PSI - Issue 50

4

Dmitry Parshin et al. / Procedia Structural Integrity 50 (2023) 320–326 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

323

Here it is important to emphasize the fact, inherent in our research, that the lower limit of integration in (1) essentially depends on r since all points of a growing body are implicated in the deformation process at different instants in time. We approximate the measure of shear creep by the expression proposed by Arutyunyan (1966):

( ) t

 



](  



.

(2)

( , ) [1 

),

, C C  

, ,

const

C t

e

 C Ce 

 

  

For approximation (2), a closed analytical inversion of relationship (1) is possible, which may simplify the numeral analysis of the problems under consideration. Changing of the elastic modulus with age can be approximated by also an exponential expression (Arutyunyan and Manzhirov, 1999):

,   G G Ge ( )   

.

(3)

, G G 

,   

const



Remark that, according to (2) and (3), the creep resource decreases and the modulus of elasticity increases with age. This is consistent with the experimental data on aging materials and is decisively for the further results. In the paper by Manzhirov and Parshin (2015), a mathematical model of growing bodies mechanics is devised in the small strain suitability for the above given example of the large-sized structure layerwise construction. Next, we will proceed from this theoretical model and carry out corresponding numeral calculations for specific values of constants describing the material properties and specific quantitative characteristics of the technological process under consideration. 4. Relevant calculations In our calculations, we take for considered approximations (2) and (3) of the material properties (Arutyunyan and Manzhirov, 1999; remark that selected values (4) of the material constants are consistent with experimental data on the creep and aging of such structural materials as concrete) and introduce the (dimensionless) relative values of the polar radius, time, and stress variables, respectively, according to the formulas ) ( , , gb t t b          . (5) Note that, in accordance with (5), the flow rate of dimensionless time t is determined in relation to the rate of creeping process in the used material. We take geometric parameters of the structure and the program of its layerwise construction as follows: 2.000 0.517, 0.500, 4.000, 0.552,         GG    CG     C G (4)

0.9,

0.7

;

(6)

0 0 a a b

stop a a b stop 

 



( )

( a Ab t t   

),

[ t t 

,

], where

( A a a  

) (

)

.

(7)

a t

t

t

t



0

start

start stop

0 stop

stop

start

Set radius values (6) indicate a significant wall thinness of the arched structure under consideration. Chosen linear law (7) of changing the structure internal radius, despite its particularity, will allow us to fundamentally draw useful conclusions about the mechanical behavior of the large-sized structure during its construction at different rates. The dimensionless constant 0  A to be set in (7) for calculations performance determines the pace of material adding to the structure in its construction process and can be considered as an influence factor for controlling the structure stress state obtained in this process.