Twisting a thin periodically perforated elastic rod

Abstract

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:

• thin rod
• homogenization
• periodic structure

AMS Subject Classifications:

• 35K20
• 35Q35
• 35R60

Acknowledgement

A part of this work was done during the visit of A. Shamaev at Narvik University college, whose support is gratefully acknowledged.