PSI - Issue 58

Victor Rizov et al. / Procedia Structural Integrity 58 (2024) 137–143 V. Rizov / Structural Integrity Procedia 00 (2019) 000–000

140

4

h 2

z



4 

g B B e 

h

,

(7)

h 2

z



5 

g D D e 

h

,

(8)

h 2

z



6 

g P P e 

h

,

(9)

h 2

z



7 

g Q Q e 

h

,

(10)

where

z h    .

2 h

(11)

2

In formulas (4) – (11),    are parameters, h is the beam thickness. The viscoelastic model in Fig. 2 is under strain,  , variation of which with respect to time is expressed by   t    sin 0  , (12) where 0  is a parameter. The stress,  , in the viscoelastic model is determined by 7 1 2 , ,..., Since the beam analyzed here has a high length to thickness ratio, the distribution of strains in the beam cross section is written in the form z y z y C        , (14) where C  is the strain in the centre, y  and z  are the beam curvatures in xy and xz planes, respectively. We use the following approach for deriving C  , y  and z  . First, by applying the integrals of Maxwell-Mohr for expressing the free beam end angle of rotation and projecting it on y and z , we get nld nls    2 E     . (13)

cos

 





,

(15)

y

l

sin

 

z 



.

(16)

l

We use equilibrium equation (18) for obtaining C  .