A Computationally Efficient Solution Procedure for Stationary Two-State Problems in Stochastic Mechanics

by 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,



Document Type: Proceeding Paper

Part of: Structural Safety and Reliability

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: Stochastic processes | Stationary processes | Markov process | Finite difference method | Cracking | Numerical methods | Finite element method

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