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1.
The dynamic problem in micropolar viscoelastic medium has been investigated by employing eigen value approach after applying
Laplace and Fourier transformations. An example of infinite space with concentrated force at the origin has been presented
to illustrate the application of the approach. The integral transforms have been inverted by using a numerical technique to
obtain the displacement components, force stresses, couple stress and microrotation in the physical domain. The results for
these quantities are given and illustrated graphically. 相似文献
2.
In this study, the dynamic response of a poroelastic half‐space to a point fluid sink is investigated using Biot's dynamic theory of poroelasticity. Based on Biot's theory, the governing field equations are re‐formulated in frequency domain with solid displacement and pore pressure. In a cylindrical coordinate system, a method of displacement potentials for axisymmetric displacement field is proposed to decouple the Biot's field equations to three scalar Helmholtz equations, and then the general solution to axisymmetric problems are obtained. The full‐space fundamental singular solution for a point sink is also derived using potential methods. The mirror‐image method is finally applied to construct the fundamental solution for a point sink buried in a poroelastic half‐space. Furthermore, a numerical study is conducted for a rock, that is, Berea sandstone, as a representative example. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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Morteza Eskandari‐Ghadi Azizollah Ardeshir‐Behrestaghi Ronald Y. S. Pak Mostafa Karimi Masoud Momeni‐Badeleh 《国际地质力学数值与分析法杂志》2013,37(14):2301-2320
An analytical investigation of a half‐space containing transversely isotropic material under forced vertical and horizontal displacements applied on a rectangular rigid foundation is presented in this paper. With the goal of a rigorous solution to the shape‐ and rigidity‐ induced singular mixed boundary value problem, the formulation employs scalar potential representation, the Fourier expansion and the Hankel integral transforms method to obtain the surface arbitrary point‐load solution in cylindrical coordinate system. The obtained Green's functions are rewritten in rectangular coordinate system, allowing the response of the half‐space because of an arbitrary distributed load on a rectangular surface area be given in terms of a double integral. The numerical evaluations of stresses are done with the use of an element, which is singular at the edge and the corner of the rectangle. Upon the imposition of the rigidity displacement boundary condition for a rigid foundation and the use of a set of two‐dimensional adaptive‐gradient elements, which can capture the singular behavior in the contact stress effectively, a set of new numerical results are presented to illustrate the effect of transverse isotropy on the foundation response. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
4.
The problem of the dynamic responses of a semi‐infinite unsaturated poroelastic medium subjected to a moving rectangular load is investigated analytical/numerically. The dynamic governing equations are obtained with consideration of the compressibility of solid grain and pore fluid, inertial coupling, and viscous drag as well as capillary pressure in the unsaturated soil, and they can be easily degraded to the complete Biot's theory. Using the Fourier transform, the general solution for the equations is derived in the transformed domain, and then a corresponding boundary value problem is formulated. By introducing fast Fourier transform algorithm, the unsaturated soil vertical displacements, effective stresses, and pore pressures induced by moving load are computed, and some of the calculated results are compared with those for the degenerated solution of saturated soils and confirmed. The influences of the saturation, the load speed, and excitation frequency on the response of the unsaturated half‐space soil are investigated. The numerical results reveal that the effects of these parameters on the dynamic response of the unsaturated soil are significant. 相似文献
5.
Deformation of a poroelastic layer overlying an elastic half‐space due to dip‐slip faulting 
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下载免费PDF全文 An analytical solution of the plane strain problem of the deformation of a homogeneous, isotropic, poroelastic layer of uniform thickness overlying a homogeneous, isotropic, elastic half‐space due to two‐dimensional seismic sources buried in the elastic half‐space has been obtained. The integral expressions for the displacements, stresses and pore pressure have been obtained using the stress function approach by applying suitable boundary conditions at the free surface and the interface. The solution obtained is in the Laplace–Fourier transform domain. The case of a vertical dip‐slip line dislocation for the oceanic crust model of Earth is studied in detail. Schapery's formula is used for the Laplace inversion and the extended Simpson's formula for the Fourier inversion. Diffusion of pore pressure in the layer is studied numerically. Contour maps showing the pore pressure in the poroelastic layer have been plotted. The effect of the compressibility of the solid and fluid constituents on pore pressure has also been studied. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
6.
移动荷载下黏弹性半空间体上双层板的动力响应 总被引：1，自引：0，他引：1
采用黏弹性半空间体上无限大双层板模型模拟路面结构,通过三重Fourier积分变换得到单位脉冲荷载作用下路面动力响应的Green函数。根据线性系统的叠加原理,利用广义Duhamel积分推导出移动荷载作用下路面动力响应的解析解。采用自适应Simpson法编制了计算奇异、振荡函数的广义积分计算程序,完成了路面动力响应从波数-频率域到时间-空间域的转换。结合算例,对移动荷载作用下路面的振动规律进行研究,讨论上、下层板厚度和板材料的弹性模量对路面动力响应的影响,明确了路面结构的振动特性,研究结果可为路面结构的设计、施工提供理论指导。 相似文献
7.
动力响应问题的求解对于地基在外荷载作用下引起的弹性波动问题研究有重要的意义。本文提出了一种求解横观各向同性层状地基在施加时间简谐荷载作用下任意点的应力响应的算法。此算法利用傅里叶变换将广义平面应变问题频率-空间域的动力方程转化到频率-波数域内,结合对偶变量的引入,利用高精度的精细积分算法对状态方程进行求解,在得到频率-波数域内的位移响应的基础上,利用傅里叶逆变换得到任意点的动应力响应。简谐荷载不仅可以施加在地基表面,而且可以施加在地基内部。对比算例验证了本文算法的准确性,同时对地基各向异性特性、激励频率和阻尼比对动应力响应的影响进行了参数分析,为工程实际提供可靠的数值依据。 相似文献
8.
This paper presents a three‐dimensional energy‐based solution for the time‐dependent response of a deeply embedded and unsupported semi‐infinite tunnel of circular cross‐section. The tunnel is taken to be excavated quasi‐instantaneously from an infinite rock body that initially exhibits an isotropic stress state and that is made up of a homogeneous, isotropic and viscoelastic material. The viscoelastic behaviour is modelled by means of Burger's model, and the rock is taken to behave volumetrically linear elastic and to exhibit exclusively deviatoric creep. This viscoelastic problem is transformed into the Laplace domain, where it represents a quasi‐elastic problem. The displacement fields in the new solution are taken to be the products of independent functions that vary in the radial and longitudinal directions. The differential equations governing the displacements of the system and appropriate boundary conditions are obtained using the principle of minimum potential energy. The solutions for these governing equations in the Laplace domain are then obtained analytically and numerically using a one‐dimensional finite difference technique. The results are then transformed back into the time domain using an efficient numerical scheme. The accuracy of the new solution is comparable with that of a finite element analysis but requires much less computation effort. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
9.
Moche Ziv 《国际地质力学数值与分析法杂志》2002,26(4):373-406
First, the response of an ideal elastic half‐space to a line‐concentrated impulsive normal load applied to its surface is obtained by a computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. Then, the geometry is determined of the obtained waves and the source signature—the latter is the imprint of the spatiotemporal configuration of the excitation source in the resultant response. Behind the dilatational precursor wave, there exists a pencil of three plane waves extending from the vertex at the impingement point of the precursor wave on the stress‐free surface of the half‐space to three points located on the other two boundaries of the solution domain. These four wave‐arresting points (end points) of the three plane waves constitute the source signature. One wave is an inhibitor front in the behaviour of the normal stress components and the particle velocity, while in the behaviour of the shear stress component, it is a surface‐axis wave. The second is a surface wave in the behaviour of the horizontal components of the dependent variables, while the third is an inhibitor wave in the behaviour of the shear stress component. An inhibitor wave is so named, since beyond it, the material motion is dying or becomes uniform. A surface‐axis wave is so named, since upon its arrival, like a surface wave, the dependent variable in question features an extreme value, but unlike a surface wave, it exists in the entire depth of the solution domain. It is evident from this work that Saint‐Venant's principle for wave propagation problems cannot be formulated; therefore, the above results are a consequence of the particular model proposed here for the line‐concentrated normal load. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
10.
This paper is dedicated to study the dynamic response of a thin‐plate resting on a layered poroelastic half‐space under a moving traffic load. Based on the dynamic poroelastic theory of Biot, the general solutions of the homogeneous poroelastic foundation are obtained by Fourier translation. By using the transmission and reflection matrices method in the frequency domain, the equivalent stiffness of the layered poroelastic half‐space is presented. Kirchhoff's hypotheses are applied to obtain the vertical displacement of the thin plate. By using the inverse Fourier transform, the time domain solution is obtained. As an example of three layers, the influences of the load velocity, the material properties of poroelastic layers, and the flexural rigidity of the plate on the response of the pavement system are examined. Analyses show that a soft intermediate layer results in the significant increase of vertical displacement of road pavement. Comparison with the existing work validates the present model. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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假定土骨架服从标准线性固体黏弹性本构关系,研究了深埋圆形隧洞的饱和黏弹性土-弹性衬砌耦合系统在轴对称爆炸作用下的瞬态动力响应。首先,基于饱和土的Biot模型和衬砌的弹性理论,通过引入势函数和Laplace变换,利用弹性衬砌和饱和黏弹性土界面处的连续性条件以及边界条件,得到饱和黏弹性土体和弹性衬砌位移、应力和孔隙水压力等在Laplace变换域中的解析解。其次,利用Laplace数值Crump逆变换得到耦合系统在时间域的动力响应,数值分析了不同土体模型下土体-衬砌耦合系统的径向位移和环向应力以及土体孔隙水压力等。结果表明：对不同土体模型的土体-衬砌耦合系统,其在爆炸载荷作用下的动力响应性态基本一致,但动力响应的振动周期和幅值等具有明显的差异。同时,对于饱和黏弹性土-弹性衬砌系统,土体黏性参数对土体径向位移和孔隙水压力有明显的影响,但对土体环向应力影响较小。 相似文献
13.
埋置简谐扭转荷载作用下广义Gibson饱和地基动力响应 总被引：1，自引：0，他引：1
考虑地基为饱和半空间,研究了广义Gibson饱和地基内作用简谐扭转动荷载时地基的动力响应问题。从Biot饱和地基固结理论出发,结合扭转振动的特点,建立了剪切模量随深度线性变化的饱和地基扭转振动的动力微分方程,通过Hankel变换求解此微分方程,给出了Hankel变换域内的切向位移和剪应力关于待定系数的表达式。根据饱和地基表面为自由表面,荷载作用面位移连续、剪应力差等于动荷载大小,波的辐射条件等边界条件求解出待定系数,借助Hankel逆变换给出地基内的位移和应力的表达式。通过数值算例研究发现:在同一水平面内,地基内的切向位移和剪应力曲线的实部和虚部都呈现出非常明显的波动变化规律;在竖向平面内,动荷载作用面上部区域内随深度逐渐增大时,地基内切向位移和剪应力曲线的实部逐渐增大,而在动荷载作用面下部区域则正好相反;扭转动荷载的影响范围主要是荷载作用面上下2倍半径区域。 相似文献
14.
P. L. A. Barros 《国际地质力学数值与分析法杂志》2006,30(7):683-702
A complete formulation and implementation for assessment of the response to dynamic loads of cylindrical rigid structures embedded in transversely isotropic elastic half‐spaces is presented. The analysis is performed in the frequency domain and the steady‐state structure response is obtained. The method is based on a non‐singular version of the indirect boundary element method which uses influence functions, instead of Green's functions, as fundamental solutions. These influence functions are the response of an elastic half‐space to distributed, internally applied loads. The proposed method imposes full bonding contact between the foundation and the surrounding soil. Numerical results for displacement (vertical and horizontal) and rotation (twisting and rocking) impedances, showing the influence of the soil anisotropy, are presented. Results for the soil–structure interface tractions and for the displacement field throughout the half‐space are also shown. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
15.
基于Biot波动理论和广义热弹性理论,对简谐线源荷载（力荷载和热荷载）作用下的热-流-固耦合地基的动力响应问题进行了研究。将地基看成是均质各向同性、完全饱和的多孔半空间介质,利用无量纲化和Fourier变换方法对热-流-固耦合控制方程进行简化,得到了变换域内应力分量、位移分量、温度分布及超孔隙水压力的一般解,并利用Fourier逆变换得到了相应的积分形式解答。通过数值计算对按热-流-固耦合理论、饱和多孔弹性理论和热弹性理论得到的结果进行了比较,同时分析了热-流-固耦合条件下热荷载激振频率对竖向应力、竖向位移、温度分布以及超孔隙水压力的影响。 相似文献
16.
Elastic lateral dynamic impedance functions are defined as the ratio of the lateral dynamic force/moment to the corresponding lateral displacement/rotation at the top ending of a foundation at very small strains. Elastic lateral dynamic impedance functions have a defining influence on the natural frequencies of offshore wind turbines supported on cylindrical shell type foundations, such as suction caissons, bucket foundations, and monopiles. This paper considers the coupled horizontal and rocking vibration of a cylindrical shell type foundation embedded in a fully saturated poroelastic seabed in contact with a seawater half‐space. The formulation of the coupled seawater–shell–seabed vibration problem is simplified by treating the shell as a rigid one. The rigid shell vibration problem is approached by the integral equation method using ring‐load Green's functions for a layered seawater‐seabed half‐space. By considering the boundary conditions at the shell–soil interface, the shell vibration problem is reduced to Fredholm integral equations. Through an analysis of the corresponding Cauchy singular equations, the intrinsic singular characteristics of the problem are rendered explicit. With the singularities incorporated into the solution representation, an effective numerical method involving Gauss–Chebyshev method is developed for the governing Fredholm equations. Selected numerical results for the dynamic contact load distributions, displacements of the shell, and lateral dynamic impedance functions are examined for different shell length–radius ratio, poroelastic materials, and frequencies of excitation. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
17.
This paper presents an exact analytical solution to fully coupled axisymmetric consolidation of a semi‐infinite, transversely isotropic saturated soil subjected to a uniform circular loading at the ground surface. The analysis is under the framework of Biot's general theory of consolidation. First, the governing equations of consolidation are transformed into a set of equivalent partial differential equations with the introduction of two auxiliary variables. These partial differential equations are then solved using Hankel–Laplace integral transforms. Once solutions in the transformed domain have been obtained, the actual solutions in the physical domain for displacements and stress components of the solid matrix, pore‐water pressure and fluid discharge can be finally obtained by direct numerical inversion. The accuracy of the numerical solutions developed is confirmed by comparison with an existing exact solution for an isotropic and saturated soil that is a special case of the more general problem addressed. Numerical analyses are also presented to investigate the influence of the degree of material anisotropy on the consolidation settlement. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
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Moche Ziv 《国际地质力学数值与分析法杂志》2003,27(3):233-258
The transient deformation of an elastic half‐space under a line‐concentrated impulsive vector shear load applied momentarily is disclosed in this paper. While in an earlier work, the author gave an analytical–numerical method for the solution to this transient boundary‐value problem, here, the resultant response of the half‐space is presented and interpreted. In particular, a probe is set up for the kinematics of the source signature and wave fronts, both explicitly revealed in the strained half‐space by the solution method. The source signature is the imprint of the spatiotemporal configuration of the excitation source in the resultant response. Fourteen wave fronts exist behind the precursor shear wave S: four concentric cylindrical, eight plane, and two relativistic cylindrical initiated at propagating centres that are located on the stationary boundaries of the solution domain. A snapshot of the stressed half‐space reveals that none of the 14 wave fronts fully extend laterally. Instead, each is enclosed within point bounds. These wave arresting points and the two propagating centres of the relativistic waves constitute the source signature. The obtained 14 wave fronts are further combined into 11 disparate wave fronts that are grouped into four categories: an axis of symmetry wave—so named here by reason of being a wave front that is contiguous to the axis of symmetry, three body waves, five surface waves and two inhibitor waves—so named here by reason that beyond them the material motion dies out. Of the three body waves, the first is an unloading shear wave, the second is a diffracted wave and the third is a reflected longitudinal two‐branch wave. Of the two inhibitor waves, the first is a two‐joint relativistic wave, while the second is a two‐branch wave. The wave system, however, is not the same for all the dependent variables; a wave front that appears in the behaviour of one dependent variable may not exist in the behaviour of another. It is evident from this work that Saint–Venant's principle for wave propagation problems cannot be formulated. Therefore, the above results are valid for the particular proposed model for the momentary line‐concentrated shear load. The formulation of the source signature, the wave system, and their role in the half‐space transient deformation are presented here. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
20.
粘弹性准饱和土中球空腔的动力响应 总被引：2，自引：0，他引：2
从工程实际出发,采用粘弹性两相介质模型,考虑土骨架的粘性以及流体与固体之间的耦合作用,利用Laplace变换求解了粘弹性准饱和土中球空腔的动力响应问题,得到了变换域内的解析解。借助数值Laplace反变换,数值分析了粘弹性准饱和土中球空腔动力响应的位移、应力及孔压的变化规律。为分析地下结构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。 相似文献