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1.
An efficient method for modelling the propagation of elastic waves in unbounded domains is developed. It is applicable to soil–structure interaction problems involving scalar and vector waves, unbounded domains of arbitrary geometry and anisotropic soil. The scaled boundary finite element method is employed to derive a novel equation for the displacement unit-impulse response matrix on the soil–structure interface. The proposed method is based on a piecewise linear approximation of the first derivative of the displacement unit-impulse response matrix and on the introduction of an extrapolation parameter in order to improve the numerical stability. In combination, these two ideas allow for the choice of significantly larger time steps compared to conventional methods, and thus lead to increased efficiency. As the displacement unit-impulse response approaches zero, the convolution integral representing the force–displacement relationship can be truncated. After the truncation the computational effort only increases linearly with time. Thus, a considerable reduction of computational effort is achieved in a time domain analysis. Numerical examples demonstrate the accuracy and high efficiency of the new method for two-dimensional soil–structure interaction problems. 相似文献
2.
A systematic procedure to construct the (symmetric) static-stiffness, damping and mass matrices representing the unbounded medium is presented addressing the unit-impulse response matrix corresponding to the degrees of freedom on the structure–medium interface. The unit-impulse response matrix is first diagonalized which then permits each term to be modelled independently from the others using expansions in a series of Legendre polynomials in the time domain. This leads to a rational approximation in the frequency domain of the dynamic-stiffness coefficient. Using a lumped-parameter model which provides physical insight the property matrices are constructed. 相似文献
3.
A new numerical procedure is proposed for the analysis of three-dimensional dynamic soil–structure interaction in the time domain. In this study, the soil is modelled as a linear elastic solid, however, the methods developed can be adapted to include the effects of soil non-linearities and hysteretic damping in the soil. A substructure method, in which the unbounded soil is modelled by the scaled boundary finite-element method, is used and the structure is modelled by 8–21 variable-number-node three-dimensional isoparametric or subparametric hexahedral curvilinear elements. Approximations in both time and space, which lead to efficient schemes for calculation of the acceleration unit-impulse response matrix, are proposed for the scaled boundary finite-element method resulting in significant reduction in computational effort with little loss of accuracy. The approximations also lead to a very efficient scheme for evaluation of convolution integrals in the calculation of soil–structure interaction forces. The approximations proposed in this paper are also applicable to the boundary element method. These approximations result in an improvement over current methods. A three-dimensional Dynamic Soil–Structure Interaction Analysis program (DSSIA-3D) is developed, and seismic excitations (S-waves, P-waves, and surface waves) and externally applied transient loadings can be considered in analysis. The computer program developed can be used in the analysis of three-dimensional dynamic soil–structure interaction as well as in the analysis of wave scattering and diffraction by three-dimensional surface irregularities. The scattering and diffraction of seismic waves (P-, S-, and Rayleigh waves) by various three-dimensional surface irregularities are studied in detail, and the numerical results obtained are in good agreement with those given by other authors. Numerical studies show that the new procedure is suitable and very efficient for problems which involve low frequencies of interest for earthquake engineering. Copyright © 1999 John Wiley & Sons Ltd 相似文献
4.
A seismic free field input formulation of the coupling procedure of the finite element (FE) and the scaled boundary finite-element
(SBFE) is proposed to perform the unbounded soil-structure interaction analysis in time domain. Based on the substructure
technique, seismic excitation of the soil-structure system is represented by the free-field motion of an elastic half-space.
To reduce the computational effort, the acceleration unit-impulse response function of the unbounded soil is decomposed into
two functions; linear and residual. The latter converges to zero and can be truncated as required. With the prescribed tolerance
parameter, the balance between accuracy and efficiency of the procedure can be controlled. The validity of the model is verified
by the scattering analysis of a hemi-spherical canyon subjected to plane harmonic P, SV and SH wave incidence. Numerical results
show that the new procedure is very efficient for seismic problems within a normal range of frequency. The coupling procedure
presented herein can be applied to linear and nonlinear earthquake response analysis of practical structures which are built
on unbounded soil.
Supproted by: the National Key Basic Research and Development Program under Grant No. 2002CB412709 相似文献
5.
To calculate the dynamic-stiffness matrix in the time domain (unit-impulse response functions) of the unbounded medium, the infinitesimal finite element cell method based solely on the finite element formulation and working exclusively in the time domain is developed. As in the cloning algorithm, the approach is based on similarity of the unbounded media corresponding to the interior and exterior boundaries of the infinitesimal finite element cell. The derivation can be performed exclusively in the time domain, or alternatively in the frequency domain. At each time station a linear system of equations is solved. The consistent-boundary method to analyse a layered medium in the frequency domain and the viscous-dashpot boundary method are special cases of the infinitesimal finite element cell method. The error is governed by the finite element discretization in the circumferential direction, as the width of the finite-element cell in the radial direction is infinitesimal. The infinitesimal finite element cell method is thus ‘exact in the finite-element sense’. This method leads to highly accurate results for a vast class of problems, ranging from a one-dimensional spherical cavity to a rectangular foundation embedded in a half-plane. 相似文献
6.
An approximate‐simple method for nonlinear response estimates of reinforced concrete frames subjected to near‐field and far‐field records is presented in this paper. The approximate method is based on equivalent single‐degree‐of‐freedom and linear multi‐degree‐of‐freedom models. In this procedure, the nonlinear maximum roof displacement is estimated using an effective period factor and elastic response spectrum with an equivalent damping. The effective period factor was proposed for far‐field and near‐field ground motion records. For regions of high seismicity, the maximum roof displacement can be estimated by applying an effective period factor of 2.3 and 2.1 for near‐field and far‐field records, respectively, and 9% damped displacement response spectrum. For regions of moderate seismicity, a lower effective period factor of 1.9 and 1.8, for near‐field and far‐field records, respectively, can be applied to estimate the maximum roof displacement. A relationship between linear and nonlinear response of multi‐degree‐of‐freedom systems was also proposed to obtain estimates of the maximum inter‐story drift of nonlinear responding reinforced concrete frames. In addition, the effects of number of ground motion records used in the analyses on the scatters of results were investigated. The required number of ground motions to produce a reliable response was proposed. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
7.
An axisymmetric infinite element and a three-dimensional infinite element are developed to solve three-dimensional elastic wave propagation problems in unbounded media. The elements are capable of transmitting Rayleigh, shear and compressional waves in the frequency domain. A scheme to integrate numerically the characteristic matrices of the elements is formulated based upon Gauss—Laguerre quadrature. Finally, the axisymmetric infinite element is used to find the compliance functions of a rigid circular plate subjected to harmonic loading on a semi-infinite medium. By using infinite elements, the size of the near field may be kept small. Consequently, the system is characterized by relatively few degrees of freedom, thus providing the analyst with an inexpensive solution. 相似文献
8.
John P. Wolf 《地震工程与结构动力学》2002,31(1):15-32
The scaled boundary finite‐element method is a powerful semi‐analytical computational procedure to calculate the dynamic stiffness of the unbounded soil at the structure–soil interface. This permits the analysis of dynamic soil–structure interaction using the substructure method. The response in the neighbouring soil can also be determined analytically. The method is extended to calculate numerically the response throughout the unbounded soil including the far field. The three‐dimensional vector‐wave equation of elasto‐dynamics is addressed. The radiation condition at infinity is satisfied exactly. By solving an eigenvalue problem, the high‐frequency limit of the dynamic stiffness is constructed to be positive definite. However, a direct determination using impedances is also possible. Solving two first‐order ordinary differential equations numerically permits the radiation condition and the boundary condition of the structure–soil interface to be satisfied sequentially, leading to the displacements in the unbounded soil. A generalization to viscoelastic material using the correspondence principle is straightforward. Alternatively, the displacements can also be calculated analytically in the far field. Good agreement of displacements along the free surface and below a prism foundation embedded in a half‐space with the results of the boundary‐element method is observed. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
9.
Exact representation of unbounded soil contains the single output–single input relationship between force and displacement in the physical or transformed space. This relationship is a global convolution integral in the time domain. Rational approximation to its frequency response function (frequency‐domain convolution kernel) in the frequency domain, which is then realized into the time domain as a lumped‐parameter model or recursive formula, is an effective method to obtain the temporally local representation of unbounded soil. Stability and identification for the rational approximation are studied in this paper. A necessary and sufficient stability condition is presented based on the stability theory of linear system. A parameter identification method is further developed by directly solving a nonlinear least‐squares fitting problem using the hybrid genetic‐simplex optimization algorithm, in which the proposed stability condition as constraint is enforced by the penalty function method. The stability is thus guaranteed a priori. The infrequent and undesirable resonance phenomenon in stable system is also discussed. The proposed stability condition and identification method are verified by several dynamic soil–structure‐interaction examples. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
10.
挡土墙地震反应非线性波动模拟 总被引：3，自引：0，他引：3
本文运用解耦近场非线性波动数值模拟方法研究挡土墙地震反应，为反映墙土体系在地震作用下的位移机制，引入了Desai薄层单元模拟墙土间接触面，并采用双线型本构关系作为接触面单元和土体的非线性模型，在此基础上给出了解决P—SV问题的非线性显式有限元时域递推公式，为进一步发展非线性波动数值模拟技术提供了有益经验。为验证本文方法及适用性，将数值模拟结果与Zeng，X．和Madabhushi，X．P．G．等的离心机试验和弹塑性数值模拟结果进行对比。结果表明：墙土体系加速度、挡土墙顶底相对滑移、沉降和墙体倾角等同离心机试验模拟结果基本吻合，与弹塑性数值模拟结果相似。 相似文献
11.
12.
The response of massive caisson foundations to combined vertical (N), horizontal (Q) and moment (M) loading is investigated parametrically by a series of three-dimensional finite element analyses. The study considers foundations in cohesive soil, with due consideration to the caisson-soil contact interface conditions. The ultimate limit states are presented by failure envelopes in dimensionless and normalized forms and the effects of the embedment ratio, vertical load and interface friction on the bearing capacity are studied in detail. Particular emphasis is given on the physical and geometrical interpretation of the kinematic mechanisms that accompany failure, with respect to the loading ratio M/Q. Exploiting the numerical results, analytical expressions are derived for the capacities under pure horizontal, moment and vertical loading, for certain conditions. For the case of fully bonded interface conditions, comparison is given with upper bound limit equilibrium solutions based on Brinch Hansen theory for the ultimate lateral soil reaction. A generalized closed-form expression for the failure envelope in M–Q–N space is then proposed and validated for all cases examined. It is shown that the incremental displacement vector of the caisson at failure follows an associated flow rule, with respect to the envelope, irrespective of: (a) the caisson geometry, and (b) the interface conditions. A simplified geometrical explanation and physical interpretation of the associativity in M-Q load space is also provided. Finally, the derived failure envelope is validated against low (0.67 Hz) and high frequency (5 Hz) dynamic loading tests and the role of radiation damping on the response of the caisson at near failure conditions is unraveled. 相似文献
13.
A three dimensional numerical model is presented capable of modelling the propagation and transmission of ground vibration in the vicinity of high speed railways. It is used to investigate the effect of embankment constituent material on ground borne vibration levels at various distances from the track.The model is a time domain explicit, dynamic finite element model capable of simulating non-linear excitation mechanisms. The entire model, including the wheel/rail interface is fully coupled. To account for the unbounded nature of the soil structure an absorbing boundary condition (infinite element) is placed at the truncated interfaces. To increase boundary absorption performance, the soil structure is modelled using an elongated spherical geometry.The complex geometries associated with the track components are modelled in detail thus allowing a highly realistic simulation of force transmission from vehicle to embankment. Lastly, quasi-static and dynamic excitation mechanisms of the vehicle locomotives are described using a multi-body approach which is fully coupled to the track using non-linear Hertzian contact theory.The resulting model is verified using experimental ground borne vibration data from high speed trains, gathered through field trials. It is then used to investigate the role of embankments in the transmission of vibration. It is found that soft embankments exhibit large deflections and act as a waveguide for railway vibrations which are trapped within the structure. This results in increased vibration levels both inside the embankment and in the surrounding soil. In contrast it is found that embankments formed from stiffer material reduce vibrations in the near and far fields. 相似文献
14.
Formulation of a matrix‐valued force–displacement relationship which can take radiation damping into account is of major importance when modelling unbounded domains. This can be done by means of fundamental solutions in space and time in connection with convolution integrals or by means of a frequency dependent boundary element representation, but for discrete frequencies Ω only. In this paper a method for interpolating discrete values of dynamic stiffness matrices by a continuous matrix valued rational function is proposed. The coupling between interface degrees of freedom is fully preserved. Another crucial point in soil–structure interaction analysis is how to implement an approximation in the spectral domain into a time‐domain analysis. Well‐known approaches for the scalar case are based on the partial‐fraction expansion of a scalar rational function. Here, a more general procedure, applicable to MDOF‐systems, for the transformation of spectral rational approximations into the time‐domain is introduced. Evaluation of the partial‐fraction expansion is avoided by using the so‐called mixed variables. Thus, unknowns in the time‐domain are displacements as well as forces. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
15.
3D viscous-spring artificial boundary in time domain 总被引：8，自引：1，他引：7
After a brief review of studies on artificial boundaries in dynamic soil-structure interaction, a three-dimensional viscous-spring artificial boundary （VSAB） in the time domain is developed in this paper. First, the 3D VSAB equations in the normal and tangential directions are derived based on the elastic wave motion theory. Secondly, a numerical simulation technique of wave motion equations along with the VSAB condition in the time domain is studied. Finally, numerical examples of some classical elastic wave motion problems are presented and the results are compared with the associated theoretical solutions, demonstrating that high precision and adequate stability can be achieved by using the proposed 3D VSAB. The proposed 3D VSAB can be conveniently incorporated in the general finite element program, which is commonly used to study dynamic soil-structure interaction problems. 相似文献
16.
When modelling unbounded domains, formulation of a matrix‐valued force–displacement relationship which can take radiation damping into account is of major importance. In this paper, a method to describe the dynamic stiffness by a system of fractional differential equations in the time‐domain is presented. Here, a doubly asymptotic rational approximation of the low‐frequency force–displacement relationship is used, whereas a direct interpretation of the asymptotic part as a fractional derivative is possible. The numerical solution of the corresponding system of fractional differential equations is demonstrated using the infinite beam on elastic foundation as an example. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
17.
We propose a domain decomposition method based on the spectral element method(DDM-SEM)for elastic wave computation in frequency domain.It combines the high accuracy of the spectral element method and the high degree of parallelism of a domain decomposition technique,which makes this method suitable for accurate and efficient simulations of large scale problems in elastodynamics.In the DDM-SEM,the original large-scale problem is divided into a number of well designed subdomains.We use the spectral element method independently for each subdomain,and the neighboring subdomains are connected by a frequency-domain version of Riemann transmission condition(RTC)for elastic waves.For the proposed method,we can employ the non-conforming meshes and different interpolation orders in different subdomains to maximize the efficiency.By separating the internal and boundary unknowns of each subdomain,an efficient and naturally parallelizable block LDU direct solver is developed to solve the final system matrix.Numerical experiments verify its accuracy and efficiency,and show that the proposed DDM-SEM can be a promising numerical tool for accurately and effectively solving large and multi-scale problems of elastic waves.It is potentially valuable for the frequency domain seismic inversion where multiple source illuminations are required. 相似文献
18.
We present and evaluate the formulation of a reduced‐dimension (one‐dimensional) finite element for the nonlinear analysis of a vibrating disk in a two‐dimensional unbounded domain. As this problem is relevant in studies of the dynamic response of laterally loaded piles, numerous spring‐and‐dashpot representations of the disk undergoing displacement in an unbounded material domain have been developed to date: static and dynamic, linear and nonlinear. With the focus on material nonlinearity, the present simplified formulation circumvents the complications associated with nonlinear springs and dashpots. Indeed, the continuum‐based treatment described herein accounts for the interaction between the two modes of energy dissipation, due to wave propagation in the unbounded domain and loss associated with inelastic behavior. The formulation is a good compromise between the competing desires for realistic representation and efficient computation. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
19.
Starting from the unit-impulse response matrix of the unbounded medium, a discrete-time formulation permitting the recursive evaluation of the interaction forces and a continuous-time formulation yielding property matrices corresponding to a model with a finite number of degrees of freedom are discussed. This is achieved using the balancing approximation method which is easily automated, guarantees stability and leads to highly accurate results. © 1998 John Wiley & Sons Ltd. 相似文献
20.
This paper presents a time-dependent semi-analytical artificial boundary for numerically simulating elastic wave propagation problems in a two-dimensional homogeneous half space. A polygonal boundary is considered in the half space to truncate the semi-infinite domain, with an appropriate boundary condition imposed. Using the concept of the scaled boundary finite element method, the wave equation of the truncated semi-infinite domain is represented by the partial differential equation of non-constant coefficients. The resulting partial differential equation has only one spatial coordinate variable and time variable. Through introducing a few auxiliary functions at the truncated boundary, the resulting partial differential equations are further transformed into linear time-dependent equations. This allows an artificial boundary to be derived from the time-dependent equations. The proposed artificial boundary is local in time, global at the truncated boundary and semi-analytical in the finite element sense. Compared with the scaled boundary finite element method, the main advantage in using the proposed artificial boundary is that the requirement for solving a matrix form of Lyapunov equation to obtain the unit-impulse response matrix is avoided, so that computer efforts are significantly reduced. The related numerical results from some typical examples have demonstrated that the proposed artificial boundary is of high accuracy in dealing with time-dependent elastic wave propagation in two-dimensional homogeneous semi-infinite domains. 相似文献