PSI - Issue 28

Victor Rizov et al. / Procedia Structural Integrity 28 (2020) 1212–1225 Author name / Structural Integrity Procedia 00 (2019) 000–000

1217

6





G G t 

2 0 0 

g







 G G G e     

,

(14)

0

0

0

g

g

where

0 G G G g  

0 02

.

(15)

G G

0

02

02 G , in radial direction of the beam is expressed as

The variation of the shear modulus,

4 R h R

02 C G G e  02

,

(16)

where

4 0 R R   .

(17)

In (16), C G 02 is the value of 02 G in the centre of the beam cross-section, h is a parameter that controls the distribution of 02 G in radial direction. The variation of C G 02 in the length direction of the beam is written as

l m x

D C G G e 02 02  ,

(18)

where

x l   0 .

(19)

D G 02 is the value of

C G 02 at the free end of the beam, m is a parameter that controls the variation of

In (18),

C G 02 along the beam length. The distribution of 2  in radial direction is expressed as

4 R n R C e    , 2

(20)

2

where

4 0 R R   .

(21)

C 2  in the centre of the beam cross-section, n is a parameter that controls the

In (20), 2  is the value of

distribution of 2  in radial direction. The distribution of

C 2  along the beam length is written as

l s x

D e 2

C   2



,

(22)

where