Vol. 9, No. 1, 2014

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Planar grained structures with traction-smoothing inclusions: an elastostatic numerical analysis for shear and torsion

Shmuel Vigdergauz

Vol. 9 (2014), No. 1, 87–103

The topical problem of optimizing the stress state in a bimaterial plate by proper shaping of the matrix/inclusion interface is considered with respect to a recently advanced criterion of minimizing the global variations of the contact stresses. Mathematically, the variations provide an integral-type assessment of the local stresses which requires less computational effort than direct minimization of the stress concentration factor. The proposed criterion can thus be easily incorporated in the numerical optimization scheme previously proposed by the author for similar inverse problems. It consists of an efficient complex-valued direct solver and an ordinary evolutionary search enhanced with an economical shape parametrization tool. The attendant problem of optimizing the effective shear moduli is also solved for comparison purposes. Though methodologically the paper continues the previous works of the author, the primary emphasis is now placed on developing a systematic optimization approach to obtain comprehensive numerical results for nonbiaxial loadings. This setup is of special interest since it differs drastically from the biaxial case, where the analytically known equistress interfaces serve as an efficient benchmark for both theory and computations. Consequently, given the lack of structurally specific analytical assessments, the simulations performed for a wide range of values of the governing parameters provide detailed numerical insight into the chosen case. The elastic behavior of the optimal square-symmetric structures with strongly contrasting well-ordered constituents is conveniently detailed in a set of figures.

plane elasticity problem, shape optimization, Kolosov–Muskhelishvili potentials, hoop stresses, extremal elastic structures, genetic algorithm
Received: 15 July 2013
Revised: 16 October 2013
Accepted: 3 December 2013
Published: 23 March 2014
Shmuel Vigdergauz
Research and Development Division
The Israel Electric Corporation Ltd.
P.O. Box 10
1, Nativ-ha-Or
31000 Haifa