ABSTRACTComplex method and Green's function method are used here to investigate the dynamic analysis for circular inclusion near interfacial crack impacted by SH-wave in bi-material half-space. Firstly, the displacement expression of the scattering wave was constructed which satisfied the free boundary conditions, then Green's function could be constructed, which was an essential solution to the displacement field for an elastic right-angle space with a circular inclusion impacted by out-plane harmonic line source loading at vertical surface. Secondly, crack was made out with “crack-division” technique. Meanwhile, the bi-material media was divided into two parts along the bi-material interface based on the idea of interface “conjunction”, and then the vertical surfaces of the two right-angle spaces were loaded with undetermined anti-plane forces in order to satisfy displacement continuity and stress continuity conditions at linking section. So a series of algebraic equations for determining the unknown forces could be set up through continuity conditions and the Green's function. Finally, some examples and results for dynamic stress concentration factor of the circular elastic inclusion were given. Numerical results show that they are influenced by interfacial crack, the incident wave number and the free boundary in some degree.
Mean curvature flow of entire graphs in a half-space with a free boundary
