半空间饱和土中圆柱形衬砌内荷载引起的动力响应解答

地下衬砌结构经常会受到内部动荷载的作用,内荷载引起的衬砌结构的动应力集中备受关注。采用Laplace变换和波函数展开法,对半空间饱和土中均布突加荷载作用下圆柱形衬砌结构的动力响应进行了研究。对以大半径凸圆弧来近似半空间表面,将半空间饱和土中的波动方程展开成无穷级数的形式,应用Graff加法公式进行坐标变换,根据连续条件和边界条件,确定波函数展开式中的未知系数,求得了半空间饱和土中均布突加荷载作用下圆柱形衬砌的动力响应解答,讨论了衬砌埋深对圆柱形衬砌动力响应的影响。该问题的求解,为地下结构的动力分析提供了一种有效方法。     

内部荷载作用下圆柱形孔洞的动力响应解答

考虑土与衬砌结构的动力相互作用,本文研究了内源荷载作用下,圆柱形孔洞的动力响应问题.将土体和衬砌结构视为弹性均匀介质,通过引入势函数将位移控制方程化为二维轴对称波动方程.采用拉普拉斯变换,得到土体及衬砌的位移应力的表达式.利用土体与衬砌结构之间的连续性条件和衬砌结构内边界上的边界条件,可确定表达式的未知系数.采用逆拉普拉斯变换的数值方法,给出了问题的数值解.分析了土中圆形衬砌结构的动力响应随土体和衬砌结构参数的变化规律.     

层状地基中单桩扭转振动特性分析

采用积分变换和Muki的方法求解了层状地基中单桩的扭转振动问题.在分析过程中,首先对基本控制方程进行Hankel变换,建立了单层地基的初参数解答和刚度矩阵,得到层状地基的递推矩阵;然后利用递推矩阵、边界条件和桩-土变形协调条件建立了层状地基中单桩扭转振动问题的基本积分方程并进行数值求解.文末数值算例给出了退化的层状地基中刚性单桩的扭转变形,其结果与已有经典解答吻合良好.同时,并研究了两层地基中单桩的扭转动力响应,分析了桩-土参数对动力响应的影响,所得结论对工程实践和桩基扭转波检测有一定的指导意义.     

饱和土中球空腔的瞬态动力响应

采用工程上通用的饱和土力学模型,考虑流体与固全之间的耦合作用,利用Ｌａｐｌａｃｅ变换求解了饱和土中球空腔的瞬态动力响应问题,得到了变换域内的解析解,借助数值Ｌａｐｌａｃｅ换求解了饱和土中球空腔瞬态动力响应的位移、应力及孔压的变化规律,为分析地下结构瞬态动力响应提供了一种有效的方法,模型符合工程实际,有一定的工程应用价值。     

饱和土与衬砌动力相互作用的圆柱形孔洞内源问题解答

考虑饱和土与衬砌结构的动力相互作用,该文研究了内源荷载作用下圆柱形孔洞的动力响应问题.将饱和土体和衬砌结构分别视为流固耦合介质和弹性均匀介质,通过引入势函数将位移控制方程化为二维轴对称波动方程.采用拉普拉斯变换,得到饱和土体位移应力的表达式及衬砌的位移应力的表达式.利用土体与衬砌结构之间的连续性条件和衬砌结构内边界上的边界条件,确定表达式的未知系数.采用逆拉普拉斯变换的数值方法,给出了问题的数值解.分析了饱和土中圆形衬砌结构随土体和衬砌结构参数变化的动力响应规律.     

高速移动简谐荷载下层状多孔饱和固体的动力响应

本文研究了匀速移动的振动荷载作用下层状多孔饱和固体的动力响应。应用Fourier变换求解该问题的控制偏微分方程,首先考虑了荷载的移动速度及振动频率对单层多孔饱和固体中应力与孔隙水压力的影响,并与相应的弹性介质的解答和半平面解答进行了比较;然后运用精确刚度矩阵法求解了层状多孔饱和固体的应力响应,并与单层问题进行了比较。结果显示层状多孔饱和固体中应力和孔隙水压力随荷载的移动速度的增加而明显变化,层状多孔饱和固体在移动荷载下的动力响应与相应的单相弹性固体和半平面固体的动力响应有较大的差别。     

粘弹性饱和土体中半封闭圆形隧洞的动力响应分析

基于Biot波动方程,研究分析了粘弹性饱和土体中半封闭圆形隧洞的动力响应问题．假定衬砌材料为多孔介质,引入了更符合工程实际的半封闭边界条件．通过引入势函数,在Laplace变换域中得到隧洞边界上作用轴对称荷载和流体压力条件下应力、位移和超孔隙水压力的解答．利用Laplace数值逆变换得到时域中的解,分析了隧洞边界的半透水特性对隧洞动力响应问题的影响,结果表明：隧洞边界的半透水特性对应力、位移场的变化和超孔隙水压力的消散有很大的影响,透水和不透水下条件的解仅是本文的两个特例。     

一维流体饱和粘弹性多孔介质层的动力响应

本文研究了不可压流体饱和粘弹性多孔介质层的一维动力响应问题。基于粘弹性理论和多孔介质理论，在流相和固相微观不可压、固相骨架服从粘弹性积分型本构关系和小变形的假定下，建立了不可压流体饱和粘弹性多孔介质层一维动力响应的数学模型，利用Laplace变换，求得了原初边值问题在变换空间中的解析解，并利用Laplace逆变换的Crump数值反演方法，得到原动力响应问题的数值解。数值研究了饱和标准线性粘弹性多孔介质层的动力响应，分析了固相位移、渗流速度、孔隙压力及固相有效应力等的响应特征。结果表明，与不可压流体饱和弹性多孔介质相同，不可压流体饱和粘弹性多孔介质中亦只存在一个纵波，并且固相骨架的粘性对动力行为有显著的影响。     

内源瞬态荷载作用下弹性介质与饱和多孔介质中衬砌隧道的动力响应对比分析

衬砌隧道周围介质不同，其内源瞬态荷载作用下的动力响应不同，该文对弹性介质与饱和多孔介质中作用有内源荷载的衬砌隧道的动力响应进行对比分析。首先，令饱和多孔介质孔隙率n=0，将衬砌周围饱和介质退化为弹性介质，动力响应解答相应退化为弹性介质中的解答，退化解与已有的隧道周围为弹性介质时的动力响应解答完全一致。其次，对不同孔隙率的饱和多孔介质和理想弹性介质中衬砌隧道的动力响应进行计算，结果表明：与弹性介质相比，饱和多孔介质中衬砌内表面的动力响应较大，轴向衰减速度较快；随着孔隙率的减小，饱和土中衬砌内表面的动力响应逐渐减小，位移和应力时程曲线均趋近于弹性介质。     

两相介质饱和土三维非轴对称稳态响应分析

用积分变换方法分析饱和土三维非轴对称波动方程，用刚度矩阵方法分析层状饱和土三维非轴对称稳态响应。以数值算例对比分析了单相土介质与两相饱和土介质三维非轴对称稳态动力响应。分析中未引入势函数及传统的Helmholtz分解，推导过程及解答均非常简捷，为边界元方法在三维非轴对称饱和土与基础结构动力相互作用研究中的应用奠定基础。     

回转体局部空泡绕流的非线性分析

基于面元法, 通过在回转体和空泡壁面放置源汇,对回转体定长局部空泡的绕流问题进行了分析和讨论,并提出了求解回转体局部空泡绕流“正问题”的方法。计算结果表明：所给出的方法具有快速收敛的特征,第1次迭代和最终收敛时空泡壁面切向速度的误差不超过5％;随着回转体面元总数N的增加,局部空泡的空泡数σ趋于稳定;通过比较可知,该方法得到的理论估算值与实测值的一致性较好。     

Application of the reciprocity theorem to scattering of surface waves by a cavity

Scattering of surface waves by a cylindrical cavity at the surface of a homogenous, isotropic, linearly elastic half-space is analyzed in this paper. In the usual manner, the scattered field is shown to be equivalent to the radiation from a distribution of tractions, obtained from the incident wave on the surface of the cavity. For the approximation used in this paper, these tractions are shifted to tractions applied to the projection of the cavity on the surface of the half-space. The radiation of surface waves from a normal and a tangential line load, recently determined by the use of the reciprocity theorem, is employed to obtain the field scattered by the cavity from the superposition of displacements due to the distributed surface tractions. The vertical displacement at some distance from the cavity is compared with the solution of the scattering problem obtained by the boundary element method (BEM) for various depths and widths of the cavity. Comparisons between the analytical and BEM results are graphically displayed. The limitations of the approximate approach are discussed based on the comparisons with the BEM results.     

二维半圆孔附近的动态热应力分布

在稳态温度场中,由于弹性平面内半圆孔或半圆坑等缺陷在介质裂纹扩展和疲劳损伤机理中所起的作用,因此深入了解半圆孔或半圆坑的表面动态热应力分布显得很有必要．分析在半无限弹性平面内一半圆孔附近施加稳态调谐温度场条件下的半圆孔孔边动态热应力分布问题,利用共形映照等复变函数的方法,给出了汉克函数表示的此问题的解析解,并给出了相应动态热应力分布系数的数值结果．     

混凝土靶体计及压实效应的球腔动态膨胀模型和侵彻计算

建立了一混凝土靶体的球腔动态膨胀的侵彻模型。靶体的静水压力一体积应变关系考虑了不同的密实混凝土模型。也研究了混凝土作为多孔材料在高压下的压实效应。混凝土有拉伸强度极限值，其剪切强度与压力相关为Mohr—Coulomb定律。球腔动态膨胀模型考虑球对称空腔在无限介质里从零半径开始以常速度膨胀，产生一塑性区和一弹性区。当膨胀速度足够小时，由于介质的低拉伸强度，塑性区和弹性区之间可存在一径向裂纹区。可由解析方法获得空腔表面压力和弹塑性区界面传播速度随空腔表面扩张速度变化的曲线，再由球腔动态膨胀模型所得的空腔表面压力分布用于计算混凝土靶体的刚性杆弹侵彻深度。本文模型的计算结果与经验公式，不可压缩和线性可压缩混凝土模型的进行了比较。     

非定常空泡闭合区域最大压力的理论研究

当物体在流体中高速运动产生空泡时,空泡通常以回射流的形式闭合在物体表面上,并在闭合位置对物体表面产生流体超压. 在物体表面上的空泡闭合位置一般不是固定的,其位置根据物体运动速度的变化、空泡压力的变化及重力场中的位置等因素而在物体表面发 生快速移动,在非对称情况下,这种移动超压会极大影响运动物体的稳定性. 基于势流理论研究了重力场中非定常垂直空泡闭合区域中最大压力的存在位置,推导了最大压力的理论公式,揭示了最大压力与空泡发 展速度之间的关系,证明了最大压力点的两个特殊流体性质. 最后设计了测量空泡闭合区域最大压力的验证性试验,并将理论计算结果与试 验测量结果进行了对比,验证了理论研究结果.     

浅埋圆形孔洞附近的半圆形凸起对SH波的散射

采用"契合"的思想，给出了地下孔洞与地面上的半圆形凸起地形对SH波散射问题的 解答. 将整个求解区域分割成两部分来处理. 其一为包括半圆形凸起地形在内的一个圆形区 域I，其余为区域II. 在区域I和II中分别构造位移解，并在两个区域的"公共边界"上 实施"契合". 在区域I中构造一个上半部边界应力为零，而其余部分位移、应力任意的驻 波解，在区域II中构造出半圆形凹陷和浅埋圆孔的散射波，且要求它满足水平界面上应力 为零的约束条件. 然后再通过移动坐标，满足"公共边界"的"契合"条件和地下孔洞的边 界条件，建立起求解该问题的无穷代数方程组. 最后，给出了分析例题和数值结果，并 对其进行了讨论.     

A HYBRID METHOD FOR ANALYZING THE DYNAMIC RESPONSES OF CAVITIES OR SHELLS BURIED IN AN ELASTIC HALF-PLANE

In this paper, based on a variational formalism which originally proposed by Mei [1] for infinite elastic medium and extended by Yeh, et al. [2,3] for elastic half-plane, a hybrid method which combines the finite element and series expansion method is implemented to solve the diffraction of plane waves by a cavity buried in an elastic half-plane. The finite domain which encloses all inhomogeneities including the cavity can be easily formulated by finite element methods. The unknown boundary data obtained by subtracting the known free fields from the total fields which include the boundary nodal displacements and tractions at the interface between the finite domain and the surrounding elastic half-plane are not independent of each other and can be correlated through aseries repre sentation. Due to the continuity condition at the interface, the same series representation is still valid for the exterior elastic half-plane to represents the scattered wave. The unknown coefficients of this series are treated as generalized coordinates and can be easily formulated by the same variational principle. The expansion function of the series is composed of basis function. Each basis function is constructed from the basis function for an infinite plane by superimposing an additional homogeneous reflective term to satisfy both traction free conditions at ground surface and radiation conditions at infinity. The numerical results are made against those obtained by boundary element methods, and good agreements are found.     

Multiple scattering of electro-elastic waves from a buried cavity in a functionally graded piezoelectric material layer

This paper presents a theoretical method to investigate the multiple scattering of electro-elastic waves and the dynamic stress around a buried cavity in a functionally graded piezoelectric material layer bonded to a homogeneous piezoelectric material. The analytical solutions of wave fields are expressed by employing wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions around the cavity. The image method is used to satisfy the mechanical and electrically short conditions at the free surface of the structure. According to the analytical expression of this problem, the numerical solutions of the dynamic stress concentration factor around the cavity are presented. The effects of the piezoelectric property, the position of the cavity in the layer, the incident wave number and the material properties on the dynamic stress around the cavity are analyzed. Analyses show that the piezoelectric property has great effect on the dynamic stress in the region of higher frequencies, and the effect increases with the decrease of the thickness of FGPM layer. If the material properties of the homogeneous piezoelectric material are greater than those at the surface of the structure, the dynamic stress resulting from the piezoelectric property is greater. The effect material properties at the two boundaries of FGPM layer on the distribution of dynamic stress around the cavity is also examined.     

各向异性介质中SH波引起的圆孔附近的动应力集中

本文利用复变函数方法求解无限的各向异性介质中入射的SH波对圆形孔洞的散射问题,指出动应力集中系数与入射波波数K_σ和圆孔半径r有关,最后给出了圆孔附近动应力集中系数的数值结果。     

Approximate method of solving the problem of characteristic oscillations of a liquid in cavities of revolution

The problem of the characteristic oscillations of a liquid in axisymmetric cavities of rotation has been fairly fully studied [1–5], its solution in the general case being found by the variational method. Analysis of numerical results using the variational method shows that to achieve acceptable accuracy it is necessary to retain an appreciable number of coordinate functions, which entails the solution of a matrix eigenvalue problem of high order, this applying especially to the case when it is necessary to determine several eigenfrequencies and the shapes of the oscillations. In the present paper, a method proposed earlier by Shmakov [6] is developed, the velocity potential being sought in the form of a sun of two potentials. The first (base) potential is a solution to the problem of the characteristic oscillations of a liquid in a cavity whose free surface coincides with the free surface of the original cavity, and the second (correcting) potential is chosen in the form of a system of harmonic functions, this system being complete and orthogonal on the wetted surface of the cavity. Cavities of revolution are analyzed as examples, and a detailed investigation of numerical results is made for a spherical cavity. The numerical analysis shows that a sufficiently accurate result in the determination of a frequency is obtained if one term of the base problem is retained and only the correcting potential is used to make this more accurate. As a result, it is only necessary to solve an algebraic equation of first degree in the square of the frequency.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–8, September–October, 1983.