PSI - Issue 20

D. Reznikov / Procedia Structural Integrity 20 (2019) 17–23 D. Reznikov / Structural Integrity Procedia 00 (2019) 000–000

19

3

Then vectors of demand { D }={ d 1 , d 2 , …, d n } and capacity { C }={ c 1 , c 2 , …, c n } parameters can be introduced to describe the position of the system in the space of its design parameters. The coordinates of these vectors are defined as follows:

1 d t

( ) t

d t

( ) t

( ) d t  

, 5 ( ) d t

( ) N t   ;

( )

( )

 

 

, 3 ( ) ( ) max d t K t  , 4 I

, 2

max

max

max

c t

( ) C t   , 2 ( ) c t

( ) C t   , 3 ( ) c t

( ) IC K t  , 4 ( )

C c t   , 5 ( ) c t

1 ( )

C N t 

( )



.

Then the condition of ensuring structural integrity can be written in the following form:

( ) ( ) d t c t 

for i

n and t

[0; ] T

[1, 2,..., ]

 

 

,

(1)

i

i

d

where T d is the design service life of the TS , and n is the number of failure mechanisms. One should note that parameters { d 1 , d 2 , …, d n } and { c 1 , c 2 , …, c n } have a random nature and should be considered as random functions of time. It means that the structural integrity of the system is to be ensured in presence of high level of uncertainties related to natural variability of loads acting on the system, scatter of mechanical properties of structural materials, inaccuracies of geometrical dimensions, imperfections of test equipment and design models. In the view of these uncertainties two basic approaches to securing structural integrity can be distinguished: - Deterministic (standard-based) approach. Here so called safety factors are introduced into the design equation to compensate uncertainties. - Probabilistic (reliability-based) approach. According to this approach the probability of structural failure occurrence should not exceed some allowable limiting value [ P f ] which is considered by a society as acceptable at the current stage of the technological development, available resources and the wiliness of the society to pay for the implementation of protection measures. 2. Deterministic approach to securing structural integrity When the deterministic approach is implemented, the uncertain functions c i ( t ) and d i ( t ) in (1) are replaced with certain deterministic estimates: such as mathematical means of these functions E { c i ( t )} and E { d i ( t )}. In order to take into account the uncertainty, minimum allowable (or normative) safety factor [ n i ]>1 against the i -th failure mechanism is introduced in equation (1):     ( ) [ ] ( ) 0 i i i E c t n E d t    [0; ], 1, 2, , d t T i k      . (2) one can write down the condition for ensuring structural integrity for i -th failure mechanism which is written in terms of safety factors: (3) The values of normative safety factors [ n i ] are specified by regulatory bodies taking into account the accumulated experience gained through operating TS of the specific type (Table 1). They are closely linked to the level of technology in a particular industry and with the methods used in calculations. When assigning the values of normative safety factors the severity of possible consequences of the system’s failure should also be taken into account. Then introducing the concept of the design value of the central safety factor     ( ) ( ) E d t ( ) i i i n t E c t  ( ) [ ], n  [0; ],     1, 2, ,  i i d n t t T i k .