单侧接触埋置结构与波的动力相互作用
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摘要
本文利用瞬态时域边界元数值工具对单侧接触约束埋置结构与波的动力相互作用进行了研究。单侧接触约束界面问题是一类边界非线性问题,数学上的处理非常困难。对这类问题,边界积分方程和离散技术是十分有效的,特别是无限域和半无限域中的波动问题,边界元具有其独特的优点。本文详细地介绍了瞬态时域边界元法基本列式的推导,给出了摩擦接触边界非线性问题的数学模型,研究了单侧接触边界条件判断准则,讨论了应用时域边界元方法求解动接触问题的数值技术,给出了有效的且收敛速度快的迭代方法。
应用区域分解技术,对无限域和埋置区域分别给出瞬态时域边界元列式,由浅入深地研究了若干典型问题。首先研究反平面波与埋置结构动力相互作用问题,其次分忻了单侧光滑接触埋置结构与平面波的动力相互作用问题,最后进一步研究了平面波与无分离和有分离单侧摩擦接触埋置结构的动力相互作用问题,编制了相应的计算机程序。通过数值求解得到问题的近场解,给出了内外边界的位移和面力、相对滑移速度、位移间断等响应参量,以及界面状态随时间的变化。对不同的埋置结构进行了计算,并与完好粘着的情况进行了比较,文中给出了大量的数值结果。
本文的结果显示足够强的入射波在埋置结构与周围介质之间的接触界面上造成局部的分离和滑移。界面的状态预先未知,且随时间变化。对于这样具有边界非线性的弹性动力学问题,本文给出的数值方法被证明是有效的,且具有较好的收敛性和精度。
界面的局部分离和滑移对传播的波形有重要的影响,如对简谐形式的入射波,经历若干周期后其响应波与简谐波形相去甚远。这种波形的畸变说明有高频波成份的产生,这也是该问题的非线性所引起的内在特性。另外,界面的局部分离和滑移还阻隔了波透过界面的传播,使得埋置结构中的波动较外部介质的波动强度明显减少。即使光滑接触的情况,虽不象摩擦滑移那样造成波在界面上的能量耗散,仍然对波传播有明显的阻隔作用。
本文的分忻结果对丰富弹性波传播理论和促进其在工程中的应用具有积极的意义。
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 proposed
By 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 medium
It 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 precision
The 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
应用区域分解技术,对无限域和埋置区域分别给出瞬态时域边界元列式,由浅入深地研究了若干典型问题。首先研究反平面波与埋置结构动力相互作用问题,其次分忻了单侧光滑接触埋置结构与平面波的动力相互作用问题,最后进一步研究了平面波与无分离和有分离单侧摩擦接触埋置结构的动力相互作用问题,编制了相应的计算机程序。通过数值求解得到问题的近场解,给出了内外边界的位移和面力、相对滑移速度、位移间断等响应参量,以及界面状态随时间的变化。对不同的埋置结构进行了计算,并与完好粘着的情况进行了比较,文中给出了大量的数值结果。
本文的结果显示足够强的入射波在埋置结构与周围介质之间的接触界面上造成局部的分离和滑移。界面的状态预先未知,且随时间变化。对于这样具有边界非线性的弹性动力学问题,本文给出的数值方法被证明是有效的,且具有较好的收敛性和精度。
界面的局部分离和滑移对传播的波形有重要的影响,如对简谐形式的入射波,经历若干周期后其响应波与简谐波形相去甚远。这种波形的畸变说明有高频波成份的产生,这也是该问题的非线性所引起的内在特性。另外,界面的局部分离和滑移还阻隔了波透过界面的传播,使得埋置结构中的波动较外部介质的波动强度明显减少。即使光滑接触的情况,虽不象摩擦滑移那样造成波在界面上的能量耗散,仍然对波传播有明显的阻隔作用。
本文的分忻结果对丰富弹性波传播理论和促进其在工程中的应用具有积极的意义。
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 proposed
By 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 medium
It 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 precision
The 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
引文
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