Periodic system of rigid inclusions in a spatial elastic wedge

Abstract

A periodic contact problem (tangential contact) on a chain of thin rigid inclusions located along the edge of a three-dimensional elastic wedge of a dihedral angle in its middle half-plane (rigid sealing of the wedge faces, the axis of the chain of inclusions is parallel to the edge of the wedge) is considered. To derive the integral equation, the previously obtained fundamental solution of the problem of the action of a concentrated force inside a three-dimensional elastic wedge is used. The nucleus has latent symmetry, then it is reduced to a form with explicit symmetry. To solve the integral equation, a regular asymptotic method is used, which is effective for relatively sparse and far from the edge chains of inclusions in a three-dimensional elastic wedge. Contact characteristics are calculated for different values of dimensionless geometric parameters. Previously, similar problems were considered about one inclusion (stringer) in a strip [1] and a three-dimensional wedge [2], as well as in an unbounded elastic body [1].