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

The transition from two-dimensional (2D) wave propagation throughthe square periodic structure in anti-plane shear time-harmoniccase to a discretised model of a 2D lattice with masses connectedby springs is considered. A model of a defect in the middlepart of the thin-walled bridges is presented. As a first partof the asymptotic model, the effective transmission conditionin the vicinity of the transverse cut of the thin-walled bridgesis discussed. Then, a boundary layer determining the asymptoticexpansion of the field near the tip of the crack is constructed.Stress intensity factors are evaluated for deep cracks in thejunction regions. The corresponding boundary layer analysisis non-trivial and has not been attempted elsewhere.