Introduction to Optimum Design phần 8 pot

... 1300 156 3 .83 0W36 ¥ 280 82 .40 36.52 0 .88 5 16.595 1.570 189 00 1030 15.10 1200 144 3 .81 0W36 ¥ 260 76.50 36.26 0 .84 0 16.550 1.440 17300 953 15.00 1090 132 3. 780 W36 ¥ 245 72.10 36. 08 0 .80 0 16.510 ... Applications involving526 INTRODUCTION TO OPTIMUM DESIGN TABLE 15-3 Some Wide Flange Standard SectionsSection A d twbtfIxSxrxIySyryW36 ¥ 300 88 .30 36.74 0.945 16.655 1. 680 20300 1110 15.20 ... operators are used to accomplish this task: reproduction, crossover,and mutation. Reproduction is an operator where an old design (D-string) is copied into thenew population according to the design s...

Introduction to Optimum Design phần 6 potx

... trial design point is(n)The cost and constraint functions at the new trial design point are calculated as(o)ffg112152 8 0 725 52 8 320 52 8 0 725 15 03752 8 0 72552 8 60 0 7251 0 21 38 ... that has worked fairly well is 388 INTRODUCTION TO OPTIMUM DESIGN Table 11-1 Simplex Solution Procedure for QP Problem of Example 11.2X1X2X3X4X5X6X7X 8 Y1Y2Y3Y4DInitialY120 ... sizedetermination.ad d d321 6 18 1 6 18 0 1 1 6 18 0 1 2 6 18 0 1 0 5236=+ + = +()+()= F02 02 0211 416 3 24 280 0 4022 21 182 ,, ,,. , . ,=+ = +()()=fRVV010 0 2594 0 4022 46 70 0 6 18 0 4022,max ;...

Introduction to Optimum Design phần 7 pot

... ÈÎÍÍÍ˘˚˙˙˙KxxU 10 033 1214 9 3642 87 86 1 28 585 0 28 4540 3 300 28 585 0 28 4540 3 300. E∂()∂=-+-++ÈÎÍÍÍ˘˚˙˙˙KxUd3 1214 032 85 85 042 85 85 04.. .EEE∂∂=-ÈÎÍÍÍ˘˚˙˙˙∂∂=-ÈÎÍÍÍ˘˚˙˙˙gg114 ... 4.3230E-01 9. 083 7E+00 8 CCC 3.53358E-02 1.67623E-02 1.19 085 E-02 5.2692E-02 3 .88 96E-01 9. 082 8E+009 CCC 4.24950E-04 1.67623E-02 1.27298E-02 5.3 485 E-02 4.0151E-01 9. 083 1E+0010 CCS 1. 089 57E-04 1.67623E-02 ... constraints.4 58 INTRODUCTION TO OPTIMUM DESIGN 11 10 9 8 7 6 5 4 3 2 1 0123Iteration no. Design variable value456 789 1011121314FIGURE 13-5 History of design variables for the spring design...

Introduction to Optimum Design phần 1 pdf

... Minimization Subproblem 282 8. 2.2 Analytical Method to Compute Step Size 283 8. 2.3 Concepts Related to Numerical Methods to Compute Step Size 285 8. 2.4 Equal Interval Search 286 8. 2.5 Alternate Equal ... Algorithm 579 18. 4.2 Domain Elimination Method 580 18. 4.3 Stochastic Zooming Method 582 18. 4.4 Operations Analysis of the Methods 583 18. 5 Numerical Performance of Methods 585 18. 5.1 Summary of ... of Methods 585 18. 5.2 Performance of Some Methods Using Unconstrained Problems 586 Contents xix14 INTRODUCTION TO OPTIMUM DESIGN TABLE 1-1 continued To convert from U.S British To SI units...

Introduction to Optimum Design phần 2 pdf

... asPlotg4=ContourPlot[g4,{x1,-1,25},{x2,-1,25}, ContourShadingÆFalse, ContoursÆ{0,.35}, ContourStyleÆ{{Thickness[.01]}, {GrayLevel[ .8] ,Thickness[.02]}}, DisplayFunctionÆIdentity];62 INTRODUCTION TO OPTIMUM ... of a design problemmay not be linear, in which case curves must be plotted to identify the feasible region, andcontours or iso-cost curves must be drawn to identify the optimum design. To plot ... global (absolute) minimumat x* ifSh j pg i mji=()==()£={}xx x01 01,; ;to to 84 INTRODUCTION TO OPTIMUM DESIGN Optimization methodsOptimality criteria(indirect methods)Search methods(direct...

Introduction to Optimum Design phần 3 pptx

... changes in the cost function.bbdbd-¥()==¥() 480 100 4 80 10 8 323 8 .;.ordbdbd-¥()==¥()240 100 2 40 10 8 2223 8 .;.or Optimum Design Concepts 1654.6.2 Convex FunctionsConsider ... dfdfdssudgdssjj**==dfdsfgdgdsudgdsjjjjxx***()=∂()∂=∂()∂==fguj mjjx**, 1to 1 48 INTRODUCTION TO OPTIMUM DESIGN As in Example 4.31, only the case with = 0 gives candidate optimum points. Solvingthis case, we get the two ... miijjx0,0 x0,0**;**;1 1to and to 144 INTRODUCTION TO OPTIMUM DESIGN 4.51 Consider the following problem with equality constraints:Minimize (x1- 1)2+ (x2- 1)2subject to x1+ x2- 4 = 0x1-...

Introduction to Optimum Design phần 4 pdf

... 4x2subject to x1+ 2x2£ 52x1+ x2= 4254 INTRODUCTION TO OPTIMUM DESIGN 232 INTRODUCTION TO OPTIMUM DESIGN 1. For 2x1+ x2£ 9: y1= 1.6 (c¢3in column x3)2. For x1- 2x2£ 2: y2= 1 .8 ... 20x1- 6x2subject to 3x1- x2≥ 3Linear Programming Methods for Optimum Design 2472 28 INTRODUCTION TO OPTIMUM DESIGN TABLE 6-17 ContinuedThird tableau: x4is identiﬁed to be replaced with ... used to solve the auxiliary problem. This is called Phase I of the Simplex2 08 INTRODUCTION TO OPTIMUM DESIGN 42x1 + x2 = 44x1 + 3x2 = 12x1 + 2x2 = 443322110ABCDFEOptimum...

Introduction to Optimum Design phần 5 pptx

... method. 8. 41 Exercise 8. 21 8. 42 Exercise 8. 22 8. 43 Exercise 8. 23 8. 44 Exercise 8. 24 8. 45 Exercise 8. 25 8. 46 Exercise 8. 26 8. 47 Exercise 8. 27 8. 48 Exercise 8. 28 8.49 Exercise 8. 29 8. 50 Exercise 8. 30Section ... direction. 8. 31 Exercise 8. 21 8. 32 Exercise 8. 22 8. 33 Exercise 8. 23 8. 34 Exercise 8. 24 8. 35 Exercise 8. 25 8. 36 Exercise 8. 26 8. 37 Exercise 8. 27 8. 38 Exercise 8. 28 8.39 Exercise 8. 29 8. 40 Exercise 8. 30Numerical ... is always positive.300 INTRODUCTION TO OPTIMUM DESIGN 322 INTRODUCTION TO OPTIMUM DESIGN FIGURE 9-7 Iteration history for Example 9.7 with Newton’s method.TABLE 9-2 Optimum Solution for Example...

Introduction to Optimum Design phần 9 ppsx

... Optimum Design 591 18. 6 (Hock and Schittkowski, 1 981 )minimizesubject to 18. 7 (Hock and Schittkowski, 1 981 )minimizesubject to 18. 8 (Hock and Schittkowski, 1 981 )minimizesubject to xx2121250-≥xx12700 ... (1. 281 4E-03, 3.4050E-04),(2.2660E-07, 1.6638E-06), (2.5645E-01, 3.5256E-05). 18. 9 (Hock and Schittkowski, 1 981 )minimizesubject to 18. 10 (Hock and Schittkowski, 1 981 )minimizesubject to xxx13 ... 12 84 8 602 09,, ., , .,$,.where the parameters (bi, ci) (i = 1 to 8) are given as(3 .81 12E+00, 3.4604E-03), (2.0567E-03, 1.3514E-05),(1.0345E-05, 5.2375E-06), (6 .83 06E+00, 6.3000E- 08) ,(3.0234E-02,...

Introduction to Optimum Design phần 10 ppsx

... f(a) = 6 .88 747 ¥ 109a4- 3.6111744 ¥ 10 8 a3+ 5 .80 9444 ¥106a2- 2 784 4a+ 41. 8. 24 f(a) = 8 a2- 8 a+ 2. 8. 25 f(a) = 18. 5a2- 85 a- 13.5. 8. 26f(a) = 288 a2- 96a+ 8. 8. 27 ... 0.0 280 ). 8. 57 x(2)= (0.259, -0.225, 0.145). 8. 58 x(2)= (4.2 680 , 0.2244). 8. 59 x(2)= (3 .84 15, 0. 480 87). 8. 60 x(2)= (-1.590, 2.592). 8. 61x(2)= (2.93529, 0.33976, 1.4 287 9, 2.29679). 8. 62 ... 0.16665. 8. 37a*= 0.5. 8. 38 a* = 0.40145. 8. 39a* = 0.5. 8. 40a* = 0.5. 8. 41a* = 0.6097. 8. 42a* = 0.5. 8. 43a* = 3.45492E-03. 8. 44a* = 0.5. 8. 45a* = 2.2974. 8. 46a* =0.1667. 8. 47a*...

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