Engineering Optimization: Theory and Practice, Fourth Edition

8.11 Complementary Geometric Programming 523 Degree of Difficulty. The degree of difficulty of a complementary geometric pro- gr ...

524 Geometric Programming they can each be approximated by a single-term posynomial with the help of Eq. (8.78) as ̃ Q 1 (X, ̃ X ...

8.12 Applications of Geometric Programming 525 Next we chooseX(^2 )to be the optimal solution of OGP 1 [i.e.,X(o^1 pt)] and appr ...

526 Geometric Programming If the maximum feed allowable on the lathe isFmax, we have the constraint C 11 F≤ 1 (E 4 ) where C 11 ...

8.12 Applications of Geometric Programming 527 where C 31 =a 2 Sm−^1 ax (E 9 ) If the constraint (E 8 ) s also included, the pro ...

528 Geometric Programming Figure 8.2 Cantilever beam of rectangular cross section. SOLUTION The width and depth of the beam are ...

8.12 Applications of Geometric Programming 529 The axial force applied (F )and the torque developed (T) are given by [8.37] F= ∫ ...

530 Geometric Programming Table 8.3 Results for Example 8.10 Iteration Starting Ordinary geometric programming Solution number d ...

8.12 Applications of Geometric Programming 531 To avoid fatigue failure, the natural frequency of the spring (fn) is to be restr ...

532 Geometric Programming of the shaft,Rthe radius of the journal,Lthe half-length of the bearing,Sethe shear stress,lthe length ...

8.12 Applications of Geometric Programming 533 subject to 8. 62 R−^1 L^3 ≤ 1 (E 13 ) The solution of this one-degree-of-difficul ...

534 Geometric Programming or 1. 75 √ 900 +h^2 dh ≤ 1 (E 2 ) It can be seen that the functions in Eqs. (E 1 ) nd (Ea 2 ) re not p ...

8.12 Applications of Geometric Programming 535 The optimum values ofxican be found from Eqs. (8.62) and (8.63): 1 = 0. 188 y∗d∗ ...

536 Geometric Programming The objective function for minimization is taken as the sum of squares of structural error at a number ...

References and Bibliography 537 subject to 3 a d ≤ 1 Noting thatc 1 = 0. 1 563,c 2 = 0 .76,andc 3 = 3 /d, we see that Eq. (E 12 ...

538 Geometric Programming 8.11 D. Wilde, Monotonicity and dominance in optimal hydraulic cylinder design, Jour- nal of Engineeri ...

Review Questions 539 interpretation, pp. 15–21, inProgress in Engineering Optimization–1981, R. W. Mayne and K. M. Ragsdell, Eds ...

540 Geometric Programming 8.5 What is normality condition in a geometric programming problem? 8.6 Define a complementary geometr ...

Problems 541 8.12 Minimizef (X)=x− 12 +^14 x^22 x 3 subject to 3 4 x 2 1 x − 2 2 + 3 8 x^2 x − 2 3 ≤^1 xi> 0 , i= 1 , 2 , 3 8 ...

542 Geometric Programming Figure 8.5 Floor consisting of a plate with supporting beams [8.36]. 8.21 A rectangular area of dimens ...