Abstract
A hybrid polygonal element method is proposed for the micromechanical analysis of heterogeneous materials with randomly distributed rigid ellipses or elliptical voids. An arbitrarily-shaped n-sided polygonal mesh is used to discretize a random heterogeneous medium. The conformal mapping technique is employed to construct special shape functions for a polygonal super-element containing an elliptical inclusion. The performance of the developed polygonal super-element is verified against analytical solutions. As in the case of circular inclusion, one polygonal super-element containing an elliptical inclusion replaces many traditional displacement-based elements without sacrificing numerical accuracy. The versatility of the polygonal element method is demonstrated by applying the method to a random heterogeneous cantilever beam problem.
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