Issue 51

E. Mousavian et alii, Frattura ed Integrità Strutturale, 51 (2020) 336-355; DOI: 10.3221/IGF-ESIS.51.25





b

b

b  

b

,lim N S  j

H

cos α γ

cosα

(15)

j

j

j

j

j

,lim





b

b

b  

b

,lim T S  j

H

sin α γ

sinα

(16)

j

j

j

j

j

,lim

=  N b j, lim

Taking into account that T b j, lim

, the limiting hoop force resultant H b j, l im is:











 

μcos α γ sin α γ sin α μcosα b b b j j j j j     

S

b j



(17)

H

,lim

j

j

So, the parallel sliding constraint can be formulated as:

b

b

b

,lim j H H H    i j

(18)

1,lim

It should be observed that this constraint is more accurate than that proposed in the previous work [1] and therefore different results can be expected.

(a)

(b)

Figure 7 : a) Resultant of the hoop stresses H i b per unit length of parallels passing through the corresponding control point at level z i and equilibrium diagram for forces per unit length of parallels; b) meridional forces at the two interfaces ( S j -1 b and S j b ) whose horizontal components are H j -1 b and H j b , respectively. Lastly, the optimization problem can be stated as follows: t /2 = Min max     2 2 b i i x z R         (19)

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