PSI - Issue 30

Dmitry O. Reznikov et al. / Procedia Structural Integrity 30 (2020) 128–135 Dmitry O. Reznikov/ Structural Integrity Procedia 00 (2020) 000–000

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ductility and its ability to redistribute loads between mesovolumes it does not mean immediate fracture of the component, but triggers failure scenario at the component level that could lead to some local damage resulting in a component fracture (through scenario s j (c) , Fig. 2b). At the macroscale level the system is designed to fulfill the so-called success scenario S 0 (i.e. a transition from its initial state IS to the designed end state ES 0 ( s ) ). Since any failure scenario S m F presents a deviation from the success scenario S 0 that corresponds to the successful functioning of the CTS , the scenario S m F must have a disturbance point at which some local damage occurs . When the structural component of CTS reaches local damaged state LD j it does not mean obligatory and instant destruction of the system as a whole. In view of the existence of redundant links and alternative load paths, the load that was previously taken by the destroyed component, can be redistributed to the remaining ones. This, in turn, can initiate a sequence of destruction of these parts and the system as a whole (through scenario S k , Fig. 2c). Thus, each local damage event may give rise to a branch of a scenario tree which has a corresponding set of scenarios S i that end in an end state ( ES i ).

( m ) is a material damage accumulation

Fig. 2. Multilevel vulnerability assessment L k is a loading regime , MD i denotes material damage state, s i

scenario, s i LS is a component limit state function, LD j denotes local damage, F is the system failure region, F   is the system survival region, S LS is the system limit state function, IS denotes initial (undamaged) state of the system after its construction, ES 0 ( s ) is the designed end state of the system, ES i,F ( s ) denotes failed end state of the system, ES δ ( s ) is a survival end state located within survival region δ , S i ( δ ) is the survival structural scenario, S F ( s ) is the failure structural scenario ( c ) is a component damage scenario, C

The results of the probabilistic multilevel vulnerability assessment can be described by the matrix equation:

( ) s

s

)

   

    

( P ES LD P ES LD  ( | ) ( |

)

1 1 1 | ] P MD L P MD L P LD    [ | ] [ ( m

( P LD M |

D

| MD )

)

    





1

q

0

1

l

1

1

1

   



  

   

 



s

s

)

)

( 0    1 ); ; ( ) ( );. . .; ( ) P L q n P ES P L ( P ES (

. . .









 

1   [ P MD L P MD L | ] n [ | ] m n

( ) s P LD MD P LD MD P ES LD P ES LD      ( ) s 0 1 ( | ) ( | ) ( | ) ( | ) m m l q l l  

( ) { } s ES

{L}



Mat [V ]

Comp [V ]

Str [V ]



) m P MD P MD  (

{MD} { ( 

)}

1



l P LD P LD 

1 {LD} { ( ) 

( )}

( ) ( ) 0 { } ( ); ; ( s s ES P ES     (5)  ( ) s ) q P ES 

    

 