SUMMARYThe shape of grains or of cross-sections of ÿbres in a two-phase elastic material has an important in uence on the overall mechanical behaviour of the composite. In this paper a numerical scheme is devised for determining the optimal shape of a two-dimensional grain or of a ÿbre's cross-section. The optimization problem is ÿrst posed mathematically, using a global objective function, and then solved numerically by the ÿnite element method and a specially designed global optimization scheme. Excellent agreement is obtained with analytical results available for extreme cases. In addition, optimal shapes are obtained under more general conditions.

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