Rhombic lattice of equi-stress inclusions in an elastic plate

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Abstract
The objective of this paper is to extend the equi-strength concept to optimize the elastic behaviour of two-dimensional grained composites in which identical foreign inclusions form a rhombic network interacting with the principal material. The analytical solution based upon the complex potentials of Kolosov and Muskhelishvili employs the doubly-periodic Weierstrass elliptic function of a negative determinant to obtain, explicitly, the parametric equations of the equi-stress contours. It is shown that the lattice type has little influence on the stress field in the composites, but is predominant for the shaping of the optimal inclusions.

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