教程5.13g加密所屬

1、SECTION 5SPECIAL MODELING TOPICS ITABLE OF CONTENTSPAGEDESIGN VARIABLE LINKING5-3REDUCED BASIS FORMULATIONS 5-8DESIGN RESPONSES AND CASE CONTROL 5-13TOTAL WEIGHT RESPONSE 5-16MODE TRACKING FEATURES 5-18EQUALITY CONSTRAINTS 5-22FREQUENCY MATCHING 5-23DISCRETE VARIABLE OPTIMIZATION5-24FULL STRESSED DE

2、SIGN5-32DESIGN VARIABLE LINKINGDesign variable linking enforces a dependence of a design variable or on other, independent variables.The DLINK entry is used to write this dependence.Relates one design variable to one or more other design variables.Format:Example:12345678910DLINKIDDDVIDCOCMULTIDV1C1I

3、DV2C3IDV3C3-etc.-DLINK1020.10.3322.06-1.087.0DLINK entry (Cont.)Field ContentsID Unique identification number. (Integer 0)DDVID Dependent design variable identification number. (Integer 0)CO Constant term (Real; Default = 0.0)CMULT Constant multiplier (Real; Default = 1.0)IDVi Independent Coefficien

4、t I corresponding to IDVi. (Real)Ci Coefficient I corresponding to IDVi. (Real)DESIGN VARIABLE LINKING (Cont.)DLINK (Cont.)DLINK entry (Cont.)Remarks:DLINK defines the relationshipThis capability provides a means of linking physical design variables such as element thicknesses to nonphysical design

5、variables such as the coefficients of interpolating functions.CMULT provides a simple means of scaling the Ci. For example if Ci = 1/7, 2/7, 4/7, etc. is desired, then CMULT = 1/7 and Ci = 1, 2, 4, etc., may be input.An independent IDVi must not occur on the same DLINK entry more than once.ID is for

6、 user reference only.DESIGN VARIABLE LINKING (Cont.)For example, consider a simple plate, in which the redesigned thickness distribution is to vary linearly:so,DESIGN VARIABLE LINKING (Cont.)The DLINK entries can be written as:The only independent variables are t1 and t4. t2 and t3 are the dependent

7、 quantities. The design space is now two-dimensional, rather than four.Reducing the number of independent design variables offers greater advantages for large design problems.DESVAR, 1, T1, 1., 0.01, 5.DESVAR, 2, T2, 1., 0.01, 5.DESVAR, 3, T3, 1., 0.01, 5.DESVAR, 4, T4, 1., 0.01, 5.$DLINK, 11, 2, 0.

8、, 0.333, 1, 2., 4, 1.DLINK, 12, 3, 0., 0.333, 1, 1., 4, 2.$DVPREL1,21, PSHELL, 101, T, 0.01, 5., , , +, 1, 1.0DVPREL1,22, PSHELL, 102, T, 0.01, 5., , , +, 2, 1.0DVPREL1,23, PSHELL, 103, T, 0.01, 5., , , +, 3, 1.0DVPREL1,24, PSHELL, 104, T, 0.01, 5., , , +, 4, 1.0$234567890REDUCED BASIS FORMULATIONSR

9、educed basis formulations are conceptually similar to design variable linking, but can be implemented in a number of ways.Consider a plate to be designed with smoothly varying thickness distribution:Plate Thickness DistributionREDUCED BASIS FORMULATIONS (Cont.)Basis FunctionsREDUCED BASIS FORMULATIO

10、NS (Cont.)These variations can be written as linear combinations of basis vectors (X is varied from 0.0 to 1.0):REDUCED BASIS FORMULATIONS (Cont.)In general, a reduced basis formulation is expressed as:where M NSince these are linear design variable to property relations, we can use DVPREL1 entries:

11、$PSHELL,PID, MID1, T, MID2, 12I/T3 MID3PSHELL, 101, 100, 1.0, 100, , 100PSHELL, 102, 100, 1.0, 100, , 100PSHELL, 103, 100, 1.0, 100, , 100PSHELL, 104, 100, 1.0, 100, , 100PSHELL, 105, 100, 1.0, 100, , 100PSHELL, 106, 100, 1.0, 100, , 100PSHELL, 107, 100, 1.0, 100, , 100PSHELL, 108, 100, 1.0, 100, ,

12、100PSHELL, 109, 100, 1.0, 100, , 100PSHELL, 110, 100, 1.0, 100, , 100$DESVAR,ID, LABEL, XINIT, XLB, XUB, DELXVDESVAR, 1, X1, 0.33, -1.0, +1.0DESVAR, 2, X2, 0.33, -1.0, +1.0DESVAR, 3, X3, 0.33, -1.0, +1.0$REDUCED BASIS FORMULATIONS (Cont.)Linear design variable to property relations (Cont.)$DVPREL1,I

13、D, TYPE, PID, FID, PMIN, PMAX, C0, , +$+, DVID1, COEF1, DVID2, COEF2, .DVPREL1,201, PSHELL, 101, T, 0.01, , , , +, 1, 1.0, 2, 1.0, 3, 1.0DVPREL1,202, PSHELL, 102, T, 0.01, , , , +, 1, 1.0, 2, 0.9, 3, 0.81DVPREL1,203, PSHELL, 103, T, 0.01, , , , +, 1, 1.0, 2, 0.8, 3, 0.64DVPREL1,204, PSHELL, 104, T,

14、0.01, , , , +, 1, 1.0, 2, 0.7, 3, 0.49DVPREL1,205, PSHELL, 105, T, 0.01, , , , +, 1, 1.0, 2, 0.6, 3, 0.36DVPREL1,206, PSHELL, 106, T, 0.01, , , , +, 1, 1.0, 2, 0.5, 3, 0.25DVPREL1,207, PSHELL, 107, T, 0.01, , , , +, 1, 1.0, 2, 0.4, 3, 0.16DVPREL1,208, PSHELL, 108, T, 0.01, , , , +, 1, 1.0, 2, 0.3, 3

15、, 0.09DVPREL1,209, PSHELL, 109, T, 0.01, , , , +, 1, 1.0, 2, 0.2, 3, 0.04DVPREL1,210, PSHELL, 110, T, 0.01, , , , +, 1, 1.0, 2, 0.1, 3, 0.01DESIGN RESPONSES AND CASE CONTROLSpecifying DRESP1 entries ensures that all necessary data recovery is done automatically. (Internally, design optimization Case

16、 Control Sections are written to ensure all necessary responses are recovered.)In general, Case Control output requests are for output/ post-processing purposes only. (PARAM, NASPRT, n can be used to control frequency of this output.)Exceptions:Dynamic ResponsesMagnitude/phase or real/imaginary repr

17、esentations are selected using Case ControlExample:SUBCASE 10 ANALYSIS = DFREQ SET 200 = 1000,1001,1003 DISPLACEMENT(PHASE) = 200DESIGN RESPONSES AND CASE CONTROL (Cont.)All displacement components will be in magnitude/phase form both in the design model and in the analysis output. The SET request h

18、as no relation to the DRESP1 entries.Stress/StrainVon Mises, or maximum shear, are selectable in Case Control, both for data recovery and for the design model.Example:SUBCASE 20 ANALYSIS = STATICS SET 200 = 1000,1001,1003 STRESS(MAXS) = 200Stresses for all elements are represented as maximum shears,

19、 both for data recovery of the analysis model and for response retrieval of the design model.DESIGN RESPONSES AND CASE CONTROL (Cont.)Corner StressesIf corner stresses/strains are desired for the DRESP1, the corner or BILIN option must be present in the STRESS/STRAIN request for the first sub-case.I

20、f corner stresses are not desired, the corner or BILIN option must not be present in the STRESS/STRAIN request for the first sub-case. Note that item codes for corner stresses differ from those for center points.TOTAL WEIGHT RESPONSEBenefitInclude the weight from element densities and the weight fro

21、m concentrated and non-structural weights.Produce accurate total weight response and its sensitivities.Include all the rigid body weight matrix terms.Enable designing of center of gravity locations.InputThe ATTA and ATTB fields refer to row and column numbers of the rigid body weight matrix. Both fi

22、elds are default to 3 that specify weight in Z direction. $DRESP1RIDLABELRTYPEATTAATTBATTi DRESP1100WWEIGHTRow NO.Col No. SEID/All/Blank/TOTAL WEIGHT RESPONSE (Cont.)Rigid Body Weight MatrixGuidelines and limitationsWeight of scalar point is not included.Changes in GRID coordinate system from shape

23、variations are ignored in shape-variable/weight-sensitivity calculation. Use RTYPE=VOLUME in such Cases.Use RTYPE=VOLUME to avoid the numerically insignificant weight sensitivities due to the large invariant weights.MODE TRACKING FEATURESUseful when eigenvalues (e.g., first roof bending, first torsi

24、onal, etc.) are being designedModes are “tracked” based on a cross-orthogonality check:All the updated DRESP1 entries that are type FREQ or EIGN are written to the .pch file$Mode Tracking has been performed successfully. Updated DRESP1 entries are:DRESP1 301LFREQ FREQ 2DRESP1 303HFREQ FREQ 4If mode

25、tracking fails, correlation data for the untracked mode(s) is printed and the run is terminated.Mode tracking is requested by Case Control entry: MODTRAK.Parameters for mode tracking are specified by Bulk Data Entry: MODTRAK.Mode tracking Case Control commandSelects mode tracking options in design o

26、ptimization (SOL 200).Format:MODTRAK = nExample:MODTRAK = 100DescriberMeaningnSet identification of MODTRAK Bulk Data entry. (Integer 0)Remark:Selection of a MODTRAK Bulk Data entry with the MODTRAK Case Control command activates mode tracking for the current sub-case. This request is limited to nor

27、mal modes sub-cases (ANALYSIS = MODES) in design optimization (SOL 200).MODE TRACKING FEATURES (Cont.)Mode tracking Bulk Data entrySpecifies parameters for mode tracking in design optimization (SOL 200).Format:Example:FieldContentsSIDSets identification number that is selected in the Case Control se

28、ction with the MODTRAK command. (Integer; No Default) See Remark 1.LOWRNGLowest mode number in range to search. See Remark 2. (Integer 0, Default = 0, If nonzero, LOWRNG 0, Default = number of eigenvalues extracted. If nonzerp, LOWRNG 0, performs the discrete processing at the n-th design cycle (and

29、 all subsequent ones). But results from the discrete processing are not used by the optimizer in subsequent design cyclesDISCRETE VARIABLE OPTIMIZATION (Cont.)For each Discrete step, the feasibility is checked based on both the approximate and exact reanalysisThe results based on the approximate mod

30、el are labeled as either FEASIBLE or INFEASIBLE “SOFT” based on whether constraints are violatedThe results based on the exact analysis are labeled as either FEASIBLE or INFEASIBLE “HARD”* A HARD FEASIBLE DISCRETE SOLUTION FOUND (HARD FEASIBILITY DISCRETE SOLUTION CHECK LOGIC) * MAXIMUM CONSTRAINT V

31、ALUE : -1.9044E-02 MUST BE LESS THAN 5.0000E-03* A SOFT FEASIBLE DISCRETE SOLUTION FOUND (SOFT FEASIBILITY DISCRETE SOLUTION CHECK LOGIC) * MAXIMUM CONSTRAINT VALUE : -1.8838E-02 MUST BE LESS THAN 5.0000E-03*OutputThe output from the Continuous steps is not affected. But the new title output from a

32、discrete design cycle is given below:* * D I S C R E T E D E S I G N C Y C L E 1D * * * OPTIMIZATION RESULTS BASED ON AN EXACT ANALYSIS *DISCRETE VARIABLE OPTIMIZATION (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 COMP

33、LETED 5 NUMBER OF OPTIMIZATIONS W.R.T. APPROXIMATE MODELS 3 NUMBER OF DISCRETE PROCESSING ANALYSES COMPLETED 1 OBJECTIVE AND MAXIMUM CONSTRAINT HISTORY OBJECTIVE FROM OBJECTIVE FROM FRACTIONAL ERROR MAXIMUM VALUE CYCLE APPROXIMATE EXACT OF OF NUMBER OPTIMIZATION ANALYSIS APPROXIMATION CONSTRAINT INI

34、TIAL 6.614414E+02 1.102773E-01 1 5.662242E+02 5.662401E+02 -2.791767E-05 9.536743E-06 2 5.474170E+02 5.474160E+02 1.783949E-06 2.966779E-03 3 5.474160E+02 5.474160E+02 0.000000E+00 2.966779E-03 3D 5.291842E+02 5.291818E+02 4.613550E-06 3.849362E-02 0 DESIGN VARIABLE HISTORY INTERNAL | EXTERNAL | | D

35、V. ID. | DV. ID. | LABEL | INITIAL : 1 : 2 : 3 : 3D : 4 : 1 | 1 | X1 | 2.0000E+00 : 1.0000E-01 : 1.0000E-01 : 1.0000E-01 : 1.0000E-01 : 2 | 2 | X2 | 2.0000E+00 : 2.0166E+00 : 2.0266E+00 : 2.0266E+00 : 2.0000E+00 : 3 | 3 | X3 | 2.0000E+00 : 2.8267E+00 : 2.9868E+00 : 2.9868E+00 : 3.0000E+00 : 4 | 4 |

36、X4 | 2.0000E+00 : 1.0000E-01 : 1.0000E-01 : 1.0000E-01 : 1.0000E-01 : 5 | 5 | X5 | 2.0000E+00 : 3.5169E-01 : 1.0000E-01 : 1.0000E-01 : 1.0000E-01 : 6 | 6 | X6 | 2.0000E+00 : 7.8165E-01 : 6.8127E-01 : 6.8127E-01 : 7.0000E-01 : 7 | 7 | X7 | 2.0000E+00 : 1.7342E+00 : 1.6301E+00 : 1.6301E+00 : 1.5000E+0

37、0 : 8 | 8 | X8 | 2.0000E+00 : 2.8171E+00 : 2.6749E+00 : 2.6749E+00 : 2.5000E+00 :DISCRETE VARIABLE OPTIMIZATION (Cont.)DISCRETE VARIABLE OPTIMIZATION (Cont.)Limitations1 CDD and DOE are not guaranteed to produce feasible design solutions (especially with widely-spaced discrete design variables) due

38、to the nature of the approximation analysis2 DOE is not guaranteed to produce a best discrete design, as the search is limited to a subset of the possible discrete combinations3 CDD is not guaranteed to produce a “truly conservative design” since the interaction of the discrete variables is ignoredF

39、ULLY STRESSED DESIGNThe basic concept of FSD can be described as follows:where: t = designed property i = index to indicate which property contains the design parameter and the design response = response quantity, such as stress = a real number (0.0 1.0)And the old and the new superscripts refer to

40、before and after resizing.FULLY STRESSED DESIGN (Cont.)Fully Stressed Design (FSD) is an alternate approach to the Mathematical Programming (MP) approach for performing automated design tasks. It resizes the element properties so that each element is at its limit value under at least one of the appl

41、ied load conditions.It produces a quick-look design with a fraction of the computational cost and can handle tens of thousand independent design variables.The FSD can be used either as a stand-alone tool or as a starting design for an MP run.FULLY STRESSED DESIGN (Cont.)During FSD, the optimizer is

42、not utilized although the standard design model input is usedInvoking the FSD feature is based on two parameters on the DOPTPRM entry:FSDALP Relaxation parameter applied in Fully Stressed Design (Real, 0.0FSDALP=1.0, Default=0.90)FSDMAX Specifies the number of Fully Stressed Design Cycles that are t

43、o be performed (Integer, Default=0)If requested, Fully Stressed Design is performed for up to FSDMAX steps, then the MP (mathematical programming) method (the optimizer) is used for any additional stepsSmaller values of FSDALP may find an improved final design at the cost of more design iterations.F

44、ULLY STRESSED DESIGN (Cont.)Output:Follow the standard output from Optimization, except:There is no approximate analysis, so the message Will be displayed after each cycle The SUMMARY OF THE DESIGN CYCLE HISTORY will indicate FSD cycles and will not have a FRACTIONAL ERROR OF APPROXIMATION for these

45、 steps (as a finite element analysis is done at each cycle)* * D E S I G N C Y C L E 1 * * * OPTIMIZATION RESULTS BASED ON AN EXACT ANALYSIS *FULLY STRESSED DESIGN (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)(SOFT CONVERGENCE ACHIEVED)NUMBER OF FINITE ELE

46、MENT ANALYSES COMPLETED 10NUMBER OF FULLY STRESSED DESIGN CYCLES COMPLETED 5NUMBER OF OPTIMIZATIONS W.R.T. APPROXIMATE MODELS 4OBJECTIVE AND MAXIMUM CONSTRAINT HISTORY OBJECTIVE FROM OBJECTIVE FROM FRACTIONAL ERROR MAXIMUM VALUE CYCLE APPROXIMATE EXACT OF OFNUMBER OPTIMIZATION ANALYSIS APPROXIMATION

47、 CONSTRAINTINITIAL 4.962552E-01 -3.499151E-011 FSD 3.970042E-01 N/A -1.873938E-01 .5 FSD 1.877756E-01 N/A -2.075195E-056 1.701204E-01 1.701193E-01 6.744617E-06 2.066393E-037 1.566132E-01 1.566075E-01 3.634719E-05 2.066393E-038 1.519279E-01 1.519300E-01 -1.363300E-05 2.066393E-039 1.519300E-01 1.5193

48、00E-01 0.000000E+00 2.066393E-03FULLY STRESSED DESIGN (Cont.)Guidelines/Limitations:FSD is only available for ANALYSIS=STATICS and SAERO (other ANALYSIS options will be ignored during FSD)FSDMAX is independent of DESMAX that is the program will perform up to FSDMAX steps of FSD, followed by up to DE

49、SMAX steps of MP (if you want FSD only, set DESMAX to 0)Multiple BC and subcases are supportedComposites are supported (thickness of individual layers may be sized)Allowables can be on element STRESS and/or STRAINPROD areas and shell thicknesses (PSHEAR, PSHELL, P) are supported (Shape, material, ot

50、her property entries, and connectivity items are not)BAR and BEAM cross-sections are not designedIf an element has constraints, but its properties are not related to DESVAR entries, it is not re-sizedIf a property is related to on a DESVAR, but the associated elements have no constraints, it will no

51、t be re-sizedFULLY STRESSED DESIGN (Cont.)Sample roof truss design (sample 1 from NAS101)FULLY STRESSED DESIGN (Cont.)Analysis Model DescriptionThe truss is modeled with ROD elements. Each element has its own property entry.A single load case is defined (See the figure in the previous page)The eleme

52、nt stress response is of interestDesign Model DescriptionDesign variable Cross-sectional area of 11 RODsDesign Constraints 11 element stresses are within the range of 1900 and 1900FSD strategy: resize each cross-sectional area of the ROD elementFULLY STRESSED DESIGN (Cont.)dconstr,15,11,-1900.,1900.

53、dconstr,15,12,-1900.,1900.dconstr,15,13,-1900.,1900.dconstr,15,14,-1900.,1900.dconstr,15,15,-1900.,1900.dconstr,15,16,-1900.,1900.dconstr,15,17,-1900.,1900.dconstr,15,18,-1900.,1900.dconstr,15,19,-1900.,1900.dconstr,15,20,-1900.,1900.dconstr,15,21,-1900.,1900.desvar,1,a1,5.25,.01,10.dvprel1,1,prod,1

54、,A,1.,10.,1,1.desvar,2,a2,5.25,.01,10.dvprel1,2,prod,2,A,1.,10.,2,1.desvar,3,a3,5.25,.01,10.dvprel1,3,prod,3,A,1.,10.,3,1.desvar,4,a4,5.25,.01,10.dvprel1,4,prod,4,A,1.,10.,4,1.desvar,5,a5,5.25,.01,10.dvprel1,5,prod,5,A,1.,10.,5,1.desvar,6,a6,5.25,.01,10.dvprel1,6,prod,6,A,1.,10.,6,1.ID SEMINAR, PROB

55、2$ fully_stressed2.datSOL 200CENDTITLE= Truss optimization-FSDlabel = vary all propertiesdesobj = 5 $ weightSUBCASE 1 analysis = statics SPC = 2 LOAD = 2 STRESS = ALL dessub = 15 $ stress constraintsBEGIN BULKdresp1,5,weight,weightdresp1,11,stress,stress,prod,2,1dresp1,12,stress,stress,prod,2,2dresp

56、1,13,stress,stress,prod,2,3dresp1,14,stress,stress,prod,2,4dresp1,15,stress,stress,prod,2,5dresp1,16,stress,stress,prod,2,6dresp1,17,stress,stress,prod,2,7dresp1,18,stress,stress,prod,2,8dresp1,19,stress,stress,prod,2,9dresp1,20,stress,stress,prod,2,10dresp1,21,stress,stress,prod,2,11desvar,7,a7,5.2

57、5,.01,10.dvprel1,7,prod,7,A,1.,10.,7,1.desvar,8,a8,5.25,.01,10.dvprel1,8,prod,8,A,1.,10.,8,1.desvar,9,a9,5.25,.01,10.dvprel1,9,prod,9,A,1.,10.,9,1.desvar,10,a10,5.25,.01,10.dvprel1,10,prod,10,A,1.,10.,10,1.desvar,11,a11,5.25,.01,10.dvprel1,11,prod,11,A,1.,10.,11,1.doptprm,fsdmax,10,p1,1,p2,11PROD 1

58、1 5.25PROD 2 1 5.25PROD 3 1 5.25PROD 4 1 5.25PROD 5 1 5.25PROD 6 1 5.25PROD 7 1 5.25PROD 8 1 5.25PROD 9 1 5.25PROD 10 1 5.25PROD 11 1 5.25$ modelENDDATAUser Input File Initial Stress Output VARY ALL PROPERTIES SUBCASE 1 S T R E S S E S I N R O D E L E M E N T S ( C R O D ) ELEMENT AXIAL SAFETY TORSI

59、ONAL SAFETY ELEMENT AXIAL SAFETY TORSIONAL SAFETY ID. STRESS MARGIN STRESS MARGIN ID. STRESS MARGIN STRESS MARGIN 1 -1.235161E+03 5.4E-01 0.0 2 -8.678073E+02 1.2E+00 0.0 3 -7.293841E+02 1.6E+00 0.0 4 -6.814683E+02 1.8E+00 0.0 5 -1.459390E+02 1.2E+01 0.0 6 1.459390E+02 1.2E+01 0.0 7 3.691398E+02 4.1E

60、+00 0.0 8 -3.691398E+02 4.1E+00 0.0 9 3.619048E+02 4.2E+00 0.0 10 2.000000E+02 8.5E+00 0.0 11 6.095238E+02 2.1E+00 0.0 Final stress output VARY ALL PROPERTIES SUBCASE 1 S T R E S S E S I N R O D E L E M E N T S ( C R O D ) ELEMENT AXIAL SAFETY TORSIONAL SAFETY ELEMENT AXIAL SAFETY TORSIONAL SAFETY I