... takes into account local stress distribution, initial statistical distribution of defects versus their size, crack location, and orientation, and material fatigue resistance parameters. The assumptions used for the new model derivation are stated clearly and their validity is discussed. The model...

... nonlinear dynamical systems statistical distributions Markov processes Gaussian noise white noise Fokker-Planck equation Galerkin method series (mathematics) eigenvalues and eigenfunctions boundary-value problems The response of nonlinear oscillators subjected to random excitations has been...

... , “ A Statistical Distribution Function of Wide Applicability ,” J. Appl. Mech. 0021-8936 , 18 ( 3 ), pp. 293 – 297 . Ballarini , R. , Mullen , R. L. , and Heuer , A. H. , 1999 , “ The Effects of Heterogeneity and Anisotropy on the Size Effect in Cracked Polycrystalline Films ,” Int. J...