Optimal design of functionally graded materials using a procedural model and particle swarm optimization

Authors:
X. Y. Kou;G. T. Parks;S. T. Tan
Affiliations:
Department of Mechanical Engineering, the University of Hong Kong, Pokfulam Road, Hong Kong, China;Department of Engineering, the University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, United Kingdom;Department of Mechanical Engineering, the University of Hong Kong, Pokfulam Road, Hong Kong, China
Venue:
Computer-Aided Design
Year:
2012

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Abstract

A new method for the optimal design of Functionally Graded Materials (FGM) is proposed in this paper. Instead of using the widely used explicit functional models, a feature tree based procedural model is proposed to represent generic material heterogeneities. A procedural model of this sort allows more than one explicit function to be incorporated to describe versatile material gradations and the material composition at a given location is no longer computed by simple evaluation of an analytic function, but obtained by execution of customizable procedures. This enables generic and diverse types of material variations to be represented, and most importantly, by a reasonably small number of design variables. The descriptive flexibility in the material heterogeneity formulation as well as the low dimensionality of the design vectors help facilitate the optimal design of functionally graded materials. Using the nature-inspired Particle Swarm Optimization (PSO) method, functionally graded materials with generic distributions can be efficiently optimized. We demonstrate, for the first time, that a PSO based optimizer outperforms classical mathematical programming based methods, such as active set and trust region algorithms, in the optimal design of functionally graded materials. The underlying reason for this performance boost is also elucidated with the help of benchmarked examples.