The Elastic Polarization Matrix for a Junction of Isotropic Half-Strips

Abstract

We introduce an elastic polarization matrix M for a junction Ξ of isotropic homogeneous half-strips Π¹, . . . ,Π^J. Thematrix M is used to describe the boundary layer phenomenon near nodes of elastic lattices and is formed by coefficients in expansions at infinity of special solutions to the problem of elasticity theory for the body Ξ. It is shown that the 3J × 3J-matrix M is symmetric and degenerate on a subspace of dimension three, but, under the “correct” choice of local coordinates in the half-strips, it corrsponds to a positive definite operator on the orthogonal complement of this subspace.