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1.
The formulation of an axi-symmetric infinite element for transient analysis of flow problems in unbounded domain is presented. The theoretical basis as well as the implementation of the element is discussed, and the element decay function is derived using the analytical solution of a one-dimensional axially symmetric configuration. The form of decay within the element is described as a function of both time and space, and thus the hydraulic head distribution in the far field is simulated rigorously. The accuracy and the efficiency of the proposed element are demonstrated through several numerical examples in infinite media. In general, it is shown that using the present infinite element transient flow problems in unbounded domains can be simulated effectively. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
2.
研究了文献[2]提出的结线动力无穷元的特性及其参数确定。由于这种单元将衰减函数定义在无穷向结线上,从而不仅可同时考虑多种波动形式,而且对于不同介质,不必通过改变节点坐标分布的形式实现介质间的过渡,而直接以结线上参数的改变来实现,因而可以更好地模拟无穷波动场,使用起来更方便．更容易推广。 相似文献
3.
Axisymmetric thermal consolidation of multilayered porous thermoelastic media due to a heat source 
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下载免费PDF全文 This paper presents an analytical layer element solution to axisymmetric thermal consolidation of multilayered porous thermoelastic media containing a deep buried heat source. By applying the Laplace–Hankel transform to the state variables involved in the basic governing equations of porous thermoelasticity, the analytical layer elements that describe the relationship between the transformed generalized stresses and displacements of a finite layer and a half‐space are derived. The global stiffness matrix equation is obtained by assembling the interrelated layer elements, and the real solutions in the physical domain are achieved by numerical inversion of the Laplace–Hankel transform after obtaining the solutions in the transformed domain. Finally, numerical calculations are performed to demonstrate the accuracy of this method and to investigate the influence of heat source's types, layering, and the porous thermoelastic material parameters on thermal consolidation behavior. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
4.
Transient dynamic response of multilayered saturated media subjected to impulsive loadings 下载免费PDF全文
下载免费PDF全文 This paper presents a stable and efficient method for calculating the transient solution of layered saturated media subjected to impulsive loadings by means of the analytical layer element method. Starting with the field equations based on Biot's linear theory for porous, fluid‐saturated media, and the seepage continuity equation, an analytical layer element for a single layer is established by applying Laplace‐Hankel integral transform. The global stiffness matrix in the transform domain for a layered saturated half‐space subjected to a transient circular patch loading is obtained by assembling the layer elements of each layer. The displacements in the time domain are derived by Laplace‐Hankel inverse transform of the global stiffness matrix. Numerical examples are conducted to verify the accuracy of the method and to demonstrate the influences of type of transient loading, buried depth of loading, permeability, and stratification of materials on the transient response of the multilayered saturated poroelastic media. 相似文献
5.
The leakage effect in porous fissured media has been considered in a general sense by introducing a new expression of the leakage term in this paper. The double porosity concept is employed and the related expressions are formulated using the upwind finite element approach. Considering the infinite extension of the problem domain, a mapped transient infinite element has been presented to simulate the far field of the infinite medium. Since the mass transfer function of the present mapped transient infinite element is dependent on both space and time variables, the mechanism of transient contaminant migration problems in infinite porous fractured media can be rigorously simulated because the property matrices of the element are evaluated at any time of interest. By comparing the current numerical results with the analytical ones, the accuracy, correctness and effectiveness of the present method have been established. Three different time discretization schemes were examined and it was found that either the central difference or the backward difference approximation is suitable for the upwind finite element simulation of transient contaminant migration problems. 相似文献
6.
Biot's equations of wave propagation through fluid-saturated porous elastic media are discretized spatially using the finite element method in conjunction with Galerkin's procedure. Laplace transformation of the discretized equations is used to suppress the time variable. Introducing Laplace transforms of constituent velocities at nodal points as additional variables, the quadratic set of equations in the Laplace transform parameter is reduced to a linear form. The solution in the Laplace transform space is inverted, term by term, to get the complete time history of the solid and fluid displacements and velocities. Since the solution is exact in the time domain, the error in the calculated response is entirely due to the spatial approximation. The procedure is applied to one-dimensional wave propagation in a linear elastic material and in a fluid-saturated elastic soil layer with ‘weak’, ‘strong’ as well as ‘moderate’ coupling. With refinement of the spatial mesh, convergence to the exact solution is established. The procedure can provide a useful benchmark for validation of approximate temporal discretization schemes and estimation of errors due to spatial discretization. 相似文献
7.
土层场地对地震动的影响明显,研究成层场地局部复杂地形的波动场特性,对于抗震设防具有重要意义。基于土-结构相互作用理论,含有局部复杂地形的成层场地,可分解成广义结构（即近场复杂地形及其周围土体）和具有规则开挖边界的成层无限地基（即远场）。远场的格林函数可通过精细积分求解频域-波数域内的对偶波动方程获得,利用傅里叶逆变换得到频域-空间域内的柔度矩阵。近场可采用比例边界有限元进行模拟,通过高性能连分式的传递边界求解动刚度。自由场波动可通过传递矩阵法求得,将动刚度和自由场波动位移代入控制方程即可得到散射场的动力响应。数值算例验证了方法的准确性,并利用提出的方法讨论含有软夹层场地局部复杂场地的波动场特性。 相似文献
8.
Unsaturated soils are considered as porous continua, composed of porous skeleton with its pores filled by water and air. The governing partial differential equations (PDE) are derived based on the mechanics for isothermal and infinitesimal evolution of unsaturated porous media in terms of skeleton displacement vector, liquid, and gas scalar pressures. Meanwhile, isotropic linear elastic behavior and liquid retention curve are presented in terms of net stress and capillary pressure as constitutive relations. Later, an explicit 3D Laplace transform domain fundamental solution is obtained for governing PDE and then closed‐form analytical transient 3D fundamental solution is presented by means of analytical inverse Laplace transform technique. Finally, a numerical example is presented to validate the assumptions used to derive the analytical solution by comparing them with the numerically inverted ones. The transient fundamental solutions represent important features of the elastic wave propagation theory in the unsaturated soils. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
9.
This paper develops a semi-analytical solution for the transient response of an unsaturated single-layer poroviscoelastic medium with two immiscible fluids by using the Laplace transformation and the state-space method. Using the elastic–viscoelastic correspondence principle, we first introduce the Kelvin–Voigt model into Zienkiewicz’s unsaturated poroelastic model. The vibrational response for unsaturated porous material can be obtained by combining these two models and assuming that the wetting and non-wetting fluids are compressible, the solid skeleton and solid particles are viscoelastic, and the inertial and mechanical couplings are taken into account. The Laplace transformation and state-space method are used to solve the basic equations with the associated initial and boundary conditions, and the analytical solution in the Laplace domain is developed. To evaluate the responses in the time domain, Durbin’s numerical inverse Laplace transform method is used to obtain the semi-analytical solution. There are three compressional waves in porous media with two immiscible fluids. Moreover, to observe the three compressional waves clearly, we assume the two immiscible fluids are water and oil. Finally, several examples are provided to show the validity of the semi-analytical solution and to assess the influences of the viscosity coefficients and dynamic permeability coefficients on the behavior of the three compressional waves. 相似文献
10.
This paper presents a method for the analysis of free field ground motions at various depths from actual seismograph records. The proposed method replaces the propagating rupture on the fault surface by a fictitious focal point and a seismograph station in the vicinity of the given soil site. A fictitious focal point and seismograph station scheme is used to calibrate the free field ground motion of the soil site. The harmonic vibration analysis of the half space, which elastodynamic infinite elements are adopted in the far field and finite elements in the near field, yields the Fourier transform of any constituent wave in terms of the amplitude of the forces applied at the focal point, thus in terms of the Fourier transforms of the accelerations in three orthogonal directions recorded at a seismograph station. If a seismograph station is in the far field (as it is usually), the recorded values there can be transformed into the values at the infinite element node by means of appropriate shape functions. The results can be more refined in case of the availability of simultaneous records at more seismograph stations. In case of N stations, we assume N fictitious focal points, and solve a set of 3N simultaneous equations of 3N forces, three orthogonal forces at each focal point. Naturally, only the results by the present method were ‘exact’ at the calibrated points, and should be accurate in-between and near those points. The accelerations at the points near seismograph stations at various depths can also be obtained. An appropriate inverse Fourier transform algorithm will properly yields all results as time functions. 相似文献
11.
A plain strain problem of an isotropic elastic liquid-saturated porous medium in poroelasticity has been studied. The eigenvalue
approach using the Laplace and Fourier transforms has been employed and these transforms have been inverted by using a numerical
technique. An application of infinite space with concentrated force at the origin has been presented to illustrate the utility
of the approach. The displacement and stress components in the physical domain are obtained numerically. The results are shown
graphically and can be used for a broad class of problems related to liquid-saturated porous media. 相似文献
12.
This paper presents a coupling technique for integrating the element-free Galerkin method (EFGM) with the fractal finite element method (FFEM) to analyze unbounded problems in the half-space. FFEM is adopted to model the far field of an unbounded domain and EFGM is used in the near field. In the transition region interface elements are employed. The shape functions of interface elements which comprise both the element-free Galerkin and the finite element shape functions, satisfy the consistency condition thus ensuring convergence of the proposed coupled EFGM–FFEM. The proposed method combines the best features of EFGM and FFEM, in the sense that no structured mesh or special enriched basis functions are necessary. The numerical results show that the proposed method performs extremely well converging rapidly to the analytical solution. Also a parametric study is carried out to examine the effects of the integration order, the similarity ratio, the weight function, the scaling parameter and the number of transformation terms, on the quality of the numerical solutions. 相似文献
13.
Practical civil engineering problems are usually formulated in an infinite half-space domain, and a selected finite domain is required to analyze the dynamic responses of a fluid-saturated porous medium by the finite element method (FEM). Devising a method to deal with the boundaries of the finite domain is the key issue for this open system. In this paper, a two-dimensional spring–dashpot artificial boundary (SDAB) for transient analysis in a fluid-saturated porous media is developed. Based on Biot’s dynamic theory of fluid-saturated porous media, the normal and tangential boundary stress formulae are deduced for out-going cylindrical body waves. The boundary stress is proportional to displacement and velocity, thus continuously distributed dashpots and springs can be placed on the artificial boundaries in the normal and tangential directions to simulate the energy absorption of the infinite media outside of the finite domain for the interior distributed source problems. In this paper, the input seismic motion can be realized by applying an equivalent load on the SDAB for the seismic scattering problems of exterior distributed sources. Numerical examples are given and the analyzed results show that the SDAB and the method of wave motion input have good stability and acceptable accuracy. 相似文献
14.
In modeling of many geomechanics problems such as underground openings, soil-foundation structure interaction problems, and in wave propagation problems through semi-infinite soil medium the soil is represented as a region of either infinite or semi-infinite extent. Numerical modeling of such problems using conventional finite elements involves a truncation of the far field in which the infinite boundary is terminated at a finite distance. In these problems, appropriate boundary conditions are introduced to approximate the solution of the infinite or semi-infinite boundaries as closely as possible. However, the task of positioning the finite boundary in conventional finite element discretization and the definition of the boundary and its conditions is very delicate and depends on the modeller's skill and intuition. Moreover, such a choice is influenced by the size of the domain to be discretized. Consequently, the dimensions of the global matrices and the time required for solution of the problem will increase considerably and also selection of the arbitrary location of truncated boundary may lead to erroneous result. In order to over come these problems, mapped infinite elements have been developed by earlier researchers (Simoni and Schrefier, 1987). In the present work the applicability of infinite element technique is examined for different geomechanics problems. A computer program INFEMEP is developed based on the conventional finite element and mapped infinite element technique. It is then validated using selected problems such as strip footing and circular footing. CPU time taken to obtain solutions using finite element approach and infinite element approach was estimated and presented to show the capability of coupled modeling in improving the computational efficiency. Mesh configurations of different sizes were used to explore the enhancement of both computational economy and solution accuracy achieved by incorporation of infinite elements to solve elastic and elasto-plastic problems in semi-infinite/finite domain as applied to geotechnical engineering. © Rapid Science Ltd. 1998 相似文献
15.
在考虑横观各向同性含液饱和多孔介质固体骨架和流体可压缩性以及固体骨架的黏弹性特征下,基于横观各向同性含液饱和多孔介质u-w形式的三维动力控制方程,以固相位移u、液相相对位移w为基本未知量,综合运用Laplace变换、双重Fourier变换等方法,在直角坐标系下通过引入中间变量,将六元2阶动力控制方程组化为两组各含4个未知变量的常微分方程组,给出了直角坐标系下横观各向同性含液饱和多孔介质三维黏弹性动力反应的积分形式一般解;作为理论推导的验证,通过引入初始条件和边界条件,对横观各向同性含液饱和多孔介质半空间黏弹性瞬态反应问题进行了求解。解答的退化验证表明,所推导的理论解是正确的。 相似文献
16.
Normalized, coupled governing equations for one-dimensional thermal consolidation problems are established. The non-dimensional coefficients of thermal consolidation and thermal diffusivity are defined accordingly. An analytical solution is deduced by using the Laplace transform and the Gauss–Legendre method of Laplace transform inversion. The responses of saturated porous media subjected to cyclic thermal loading are studied. The evolution of temperature, pore pressure and displacement from instantaneous state to quasi-steady state, with elapsed time, are analysed. The characteristics of cyclic fluctuation and the attenuation of the field variables with increased depth are also analysed. The influences of the permeability of media on thermal responses are discussed. 相似文献
17.
结构-地基动力相互作用是结构地震响应分析及安全评估的一个非常重要课题。基于比例边界有限元法,提出了一种新颖的结构-地基动力相互作用的时域模型,即采用比例边界有限元子域模拟近场有限域部分,采用高阶透射边界模拟远场无限域部分。通过采用连分式展开和引入辅助变量,有限域的动力方程采用高阶的静力刚度矩阵和质量矩阵表示。高阶透射边界精确满足无限远处的辐射边界条件,具有全局精确、时间局部和收敛速度快等优点。它是基于改进的连分式法求解无限域动力刚度矩阵而建立的,在时域里表示为一阶常微分方程组。通过联立有限域和无限域的运动方程,建立了结构-地基相互作用的标准动力学方程,采用Newmark法可直接求解。3个算例结果表明,该算法在时域里比黏弹性边界更精确、有效。 相似文献
18.
This paper presents a non‐linear coupled finite element–boundary element approach for the prediction of free field vibrations due to vibratory and impact pile driving. Both the non‐linear constitutive behavior of the soil in the vicinity of the pile and the dynamic interaction between the pile and the soil are accounted for. A subdomain approach is used, defining a generalized structure consisting of the pile and a bounded region of soil around the pile, and an unbounded exterior linear soil domain. The soil around the pile may exhibit non‐linear constitutive behavior and is modelled with a time‐domain finite element method. The dynamic stiffness matrix of the exterior unbounded soil domain is calculated using a boundary element formulation in the frequency domain based on a limited number of modes defined on the interface between the generalized structure and the unbounded soil. The soil–structure interaction forces are evaluated as a convolution of the displacement history and the soil flexibility matrices, which are obtained by an inverse Fourier transformation from the frequency to the time domain. This results in a hybrid frequency–time domain formulation of the non‐linear dynamic soil–structure interaction problem, which is solved in the time domain using Newmark's time integration method; the interaction force time history is evaluated using the θ‐scheme in order to obtain stable solutions. The proposed hybrid formulation is validated for linear problems of vibratory and impact pile driving, showing very good agreement with the results obtained with a frequency‐domain solution. Linear predictions, however, overestimate the free field peak particle velocities as observed in reported field experiments during vibratory and impact pile driving at comparable levels of the transferred energy. This is mainly due to energy dissipation related to plastic deformations in the soil around the pile. Ground vibrations due to vibratory and impact pile driving are, therefore, also computed with a non‐linear model where the soil is modelled as an isotropic elastic, perfectly plastic solid, which yields according to the Drucker–Prager failure criterion. This results in lower predicted free field vibrations with respect to linear predictions, which are also in much better agreement with experimental results recorded during vibratory and impact pile driving. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
19.
Twana Kamal Haji Asaad Faramarzi Nicole Metje David Chapman Farough Rahimzadeh 《国际地质力学数值与分析法杂志》2020,44(3):418-431
The accurate modelling of gravity is of crucial importance for a variety of issues including, but not restricted to, the identification of buried objects. Gravity is an unbounded problem, which causes challenges when applying numerical models, i..e.., it results in computational difficulties when specifying the relevant boundary conditions. In order to address this, previous research has tended to generate artificial boundary conditions, e.g., truncating the simulated domain and adding many unrealistic zero-density layers, which introduces more unknown parameters and unnecessarily excessive computational time. In order to overcome such inaccuracies, this paper proposes an innovative development of the finite element modelling technique, which represents a step change in the field of gravity forward modelling. A comprehensive formulation of an infinite element to reproduce the far-field boundary effect using only one layer of infinite elements is presented. The developed model considerably reduces the computational time while obtaining high degrees of accuracy. The model is validated against the exact solution of the problem, and its results show an excellent performance. The proposed method can significantly improve the postprocessing and interpretation stages of data analysis relevant to micro-gravity sensors. The new method is applied to subsurface civil engineering although its applicability is manifold. 相似文献
20.
This paper presents a time integration scheme capable of simulating blast loading of relatively high frequency on porous media, using coarse meshes. The scheme is based on the partition of unity finite element method. The discontinuity is imposed on the velocity field, while the displacement field is kept continuous. The velocity discontinuity is postulated to occur in the time domain. The developed time integration scheme is unconditionally stable and has controllable numerical dissipation in the high frequency range. An important feature of the time scheme is that it allows for controlling the numerical damping in a consistent way. The time scheme has been implemented in combination with Biot’s theory of wave propagation in saturated porous media. Numerical examples have demonstrated that the proposed time scheme is, in addition to being accurate and stable, highly effective for coarse meshes. This makes the developed scheme suitable for large scale finite element analysis. 相似文献