop example 1 take into account the modified geometry and use 20 units as the ’’Global Edge Length ’’.Fix the nodes 1, 26, 376, 401 in x- and y- direction and "smear" the single force F = 600N over the nodes 25, 50, 75.Create the Nastran Input Deck topo_var.bdf for the optimization with MSC/PATRAN.1.2Creation of the MSC/NASTRAN Input Deck without MSC/PATRANThe generated MSC/NASTRAN input deck has to be modified for the optimization process like in workshop example No. 1 (see page 1-12)1.3Create the parameter file for the topology optimization in MSC/PATRAN1.3.1 Start the MSC/CONSTRUCT Interface in MSC/PATRAN.MSC/CONSTRUCT Action: Create Object: Parameter File Method:Topology Parameter FilesName: simpleInput Parameter...2-6MSC/CONSTRUCT Exercise Workbook1.3.2 Create the Data Input SectionLoad the FE-Model data (nodes and elements) for the optimization 1.3.3.Create the Object Definition SectionInclude all elements in the optimization group..1.3.4.Create the Optimization SectionSpecify the formula for the stress calculation --> Stress hypothesis: von Mises hypothesis Select Input File Select Input File Input Files:topo_var.bdfOK CreateGroups Group Name:DESIGN_ELEM Type:Element Select Elements:Elm 1:384Add CreateLoad Calculation Load Calc Name:LOAD_CALC_1Type:Hypo Component:MisesCreateWorkshop 2Topology optimization of a plateMSC/CONSTRUCT Exercise Workbook2-7Define the objective function --> Objective function is the relative volume Specify the optimization type and assign the design variables, an objective function and the stress hypothesis. Highlight the names in the boxes.- Specify the maximum number of iteration cycles 1.3.5 Create the Output SectionObjective Function Objective Name:OBJ_FUNC_1Type:Relative Volume Variable:None Value:0.60CreateOptimization Existing Groups:DESIGN_ELM Existing Load Calc:LOAD_CALC_1Existing Objective:OBJ_FUNC_1CreateTermination Criteria Type:Maximum Iteration Number of Iteration:30CreateOutput Request Predefined Macros:uf_topo_pat.macCreate2-8MSC/CONSTRUCT Exercise WorkbookEnd the Construct Interface and save the parameter file.The created parameter file is shown in Figure 2.2Figure 2.2 Parameter file simple.par !! INPUT FILE FOR TOPOLOGY OPTIMIZATION ! MODEL :simple ! AUTHOR :training! DATE :08-Dec-97 10:19:18! LAST CHANGE :! REMARKS :! DESCRIPTION :! - - - - -DATA INPUT SECTION READ, topo_var.bdf! - - - - -OBJECT DEFINITION SECTION SELECT, ELEM, S, ELEM, 1,384,1GROUP_DEF,ELEM, DESIGN_ELEM! - - - - -OPTIMIZATION SECTIONLOAD_CALC, LOC_DEF_1, HYPO, MISESOBJ_FUNC, USER_OBJ_FUNC_1,REL_VOL, 0.60OPTIMIZE, TOPO, DESIGN_ELEM, USER_OBJ_FUNC_1,LOC_DEF_1STOP, ITER_MAX, 30! - - - - -OUTPUT SECTION INCLUDE, uf_topo_pat.mac SA VE EXITEnd you patran session.1.4Carry out the optimizationBecause the name of the parameter file and the MSC/NASTRAN input file are not the same you have to start the optimization with the command:construct -type all -job simple -nas topo_var.bdfOK ApplyWorkshop 2Topology optimization of a plateMSC/CONSTRUCT Exercise Workbook2-91.5Postprocessing1.5.1 Material distributionFigure 2.3 Material distribution after the 14th iteration1.5.2 AnimationWithin MSC/PATRAN with the Insight tool you can create an animation of the material removal from the first to the last iteration.In order to animate the model you have to carry out the following steps:x Insight Action: Create Tool:Isosurface Isosurface Value: x ResultsResult Selection Current Load Case:select all iterationsUpdate resultsAnimation AttributesÌEnable AnimationAnimation Type:x Global VariableGlobal Variable: IterationOKIsosurface Result MP, ValueIsovalue SetupIsovalue:10000OK x Global VariableResult OptionsElement Result Mapping:x Element ConstantOKOKIsosurface AttributesÌClip at Isosurface< Display:Free Edge> Display:ShadedOKApplyFor start the animation go to in the menubar toInsight Control / Animation ControlSetup ...Animation Mode Animate Tools - 3DAnimation Tool Is-Isos_1 IterationFrames:17Animate2-10MSC/CONSTRUCT Exercise WorkbookWorkshop 2Topology optimization of a plate If you want to finish the animation click on Clear.In general: all SELECT and GROUPING operations as well as all otheroperations can be carried out with the MSC/CONSTRUCT preprozessorfor non MSC/PATRAN user. But for more complicated problems thisbecomes very tedious as one explicitly has to extract nodal and/orelement information from the finite element model.2. Restricted Topology Optimization2.1Explizit definition of the design spaceExclude two element rows from the design space which are attached to the left edge of the plate as well as these elements which are involved in the introduction of the load.Define additional the volume reduction in the first iteration and the speed for the volume reduction in the second and subsequent iteration.Modify the Object Definition Section and the Optimization Section in the existing parameter file simple.par and generate a new one, called design.par .2.1.1 Read in the existing parameter file simple.par .2.1.2 Modify the Object Definition SectionDefine the design space without the two element rows on the left edge as well as the elements which are assigned with the load ( see in the following picture, Figure 2.4)MSC/Construct Action: ReadObject:Parameter FileSelect Parameter File Parameter File Name:.../simple Apply Action: Create Object: Parameter File Method:Topology Parameter File Name:.../simple.par Input ParameterWorkshop 2Topology optimization of a plate Figure 2.4 Design Elements.GroupsGroup Name:DESIGN_ELEMType:ElementSelect Elements:Element 3:23 27:47 51:7275:96 99:120 123:144147:168 171:192 195:216219:240 243:264 267:288291:312 315:336 339:360363:384AddCreate2.1.3 Modify the Optimization Section.Define the volume reduction in the first iteration Define the speed for the volume reduction in the second and subsequent iteration.Save the parameter file under the new name design.parSolution Control Type:Start Option:Percent Value:0.1Existing Groups:DESIGN_ELEMCreateSolution Control Type:Speed Option:Moderate Existing Groups:DESIGN_ELEMCreateWorkshop 2Topology optimization of a plateFigure 2.5 Parameter file design.par! INPUT FILE FOR TOPOLOGY OPTIMIZATION! MODEL :design! AUTHOR :training! DATE :08-Dec-97 10:19:18! LAST CHANGE :! REMARKS :! DESCRIPTION :! - - - - -DATA INPUT SECTIONREAD,topo_var.bdf! - - - - OBJECT DEFINITION SECTIONSELECT, ELEM, S, ELEM, 3, 23, 1SELECT, ELEM, A, ELEM, 27, 47, 1SELECT, ELEM, A, ELEM, 51, 72, 1SELECT, ELEM, A, ELEM, 75, 96, 1SELECT, ELEM, A, ELEM, 99, 120, 1SELECT, ELEM, A, ELEM, 123, 144, 1SELECT, ELEM, A, ELEM, 147, 168, 1SELECT, ELEM, A, ELEM, 171, 192, 1SELECT, ELEM, A, ELEM, 195, 216, 1SELECT, ELEM, A, ELEM, 219, 240, 1SELECT, ELEM, A, ELEM, 243, 264, 1SELECT, ELEM, A, ELEM, 267, 288, 1SELECT, ELEM, A, ELEM, 291, 312, 1SELECT, ELEM, A, ELEM, 315, 336, 1SELECT, ELEM, A, ELEM, 339, 360, 1SELECT, ELEM, A, ELEM, 363, 384, 1! - - - -OPTIMIZA TION SECTION!LOAD_CALC, LOC_DEF_1, HYPO, MISESOBJ_FUNC, USER_REF_1,REL_VOLUM, 0.60OPTIMIZE, TOPO, DESIGN_ELEM, USER_REF_1,LOC_DEF_1CONT_TOPO, DESIGN_ELEM, START, PROZ, 0.1CONT_TOPO, DESIGN_ELEM, SPEED_TOPO, MODERA TESTOP, ITER_MAX, 30! - - - - -OUTPUT SECTIONINCLUDE,uf_topo_pat.macSA VEEXITStart the optimization and check the results.Figure 2.6 Material distribution after the 18th optimization cycleWorkshop 2Topology optimization of a plate2.2 Use frozen elementsDefines which elements are excluded from the optimization. The volume of these elements however is included in determining the objective function. (difference to the further example )2.2.1 Read in the existing parameter file simple.par .Look page 2-12 in order to read in an existing parameter file.2.2.2 Modify the Object Definition SectionDefine all elements as Design Elements Define the Frozen ElementsAll elements which were excluded from the design space in workshop example 2.1 now should be assigned to a frozen element group. Select these elements and create a group called Frozen_Elem ( Figure 2.7 )Groups Group Name:DESIGN_ELEM Type:Element Select Elements:Element 1:384Add CreateFigure 2.7 Frozen ElementsAnother possibility to create a construct group is at first to create a MSC/ PATRAN group with the neccassary elements and then to create the MSC/ CONSTRUCT group from the MSC/PATRAN group.Create the MSC/PATRAN group in the Group-Menu in PatranGroup/CreateNew Group Name:Frozen_ElemType:ElementEntity Selection:Elm 1, 2, 24, 25, 26, 48, 49, 50,73, 74, 97, 98, 121, 122, 145,146, 169, 170, 193, 194, 217,218, 241, 242, 265, 266, 289, 290313, 314, 337, 338, 361, 362ApplyWorkshop 2Topology optimization of a plateCreate the MSC/CONSTRUCT group in the Construct-Menu 2.2.3 Modify the Optimization Section.- Define which elements during the optimization may be not modified as a restrictionDefine the speed for the volume reduction in the second and subsequent iteration.Groups Type:Element Patran Groups:Frozen_ElemCreateTopology Restrictions Type:Frozen Existing Element Group:Frozen_ElemCreateSolution Control Type:Speed Option:Moderate Existing Groups:DESIGN_ELEMCreateSave the parameter file under the new name frozen.par Figure 2.8 Parameter file frozen.par! INPUT FILE FOR TOPOLOGY OPTIMIZATION! MODEL :frozen! AUTHOR :training! DATE :09-Dec-97 14:49:18! LAST CHANGE :! REMARKS :! DESCRIPTION :! - - - - -DATA INPUT SECTIONREAD, topo_var.bdf! - - - - OBJECT DEFINITION SECTIONSELECT, ELEM, S, ELEM, 1, 384, 1GROUP_DEF, ELEM, DESIGN_ELEMSELECT, ELEM, S, ELEM, 1SELECT, ELEM, A, ELEM, 2SELECT, ELEM, A, ELEM, 24, 26, 1SELECT, ELEM, A, ELEM, 48, 50, 1SELECT, ELEM, A, ELEM, 73SELECT, ELEM, A, ELEM, 74SELECT, ELEM, A, ELEM, 97SELECT, ELEM, A, ELEM, 98SELECT, ELEM, A, ELEM, 121SELECT, ELEM, A, ELEM, 122SELECT, ELEM, A, ELEM, 145SELECT, ELEM, A, ELEM, 146SELECT, ELEM, A, ELEM, 169SELECT, ELEM, A, ELEM, 170SELECT, ELEM, A, ELEM, 193SELECT, ELEM, A, ELEM, 194SELECT, ELEM, A, ELEM, 217SELECT, ELEM, A, ELEM, 218SELECT, ELEM, A, ELEM, 241SELECT, ELEM, A, ELEM, 242SELECT, ELEM, A, ELEM, 265SELECT, ELEM, A, ELEM, 266SELECT, ELEM, A, ELEM, 289SELECT, ELEM, A, ELEM, 290SELECT, ELEM, A, ELEM, 313SELECT, ELEM, A, ELEM, 314SELECT, ELEM, A, ELEM, 337SELECT, ELEM, A, ELEM, 338SELECT, ELEM, A, ELEM, 361SELECT, ELEM, A, ELEM, 362GROUP_DEF, ELEM, Frozen_Elem! - - - - -OPTIMIZATION SECTIONLOAD_CALC, LOC_DEF_1, HYPO, MISESOBJ_FUNC, USER_REF_1,REL_VOLUM, 0.60OPTIMIZE, TOPO, DESIGN_ELEM, USER_REF_1,LOC_DEF_1 CONT_TOPO, DESIGN_ELEM, SPEED_TOPO, MODERATEREST_TOPO, FROZEN_ELEM, FROZENSTOP, ITER_MAX, 30! - - - - -OUTPUT SECTIONINCLUDE, uf_topo_pat.macSA VEEXITWorkshop 2Topology optimization of a plateStart the optimization and check the resultsFigure 2.9 Material distribution after the 20th optimization cycle usingFrozen ElementsWith the same objective function (60% material removal) more materialwill be removed using frozen elements rather then excluding elementsfrom the design space ( compare Figure 2.6 with Figure 2.9). The reasonis that the volume of the frozen elements is included in the determinationof the objective function.2.3Use frozen and initial elementsBy specifying initial elements the location where material will be removed first, can be determined. This may be necassary for symmetrical loaded and constraint structures.Figure 2.10 shows the initial elements (black shaded) proposed for this example. They have to be selected and grouped first and then defined in the optimization section of the parameter file according to Figure 2.11.In addition these elements should be frozen at which boundary conditions ( forces and supports) are applied.Figure 2.10 Initial Elements2.2.1 Read in the existing parameter file simple.par.Read in the existing parameter file how it is described in page 2-122.2.2 Modify the Object Definition SectionUse the defined MSC/CONSTRUCT group Design_Elem from the readed parameter fileWorkshop 2Topology optimization of a plateDefine the Initial ElementsInclude as Initial Elements these elements which are in the upper edge (see Figure 2.11).Define the Frozen ElementsInclude as Frozen Elements these elements which are applied with the load and the boundary conditions.2.2.3 Modify the Optimization Section.- Define which elements during the optimization may be not modified as a restrictionGroups Group Name:Initial_Elem Type:ElementSelect Elements:Element 264:360:24 380:384Add CreateGroups Group Name:Frozen_Elem Type:Element Select Elements:Elm 1 24 48 361Add CreateTopology Restrictions Type:Frozen Existing Element Group:Frozen_ElemCreate- Define the initial restiction Save the parameter file under the new name initial.par according Figure 2.12, carry out the optimization and compare the material distribution after 17th iteration with Figure 2.13.Figure 2.12 Parameter file with initial elements! INPUT FILE FOR TOPOLOGY OPTIMIZATION ! MODEL :initila ! AUTHOR :training! DATE :15-Dec-97 10:19:18! LAST CHANGE :! REMARKS :! DESCRIPTION :! - - - - -DATA INPUT SECTION READ, topo_var.bdf! - - - - OBJECT DEFINITION SECTION SEL, ELEM, S,1,384,1GROUP_DEF,ELEM, DESIGN_ELEM SELECT, ELEM, S, 380SELECT, ELEM, A, 381SELECT, ELEM, A, 382SELECT, ELEM, A, 383SELECT, ELEM, A, 384SELECT, ELEM, A, 288SELECT, ELEM, A, 312SELECT, ELEM, A, 336SELECT, ELEM, A, 360GROUP_DEF, ELEM, Initial-Elem SELECT, ELEM, S, 1SELECT, ELEM, A, 361SELECT, ELEM, A, 24SELECT, ELEM, A, 48GROUP_DEF, ELEM, Frozen_Elem! -- - - -OPTIMIZATION SECTIONLOAD_CALC, LOC_DEF_1, HYPO, MISESOBJ_FUNC, USER_OBJ_FUNC_FUNC_1, REL_VOLUM, 0.50OPTIMIZE, TOPO, DESIGN_ELEM, USER_REF_1,LOC_DEF_1REST_TOPO, Initial_Elem, INITIAL, LINE REST_TOPO, Froezen_Elem, FROZEN STOP, ITER_MAX, 30! - - - - -OUTPUT SECTION INCLUDE.uf_topo_pat.mac SA VE EXITTopology Restrictions Type:Initial Option:Line Existing Element Group:Initial_ElemCreateWorkshop 2Topology optimization of a plate Figure 2.13 Material distribution after 17th iteration3. Global stiffness / ComplianceThe global stiffness is declared as the objective function when the maximum allowed displacement of the structure is specified.Within MSC/CONSTRUCT a maximum allowable displacement could be defined in the objective function. This displacement value is based on the maximum total displacement calculated in the first FE-analysis. The material distribution will be determined based on this results. In addition other restrictions can be used like frozen or initial elements.Besides the discussed definitions for the parameter file (element selection etc.) variables have to defined and assigned3.1Define the variables in the Object Definition Section.3.1.1 Read in the existing parameter file simple.par.Read in the existing parameter file simple.par how it is described in page2-123.1.2 Modify the Object Definition SectionDefine all elements as Design Elements except the element on which theload and boundary condition are applied.GroupsGroup Name:DESIGN_ELEMType:ElementSelect Elements:Element 2:23 25:4749:360 362:384CreateCreateWorkshop 2Topology optimization of a plateNodes are necassary for the determination of the displacement. Thats why a group has to be created which includes all nodes..q Define the maximum allowed displacement- Assign a variable to the maximum displacement value of the first FE-analysis named TAR_STIFF1- Assign a variable to the maximum allowed displacement value for the optimization named TAR_STIFF2Groups Group Name:DISP_NODES Type:Nodes Select Elements:Node 1:425Create CreateNumerical Variable Variable Name:Tar_Stiff_1Type:BASE Value:DISP_ABS Option:MAX Existing Group:DISP_NODESCreateNumerical Variable Variable Name:Tar_Stiff_2Type:FIX Value: 1.15Create- Multiply both variables and named the result TAR_STIFF33.2Define the Optimization SectionDefine the objective function 2.1.3 Modify the Optimization Section.Define the speed for the volume reduction in the second and subsequent iteration.Numerical Variable Variable Name:Tar_Stiff_3Type:OPER Value:MULT Variable:Tar_Stiff_1Variable:Tar_Stiff_2CreateObjective Function Objective Name:OBJ_FUNC_1Type:Stiffness Variable:FIRST Existing Variables:Tar_Stiff_3Existing Variables:Tar_Stiff_1CreateSolution Control Type:Speed Option:Moderate Existing Groups:DESIGN_ELEMCreateWorkshop 2Topology optimization of a plateSpecify the tolerance file accordingly.Save the parameter file under the new name stiffness.par and check the results with Figure 2.15Figure 2.14 Parameter file stiffness.par! INPUT FILE FOR TOPOLOGY OPTIMIZATION ! MODEL :stiffness ! AUTHOR :training! DATE :16-Dec-97 17:17:09! LAST CHANGE :! REMARKS :! DESCRIPTION :! - - - - -DATA INPUT SECTION READ, topo_var.bdf! - - - - OBJECT DEFINITION SECTION SELECT, ELEM, S, ELEM, 264, 360, 24SELECT, ELEM, A, ELEM, 380, 384, 1GROUP_DEF, ELEM, DESIGN_ELEM SELECT, NODE, S, NODE, 1, 425, 1GROUP_DEF, NODE, DISP_NODES! - - - - -OPTIMIZATION SECTIONLOAD_CALC, LOC_DEF_1, HYPO, MISESVARIABLE,TAR_STIFF1,BASE,DISP_ABS,MAX,DISP_NODES VARIABLE,TAR_STIFF2,FIX,1.15VARIABLE,TAR_STIFF3,OPER,MULT,TAR_STIFF1,TAR_STIFF2OBJ_FUNC, USER_REF_1,STIFFNESS,TAR_STIFF3,FIRST,TAR_STIFF1OPTIMIZE, TOPO, DESIGN_ELEM, USER_REF_1,LOC_DEF_1CONT_TOPO, DESIGN_ELEM, SPEED_TOPO, MODERATE CONT_TOPO, DESIGN_ELEM, EPSILON, PROZ, 0.05 STOP, ITER_MAX, 30! - - - - -OUTPUT SECTION INCLUDE,uf_topo_pat.mac SA VE EXITSolution Control Type:Epsilon Option:Percent Value:0.05Existing Groups:DESIGN_ELEMCreateFigure 2.15 Material distribution after the 14th iteration。
