1-10 This and the following problem may be the student’s first experience with a figure of merit.
• Formulate fom to reflect larger figure of merit for larger merit.
• Use a maximization optimization algorithm. When one gets into computer implementa-
tion and answers are not known, minimizing instead of maximizing is the largest error
one can make.
F V = F 1 sin θ − W = 0
F H = − F 1 cos θ − F 2 = 0
From which
F 1 = W / sin θ
F 2 = − W cos θ/ sin θ
fom = − S = − ¢ γ (volume)
= − . ¢ γ (l 1 A 1 + l 2 A 2 )
A 1 = F 1
S = W
S sin θ , l 2 = l 1
cos θ
= W cos θ
F 2
A 2 =
S
S sin θ
l 2
W
fom = − ¢ γ
S sin θ + l 2 W cos θ
1 + cos 2 θ
= − ¢ γ W l 2
cos θ sin θ
Set leading constant to unity
θ ◦ fom
θ * = 54 . 736 ◦ Ans.
0 −∞
fom* = − 2 . 828
20 − 5.86
Alternative:
30 − 4.04
40 − 3.22
d
= 0
45 − 3.00
d θ
50 − 2.87
And solve resulting tran-
Bạn đang xem 1- - TÀI LIỆU SHI20396 CHƯƠNG 1 PDF
