A Computationally Efficient Solution Procedure for Stationary Two-State Problems in Stochastic Mechanicsby T. J. Enneking, Univ of Notre Dame, United States,
B. F. Spencer, Jr., Univ of Notre Dame, United States,
I. P. E. Kinnmark, Univ of Notre Dame, United States,
Abstract: A numerical procedure is presented for the solution of stationary two-state Markov process problems with a single source. The proposed solution method combines finite element and finite difference methods to take advantage of the specific form of the governing differential equation. The method is illustrated by determining the stationary response of the Duffing oscillator and the statistical moments of the time to reach a critical crack size for the stochastic fatigue crack growth problem. Excellent comparisons are shown between this method, previous analytical studies, and experimental results with a significant reduction in computer processing time and storage.
Subject Headings: Stationary processes | Cracking | Finite element method | Markov process | Finite difference method | Oscillations | Statistics
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