Twisting a thin periodically perforated elastic rod

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We study the asymptotic behaviour of the displacement of a thin periodically perforated rod under the action of forces applied to one of the rod ends, another end of the rod is clamped. We show that, up to boundary layer functions arising in the vicinity of the end points of the rod, the set of solutions forms a finite dimensional space, and that in the interior of the rod any solution only depends on the resultant forces and moments. We also provide the results of numerical computations of the effective torsion rigidity for a hexagonal periodically perforated rod.

Keywords: homogenization; periodic structure; thin rod

Document Type: Research Article


Affiliations: 1: IDER, Narvik University College, 8505 Narvik, Norway 2: IDER, Narvik University College, 8505 Narvik, Norway,P.N. Lebedev Physical Institute of RAS, Moscow 119991, Russian Federation 3: Institute for Problems in Mechanics of RAS, Moscow 119526, Russian Federation

Publication date: October 1, 2009

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