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TECHNICAL PAPERS

# On the Fatigue Analysis of Non-Gaussian Stress Processes With Asymmetric Distribution

[+] Author and Article Information
Xiangyu Wang

Department of Mechanical Engineering, University of Delaware, Newark, DE 19716

J. Q. Sun1

Department of Mechanical Engineering, University of Delaware, Newark, DE 19716sun@me.udel.edu

1

Corresponding author.

J. Vib. Acoust 127(6), 556-565 (Jan 31, 2005) (10 pages) doi:10.1115/1.2110879 History: Received June 09, 2004; Revised January 31, 2005

## Abstract

This paper presents a multistage regression method to obtain an empirical joint probability density function (PDF) for rainflow amplitudes and means of non-Gaussian stress processes with asymmetric distribution. The proposed PDF model captures a wide range of non-Gaussian stress processes characterized by five parameters: Standard deviation, skewness, kurtosis, irregularity factor and mean frequency. It is shown that the fatigue prediction from the closed-form empirical PDF based on the multistage regression analysis agrees well with that from extensive Monte Carlo simulations. The ultimate purpose of the method is to provide a tool for engineers to predict the remaining fatigue life of a structure with direct measurements of stress responses at critical locations on a structure or stress responses at various hot-spots on a structure from the finite element analysis without conducting further Monte Carlo simulations.

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## Figures

Figure 7

The regression results of μi1 and μi2(i=1,2) with respect to α4 in the forth stage regression. ∗: The third stage regression. Solid line: The prediction from Eq. 22.

Figure 8

Examples of the regression results of the parameters δ1, δ3, δ4, and δ5. Symbols: The regression analysis of the rainflow mean distribution. Lines: The prediction from the regression models. (a) α4=17. ∗ and solid line: α3=0. 엯 and dashed line: α3=1.067. ◻ and dashdot line: α3=2.041. (b) α4=24. ∗ and solid line: α3=1.067. 엯 and dashed line: α3=1.515. ◻ and dashdot line: α3=2.041. xδ5=r+m. (c) α4=14. ∗ and solid line: α3=1.067. 엯 and dashed line: α3=1.515. ◻ and dashdot line: α3=2.041. xδ4=(2r2−m)∕(0.2r+1). (d) α4=20. ∗ and solid line: α3=0.509. 엯 and dashed line: α3=1.067. ◻ and dashdot line: α3=1.515.

Figure 9

PDF of the rainflow amplitude of stress processes with kurtosis α4=10, irregularity factor r=0.799, mean frequency m=0.699, and different skewness values. Solid line: Prediction from Eq. 31. ▿: α3=0. ●: α3=0.509. 엯: α3=1.067. ∗: α3=1.515. ◻: α3=2.041. ◇: α3=−0.509. ×: α3=−1.067. +: α3=−1.515. ▵: α3=−2.041.

Figure 10

Validation of the regression model for the PDF of rainflow amplitude. Solid line: The prediction from Eq. 31. Dashed line: The estimate from the adaptive kernel method. (a) α3=−2.041, α4=12, r=0.798, m=0.696. (b) α3=0.509, α4=22, r=0.325, m=0.166.

Figure 11

Validation of the regression model for the PDF of rainflow mean. Solid line: The prediction from Eq. 18. Dashed line: The estimate from the adaptive kernel method. (a) α3=2.041, α4=22, r=0.794, m=0.693. (b) α3=−1.067, α4=16, r=0.520, m=0.392.

Figure 1

Typical PSD of Gaussian and non-Gaussian stress processes. Solid line: PSD of non-Gaussian processes with kurtosis α4=14 and α3=1.067. Dashed line: PSD of a multiresonance Gaussian processes with coefficients Φ1=9.9145×102, ς1=0.01, ω1=60, Φ2=1.1101×105, ς2=0.04, ω2=250.

Figure 2

PDFs of the rainflow amplitude. Dashed line: Estimates from the adaptive kernel method. Solid line: The predictions from Eq. 31. (a) α3=1.515, α4=17, r=0.521, m=0.393. (b) α3=2.041, α4=14, r=0.711, m=0.605. (c) α3=−1.515, α4=10, r=0.799, m=0.698. (d) α3=−2.041, α4=20, r=0.320, m=0.162.

Figure 3

PDFs of the rainflow mean. Dashed line: Estimates from the adaptive kernel method. Solid line: The predictions from Eq. 18. (a) α3=0.509, α4=17, r=0.316, m=0.159. (b) α3=2.041, α4=10, r=0.512, m=0.381. (c) α3=−1.067, α4=14, r=0.414, m=0.279. (d) α3=−2.041, α4=24, r=0.713, m=0.608.

Figure 4

Symmetry of PDFs of rainflow mean with a same value of skewness but opposite sign. (a) α4=24, r=0.436, m=0.298. Solid line: α3=0.509. Dashed line: α3=−0.509. (b) α4=14, r=0.798, m=0.697. Solid line: α3=1.067. Dashed line: α3=−1.067. (c) α4=10, r=0.601, m=0.480. Solid line: α3=1.515. Dashed line: α3=−1.515. (d) α4=20, r=0.320, m=0.162. Solid line: α3=2.041. Dashed line: α3=−2.041.

Figure 5

Examples of δ2 as a function of xδ2=(r−m)∕(r+m) for different stress processes. Symbols: The regression analysis of the rainflow mean distribution. Lines: The prediction from Eq. 23. (a) α4=10. ∗ and solid line: α3=0. 엯 and dashed line: α3=0.509. ◻ and dashdot line: α3=1.515. (b) α4=14. ∗ and solid line: α3=0. 엯 and dashed line: α3=1.067. ◻ and dashdot line: α3=2.041. (c) α4=17. ∗ and solid line: α3=0.509. 엯 and dashed line: α3=1.515. ◻ and dashdot line: α3=2.041. (d) α4=24. ∗ and solid line: α3=0. 엯 and dashed line: α3=1.067. ◻ and dashdot line: α3=1.515.

Figure 6

The regression results of ϵi(i=1,2) with respect to α3 in the third stage regression. Symbols: Data points from the second stage regression. Lines: The prediction from Eq. 21. ∗ and solid line: α4=10. 엯 and dashed line: α4=14. ◻ and dotted line: α4=17. ◇ and dashdot line: α4=20. ▿ and –∙– line: α4=24.

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