边界单元法点电源二维地形改正的PC-1500机程序

边界单元法是一种较新的数值模拟方法。目前,在国内外发展较快,在地球物理勘探领域也有日益扩大的势头,理由是明显的。与有限单元法相比,边界单元法具有以下优点:①精度高;②占有计算机内存少,仅需输入二维地形剖分点的坐标就可进行地改;③输入数据准备及操作简单;④可降低数值模拟的空间维数;⑤特別适合于无界域,而很多地球物理正问题都是在无界域中进行。     

6节点无界元及其应用

推导了6节点无界元的相关公式,并采用VC++和Matlab混合编程的手段,设计了基于Windows操作平台的面向对象的有限元与无界元耦合分析软件。应用该软件,成功的对某大型水电站地下硐室群的稳定性进行了有限元分析和有限元与无界元耦合分析,验证了公式的正确性。分析表明,在无限域和半无限域的岩土工程问题中引入无界元可以达到消除“边界效应”和提高计算效率的目的。     

边界单元法在高密度电阻率法二维地形改正中的应用效果

给出了高密度电阻率法二维地形改正的边界元数值解法及其探测地下煤气管道时进行二维地形改正的应用实例。     

边界单元法原理及其在地球物理勘探中的应用简介

边界单元法比有限单元法有重大的优点:1)方程组的规模小得多,2)向计算机输入数据少得多;3)适用于无界区域。这些优点使边界单元法更便于解决二维和三维地球物理正演问题。本文简单介绍边界单元法的原理及其在地球物理勘探中的应用。     

岩体初始地应力场分析方法研究

初始地应力场是影响岩土工程稳定性的重要因素之一,如何合理地模拟初始地应力场一直是岩体力学中的重要研究课题。以国内某大型水利水电工程构筑区域实测空间地应力资料为基础,以边界位移为控制对象,采用有限元（无界元）方法对工程区大范围内的岩体初始地应力场进行了分析和研究。尝试在实际边界上满足无穷远处位移为0的模型边界上引入了无界单元,实测点上的应力拟合结果有较明显的改善,这表明所采用的方法是切实可行和有效的。     

利用有限单元法模拟二维MT倾子响应

在二维地电模型中,考虑到大地电磁测深(MT)倾子响应依赖于横电(TE)模式的数值模拟问题,笔者采用矩形网格单元和双二次插值对MT的倾子响应进行求解。首先,给出了二维地电条件下的边值问题和变分问题,并通过有限单元法对模型进行单元剖分、插值、积分和整体合成;其次,通过求解复系数方程组得到了每个节点的电场值;最后,采用差分方法求得电场沿横向和垂向的偏导数值,从而计算出二维MT的倾子响应。通过对2个二维地电模型的倾子响应进行数值模拟,获得了倾子响应的实部、虚部和振幅,结果很好地反映了不均匀体的横向分布情况。     

基于二维降阶Hermite插值的铁路路基动力响应2.5D有限元模拟

2.5D有限元方法在铁路路基动力响应研究领域中的应用渐趋广泛。针对其在求解随机不平顺条件下路基动力响应时计算效率显著下降的问题,构建了基于二维降阶Hermite插值的2.5D有限元路基动力响应快速计算框架。以路基在频率-波数域动力响应的基本特征为依据确定了插值原则,讨论了插值点分布和数量对插值精度的影响。研究表明：采用二维降阶Hermite插值方法可以实现随机不平顺条件下路基动力响应的快速计算。相比插值点非均匀分布,插值点均匀分布可以兼顾幅值和相位的插值精度,适应性更好。此外,该方法的计算效率仅与插值点数量相关,不受随机不平顺谐波数量的影响,在模拟随机不平顺条件下路基动力响应方面具备显著的优势。     

自然邻点插值算法及其在二维不规则数据网格化中的应用

由于观测数据的不足,对不规则散点数据的二维插值在地球物理中应用非常广泛。这里研究并实现了自然邻点二维插值算法,并以一个大地电磁测深反演数据为例,验证了该方法的可行性与效果。实际资料试算与成图结果表明,该方法具有精度高、插值效果好、速度快以及便于模拟地形数据等优点。     

三维有限元位移场插值问题的研究和应用

对三维有限元位移场的插值问题进行了研究,提出基于Delaunay三角剖分的二次细分网格法。该法首先建立2个模型--整体模型和局部二次细分模型,对整体模型进行有限元计算和反分析得到初始地应力场和位移场;然后,基于Delaunay三角剖分,对整体模型的三维有限元位移场进行插值,插值结果作为局部模型的边界位移,局部二次细分模型再在此基础上进行有限元分析。最后,将该方法应用于工程实践,证明能提高计算效率,是切实可行的。     

弹性介质分向插值无限元

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。     

Infinite Boundary Element in Two and Three Dimensional Problems

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.     

三维结线动力无穷元及其特性研究

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。     

Non-linear analysis of geomechanical problems using coupled finite and infinite elements

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     

Explanation of locking of four‐node plane element by considering it as elastic Dirichlet‐type boundary value problem

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.     

Parametric infinite element for seepage analysis

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.     

有限单元法数据生成器

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。     

Comparative analysis of some geomechanics problems using finite and infinite element methods

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.     

FEM Data Generator

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.     

ABAQUS动力无限元人工边界研究

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。