arXiv subjects
Publications and source records attributed to Annette Meidell.
We give an example of a relation between local and effective properties for elastic structures, up to geometric constants. The model considered is a periodic structure with isotropic and homogeneous local elasticity tensor in planar linear elasticity. The corresponding physical model is a flat two dimensional body with holes as, for example, a perforated plate.
For a periodically perforated structure, for which homogenization takes place in the linear theory of elasticity, the components of the effective elasticity tensor depend in general on the geometry of the holes as well as on the local elastic properties. These dependencies were shown by Vigdergauz in [7] to be separated in an elementary way for one particular class of structures. The original proof of this relation made use of the lattice approach to describe periodic functions using complex variables. In this paper we present a proof of the so-called Vigdergauz equations for a related class of square symmetric structures. Our proof relies solely on the fundamental theorem of real variable calculus. The differences between the two mentioned classes of structures are nontrivial which makes our result a partial generalization as well.