Introduction to Optimum Design phần 3 pptx

... on the optimum solution.xx u12 3 52=- =- =-,xx u12 3 52=- = =-,xx u12 3 12==- =,xx u12 3 12== =,xxuf12000000*,*,* , ,===()= 23 032 012 12xx xx-=-+=; Optimum Design ... convex.Sh itopg j mij=()==()£={}xx x01 01,; ,to Optimum Design Concepts 1 53 14012010080604020–20–40–60–80–100–120–140–160–5 –4 3 –2 –11 234 56Function isconvex for x ≤ 2 /3 f ... x1x2+ 2x22+ 3x 3 2- 2x1x 3 4.19 F(x) = x12+ 2x2x 3 + x22+ 4x 3 24.20 F(x) = 4x12+ 2x1x 3 - x22+ 4x 3 2Section 4 .3 Unconstrained Optimum Design Problems4.21 Answer True...

Introduction to Optimum Design phần 5 pptx

... size is always positive. 30 0 INTRODUCTION TO OPTIMUM DESIGN 32 2 INTRODUCTION TO OPTIMUM DESIGN FIGURE 9-7 Iteration history for Example 9.7 with Newton’s method.TABLE 9-2 Optimum Solution for Example ... 2.0000x2 3. 9765 3. 9998 3. 9999f 3. 4564E-05 1.0 239 E-08 2.5054E-10||c|| 3. 3 236 E- 03 1.2860E-04 9. 035 7E-04No. of function 138 , 236 65 34 9evaluationsNo. of iterations 9670 22 13 8.1 .3 Convergence of AlgorithmsThe ... direction.8 .31 Exercise 8.21 8 .32 Exercise 8.228 .33 Exercise 8. 23 8 .34 Exercise 8.248 .35 Exercise 8.25 8 .36 Exercise 8.268 .37 Exercise 8.27 8 .38 Exercise 8.288 .39 Exercise 8.29 8.40 Exercise 8 .30 Numerical...

Introduction to Optimum Design phần 1 pdf

... xix14 INTRODUCTION TO OPTIMUM DESIGN TABLE 1-1 continued To convert from U.S British To SI units Multiply byVolumefoot 3 (ft 3 ) meter 3 (m 3 ) 0.02 831 685inch 3 (in 3 ) meter 3 (m 3 ) 1. 638 706 ... meter 3 (m 3 ) 2.84 130 7 E–05ounce (U.S. ﬂuid) meter 3 (m 3 ) 2.95 735 3 E–05pint (U.S. dry) meter 3 (m 3 ) 5.506105 E–04pint (U.S. liquid) meter 3 (m 3 ) 4. 731 765 E–04quart (U.S. dry) meter 3 (m 3 ) ... Function Contours 63 3.2.5 Identiﬁcation of Optimum Solution 63 3 .3 Use of MATLAB for Graphical Optimization 64 3. 3.1 Plotting of Function Contours 64 3. 3.2 Editing of Graph 64 3. 4 Design Problem...

Introduction to Optimum Design phần 2 pdf

... 165 75 28 0 .32 3. Magnesium alloy A261 1800 90 45 16 0 .35 4. Berylium 1850 110 30 0 147 0.025. Titanium 4500 165 110 42 0 .30 TorquedidolFIGURE E3 -34 Hollow torsion rod.TABLE E3 -34 (A) Rod ... x1x2subject to x1+ x22£ 0x21+ x22£ 9 3. 10 Minimize f(x1, x2) = 3x1+ 6x2subject to -3x1+ 3x2£ 24x1+ 2x2£ 4-x1+ 3x2≥ 172 INTRODUCTION TO OPTIMUM DESIGN 4.2.4 ... method. 3. 39 Solve Exercise 3. 23 for a column pinned at both ends. The buckling load for such acolumn is given as p2EI/l2. Use graphical method.76 INTRODUCTION TO OPTIMUM DESIGN TABLE E3 -34 (B)...

Introduction to Optimum Design phần 4 pdf

... x1x2x 3 x4x5x6x7x8bx 3 001-10 -10 12x5000 11 0-100x20101– 3 02– 3 0 -2– 3 2– 3 x11001– 3 0 -1– 3 01– 3 5– 3 Cost 0 0 05– 3 07– 3 0 -7– 3 f + 13 – 3 the ... 10-1000–1= 0x20100-1– 3 2– 3 1– 3 -2– 3 2– 3 Negativex11000-1– 3 -1– 3 1– 3 1– 3 5– 3 NegativeCost 0000-5– 3 7– 3 5– 3 -7– 3 f + 13 – 3 Artiﬁcial 00000 01 1w - 0Final tableau: ... 1.5x4subject to 5x1+ 3x2+ 1.5x 3 £ 81.8x1- 6x2+ 4x 3 + x4≥ 3 -3. 6x1+ 8.2x2+ 7.5x 3 + 5x4= 15xi≥ 0; i = 1 to 46.64 Minimize f = 8x - 3x2+ 15x 3 subject to 5x1- 1.8x2- 3. 6x 3 ≥...

Introduction to Optimum Design phần 6 potx

... - 13 Second iterationX2011–6-1–6001–6-1–61–600-1– 3 2– 3 Y2002– 3 1– 3 -10-10– 3 10– 3 -1– 3 102– 3 14– 3 Y 3 00 -2– 3 2– 3 01-2– 3 2– 3 -2– 3 011– 3 1– 3 X1101–2-1–2001–2-1–21–200 ... Exercise 3. 34 10.69* Exercise 3. 35 10.70* Exercise 3. 3610.71* Exercise 3. 50 10.72* Exercise 3. 51 10. 73* Exercise 3. 5210.74* Exercise 3. 53 10.75* Exercise 3. 54Numerical Methods for Constrained Optimum ... 2. 13 at the point w = 10m, d = 10m, h = 4m.10. 53 Exercise 2.14 at the point P1= 2 and P2= 1. 37 6 INTRODUCTION TO OPTIMUM DESIGN ...

Introduction to Optimum Design phần 7 pot

... 0.00000E+00 2.27873E+01 7.87500E+02 9.9 438 E+00 9.9 438 E+00 1.0000E-01 3 1.25020E-02 1 .31 993E+00 7. 130 63E+02 9.0 133 E+00 9.0 133 E+00 1.0000E-014 2.19948E-02 1. 036 43E-01 6.99 734 E+02 7.6 933 E+00 1.0000E+01 ... constraints.458 INTRODUCTION TO OPTIMUM DESIGN 11 10 9 8 7 6 5 4 3 2 1 01 23 Iteration no. Design variable value456789101112 131 4FIGURE 13- 5 History of design variables for the spring design ... 1.4 735 2E-02 5.5455E-02 4 .32 30E-01 9.0 837 E+008 CCC 3. 533 58E-02 1.67623E-02 1.19085E-02 5.2692E-02 3. 8896E-01 9.0828E+009 CCC 4.24950E-04 1.67623E-02 1.27298E-02 5 .34 85E-02 4.0151E-01 9.0 831 E+0010 CCS...

Introduction to Optimum Design phần 8 pot

... 15.00 1010 1 23 3.750W36 ¥ 230 67.60 35 .90 0.760 16.470 1.260 15000 837 14.90 940 114 3. 730 W36 ¥ 210 61.80 36 .69 0. 830 12.180 1 .36 0 132 00 719 14.60 411 67.5 2.580W36 ¥ 194 57.00 36 .49 0.765 ... 3. 830 W36 ¥ 280 82.40 36 .52 0.885 16.595 1.570 18900 1 030 15.10 1200 144 3. 810W36 ¥ 260 76.50 36 .26 0.840 16.550 1.440 1 730 0 9 53 15.00 1090 132 3. 780W36 ¥ 245 72.10 36 .08 0.800 16.510 1 .35 0 ... involving526 INTRODUCTION TO OPTIMUM DESIGN TABLE 15 -3 Some Wide Flange Standard SectionsSection A d twbtfIxSxrxIySyryW36 ¥ 30 0 88 .30 36 .74 0.945 16.655 1.680 2 030 0 1110 15.20 130 0 156 3. 830 W36...

Introduction to Optimum Design phần 9 ppsx

... 0++-≥xxx1 23 60 0++-≥07 131 4 33 3 £-+£ =+xx jjj; to 071414 33 32 £-+£ =+-xx jjj; to 07 131 4 31 32 £-+£ =+-xx jjj; to f x Ex x Ex x Exkkkkkkkx()= ()++-()++-()()++++++=Â 23 10 ... (bi, ci) (i = 1 to 8) are given as (3. 8112E+00, 3. 4604E- 03) , (2.0567E- 03, 1 .35 14E-05),(1. 034 5E-05, 5. 237 5E-06), (6. 830 6E+00, 6 .30 00E-08), (3. 0 234 E-02, 7.0000E-10), (1.2814E- 03, 3. 4050E-04),(2.2660E-07, ... ()++-()++-()()++++++=Â 23 10 4 17 10 4 22 15 4 31 31 3 32 32 2 33 33 204 15 14££ =xii; to xxxx1222 3 24240 0+++-=xxxx1 234 25 0-≥fxxxxxxx()=++()+14 1 2 3 307506512££ ££xx,xx22150...

Introduction to Optimum Design phần 10 ppsx

... 0 .33 3; for b 3 = 3: -1 £D 3 £ 1. 6.1 13 For b1= 5: -2 £D1£•; for b2=-4:5 3 1 3 7 3 5 3 2 3 5 3 7 3 5 3 1 3 2 3 7 3 16 3 5 3 2 3 13 310 3 2 3 7 3 2 3 5 3 7 3 5 3 657 33 71571 3 8 3 118982 3 5 3 690 ... 4.151 18. 43 £q£ 71.57°. 4.152q≥ 71.57°. 4.1 53 Nosolution. 4.154q£ 18. 43 .91611125 3 32pp210 3 2 3 24767271 3 4 3 1 3 4 3 192 23 40 23 48 23 11 3 5 3 13 6 23 6 13 61162476727688 ... constrained problems, 33 2 33 4steepest descent method, 2 93 296, 31 0 31 5step size determination, 30 5 31 0unconstrained optimization methods, 33 2 33 4 Design ofcabinet, 30 32 can, 18–20rectangular...

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