Scattering Of Sh-waves By Elliptical Inclusion And Crack In Bi-material Half Space

Dynamic loads acting on elastic solid or structures can produce elastic waves.Elastic waves will reflect and refract when waves encounter obstacles or defects in the process of propagation.Then the phenomenon of dynamic stress concentration occurs on the surface of the obstacles.It is hard to avoid various defects in nature materials or engineering field.In some cases,defects are made to satisfy engineering needs.So,it is of necessity to investigate the dynamic stress concentration near the defects.In engineering field,local terrain such as geological fault or underground structures or interface of different soil is not uncommon.The local terrain under the action of seismic waves may cause superposition of wave field,which may heighten the surface vibration and dynamic stress concentration phenomenon of underground structures.The final result will be the damage of underground structures.In this paper,complex structures or local terrain with interface were simplified as bi-material half space problem to investigate.Based on linear elastic theory,the analytical solution of scattering problem of SH waves by elliptical inclusion,composite defects composed of interfacial crack and elliptical inclusion and composite defects composed of beeline crack and elliptical inclusion were presented,respectively.The main work in this dissertation could be summarized into three parts as follows:In the first part,complex function method,Green's function method,conformal mapping method and interface conjunction technique were used to give the analytical solution of the scattering problem of SH waves by elliptical inclusion near vertical interface.Using the idea of partition,the theoretical model was divided into two parts along the vertical interface to study,respectively.In the right-angle plane,the total wave field and Green's function needed were constructed by using comformal mapping method and image method.Using interface‘conjunction' technique,undetermined anti-plane force systems were loaded on the linking sections of the two right-planes.Through the continuity conditions of stress and displacement on the interface,a series of Fredholm integral equations of first kind for determining the unknown forces were set up.Finally,some examples for dynamic stress concentration factor(DSCF)around the elliptical inclusion and the amplitude of ground surface displacement were given.The influence of incident wave number,medium parameters and other dimensionless parameters on the distribution of DSCF and surface displacement wasdiscussed.The second part considered the existence of interface crack.Crack dividing technique,as a new method,was used to construct the interfacial crack by applying opposite forces which had the same magnitude as the shear stresses disturbed by SH waves to the region where the crack will appear.Meanwhile,a series of unknown forces were loaded on non-crack sections of the interface to satisfy continuity conditions of stress and displacement.Then,the integral equations for determining the unknown forces were set up.Finally,some examples for DSCF around the elliptical inclusion edge and dynamic stress intensity factor(DSIF)for mode III crack at the tip were presented.The influence of dimensionless parameters on the distribution of DSCF and DSIF was discussed.In the third part,crack dividing technique continued to be used to construct the beeline crack inside the media.Some new Green's functions were constructed for the changing position of the beeline crack.The analytical solution of scattering problem of SH waves was given when beeline crack and elliptic inclusion were on one side and both sides of the interface.Finally,some examples for DSCF around the elliptical edge and DSIF for mode III crack at the tip were presented when the beeline crack and elliptical inclusion on one and both side of the interface respectively when SH waves impacted the model.The influence of dimensionless parameters on the distribution of DSCF and DSIF was discussed.