Issue 70

S.K. Shandiz et alii, Frattura ed Integrità Strutturale, 70 (2024) 24-54; DOI: 10.3221/IGF-ESIS.70.02

            

            

2

2

2

f   [ ] T i i 



T

1 1 2 2 [ ] N N N [ ] [ ] i m T T m

T

T

m

[

]

[ ] N

1 3 N [

]

M N

f

f

b

i

yi

yt

t







i

i

i

0

0

0

I

[0] [0] [0] [0] [0] [0]

0

0 0

0 0 0

0 0 0 0

0 0 0 0 0

0

m

0 0 0 0 0

0



[ ] M

(14)

m

0 0 0 0

1

m

0 0 0

2

m

0 0

t

0

m

0

t

1

[ ] C

{0}

{0}

{0} {0} {0} {0}

         

          

b

2 c b c b c b c b  2 1 1 2 2 1 1 2 2

 

1 1 c b c b   2 2 c c

[0] [0]

0 0 0 0

0 0 0 0

1 1 2 2 c b c b 

c c 

1 2

1

2





 

0 0 0 

c

c b

c

c c

 

[ ]

0  0 0

[ ] C

(15)

N N

3 1

1 1

1

1 3



c

c b

c

c c

[

]

4 2

2 2

2

2 4



c

c

[0]

0 0

0 0

t

t

1

1 c







c

c

c

2 3 N [

]

t

t

t

t

1

1

2

[ ] K

{0}

{0}

{0} {0} {0} {0}

          

          

b

2 kb k b kb k b   2



kb

k b

[0] [0]

0 0 0 0

0 0 0 0 k 

1 1

2 2

1 1

2 2

1 1

2 2

1 1 kb k b  2 2

k k 





k

k

1

2

1

2



3 1 3 1 N N x N N x 4 2 4 2 [ ] [ ] [ ] [ ] x x c c    



 

0 0 0 

k

kb

k k k



0  0 0

[ ] K

(16)

1

1 1

1

1

3



k

k b

k

k k

2

2 2

2

2

4



k

[0]

0 0

0 0

t

t

1

1







k

c

k k k

[

]

[

]



2 3 N N x t x

t

t

t

t

2

2 3

3

1

1

            

            

3

 N

f ˆ [ ] 0 0 T i i



i

0



F { }

(17)

3 1 k r x c r x k r x c r x     3 2 ( ) 4 ( ) 4

1 ( ) ( ) 2

v

v

0

2 3 ( ) k r x c r x  2 t t 

3 ( )

v

where in the Eqn. (14) and (17):

31