X j Rd , j 1, 2,....., n
(9.9)
X 0; s 0,1
(9.10)
where C ( X ; s) represents cost function, i X ; s is the behavioural constraints and
i X ; s denotes the maximum allowable value , ‘m’ and ‘n’ are the number of constraints d and design variables respectively. A given set of discrete value is expressed by R and in this
chapter objective function is taken as T
m
t 1
n 1
C X ; s ct s xntn
(9.11)
and constraint are chosen to be stress of structures as follows
i X ; s n i s with allowable tolerance i0 s for i 1,2,...., m
(9.12)
The deflection of the structure as follows 0 X ; s n max s with allowable tolerance max s
(9.13) th
Where ct is the cost coefficient of tth side and xn is the n design variable respectively, m is 0 the number of structural element, i and i0 s max s are the i stress , allowable stress and
th
allowable deflection respectively. To solve the SOWBP (P9.2), step 1 of 1.40 is used and let UCT X ;s ,UCI X ;s ,UCF X ;s be the upper bounds of truth, indeterminacy , falsity function for the objective respectively and LTC X ;s , LIC X ;s , LFC X ;s be the lower bound of truth, indeterminacy, falsity membership
functions of objective respectively then
U CT X ;s max C X 1; s , C X 2 ; s ,
(9.14)
LTf x;s min C X 1; s , C X 2 ; s ,
(9.15)
U CF X ;s U CT X ;s ,
(9.16)
LFC X ;s LTC X ;s C X ;s where 0 C X ;s U CT X ;s LTC X ;s
LIC X ;s LTC X ;s ,
(9.17) (9.18)
U CI X ;s LTC X ;s C X ;s where 0 C X ;s UCT X ;s LTC X ;s
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(9.19)