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Research Papers

An Efficient Re-Analysis Methodology for Probabilistic Vibration of Large-Scale Structures

[+] Author and Article Information
Geng Zhang

Department of Mechanical Engineering, Oakland University, Rochester, MI 48309zhanggengjj@gmail.com

Efstratios Nikolaidis

Department of Mechanical, Industrial and Manufacturing Engineering, University of Toledo, Toledo, OH 43606enikolai@eng.utoledo.edu

Zissimos P. Mourelatos1

Department of Mechanical Engineering, Oakland University, Rochester, MI 48309mourelat@oakland.edu

1

Corresponding author.

J. Mech. Des 131(5), 051007 (Apr 06, 2009) (13 pages) doi:10.1115/1.3087569 History: Received February 06, 2008; Revised January 21, 2009; Published April 06, 2009

Probabilistic analysis and design of large-scale structures requires repeated finite-element analyses of large models, and each analysis is expensive. This paper presents a methodology for probabilistic analysis and reliability-based design optimization of large-scale structures that consists of two re-analysis methods, one for estimating the deterministic vibratory response and another for estimating the probability of the response exceeding a certain level. The deterministic re-analysis method can analyze efficiently large-scale finite-element models consisting of tens or hundreds of thousand degrees of freedom and design variables that vary in a wide range. The probabilistic re-analysis method calculates very efficiently the system reliability for different probability distributions of the random variables by performing a single Monte Carlo simulation of one design. The methodology is demonstrated on probabilistic vibration analysis and reliability-based design optimization of a realistic vehicle model. It is shown that the computational cost of the proposed re-analysis method for a single reliability analysis is about 1/20 of the cost of the same analysis using MSC/NASTRAN . Moreover, the probabilistic re-analysis approach enables a designer to perform reliability-based design optimization of the vehicle at a cost almost equal to that of a single reliability analysis. Without using the probabilistic re-analysis approach, it would be impractical to perform reliability-based design optimization of the vehicle.

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Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Effect of mean value of a random variable on failure probability predicted from PRRA (solid curve) and sensitivity of failure probability

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Figure 2

Eight-story frame model; the numbers above the horizontal lines are lumped masses in slugs

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Figure 3

Truck model and components associated with random variables

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Figure 4

Response nodes on right door

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Figure 5

Forced response comparison using first- (upper panel) and second-order (lower panel) regression models

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Figure 6

Computational cost of deterministic re-analysis and NASTRAN for a MC simulation

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Figure 7

CDF with different numbers of sample points

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Figure 8

Upper region of CDF in Fig. 7

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Figure 9

Maximum door displacement CDF from PRRA and MC simulation

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Figure 10

Failure probability (crosshatched area) varies smoothly with thickness mean shifts

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Figure 11

Optimum design for allowable failure probability of 0.01

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Figure 12

Optimal designs from RBDO and their failure probabilities from MC simulation

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