Problems 777(^12)
3
P^45 °
X
Y
x x
h
Figure 14.15 Two-bar truss.
subject to
g 1 (X)=
P ( 1 +x 1 )
√
1 +x 12
2
√
2 x 1 x 2
−σ 0 ≤ 0
g 2 (X)=
P (x 1 − 1 )
√
1 +x 12
2
√
2 x 1 x 2
−σ 0 ≤ 0
xi≥xi(l), i= 1 , 2
wherex 1 =x/ h,x 2 =A/Aref, hthe depth,Eis Young’s modulus,ρthe weight density,
σ 0 the permissible stress, andxi(l)the lower bound onxi. Find the optimum solutions of
the individual objective functions subject to the stated constraints using a graphical pro-
cedure. Data:P= 10 ,000 lb, ρ= 0 .283 lb/in^3 , E= 30 × 106 psi,h=100 in.,Aref= 1
in.^2 , σ 0 = 20 ,000 psi,x(l) 1 = 0 .1, andx 2 (l)= 1 .0.
14.20 Solve the two-objective optimization problem stated in Problem 14.19 using the weight-
ing method with equal weights to the two objective functions. Use a graphical method
of solution.
14.21 Solve the two-objective optimization problem stated in Problem 14.19 using the global
criterion method withp=2. Use a graphical method of solution.
14.22 Formulate the two-objective optimization problem stated in Problem 14.19 as a goal
programming problem using the goals of 30 lb and 0.015 in. for the objectivesf 1 and
f 2 , respectively. Solve the problem using a graphical procedure.
14.23 Consider the following two-objective optimization problem:
FindX= {x 1 x 2 x 3 x 4 x 5 x 6 }T
to minimize