Engineering Optimization: Theory and Practice, Fourth Edition

7.22 Test Problems 471

l

L

h P

h

b

t

Figure 7.23 Welded beam [7.39].

Objective function:f (X)= 1. 10471 x 12 x 2 + 0. 04811 x 3 x 4 ( 41. 0 +x 2 )

Constraints:

g 1 ( X)=τ(X)−τmax≤ 0

g 2 ( X)=σ(X)−σmax≤ 0

g 3 (X)=x 1 −x 4 ≤ 0

g 4 ( X)= 0. 10471 x 12 + 0. 04811 x 3 x 4 ( 41. 0 +x 2 )− 5. 0 ≤ 0

g 5 ( X)= 0. 125 −x 1 ≤ 0

g 6 ( X)=δ(X)−δmax≤ 0

g 7 (X)=P−Pc(X)≤ 0

g 8 ( X)tog 11 ( X): 0. 1 ≤xi≤ 2. 0 , i= 1 , 4

g 12 ( X)tog 15 ( X): 0. 1 ≤xi≤ 01. 0 , i= 2 , 3

where

τ (X)=

√

(τ′)^2 + 2 τ′τ′′

x 2

2 R

+(τ′′)^2

τ′=

P

√

2 x 1 x 2

, τ′′=

MR

J

, M=P

(

L+

x 2

2

)

R=

√

x 22

4

+

(

x 1 +x 3

2

) 2