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Research Papers

A Multiscale Design Methodology for Hierarchical Systems With Random Field Uncertainty

[+] Author and Article Information
Wei Chen1

Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111weichen@northwestern.edu

Xiaolei Yin, Wing Kam Liu

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

Sanghoon Lee2

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

1

Corresponding author.

2

Also at the Korea Atomic Energy Research Institute, Republic of Korea.

J. Mech. Des 132(4), 041006 (Apr 13, 2010) (11 pages) doi:10.1115/1.4001210 History: Received June 08, 2009; Revised January 14, 2010; Published April 13, 2010; Online April 13, 2010

A multiscale design methodology is proposed for hierarchical material and product systems with random field uncertainty that propagates across multiple length scales. Using the generalized hierarchical multiscale decomposition pattern in multiscale modeling, a set of computational techniques is developed to manage the system complexity. Design of experiments and metamodeling strategies are proposed to manage the complexity of propagating random field uncertainty through three generalized levels of transformation: the material microstructure random field, the material property random field, and the probabilistic product performance. Multilevel optimization techniques are employed to find optimal design solutions at individual scales. A hierarchical multiscale design problem that involves a two-scale (submicro- and microscales) material design and a macroscale product (bracket) design is used to demonstrate the applicability and benefits of the proposed methodology.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Multiscale modeling strategies

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Figure 2

A generalized two-level multiscale modeling pattern (left) and an example (right)

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Figure 3

Metamodeling strategy I

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Figure 4

Applying metamodeling strategy II for single scale

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Figure 5

Applying metamodeling strategy II for multiple scales

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Figure 6

Two DOEs for correlated inputs

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Design pattern of multilevel optimization

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Figure 8

Flowchart of the three-scale system

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Figure 9

Scale 2 simulation and calibrated material model

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Figure 10

Scale 1 bracket product model

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Figure 11

Flow of random field uncertainty propagation

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