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Research Papers

Efficient Random Field Uncertainty Propagation in Design Using Multiscale Analysis

[+] Author and Article Information
Xiaolei Yin, Sanghoon Lee, Wei Chen, Wing Kam Liu

Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111

M. F. Horstemeyer

Department of Mechanical Engineering, Mississippi State University, Mississippi State, MS 39762

J. Mech. Des 131(2), 021006 (Jan 07, 2009) (10 pages) doi:10.1115/1.3042159 History: Received April 22, 2008; Revised October 04, 2008; Published January 07, 2009

An integrated design framework that employs multiscale analysis to facilitate concurrent product, material, and manufacturing process design is presented in this work. To account for uncertainties associated with material structures and their impact on product performance across multiple scales, efficient computational techniques are developed for propagating material uncertainty with random field representation. Random field is employed to realistically model the uncertainty existing in material microstructure, which spatially varies in a product inherited from the manufacturing process. To reduce the dimensionality of random field representation, a reduced order Karhunen–Loeve expansion is used with a discretization scheme applied to finite-element meshes. The univariate dimension reduction method and the Gaussian quadrature formula are used to efficiently quantify the uncertainties in product performance in terms of its statistical moments, which are critical information for design under uncertainty. A control arm example is used to demonstrate the proposed approach. The impact of the initial microscale porosity random field produced during a casting process on the product damage is studied and a reliability-based design of the control arm is performed.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Nodes and weights in three-node quadrature formulas for four different distributions (the vertical axis represents the values of PDF and weights)

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Figure 2

Integrated framework for design under uncertainty with multiscale modeling

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Figure 3

Procedure for uncertainty propagation from random field of microstructure

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Figure 4

Damage prediction analysis in one control arm simulation (DOE1)

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Figure 5

Regions in the control arm with two wall thicknesses as design variables

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Figure 6

Plots of coefficient of correlation with various correlation lengths

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Figure 7

Eigenvectors of initial porosity random field in Region 1 for DOE1 of geometry design

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Figure 8

Possible locations (numbered) of maximum damage in Region 1

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Figure 9

Metamodels of the mean and STD of Dmax

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