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Research Papers

Efficient Assessment of Structural Reliability in Presence of Random and Fuzzy Uncertainties

[+] Author and Article Information
A. S. Balu

Assistant Professor
Department of Civil Engineering,
National Institute of Technology Karnataka,
Surathkal,
Mangalore 575 025, India
e-mail: arunsbalu@gmail.com

B. N. Rao

Professor
Structural Engineering Division,
Department of Civil Engineering,
Indian Institute of Technology Madras,
Chennai 600 036, India
e-mail: bnrao@iitm.ac.in

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received October 7, 2013; final manuscript received January 27, 2014; published online March 21, 2014. Assoc. Editor: David Gorsich.

J. Mech. Des 136(5), 051008 (Mar 21, 2014) (11 pages) Paper No: MD-13-1452; doi: 10.1115/1.4026650 History: Received October 07, 2013; Revised January 27, 2014

This paper presents an efficient uncertainty analysis for estimating the possibility distribution of structural reliability in presence of mixed uncertain variables. The proposed method involves high dimensional model representation for the limit state function approximation, transformation technique to obtain the contribution of the fuzzy variables to the convolution integral and fast Fourier transform for solving the convolution integral. In this methodology, efforts are required in evaluating conditional responses at a selected input determined by sample points, as compared to full scale simulation methods, thus the computational efficiency is accomplished. The proposed method is applicable for structural reliability estimation involving any number of fuzzy and random variables with any kind of distribution.

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Figures

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Fig. 1

Response bounds using transformation techniques

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Fig. 2

Flowchart of coupled HDMR–FFT based reliability analysis

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Fig. 3

Sampling scheme for first-order HDMR: (a) for a function having one variable (x); (b) for a function having two variables (x1 and x2)

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Fig. 4

Membership function of reliability for hypothetical limit state function

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Fig. 6

Membership function of reliability for cantilever beam

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Fig. 8

Membership function of reliability for ten-bar truss

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Fig. 9

Edge-cracked plate: (a) Geometry, loads, and domain size (b) FEM discretization

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Fig. 10

Membership function of reliability for edge-cracked plate

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