PSI - Issue 20

Gusev E.L. et.al. / Structural Integrity Procedia 00 (2019) 000–000

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Gusev E.L. et al. / Procedia Structural Integrity 20 (2019) 294–299

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specific types of polymeric and composite materials. The development of methods to identify and study such stable qualitative patterns is the basis for the development of a new approach to improving the efficiency of methods for predicting the determining characteristics of polymer composites. On the basis of the developed approach in the framework of inverse problems of forecasting with the inclusion in the formulation of the problem of forecasting the accuracy of the forecast, can be developed scientifically based predictive solutions within the required accuracy of the forecast. The inclusion of established new qualitative laws of influence of micro-and macrostructural features of polymer composite materials on the nature of the change in the residual life, durability, in the formulation of the problem can significantly clarify the formulation of the forecasting problem, as well as significantly improve the efficiency and reliability of predicting the residual life, strength, durability of polymer composite materials . 4. Construction of a generalized mathematical model of forecasting We assume that various physical factors have an impact on the polymer composite, regardless of the impact of other factors. We will also assume that the changes caused in the composite are summarized. Then we can assume that a generalized model that describes the simultaneous impact of several factors can be represented as:   ; . ,..., , 1 , ,1 ,2 0     p j j l j j j t R R F u u u j (1) Each of the functions   ) ; , ( 1,2,..., ,..., , , ,1 ,2 p t j F u u u j j l j j j  describing the impact of the j-th factor on the polymer composite, can be represented in the form of an expansion over a system of basis functions   ; , ( 1, 2,3,...) kj kj t k    . The introduced functions most fully characterize the features of the process of increasing the damage of the material under the influence of extreme environmental factors.

 

kj    kj

) ; , 

F

u u

( , ..., u u t

( , ...,

)









j

kj

j

, j l

j

, j l

,1

,1

(2)

j

j

k

1



( 1, 2, ..., ) . j p 

In these designations: uncertain parameters of the model describing the impact of the j-th factor. Within the framework of the generalized model, it is possible to solve the problems of predicting the residual life, durability both under the influence of an indefinite number of extreme factors, and the problem of forecasting under the influence of strictly defined pre-known factors. For example, it is possible to solve forecasting problems under the influence of a factor associated with climate impact and a factor associated with hardening processes. Within the framework of the basic system of support functions, which is used to construct the decomposition of the prediction model into a series, a prediction model of optimal complexity is constructed. Under the model of optimal complexity we understand the model containing the optimal number of terms, allowing to solve the problem of forecasting with the required accuracy. Then the problem of constructing a model of optimal complexity is reduced to the solution of the following extreme problem: ., j l ,1 ., j l ) , ( ,...,  ) , ( 1, 2,..., ;  0,1, 2,...) j j kj kj j u u u u j p k   ,1 ( ,..., j