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The Quarterly Journal of Mechanics and Applied Mathematics 1996 49(4):565-580; doi:10.1093/qjmam/49.4.565
© 1996 by Oxford University Press
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RHOMBIC LATTICE OF EQUI-STRESS INCLUSIONS IN AN ELASTIC PLATE

SHMUEL VIGDERGAUZ

( Research and Development Division, The Israel Electric Corporation Ltd P.O. Box 10, Haifa 31000, Israel )

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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