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1.
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
2.
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
3.
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
4.
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
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.
Four classical geomechanics problems involving semi-infinite linear elastic media have been solved numerically using recently developed mapped infinite elements coupled to finite elements.The effect of the remoteness of the truncated boundary and the location of infinite element coupling on solution accuracy has been studied. The results of conventional analyses using finite elements over a relatively large but restricted region are compared to the coupled analyses. Comparison of the results shows that for the same number of degrees of freedom the performance of the coupled solutions is superior to the conventional approach with respect to accuracy of solution and computational efficiency. Finally, some general guidelines are proposed for the efficient numerical solution of these types of problems using the coupled finite/infinite element approach. 相似文献
7.
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
8.
本文介绍有限单元法数据生成器采用字符标识的输入数据系统和等参元插值函数的概念,人工准自动或全自动生成实际工程问题二维或三维有限元分析所需要的基本数据,如单元节点号、材料参数、节点坐标、边界条件和荷载信息等等。这个数据生成器以统一的程序和相同的输入方式来处理规则网格、不规则网格,以及它们的任意组合和各种类型的单元,便于用户的使用。 相似文献
9.
Wang Kejun 《岩土力学》1988,9(3):57-67
The FEM data generator presented in this paper is used to generate quasi-automatically or automatically the basic data for 3-d or 2-d finite element analysis of engineering projects, such as element nodal connections, material parameters, nodal coordinates, restrained boundary conditions, and the information of applied load. With the symbol-identified input data system and the concept of interpolation function of isoperimetric element, this data generator deals with regular meshes, irregular meshes, and their arbitrary combination in unified routine and the same way to input data, which is available to any kind of elements and convenient to users. The work principle of this data generator and the features of corresponding computer routines are described in detail. 相似文献
10.
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
11.
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
12.
Semih Küçükarslan 《国际地质力学数值与分析法杂志》2004,28(9):963-980
In this paper, time-domain dynamic analysis of dam–reservoir–foundation interaction is presented by coupling the dual reciprocity boundary element method (DRBEM) in the infinite reservoir and foundation domain and the finite element method in the finite dam domain. An efficient coupling procedure is formulated by using the sub-structuring method. The effects of the reservoir bottom absorption are included in the formulations. Sharan's boundary condition for the far-end of the infinite fluid domain is implemented. To verify the proposed scheme, numerical examples are carried out by comparing with the available exact solutions and finite–finite element coupling results for the dam–reservoir interaction. A complete dam–reservoir–foundation interaction is also studied by including the bottom absorption effects. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
13.
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
14.
This paper describes the application of symmetric Galerkin boundary element methods (SGBEM) for the analysis of a 2D crack propagation problem. The sub-domain SGBEM for crack problem is derived. The coefficient matrix is completely symmetric. Cohesive crack model is used to simulate crack propagation. The increment control method for crack propagation and the method for unknown crack propagation path have been derived for high-order element. Two-stage interpolation method called the ‘quasi-higher order element method’ (QHOEM) is then proposed to solve the double integrals. In the initial stage, it uses higher order elements to interpolate the field variables, and for the numerical integration involved, it further uses interpolation functions to decompose the higher order elements into lower order elements so that the existing analytical integration can be applied. A finite rectangular plate containing a centre crack growth and four-points bending beam problem have been analysed to check the accuracy of the proposed method. For actual application, a dam buttress with an edge crack has been analysed and the results are found to be in agreement with the other numerical and experimental results. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
15.
A new finite element scheme is proposed, in this paper, for solving two-dimensional wave propagation problems in multilayered soils resting on a rigid base. The multilayered soils are treated as multiple horizontal layers of lateral infinite extension in geometry. Since these horizontal layers can be truncated by two artificially truncated vertical boundaries, two high-order artificial boundary conditions are applied for propagating the incoming waves from the interior domain into the far field of the system. Both the semi-analytical method and the truncated boundary migration procedure are used to derive the high-order artificial boundary conditions, which are comprised of a physically meaningful dashpot and a generalized energy absorber. The main advantage of using the proposed finite element scheme is that the derived artificial boundary condition can be straightforwardly implemented in the finite element analysis, without violating the band/sparse structure of the conventional finite element equation. The related numerical examples have demonstrated that the proposed finite element scheme is of high accuracy in dealing with wave propagation problems in multiple horizontal layers. 相似文献
16.
The finite element method (FEM) and the boundary element method (BEM) are two well established numerical methods used for the analysis of underground openings. The advantages of both the methods are utilized by adopting FEBEM in which finite elements are coupled with boundary elements. A coupling procedure is presented in this paper. In using FEBEM, the effect of the location of interface boundary between finite element and boundary element regions, effect of Poisson's ratio and effect of stress ratio are discussed. It is shown that Poisson's ratio and stress ratio have significant effect on the accuracy of the results. Different discretization schemes are discussed to study their effect on accuracy and computation time. The use of different material properties in the FE region is presented. A comparative study is made with FEM for all the cases. It is shown that use of FEBEM is more advantageous than FEM. 相似文献
17.
In this paper evaluated a case study for jointed rock mass using element free Galerkin method and Paton??s failure. The displacement field of each block is constructed by the moving least-squares interpolation with an array of points distributed in the block. The essential boundary conditions are enforced using penalty method. It is shown that excellent results are obtained and less calculation time is required as compared to finite difference method. 相似文献
18.
In this paper a new finite element formulation for numerical analysis of diffused and localized failure behavior of saturated and partially saturated gradient poroplastic materials is proposed. The new finite element includes interpolation functions of first order (C1) for the internal variables field while classical C0 interpolation functions for the kinematic fields and pore pressure. This finite element formulation is compatible with a thermodynamically consistent gradient poroplastic theory previously proposed by the authors. In this material theory the internal variables are the only ones of non-local character. To verify the numerical efficiency of the proposed finite element formulation, the non-local gradient poroplastic constitutive theory is combined with the modified Cam Clay model for partially saturated continua. Thereby, the volumetric strain of the solid skeleton and the plastic porosity are the internal variables of the constitutive theory. The numerical results in this paper demonstrate the capabilities of the proposed finite element formulation to capture diffuse and localized failure modes of boundary value problems of porous media, depending on the acting confining pressure and on the material saturation degree. 相似文献
19.
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
20.
紧支径向基函数能使支配方程中的刚度矩阵具有稀疏性,很适合应用于无网格方法中,其缺点是在插值计算时精度不高.点插值方法的插值函数具有Delta函数性质,可以很方便的施加本质边界条件,但在计算插值函数时矩阵易出现奇异.为了提高计算精度并避免点插值法的局限性,首先对紧支径向基函数进行完备性修正,然后用完备性修正的紧支径向基函数代替多项式来形成插值函数,建立了紧支径向基函数点插值方法.由于该方法中的形函数满足Delta函数性质,因此本质边界条件可以像传统的有限元方法一样很容易施加.然后将该方法用于二维弹性静力问题的求解,导出了其相应的离散方程.最后将该方法应用于一个悬臂梁的分析中,初步验证了该方法的有效性与合理性. 相似文献