Introduction to Optimum Design phần 10 ppsx

... 7.999771).Chapter 10 Numerical Methods for Constrained Optimum Design 10. 29 x* = ( , ), u* = 1, f* = 0.5. 10. 30 x* = (1, 1), u* = 0, f* = 0. 10. 31 x* = (, ),u* = , f* = . 10. 32 x* = (2, 1), u* = 0, f* =-3. 10. 33 ... objective, 552Pareto ﬁtness, 554plotting, 61–62utility, 551Chapter 12 Introduction to Optimum Design with MATLAB12.1 For l = 0.5m, To= 10kN◊m, Tmax= 20kN◊m, x1*= 103 mm, x2*= 0.955, ... 6 .100 y1= 0, y2= , y3= 6 .101 y1=-0.5,y2=-2.5. 6 .102 y1=- , y2= 0, y3= . 6 .103 y1= 0.2, y2= 0.4. 6 .104 y1= 0.25, y2=1.25, y3= 0, y4= 0. 6 .105 y1= 2, y2= 0. 6 .106 ...

Introduction to Optimum Design phần 9 ppsx

... 1972)minimizefxxxxxxxx()=- +ÊËˆ¯++-+()421134412141212 2222.588 INTRODUCTION TO OPTIMUM DESIGN A .10 A couple deposits $100 0 in a bank at the end of every month for the next 12months (one ... 1981)minimizesubject to 18 .10 (Hock and Schittkowski, 1981)minimizesubject to xxx13 14 15 105 0++- ≥xxx 10 11 1285 0++-≥xxx78970 0++-≥xxx45650 0++-≥xxx12360 0++-≥07131433 3£-+£ =+xx jjj; to 07141433 ... B.bainjnjiij=()==cofac to toA;;11xAb=-1AAx Ab =11AB BA I==()nAppendix B Vector and Matrix Algebra 625 to unity. Once the matrix is converted to that form, the determinant is...

Introduction to Optimum Design phần 1 pdf

... ContentsPrefaceixChapter 1 Introduction to Design 11.1 The Design Process 21.2 Engineering Design versus Engineering Analysis 41.3 Conventional versus Optimum Design Process 41.4 Optimum Design versus ... the vector x. To summarize, the following considerations shouldbe given in identifying design variables for a problem.16 INTRODUCTION TO OPTIMUM DESIGN Is all theinformationavailable to solve ... conventional design process can lead to uneconomical designsand can involve a lot of calendar time. The optimum design process forces the designer to identify explicitly a set of design variables,...

Introduction to Optimum Design phần 2 pdf

... 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 ... 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 ... Mathematica command used to plot the contour of a function, say g1 = 0, is entered asPlotg1=ContourPlot[g1,{x1,0,25},{x2,0,25}, ContourShadingÆFalse, ContoursÆ{0}, ContourStyleÆ{{Thickness[.01]}},...

Introduction to Optimum Design phần 3 pptx

... 40 (100 ) or f* = 10, 250cm3. Theus u g s s i to ii i i i i=≥+=≥ =00 00 1422,, ,;∂∂=-¥()-=LAluAu222622416 10 0.∂∂=-¥()-=LAluAu111612320 10 0. Optimum Design ... 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- ... 9x2subject to x1+ 2x2£ 10 4x1- 3x2£ 20; xi≥ 0; i = 1, 24.65 Minimize f(x1, x2) = (x1- 1)2+ (x2- 1)2subject to x1+ x2- 4 £ 0170 INTRODUCTION TO OPTIMUM DESIGN In this...

Introduction to Optimum Design phần 4 pdf

... 18x1, x2≥ 06.67 Maximize z = x1+ 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 ... identiﬁed to be replaced with x1in the basic set.BasicØ x1x2x3x4x5x6x7x8b Ratiox31 210 000055–1= 5x4 2101 000044–2= 2x7 2100 -101 044–2= 2x81 -10 0 0 -101 11–1= ... 2x2subject to -x1+ 3x2£ 10 x1+ x2£ 6x1- x2£ 2x1, x2≥ 0250 INTRODUCTION TO OPTIMUM DESIGN (6.20)6.4.3 Deﬁnition of Phase I ProblemSince the artiﬁcial variables are introduced to simply...

Introduction to Optimum Design phần 5 pptx

... 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 ... called the DFP (Davidon-Fletcher-Powell) method:324 INTRODUCTION TO OPTIMUM DESIGN 290 INTRODUCTION TO OPTIMUM DESIGN In general, we continue to evaluate the function at the points(8.14)Let us ... ,∂∂ ∂∂x2x1f = 100 f = 25(0.6, 4)c = (30, 8)t = (–4, 15)d830FIGURE 9-4 Contours of function f = 25x12+ x22for f = 25 and 100 .316 INTRODUCTION TO OPTIMUM DESIGN The Hessian of...

Introduction to Optimum Design phần 6 potx

... point w = 10m, d = 10m, h = 4m. 10. 53 Exercise 2.14 at the point P1= 2 and P2= 1.376 INTRODUCTION TO OPTIMUM DESIGN ...

Introduction to Optimum Design phần 7 pot

... constraints.458 INTRODUCTION TO OPTIMUM DESIGN 11 10 9 8 7 6 5 4 3 2 1 0123Iteration no. Design variable value45678 9101 1121314FIGURE 13-5 History of design variables for the spring design ... point.9. The designer should be able to request a constraint correction at any iteration. 10. The designer should be able to request a constant cost step.11. The designer should be able to request ... progress of the iterative process toward the optimum point.2. Histories of design variables. These can be used to observe the trend in design variables and possibly used to extrapolate their values.3....

Introduction to Optimum Design phần 8 pot

... of designs for new generation (reproduction).x1 = 101 110 | 100 1x2 = = 0101 00| 101 1(A) Designs selected for crossover (parent chromosomes)x1' = 101 110 | 101 1x2' = = 0101 00| 100 1(B) ... OPTIMUM DESIGN x1 = 101 | 1101 |001 x2 = 010 | 100 1|011(A) Designs selected for crossover (parent chromosomes)x1’ = 101 | 100 1|001 x2’ = 010 | 1101 |011(B) New designs (children) ... 16.595 1.570 18900 103 0 15 .10 1200 144 3. 810 W36 ¥ 260 76.50 36.26 0.840 16.550 1.440 17300 953 15.00 109 0 132 3.780W36 ¥ 245 72 .10 36.08 0.800 16. 510 1.350 1 6100 895 15.00 101 0 123 3.750W36...

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