Dynamic Interaction Between Waves And Embedded Structures With Unilateral Contact Interfaces

In this paper,dynamic interaction between waves and embedded structures withunilateral contact interfaces is investigated by using the powerful numerical t001——transient time-domain boundary element method(BEM)Due to the non-linearityinduced by unilateral contact interfaces,the problem is hard for conventionalmathematical treatments However,boundary integral equation(BIE)together with itsdiscretion techniques has been found to be an effective tool for such problemespeciallyfor the problem of wave motion in an infinite or semi-infinite medium Forthe sake ofthis.the basic formulae for transient time.domain BEM are derived indetail Amathematical model for nonlinear boundary problems with frictional contactinterfaces is presented Criteria for the determination of the boundaxy conditionsare studied;numerical techniques for the application of transient time-domain BEMto the dynamiccontact problems are discussed and efficient iteration methods withrapid convergenceare proposedBy employing the domain decomposition technique,formulae of transienttime-domain BEM are presented for the embedded structure mad its surroundingmedium From simple to complex,some typical examples are considered As a first step,the dynamic interaction between the anti-plane waves(SH waves)and the embeddedstructure is investigated;dynamic interaction between the plane waves(P or SV waves)and the embedded structure with a unilateral and smooth COntact interface iSresearchedFinally the dynamic interaction between the plane waves mad the embeddedstructure with a unilaterally frictional contact interface where separations mayor may not is considered The corresponding computer programs are coded Throughnumerical calculation of the near field solutions,time dependence of some parameterssuch as displacements , tractions , relative slipping speeds and displacementdiscontinuities at the interface is presented and variation of the interface stateswith time is also given For various shapes of the embedded structure,comparisonsare made between the present results and those obtained from the problem that theembedded structure is perfectly bonded to its surrounding mediumIt is shown that incident waves of enough strength can induce the local separationand slip of the interface between the embedded structure and its surrounding mediumThe state of the interface is unknown beforehand and may vary with time For suchelastodynamic problems with boundary non-linearity,the present numerical method isfound to be very efficient with good convergence and precisionThe local separation and slip of the interface significantly influence the shapesof the propagating waves For exmnple,vcaves corresponding to a harmonic incidentw-ave,after several periods,may be very different from their original shapes,which implies the generation of the waves with high frequencies This is the inherentfeature induced by the non-linearity of the problem Besides,the local separationand slip can obstruct the refraction of waves through the interface As a result,the induced wave motion of the embedded structure will be less than that of itssurrounding medium Even the smooth contact can obviously obstruct the wavepropagation,though unlike the frictional contact that will result in the energy...