Asymptotic model of fields in a thin-walled structure with crack-like defects

Abstract

The transition from two-dimensional (2D) wave propagation through the square periodic structure in anti-plane shear time-harmonic case to a discretised model of a 2D lattice with masses connected by springs is considered. A model of a defect in the middle part of the thin-walled bridges is presented. As a first part of the asymptotic model, the effective transmission condition in the vicinity of the transverse cut of the thin-walled bridges is discussed. Then, a boundary layer determining the asymptotic expansion of the field near the tip of the crack is constructed. Stress intensity factors are evaluated for deep cracks in the junction regions. The corresponding boundary layer analysis is non-trivial and has not been attempted elsewhere.