电法勘探中有覆盖层的点源二维、点源三维边界元法正演

本文提出用二层介质格林函数作为余量加权函数,归化边界积分方程的边界单元法。通过对有水平覆盖层的点源二维、点源三维正演计算表明,本算法明显地优化了以往的边界元法,计算精度高,方程组规模小,节省内存空间,仅在一般微机上即可实现,扩大了边界单元法在电法勘探中的应用范围。     

A quadratic variation indirect boundary element method for traction boundary-value problems of two-dimensional elastostatics

Boundary integral equations for traction boundary-value problems of two-dimensional elastostatics are derived by the indirect boundary element method. Quadratic variation functions for the representation of geometry, fictitious forces and displacements over each boundary element are described. A system of equations approximating to the boundary integral equations is obtained by a Galerkin formulation in which the integral equation is written at Gauss integration points of elements. The method of computation of the Cauchy principal value is described. Examples of application to the analysis of stress and displacement around underground excavations demonstrate the accuracy and efficiency of the formulation.     

边界积分方程法二维电阻率层析成像

本文基于作者在文献［１］中提出的边界积分方程,建立了一种新的二维电阻率层析成像方案。与目前国内外用有限元法和α中心法的成像方法相比,该方法无需计算雅可比矩阵,也不必做线性化近似。这不仅节省了计算时间,而且使成像迭代过程稳定,可以对实际上广泛存在的大电性对比度介质获得满意的成像效果,从而大大提高了电阻率层析成像技术的实用性。文中给出的数值模拟结果显示了该方法的有效性。     

A practical and efficient numerical scheme for the analysis of steady state unconfined seepage flows

The scaled boundary finite‐element method (SBFEM), a novel semi‐analytical technique, is applied to the analysis of the confined and unconfined seepage flow. This method combines the advantages of the finite‐element method and the boundary element method. In this method, only the boundary of the domain is discretized; no fundamental solution is required, and singularity problems can be modeled rigorously. Anisotropic and nonhomogeneous materials satisfying similarity are modeled without additional efforts. In this paper, SBFE equations and solution procedures for the analysis of seepage flow are outlined. The accuracy of the proposed method in modeling singularity problems is demonstrated by analyzing seepage flow under a concrete dam with a cutoff at heel. As only the boundary is discretized, the variable mesh technique is advisable for modeling unconfined seepage analyses. The accuracy, effectiveness, and efficiency of the method are demonstrated by modeling several unconfined seepage flow problems. Copyright © 2011 John Wiley & Sons, Ltd.     

基于紧支径向基函数的点插值无网格方法

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.     

水流入渗和气体驱替过程二维问题的耦合求解

采用孔隙介质力学分析方法,把土体骨架、孔隙水和孔隙气体分别作为独立的研究对象,结合孔隙水和孔隙气体在气、液交界面上的力学条件建立耦合方程,研究非饱和土中孔隙水的入渗和孔隙气体的排出过程,为水流入渗问题的求解提供了一种新的方法。将此种方法应用于二维水流入渗问题的数值求解,利用简单的工况校验了这种计算方法的可靠性。通过对砂体和粉煤灰断面进行的二维水流入渗计算表明,孔隙气体的排出过程影响孔隙水的入渗运动。     

复杂条件下3D电磁场有限元计算方法

从电磁场的Maxwell方程出发, 根据电磁场的边值问题及变分公式建立了有限元方程组.采用可以模拟较为复杂的空间地质构造和地形起伏的四面体单元离散计算区域; 单元中的插值函数选择了精度较高的十点双二次多项式; 并采用连续的双二次多项式插值函数来模拟计算区域内单元中电导率σ的空间变化.推导出了地下变电导率σ条件下计算三维电磁场的有限元单元方程的解析表达式; 采用伽辽金方法推导出了散度效正有限元方程组.根据所推导的公式, 编制了三维有限元的计算程序.数值计算结果表明, 上述公式推导正确, 为三维电磁场的数值计算提供了一条有效的新途径.      

An indirect boundary integral equation method for poroelasticity

This paper presents an indirect boundary integral equation method for analysis of quasi-static, time-harmonic and transient boundary value problems related to infinite and semi-infinite poroelastic domains. The present analysis is based on Biot's theory for poroelastodynamics with fluid viscous dissipation. The solution to a given boundary value problem is reduced to the determination of intensities of forces and fluid sources applied on an auxiliary surface defined interior to the surface on which the boundary conditions are specified. A coupled set of integral equations is established to determine the intensities of forces and fluid sources applied on the auxiliary surface. The integral equations are solved numerically in the Laplace domain for quasi-static and transient problems, and in the frequency domain for time-harmonic excitations. The kernel functions of the integral equation correspond to appropriate Green's functions for a poroelastic full space or half-space. The convergence and numerical stability of the present scheme are established by considering a number of bench mark problems. The versatility of the present method is demonstrated by studying the quasi-static response of a rigid spheroidal anchor, and time-harmonic and transient response of a rigid semi-circular tunnel.     

越流含水层井群系统地下水流的边界元数值模拟

本文提出一种求解越流含水层井群系统的边界元方法。该法把抽水井井壁作为内边界,通过积分处理,不需要对井壁内边界进行剖分,通过推导求得水头H及其法向导数的边界积分方程,离散化后得到求解该积分方程的一组线性代数方程组、该法用于实例计算表明,计算精度较高。     

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.     

二维与三维问题的无界边界单元

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。     

A Posteriori Error Estimates for Finite Volume Element Approximations of Convection–Diffusion–Reaction Equations

We present the results of a study on a posteriori error control strategies for finite volume element approximations of second order elliptic differential equations. Finite volume methods ensure local mass conservation and, combined with some up-wind strategies, give monotone solutions. We adapt the local refinement techniques known from the finite element method to the finite volume discretizations of various boundary value problems for steady-state convection–diffusion–reaction equations. In this paper we derive and study a residual type error estimator and illustrate its practical performance on a series of computational tests in 2 and 3 dimensions. Our tests show that the discussed locally conservative approximation methods with a posteriori error control can be used successfully in numerical simulation of fluid flow and transport in porous media.     

Some numerical issues using element‐free Galerkin mesh‐less method for coupled hydro‐mechanical problems

A new formulation of the element‐free Galerkin (EFG) method is developed for solving coupled hydro‐mechanical problems. The numerical approach is based on solving the two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Spatial variables in the weak form, i.e. displacement increment and pore water pressure increment, are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on a penalty method. Numerical stability of the developed formulation is examined in order to achieve appropriate accuracy of the EFG solution for coupled hydro‐mechanical problems. Examples are studied and compared with closed‐form or finite element method solutions to demonstrate the validity of the developed model and its capabilities. The results indicate that the EFG method is capable of handling coupled problems in saturated porous media and can predict well both the soil deformation and variation of pore water pressure over time. Some guidelines are proposed to guarantee the accuracy of the EFG solution for coupled hydro‐mechanical problems. Copyright © 2008 John Wiley & Sons, Ltd.     

三维N-S方程混合有限分析多重网格方法

提出了一种求解三维定常不可压N-S方程的混合有限分析多重网格方法(HFA-FMG).以三维方腔流动作为算例,计算表明提出的数值格式能极大地节省计算工作量且稳定有效.三维方腔流动的模拟成果较好地表现方腔内复杂的流动特征并和其他成果吻合.     

A finite element approach to solve contact problems in geotechnical engineering

This paper presents a finite element approach to solve geotechnical problems with interfaces. The behaviours of interfaces obey the Mohr–Coulomb law. The FEM formulae are constructed by means of the principle of virtual displacement with contact boundary. To meet displacement compatibility conditions on contact boundary, independent degrees of freedom are taken as unknowns in FEM equations, instead of conventional nodal displacements. Examples on pressure distribution beneath a rigid strip footing, lateral earth pressure on retaining walls, behaviours of axially loaded bored piles, a shield‐driven metro tunnel, and interaction of a sliding slope with the tunnels going through it are solved with this method. The results show good agreement with analytical solutions or with in situ test results. Copyright © 2005 John Wiley & Sons, Ltd.     

Application of the edge function method to rock mechanics problems

Summary The edge function method is considered as an alternative to conventional numerical schemes for the solution of plane problems in rock mechanics. The essence of the approach is the approximation of the solution by a linear combination of solutions of the field equations. The unknowns in the linear combination are obtained from a system of equations which follows from the approximation of the boundary conditions by a boundary Galerkin energy method. No mesh generation is required over the domain or boundary of the problem. Previous edge function work in anisotropic elasticity is enhanced by the incorporation of a special solution for the effect of gravity. Examples are presented to illustrate the applicability of the method in determining stresses in various rock mechanics problems. A high level of accuracy is achieved with a relatively small number of degrees of freedom. Convergence is rapid because of the inclusion of special analytic solutions to model stress concentrations. The inclusion of the gravity force does, however, lead to a small increase in the number of degrees of freedom needed to achieve acceptable results. The optimum use of the edge function method, at present, may be as a special element within more general finite element or discrete element codes.     

A new development of the scaled boundary finite element method for wave motion in layered half-space

The scaled boundary finite element method (SBFEM) developed by Wolf and Song has shown certain parallels to the finite element method (FEM) and boundary element method (BEM). Because of its semi-analytical nature, SBFEM is particularly suitable for the analysis of wave propagation in unbounded domains. This paper makes a certain modification of the standard SBFEM. A new idea of scaling surface instead of a scaling center is introduced to formulate the governing SBFE equations for the analysis of wave propagation in multilayered half-space, which leads to simplifying the modeling and saving considerably the computational effort. In addition, by employing the proposed approach, some problems encountered in engineering practice, which are difficult to deal with by the conventional SBFEM, for example, 3D foundation impedance on half-space with irregular geographical features, can be effectively solved. The proposed approach also helps to simplify the solution of shell structures. Numerical examples are provided to validate the accuracy and efficiency of the proposed approach.     

动力固结流—固耦合模型的求解方法

以三维多孔介质中基本方程为基础，提出了动力固结问题的力学模型，给出了相应的变分原理及其有限元格式，用轴对称问题的有限单元法模拟了单点单次夯击过程，给出了详细的求解方法及算例，并将计算结果与现场实测资料作了比较。     

基于二次场二维起伏地形MT有限元数值模拟

通过计算二次场来进行二维大地电磁数值模拟;导出了二维大地电磁二次场的微分方程,利用有限单元法来解微分方程;对矩形网格进行对角线的二次剖分,更容易且真实地模拟起伏地形。对几个典型模型进行了试算,与前人总场法的计算结果做了比较,两者视电阻率曲线一致,证明本文算法是正确的;通过2个简单的算例说明复杂地表下2种极化模式的MT观测资料都有明显的异常,视电阻率在TM模式下比TE模式更易受地形影响,TE模式下视电阻率曲线形态与地形呈"正相关",TM模式下反之。