共查询到20条相似文献，搜索用时 31 毫秒
1.
A new artificial boundary approach for transient seepage problems in unbounded domain is presented. The artificial boundary condition at the truncated boundary is derived from the analytical solutions for transient seepage problems in one dimension, including solutions, respectively, for flow in one‐dimensional infinite space and for radial flow in an infinite layer, and then it is tentatively applied for some two dimensional problems in addition to the one‐dimensional problems mentioned above. The boundary conditions derived relate the time‐dependent boundary flux with the time derivative of the hydraulic head at the truncated boundary, which makes the implementation much easier compared with the infinite element method. The accuracy and efficiency of the artificial boundary are validated by several numerical examples, which shows that the proposed boundary can give very good results for one‐dimensional transient seepage problems, as expected, whereas reasonable results can be also obtained for two‐dimensional problems, such as two‐dimensional axisymmetric flow and flow in an infinite plane. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
2.
In this paper, a time-dependent infinite element which can be used to simulate transient seepage problems in infinite media is presented. The hydraulic head distribution function of the element has been derived in detail and the property matrices of the element have been well formulated. Since both space and time variables are used in the course of constructing the hydraulic head distribution function of the element, the present infinite element can be referred to as a transient one. Using the present infinite element to model the far field of a system, the mechanism of transient seepage problems in infinite media can be rigorously simulated because the property matrices of the element are evaluated at any time of interest in the analysis. Since explicit expressions can be written for the property matrices of the infinite element, they may be evaluated quite easily and this can be carried out by writing a simple subroutine in a computer program. In order to examine the accuracy and efficiency of the present infinite element, both a one-dimensional (ID) transient seepage problem in a semi-infinite medium and a 2D transient seepage problem in a full plane have been solved using the finite and infinite element technique. It has been demonstrated that the present infinite element is very useful for the numerical simulation of transient seepage problems in infinite media. 相似文献
3.
An infinite element is presented to treat wave propagation problems in unbounded saturated porous media. The porous media is modeled by Biot's theory. Conventional finite elements are used to model the near field, whereas infinite elements are used to represent the behavior of the far field. They are constructed in such a way that the Sommerfeld radiation condition is fulfilled, i.e. the waves decay with distance and are not reflected at infinity. To provide the wave information the infinite elements are formulated in Laplace domain. The time domain solution is obtained by using the convolution quadrature method as the inverse Laplace transformation. The temporal behavior of the near field is calculated using standard time integration schemes, e.g. the Newmark method. Finally, the near and far field are combined using a substructure technique for any time step. The accuracy as well as the necessity of the proposed infinite elements, when unbounded domains are considered, is demonstrated by different examples. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
4.
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
5.
A local artificial boundary for transient seepage problems with unsteady boundary conditions in unbounded domains 
下载免费PDF全文
下载免费PDF全文 Numerical analysis of transient seepage in unbounded domains with unsteady boundary conditions requires a more sophisticated artificial boundary approach to deal with the infinite character of the domain. To that end, a local artificial boundary is established by simplifying a global artificial boundary. The global artificial boundary conditions (ABCs) at the truncated boundary are derived from analytical solutions for one‐dimensional axisymmetric diffusion problems. By applying Laplace transforms and introducing some specially defined auxiliary variables, the global ABCs are simplified to local ABCs to significantly enhance the computational efficiency. The proposed local ABCs are implemented in a finite element computer program so that the solutions to various seepage problems can be calculated. The proposed approach is first verified by the computation of a one‐dimensional radial flow problem and then tentatively applied to more general two‐dimensional cylindrical problems and planar problems. The solutions obtained using the local ABCs are compared with those obtained using a large element mesh and using a previously proposed local boundary. This comparison demonstrates the satisfactory performance and obvious superiority of the newly established boundary to the other local boundary. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
6.
Transient seepage analysis in zoned anisotropic soils based on the scaled boundary finite‐element method 下载免费PDF全文
下载免费PDF全文 The scaled boundary finite‐element method, a semi‐analytical computational scheme primarily developed for dynamic stiffness of unbounded domains, is applied to the analysis of unsteady seepage flow problems. This method is based on the finite‐element technology and gains the advantages of the boundary element method as well. Only boundary of the domain is discretized, no fundamental solution is required and singularity problems can be modeled rigorously. Anisotropic and non‐homogeneous materials satisfying similarity are modeled with no additional efforts. In this study, firstly, formulation of the method for the transient seepage flow problems is derived followed by its solution procedures. The accuracy, simplicity and applicability of the method are demonstrated via four numerical examples of transient seepage flow – three of them are available in the literature. Homogenous, non‐homogenous, isotropic and anisotropic material properties are considered to show the versatility of the technique. Excellent agreement with the finite‐element method is observed. The method out‐performs the finite‐element method in modeling singularity points. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
7.
在边界积分方程离散的基础上,根据远场位移的特性,用衰减函数描述远场位移,阐述了自适应高斯积分算法,并结合前人成果—用解析法求出在远场上的强奇异积分,编制了适合于半无限域线弹性问题的计算机程序,并进行了事例验证,验证表明,该法比传统边界元具有更高的精度。 相似文献
8.
S. K. Sharan 《国际地质力学数值与分析法杂志》1989,13(5):565-570
A highly efficient technique is presented for the finite element analysis of stresses around underground openings surrounded by an infinite extent of linearly elastic rock mass. The effect of unbounded rock is incorporated in the analysis by using elastic supports around the finite element model. Expressions for stiffnesses of the elastic supports are derived and these are found to depend on the location of elastic supports, the shear modulus and Poisson's ratio of the rock, and the ratio of horizontal to vertical initial stresses. With the use of the proposed technique, the extent of the finite domain to be considered in the analysis is highly reduced. This results in a great computational advantage. The other principal merit of the proposed technique is that a standard finite element code for stress analysis may be used without making any modification. Results of some numerical tests are reported to demonstrate the effectiveness and efficiency of the proposed method. The technique has the potential of being applied to more complex problems of unbounded domains in geomechanics. 相似文献
9.
Unbounded plane stress and plane strain domains subjected to static loading undergo infinite displacements, even when the zero displacement boundary condition at infinity is enforced. However, the stress and strain fields are well behaved, and are of practical interest. This causes significant difficulty when analysis is attempted using displacement‐based numerical methods, such as the finite‐element method. To circumvent this difficulty problems of this nature are often changed subtly before analysis to limit the displacements to finite values. Such a process is unsatisfactory, as it distorts the solution in some way, and may lead to a stiffness matrix that is nearly singular. In this paper, the semi‐analytical scaled boundary finite‐element method is extended to permit the analysis of such problems without requiring any modification of the problem itself. This is possible because the governing differential equations are solved analytically in the radial direction. The displacement solutions so obtained include an infinite component, but relative motion between any two points in the unbounded domain can be computed accurately. No small arbitrary constants are introduced, no arbitrary truncation of the domain is performed, and no ill‐conditioned matrices are inverted. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
10.
A set of mapping functions in the form of convergent series for an infinite element, which is capable to include the infinitely distanced constant head boundary condition from the area of disturbance (e.g. pumping), is proposed based on the asymptotic far-field behaviour of typical seepage flow problems. The derived mapping functions have been successfully used in three-dimensional point symmetric, two-dimensional axi-symmetric and one-dimensional unidirectional flow for the fixed head boundary at infinite distance. The result shows excellent agreement with analytical solution. For the first time, the mapping function of an infinite element is presented in the form of a convergent series. The infinite elements are really capable of reducing the cost and efficiency of conventional finite element analysis. Finally, a figure is also proposed to indicate the required size of the near field to obtain accurate drawdown at specified locations based on some calculations for two-dimensional radial flow case. 相似文献
11.
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
12.
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
13.
Since the attenulation of propagating waves through soil/rock is related to the localized material properties as well as the strain developed, the commonly used Rayleigh-type damping model and its variations are not suitable for dynamic finite element analysis of such materials. A linear viscoelastic material model based on the concept of the relaxation spectrum is manipualted in place of the damping model in this paper. The method proposed by Day and Minster11 to transform the convolutional form of the stress–strain relationship to a set of differential operators using the Pade approximant method is generalized to non-scalar waves and implemented for transient finite element analyses. A time-marching scheme is also proposed to incorporate the resultant differential operators into the governing equation of motion. The accuracy related to the Pade approximant method and the time-marching scheme is investigated by critically analysing some scalar wave propagation problems. The proposed technique is further verified using two one-dimensional stress wave propagation problems and a two-dimensional transient propagating wave through an unbounded linear viscoelastic medium. Some encouraging results have been obtained using the proposed technique and guidelines for using this technique are also presented. Comparisons of analytical solutions obtained by Fourier synthesis and numerical results have been provided. 相似文献
14.
针对有限元与边界元耦合法在岩土力学无异域中应用的具体实现问题进行了研究，提出了在微机上实现的具体措施和需建立的程序模块，将有限元与边界元耦合法计算结果、有限元计算结果与理论解析解进行了比较。 相似文献
15.
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
16.
In this paper, the infinite boundary elements developed previously in two and three dimensional problems are reviewed, and the shortcoming and irrationality of interpolation functions of those elements are pointed out. A new interpolation function of infinite boundary element is proposed. The divergent integration on infinite element is also discussed in this paper. 相似文献
17.
本文通过对二维与三维问题的无界边界元的分析,指出二维问题中原有边界元上插值函数的缺点和不合理性,提出一种新型的无界边界元插值形式,对无界单元上的发散积分作了一些讨论。 相似文献
18.
《Geomechanics and Geoengineering》2013,8(1):31-39
In the present paper, dynamic response of rigid pavements subjected to moving vehicular loads is presented using an analytical procedure based on the finite element method. The vehicle–pavement interaction effects are taken into account while developing the solution algorithm. The concrete pavement is discretized by finite and infinite beam elements. Infinite elements are helpful in appropriate modeling of end conditions. The main purpose of the development of infinite elements is to model the unbounded domain. The underlying soil medium is modeled by Pasternak model which assumes the existence of shear interaction between the spring elements. The moving vehicle is represented by a mass supported by a spring-dashpot system. The vehicle -pavement interaction force is modeled with Dirac-delta function. Dynamic equilibrium equation is solved with Newmark-Beta integration scheme. It has been observed that the dynamic interaction between the moving load and the pavement has significant effect on pavement response. Parametric study is carried out to investigate the effect of vehicle–pavement interaction (VPI) and soil parameters on the response of pavement. 相似文献
19.
自然单元法(NEM)是较近出现的一种无网格方法,其形函数兼有无网格的特点和传统有限元的优点,是一种理想的适合岩土工程问题计算的新型数值方法。介绍了自然单元法的基本原理和特性,并讨论了其在岩土工程中的具体应用。将Goodman单元引入自然单元法以实现对不连续面的模拟,研究表明,在NEM中加入节理单元的总体原则和具体的实施细节与FEM中完全相同;而在一般的无网格方法中,则稍微复杂一点。为了实现对岩土工程中常见的无限域或半无限域问题的模拟,引入了无界单元;由于自然单元法的特性,自然单元法和无界元可实现无缝“耦合”。具体的数值算例验证了上述思路。 相似文献
20.
The present study is aimed at working out the possible resistivity anomalies associated with hydrocarbon bearing structures. The anomaly due to a typical two-dimensional anticlinal structure filled with hydrocarbon, and overlying a basement of infinite resistivity was computed using the conformal mapping technique. A more realistic and elaborate model, which could not be simplified by conformal mapping, was studied using the finite element method. This model consisted of a two-dimensional anticlinal structure filled with oil or gas-embedded midway in a homogeneous layer which itself overlies a half-space of infinite resistivity, the electrical resistivity of the hydrocarbon bearing structure being simulated as infinite. 相似文献