共查询到20条相似文献，搜索用时 46 毫秒
1.
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
2.
A challenging computational problem arises when a discrete structure (e.g. foundation) interacts with an unbounded medium (e.g. deep soil deposit), particularly if general loading conditions and non‐linear material behaviour is assumed. In this paper, a novel method for dealing with such a problem is formulated by combining conventional three‐dimensional finite‐elements with the recently developed scaled boundary finite‐element method. The scaled boundary finite‐element method is a semi‐analytical technique based on finite‐elements that obtains a symmetric stiffness matrix with respect to degrees of freedom on a discretized boundary. The method is particularly well suited to modelling unbounded domains as analytical solutions are found in a radial co‐ordinate direction, but, unlike the boundary‐element method, no complex fundamental solution is required. A technique for coupling the stiffness matrix of bounded three‐dimensional finite‐element domain with the stiffness matrix of the unbounded scaled boundary finite‐element domain, which uses a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co‐ordinate system, is described. The accuracy and computational efficiency of the new formulation is demonstrated through the linear elastic analysis of rigid circular and square footings. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
3.
M. E. Duncan Fama 《国际地质力学数值与分析法杂志》1989,13(3):331-337
It is shown that a finite element calculation which approximates an ‘infinite medium’; problem by a mesh with finite boundaries will yield greater accuracy when stress boundary conditions are applied on the far-field boundary than is obtainable with displacement boundary conditions. In particular, with Poisson's ratio close to 0.5, the accuracy of the latter model is severely impaired, whereas the stress boundary condition model is unaffected for Poisson's ratio of 0.49 and a reasonable mesh. The eight-node quadratic isoparametric element displays superb accuracy for the axisymmetric thick cylinder with either type of boundary condition. 相似文献
4.
以重力位在场源内部满足泊松方程为依据,以重力矢量满足第三类边界条件为切入点,推导了与三度体重力矢量满足的边值问题相对应的变分问题,进而利用有限单元法实现了对变分问题的求解.立方体模型试验结果表明:文中提出的新的系数矩阵存储方式较之传统方式能够更有效地节约存储空间,且为利用预条件共轭梯度技术更加快速地求解线性方程组提供了保障;重力矢量的计算精度与边界长度及单元网格的边长息息相关,其计算效率则主要取决于所要计算的节点总数和大型稀疏线性方程组求解算法的优劣;一般情况下,当单元的边长小于场源体边长的1/10、边界长度大于场源体长度的7.5倍时,能够获得理想的结果. 相似文献
5.
The aim of this study is to arrive at a better understanding of the phenomenon of locking of low‐order compatible displacement type of finite elements in particular for the hour‐glass mode of the plane four‐node element and dilative materials. To this end the properties of finite elements are investigated in an analytical way, where a finite element is considered as a plane boundary value problem with prescribed boundary displacement (Dirichlet problem). In this paper for the sake of simplicity the simplest possible linear comparison solid, namely isotropic linear elasticity, is applied, although recognizing fully that for a dilative material elasto‐plasticity would be more realistic. From the study described in this paper it is concluded that locking of the four‐node element is not due to any particular numerical formulation of this compatible finite element since, even the analytical solution suffers from this problem. The locking of this element is not related to incompressibility of the material either as the analytical solution shows locking to occur at a parameter set which differs significantly from the one in case of incompressibility. It is shown that locking is a consequence of the combination of the dilative material behaviour and the compatible displacement type of boundary conditions, which leads to infinite isotropic stresses in the element. These infinite isotropic stresses occur at the limit of uniqueness of the solution, which for this element is shown to occur outside the parameter range of the sufficiency of uniqueness. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
6.
This paper concerns the application of a finite element squared approach for modelling hydromechanical coupling in the simulation of gallery excavation in the context of radioactive waste repositories. The micromechanics of Callovo-Oxfordian claystone is modelled at the microscale, taking into account the interaction of different mechanical constituents and its interaction with pore fluid. In a framework of computational homogenization, the micromechanical behaviour is coupled to the macroscale boundary value problem of a poromechanical continuum with local second gradient paradigm. The simulations concern several cases of the “Transverse action” benchmark by Andra, in the context of which the model is used. 相似文献
7.
无限元是一种有效的人工边界,可用于处理弹性波的传播问题。在传统动力无限元的基础上,提出了一种采用分向插值技术的新型动力无限元,详细地推导了这种无限元的形函数,建立了完全解析形式的刚度矩阵,以提高计算效率,采用该无限元边界,计算了弹性介质中的线源Lamb问题,通过对比解析解答的地基表面位移,验证了该无限元的有效性。算例分析表明,采用此类无限元时,有限元单元边长建议取不超过1/8剪切波波长,网格边界到激励源点的距离宜取5倍剪切波波长。无限单元中的幅值衰减系数对计算结果影响甚微,建议取较小值。 相似文献
8.
In this paper, the seismic response analysis of concrete gravity dams is presented using the concept of Continuum Damage Mechanics. The analysis is performed using the finite element technique and a proper material degradation/damage model. The damage criterion used here is a second order tensor model based on elastic-brittle characterization and on a power function of the principal tensile stress. The methodology employed is shown to be computationally efficient and consistent in its treatment of both damage growth and propagation. Other important features considered in the analysis are: (1) dam–foundation interaction (2) appropriate modelling of joined rock mass using continuum damage mechanics, and (3) proper modelling of unbounded domain of foundation rock. The infinite media representation of the foundation material has been achieved by using doubly asymptotic approximation. The results of the analysis indicate that the seismic response of a damaged concrete dam could be significantly different from that of an undamaged one. In particular, the analysis shows that during a seismic event, the microstructure of a damaged zone can significantly change due to growth and propagation of microcracks. 相似文献
9.
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
10.
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
11.
Keh‐Jian Shou 《国际地质力学数值与分析法杂志》2000,24(10):795-814
A superposition scheme is proposed to obtain a fundamental solution for boundary elements in multi‐layered elastic media. A three‐layered elastic region is obtained by superposing two sets of bonded half‐planes and subtracting one infinite plane. Therefore, the solution for an element in a layered media can be expressed in terms of bonded half‐plane solutions and an infinite‐plane solution. The major advantages of this superposition scheme are: (1) it is unnecessary to introduce elements at the interface, (2) it can be extended to higher‐order element, and (3) it may be applicable to three dimensions easily. The accuracy and performance of the developed model is illustrated by two examples. For the problem of a pressurized two‐dimensional crack within a three‐layered system, the comparison with other numerical results shows the model is quite accurate and efficient. The model is also used for a study of a practical two‐dimensional mining problem in South Africa, i.e. stoping through a dyke with material properties different from the host rock. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
12.
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
13.
Investigating the effect of flow direction on suffusion and its impacts on gap-graded granular soils
The flow direction is generally different from the gravity direction in geotechnical structures or slopes, the effect of which during suffusion remains unclear. This paper presents a coupled computational fluid dynamics and discrete element method approach to simulate the particle–fluid interaction relevant to this problem. The CFD-DEM approach is first benchmarked by a classic granular system problem, which is then used to investigate the characteristics of suffusion and its impact on the mechanical behavior. Five different angles between gravity and seepage directions for gap-graded soils with two fines contents are examined. Both the macroscopic and microscopic characteristics during suffusion and triaxial loading tests are analyzed. The direction angle is found to play a significant role affecting the erosion process and the mechanical consequence of soils. The results show that the greater the angle is, the harder it is for suffusion to occur and continue.
相似文献14.
扰动重力梯度是扰动重力位的二阶导数,相对于其他重力场元素能更多地反映变化的不规则地球产生的高频信息。在使用高阶次球谐系数模型获取大范围高分辨率的扰动重力梯度数据时,存在重复运算多、计算效率低下、耗时较长的问题。针对该问题,推导了简化计算公式,将中间变量提取出来作为全局参数和局部参数单独进行计算、存储,从而有效减少重复运算;并在简化公式的基础上,提出了扰动重力梯度张量快速异构并行算法,利用CUDA（compute unified device architecture）实现了梯度全张量在GPU端的并行计算。根据Txx、Tyy、Tzz三个分量满足Laplace条件验证了算法可靠性,并与传统串行算法进行了计算效率对比,实验结果表明,相较于串行算法,所提算法可减少90%以上计算耗时,可将计算效率提高60倍以上。最后利用该算法基于2 190阶EIGEN6C4模型快速构建了5′×5′分辨率的全球扰动重力梯度全张量图,计算结果显示了扰动重力梯度同地形、地球质量分布变化的相关性及其在全球范围内的数值特征。 相似文献
15.
ABAQUS动力无限元人工边界研究 总被引：2，自引：0，他引：2
针对动力场天然无限地基的数值模拟与地震波输入问题进行了一些有意义的研究,评述了现有动力计算常用无限元的优缺点,详细阐述了ABAQUS无限元理论体系框架,并加以改进,提出一种考虑外域地震动影响的ABAQUS动力无限元人工边界。采用等效边界力的叠加原理,对入射波和散射波分开处理,视入射波和散射波在边界上互不影响,将输入地震动转化为作用于有限元无限元交界面上的等效应力的方法来解决外源波的入射问题。算例验证结果表明：内源振动和固定边界会出现失真和扰动现象,同时该计算结果与黏弹性边界的计算结果对比可知,该方法对外行散射波的过滤作用优于黏弹性边界。因此,改进的ABAQUS动力无限元人工边界理论方法有效且具有一定的稳定性。 相似文献
16.
The Rapid Inversion of 3-D Potential Field and Program Design 总被引：1，自引：0，他引：1
The application of three-dimensional inversion of gravity and magnetic fields is very important not only in geophysical researches, but also in the study of geological structures. A formula of potential field in frequency-domain, developed by Parker in 1973, can be used as a rapid and effective algorithm in gravity and magnetic inversion. The technique has been improved then by Oldenburg, Sprenke, Feng and others.In addition to a brief introduction of Parker's algorithm and its applications, this paper includes the following five parts: basic computational techniques, inversion of single layer, convergence and constraints, simultaneous inversion for density and topography as well as inversion of multilayers. The authors present relevant practical iterative formulas and its varieties when density distribution varies with depth in linear or exponential relation. In order to maintain computation stability and speed up iteration convergence, some approaches are taken in the program design, for instance shifting lower interface of the studied layer, inverting corrections of topography, reducing grid boundary effects and utilizing low-pass filter. With the consideration of the nonuniqueness of the inversion, a method of using seismic data to constrain the range ofpossible models is discussed. It is pointed out that the density variation generates less effects than those of topography on the spectrum of gravity anomaly in second order. Therefore density contrast and topography can be inverted simultaneously by an alternative weighting iteration. By analogy, the inversion of multilayer model can be done in the above procedure. An approach of model decomposition is useful in the computation of multilayer model. The techniques discussed in the present paper for gravitational field are also valid for magnetic field. 相似文献
17.
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
18.
This paper presents the numerical simulation of a creeping slope in Upper Austria, using a visco-hypoplastic material law
which describes the mechanical behavior of cohesive soils allowing for viscous effects, i.e. creep and relaxation. The method
consists of: (1) determination of the parameters of the material law, based on laboratory tests on soil samples taken from
the slope; (2) simulation of the laboratory tests with an element test program in which the used material law was implemented,
in order to test whether the model holds for the soils studied; and (3) simulation of slope movements at different sections
along the slope, assuming an infinite slope. The simulation results fit well with the field measurements. This demonstrates
that despite strongly simplified boundary conditions and limited availability of subsurface data (e.g. density) the visco-hypoplastic
law is a promising tool for predicting creep movements. 相似文献
19.
20.
The fluid flow induced by an incident wave at a discontinuity separating two porous media is governed by the hydraulic permeabilities of both media and that of the interface. In the context of Biot’s theory, we derive the time-harmonic Green’s function for the two half-space problem allowing incident fast and slow dilatational waves to assess the heterogeneous modelling behaviour for diverse hydraulic conditions. It is found that when at least one of the media is permeated with inviscid fluids, heterogeneous modelling simulates open boundary conditions. On the other hand, when the model is saturated with viscous fluids, the modelling reproduces restrained fluid flow whose values correspond to sealed pore interface conditions, in agreement with the theoretical results. Therefore the numerical technique models correctly the wave diffusion and propagation phenomena attendant at the boundary. 相似文献