Issue 67

D. Scorza et alii, Frattura ed Integrità Strutturale, 67 (2024) 280-291; DOI: 10.3221/IGF-ESIS.67.20

1

    3 0

    2



0 0 

v

v

(3)

1

1

L

c

1

    3 2 c v L v L L      2 2



0

(4)

 

2 M t

1

2

L

    3 1 v L v L      2 1 1 1

     L



  L

  x







x t,L

dt

with

(5)

12 1 ,

12 ,

c

L

L

IE

1

c

c

 

1 M t

1

2

L

    3 2 1 v L v L      2 2 1

     1 0



  L

  x







t x,L

dt

with

(6)

21 1 ,

21 ,

c

L

L

IE

c

c

    1 1 2 1 v L v L 

(7)

  1 1 IE M L

        1 1 2 1 1 1 v L v L v L L v L         2 1     1 2 4 1 1 c

  



(8)

 

k k

1

1

    4 1         2 4 c v L v L v L v L L L        2 2 1 1 1 1 2 1 2 2 c     5 1         3 5 c v L v L v L v L L L        3 2 1 1 1 1 2 1 2 2 c 1 1

(9)

(10)

where v 1 and v 2 are the transverse displacements of the left and right beam segments, respectively, I is the moment of inertia, E is the elastic modulus, M 1 and M 2 are the bending moments related to the left and right beam segments, respectively, and L c is the material internal characteristic length (0.0 <  L c /L ≤  ).

(a)

y



a

L 1

O

H

x

B

L

(b)

y

k

v 2

v 1

O

H

x

B

L 1

F

L

Figure 1: Edge-cracked nanobeam: (a) undeformed configuration and (b) schematisation according to the present formulation, both in the undeformed and in the deformed configuration.

282