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RESEARCH PAPERS

Safety Envelope for Load Tolerance and its Application to Fatigue Reliability Design

[+] Author and Article Information
Haoyu Wang

Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611

Nam H. Kim

Department of Mechanical and Aerospace Engineering, University of Florida, PO Box 116250, Gainesville, FL 32611nkim@ufl.edu

Yoon-Jun Kim

 Technical Center, Caterpillar Inc., PO Box 1875, Peoria, IL 61656

J. Mech. Des 128(4), 919-927 (Dec 22, 2005) (9 pages) doi:10.1115/1.2204971 History: Received September 19, 2005; Revised December 22, 2005

In this paper, a safety envelope concept for load tolerance is introduced. This shows the capacity of the current design as a future reference for design upgrade, maintenance, and control. The safety envelope is applied to estimate the load tolerance of a structural part with respect to the fatigue reliability. First, the dynamic load history is decomposed into the average value and amplitude, which are modeled as random variables. Second, through fatigue analysis and uncertainty propagation, the reliability is calculated. Last, based on the implicit function evaluation for the reliability, the boundary of the safety envelope is calculated numerically. The effect of different distribution types of random variables is then investigated to identify the conservative envelope. In order to improve the efficiency of searching the boundary, probabilistic sensitivity information is utilized. When the relationship between the safety of the system and the load tolerance is linear or mildly nonlinear, the linear estimation of the safety envelope turns out to be accurate and efficient. During the application of the algorithm, a stochastic response surface of logarithmic fatigue life with respect to the load capacity coefficient is constructed, and the Monte Carlo simulation is utilized to calculate the reliability and its sensitivities.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Analysis procedure of constructing safety envelope

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Figure 2

Parametrization of dynamic loads using the average value and amplitude. This method preserves the fundamental characteristics of the dynamic load history, while it is flexible enough so that the various effects of the dynamic loads can be included.

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Figure 3

Flow chart for fatigue life prediction

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Figure 4

Stress-based S-N curve for the material

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Figure 5

Reliability index β with respect to random variable μγ

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Figure 6

Probability of failure Pf with respect to random variable μγ

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Figure 7

Reliability index β with respect to μγ for both normal and lognormal distributions with the same parameters

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Figure 8

Probability of failure Pf with respect to μγ for both normal and lognormal distributions with the same parameters

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Figure 9

Safety envelope for two variables and the predictor-corrector algorithm finding the boundary of the envelope. The accuracy can be improved by using a smaller size of move limit Δl.

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Figure 10

Two-dimensional safety envelope of fatigue reliability for different distribution types with the same random parameters. The normal distribution shows more conservative estimation than lognormal distribution.

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