Stochastic Design Optimization of Microstructural Features Using Linear Programming for Robust Design

Microstructure design can have a substantial effect on the performance of critical components in numerous aerospace applications. However, the stochastic nature of metallic microstructures leads to deviations in material properties from the design point and alters the performance of these critical c...

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Bibliographic Details
Published in:AIAA journal 2019-01, Vol.57 (1), p.448-455
Main Authors: Acar, Pinar, Sundararaghavan, Veera
Format: Article
Language:English
Subjects:
Aircraft components
Covariance matrix
Critical components
Design
Design optimization
Distribution functions
Finite element method
Galfenol
Linear programming
Magnetic properties
Magnetostriction
Material properties
Microstructure
Normal distribution
Robust design
Statistical analysis
Stiffness
Uncertainty analysis
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Summary:Microstructure design can have a substantial effect on the performance of critical components in numerous aerospace applications. However, the stochastic nature of metallic microstructures leads to deviations in material properties from the design point and alters the performance of these critical components. In this paper, a novel stochastic linear programming (LP) methodology is developed for microstructure design accounting for uncertainties in desired properties. The metallic microstructure is represented using a finite element discretized form of the orientation distribution function (ODF). The inverse LP problem solves the mean values and covariance matrix of the ODFs to maximize the mean values of a property, given the statistical constraints on other properties. The highlight is an analytical uncertainty quantification model via a Gaussian distribution to model propagation of microstructural uncertainties to the properties. Examples illustrate maximization of the yield strength and magnetostriction of a galfenol alloy when constrained by uncertainties in a set of stiffness constants.
ISSN:0001-1452
1533-385X
DOI:10.2514/1.J057377