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TECHNICAL PAPERS

Estimating the Probability Distribution of von Mises Stress for Structures Undergoing Random Excitation

[+] Author and Article Information
Dan Segalman, Garth Reese

Richard Field, Clay Fulcher

Sandia National Laboratories, * Organization 9234, MS 0847, PO Box 5800, Albuquerque, NM 87185

J. Vib. Acoust 122(1), 42-48 (Jul 01, 1999) (7 pages) doi:10.1115/1.568442 History: Received July 01, 1999
Copyright © 2000 by ASME
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References

Shigley, J. E., 1972, Mechanical Engineering Design, 2nd ed., McGraw-Hill, NY, pp. 232–236.
Lin, Y. K., 1967, Probabilistic Theory of Structural Dynamics, Robert E. Krieger, Pub., Malabar, FL.
Soong, T. T., and Grigoriu, M., 1993, Rundom Vibration of Mechanical and Structural Systems, Prentice-Hall, Inc., New Jersey.
Jazwinski, A. H., 1970, Stochastic Processes and Filtering Theory, Academic Press, Inc. San Diego, CA.
Segalman, D. J., Reese, G. M., Fulcher, C. W., and Field, R. V., Jr., 1998, “An Efficient Method for Calculating RMS von Mises Stress in a Random Vibration Environment,” Proceedings of the 16th International Modal Analysis Conference, Santa Barbara, California, February 1998. Also, accepted for publication in the J. Sound Vibron.
Chen,  M-T., and Harichandran,  R., 1998, “Statistics of the von Mises Stress Response for Structures Subjected to Random Excitations,” Shock Vibr. 5, pp. 13–21.
Bendat, J., and Piersol, A., 1986, Random Data: Analysis and Measurement Procedures, John Wiley & Sons, NY, pp. 244–246.
Strang, G., 1988, Linear Algebra and Its Applications, third edition. Harcourt Brace Jovanovich College Publishers, New York, pp. 442–451.
Wirsching, P. H., Paez, T. L., and Ortiz, K., 1995, Random Vibrations: Theory and Practice, John Wiley and Sons, Inc., New York.
Ang, A., and Tang, W., 1975, Probability Concepts in Engineering Planning and Design, Volume 1, Basic Principles, John Wiley & Sons, New York, NY, pp. 274–280.
Ayyub, B. M., and McCuen, R. H., 1995, “Simulation-Based Reliability Methods,” Chapter 4, Probabilistic Structural Mechanics Handbook, R. Sundararajan, ed., Chapman Hall, pp. 53–69.

Figures

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A collection of boxes entirely contained in the ellipsoid, is an admissible VL({D},Y,α).
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Finite element model of hollow cylinder
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Acceleration PSD imposed at base of cylinder
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Contours of the rank of D over the surface of the cylinder
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Probability density functions for von Mises stress at location A. Filled curve is the histogram of Monte Carlo simulation and the solid curve is that predicted by the method presented in this paper.
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Probability density functions for von Mises stress at location B. Filled curve is the histogram of Monte Carlo simulation and the solid curve is that predicted by the method presented in this paper.
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Probability density functions for von Mises stress at location C. Filled curve is the histogram of Monte Carlo simulation and the solid curve is that predicted by the method presented in this paper.
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Probability density functions for von Mises stress at location D. Filled curve is the histogram of Monte Carlo simulation and the solid curve is that predicted by the method presented in this paper.
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Cumulative probability for three cases of the matrix D, taken from Table 1
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Contours of RMS von Mises stress (kPa) resulting from random forces applied in the Y direction at the cylinder tip.
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Contour plot of the logarithm of the probability that von Mises stress is greater than 2000 kPa

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