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Research Papers: Design Automation

Reliability-Based Design Optimization of Microstructures With Analytical Formulation

[+] Author and Article Information
Pinar Acar

Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: pacar@vt.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 8, 2018; final manuscript received July 6, 2018; published online September 7, 2018. Assoc. Editor: Andres Tovar.

J. Mech. Des 140(11), 111402 (Sep 07, 2018) (9 pages) Paper No: MD-18-1108; doi: 10.1115/1.4040881 History: Received February 08, 2018; Revised July 06, 2018

Microstructures are stochastic by their nature. These aleatoric uncertainties can alter the expected material performance substantially and thus they must be considered when designing materials. One safe approach would be assuming the worst case scenario of uncertainties in design. However, design under the worst case conditions can lead to over-conservative solutions that provide less effective material properties. Here, a more powerful design approach can be developed by implementing reliability constraints into the optimization problem to achieve superior material properties while satisfying the prescribed design criteria. This is known as reliability-based design optimization (RBDO), and it has not been studied for microstructure design before. In this work, an analytical formulation that models the propagation of microstructural uncertainties to the material properties is utilized to compute the probability of failure. Next, the analytical uncertainty solution is integrated into the optimization problem to define the reliability constraints. The presented optimization under uncertainty scheme is exercised to maximize the yield stress of α-Titanium and magnetostriction of Galfenol, respectively.

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Figures

Grahic Jump Location
Fig. 1

Flowchart for the RBDO of the microstructures

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Fig. 2

Orientation distribution function representation in the Rodrigues fundamental region for hexagonal crystal symmetry

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Fig. 3

Optimum ODF probability distributions for α-Titanium

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Fig. 4

Optimum design constraint and objective function distributions for α-Titanium

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Fig. 5

Deterministic and stochastic ODF solutions for α-Titanium

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Fig. 6

Orientation distribution function representation in the Rodrigues fundamental region for BCC crystal symmetry

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Fig. 7

Optimum ODF probability distributions for Galfenol

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Fig. 8

Optimum design constraint and objective function distributions for Galfenol

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Fig. 9

Mean values of the ODFs for Galfenol

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