Lat. Am. j. solids struct. vol.11 número4

i

q

g ext

Tu =

g T

K Fext u g E K g G K

g g g

T  E  G

K K K

0 0 i i E 0 0 0 0 3 3 G 3 3 3

1 0 0

E A

, 0 0

0 0

1 0 0

F

, 0 1 0 , i 1,..., b

0 0 1

0 0 i i i l l      _{ } _  _{ }   _{ }        _{ }   _  _{ }   _       I I k I I I I I k I I I 0 _F E A E A = i l i i i i i i l  F_i

F_{i i}

i

q l 

T ext

Fitf u

ci, si l l

,

ci si q q



A_si A_ci

      ci si ci si T ext , A , A

ub ci cable ci ci ub si strut si si ci ub cable ci0

si si ub

strut si 0

Given data: E , E , , ,

min S.t. F 1: S A A F

2 : S

A A

3 : 0

E

4 : S 0

l

E A

5 : S 0

l

6 :

ci si ci si

ci ci

si si

nci ci0

nci ci0

nsi si0

q q l , l

q l

q l

l - l

l - l

l - l

                         f u   si si

si 0 0

2 min

si i

E A E

l

I

0 l

nsi si0 π

l - l

 



 

  2 

ci ci

E , A E , A_{si si}

ci0

l l_si0

n si

l l_nci

u ub strut

S ub

cable

selection

p (i)

selection

j

1 / Ft(i)

p (i)

1 / Ft( j) 



i q











No

Selection (reproduction of the fittest individuals) 9 Crossover Mutation Next generation No No

Create the random population Start

Compute the nodal displacement after applying the external loading

Calculation the other constraints using these obtained displacement if

satisfying

Remove the set of population

Evaluation of the objective fun-ction

End of the population

Yes

Termination test

Yes