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Technical Briefs

Application of Algorithms for Percentiles of von Mises Stress From Combined Random Vibration and Static Loadings

[+] Author and Article Information
Patrick A. Tibbits

 Patrick Tibbits & Associates, 608 Possum Trot Way, Aberdeen, MD 21001patrick.tibbits@gmail.com

J. Vib. Acoust 133(4), 044502 (Apr 12, 2011) (5 pages) doi:10.1115/1.4003682 History: Received September 09, 2010; Revised January 20, 2011; Published April 12, 2011; Online April 12, 2011

Gaussian time-varying loading induces Gaussian components of the stress tensor in a linear structure, where the loading is assumed stationary. For any stress component, finite element spectrum analysis obtains the standard deviation, and any percentile can be calculated as a multiple of the standard deviation. However, a yield criterion requires a percentile of von Mises stress. The distribution of von Mises stress arising from random vibration loading stymies closed-form characterization, but several algorithms estimate its percentiles. One algorithm treats combined random vibration and static loadings. This paper improves computational efficiency for special plane stress cases, e.g., combining finite element spectrum and static analyses of piping models. All the algorithms are applied to a simple test model. Results match Monte Carlo simulation. Computational efficiencies are evaluated and compared.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Analysis procedure block diagram

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Figure 2

Acceleration spectral density, g2/Hz versus Hz

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Figure 3

pdf of σvM from MC algorithm at one element of shell model of tube

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Figure 4

Shell model of tube—σvM∣99.865 from two MC simulations

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Figure 5

Shell model of tube—σvM∣99.865 from SR versus MC

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Figure 6

Piping model of tube—comparative computational efficiencies

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