PSI - Issue 83

Victor Rizov et al. / Procedia Structural Integrity 83 (2026) 105–114

110

3 L L J J J J    . 2 1 L

(22)

The quantities in the left side of Eq. (22) are the solutions in portions, 1 L , 2 L and 3 L , of the contour. 1 L J is

     

  

i n 

  

v

u





up  

cos

ds

p

J

u

p

1

1









L

L

,

(23)

1

0 1

1

1 xL i

1 yL i

1

L

L i

L

L

x

x





1

i



L

L

where up n is the number of layers in the upper delamination arm (the portion, 1 L , intersects transversely the upper delamination arm as shown in Fig. 1). The equations to determine the elements of 1 L J are written below.   i i L i d u   0 1 , (24) 1 cos 1  L  , (25)

xL i p   1 L x u L

i   1 ,

(26)

 

,

(27)

i

0 1  yL i p ,

(28) (29)

1 ds L 

dz

,

2

where

1 h    z

h

1

.

(30)

2

2

2

In Eq. (30) the following notations are used: 1 h - the thickness of the upper arm of the delamination; 2 z - the central axis of the cross-section of the upper arm of the delamination. The change of i  across the thickness of the upper arm of the delamination is   n up i z z 2 2     . (31) The notations in Eq. (31) are: up  - curvature; n z 2 - distance of the neutral axis from the centre of the cross-section of the upper arm of the delamination. Equations (32) and (33) are used to determine up  and n z 2 .

     up i i n i z 1 2 1

 N b

i dz



,

(32)

2

z

2

i

     up i i n i z 1

2 1

 M b

z dz

i 

.

(33)

2

2 2

y

z

2

i