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Application of Filtered Poisson Process in Modeling Fatigue Cracks Propagation
Author(s) -
Śniady P.,
Sieniawska R.,
Żukowski S.
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.199807815109
Subject(s) - stochastic differential equation , jump , differential equation , extension (predicate logic) , stochastic process , poisson distribution , mathematics , process (computing) , stochastic modelling , jump process , set (abstract data type) , mathematical analysis , computer science , physics , statistics , quantum mechanics , programming language , operating system
A stochastic model of fatigue crack propagation based on stochastic fatigue cracks growth equation is proposed. It is an extension of models given by Y. K. Lin, B. F. Spencer and K. Sobczyk. The model proposed includes the properties of both the continuous and the jump model and make possible to take into account the random disturbances in fatigue phenomenon, which are described by a nonnegative stochastic process. It is assumed that the process of disturbances can be described by a stochastic differential equation which together with the fatigue cracks growth equation builds a set of equations which can be treated as generalized Ito equations.