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。     

三维过渡等参单元在岩土工程有限元分析中的应用

土石坝等复杂土工结构物有限元三维建模中多采用精度较高的六面体单元辅以部分过渡用的退化单元,而退化单元由于形态不好,会导致有限元计算精度较差。解决该问题的途径之一是采用过渡性的等参元。总结了几种常遇到的过渡等参单元（楔形体、四面体、金字塔）的插值函数和高斯积分局部坐标和权重,并编入了有限元程序。通过比较六面体单元和金字塔单元剖分理想土石坝的有限元计算结果,说明所引入的金字塔单元是满足精度要求的。将各种过渡单元应用于实际土石坝工程的有限元计算,结果表明,使用过渡等参单元是可以在一定程度上提高计算精度的。最后讨论了二次单元在弹塑性有限元动力计算中的应用。二次单元的使用,可以改善动力计算中的超静孔压分布,提高计算精度。     

Finite element analysis for a finite conductivity fracture in an infinite poroelastic medium

In the technology of oil recovery, oil production rate can be increased by generation of a vertical conductive fracture adjacent to the well-bore. In this paper the seepage flow and isothermal deformation in both the oil formation and the fracture are studied by modelling the formation as a two-dimensional infinite poroelastic medium and the conductive fracture as a one-dimensional poroelastic material, saturated by a one-phase compressible fluid. The plane strain condition is employed. Solutions for a growing conductive fracture and a stationary conductive fracture in the infinite medium are obtained by means of the finite element method based on a variational principle for the formation which can impose the governing equations of the fracture. Infinite elements are used outside the finite element domain. Numerical results indicate that the injection rate, the applied pressure and the crack mouth opening displacement at the well-bore oscillate during the propagation of the conductive fracture. The production rate of a well with the conductive fracture is compared with that of a well without the conductive fracture. Finally, a new definition of the conductivity coefficient for the conductive fracture is presented. Copyright © 1999 John Wiley & Sons, Ltd.     

三维油藏中应力与渗流的摄动-有限元分析

提出了一个较为实际的石油油藏的三维力学模型。以已有的三维介质中应力与渗流耦合问题的变分原理为基础,用摄动法证明了光油藏厚度变化为小量时,三维问题或简化为平面应变问题,并可采用不同厚度的平面应变单元进行有限元分析,所得到的解即是该三维问题的零阶摄动解。给出了摄动法的推导和有限元格式,计算了一个水驱法进行油田二次开发的算例并给出了计算结果。     

Modelling of coupled fluid‐mechanical problems in fractured geological media using enriched finite elements

Geological environments, such as petroleum reservoirs, normally exhibit physical discontinuities, for example, fractures and faults. Because of the reduced thickness of these discontinuities, finite element formulations with strong discontinuity have been applied to the numerical modelling of geological environments. Until now, two relevant characteristics of petroleum reservoirs have not been addressed by these formulations. The first is the pore pressure jump in the direction normal to a discontinuity in a fluid‐mechanical coupling condition, which is present primarily in sealing faults owing to the contrast of permeability with the porous medium. The absence of this jump can affect the prediction of the deformability of a physical discontinuity. Furthermore, reservoir models frequently use coarse meshes. Thus, the method used to evaluate the pore pressure in the discontinuity may exhibit a strong dependence relative to the mesh refinement. Based on these characteristics, in this study, a formulation of an enriched finite element for application to coupled fluid‐mechanical problems with pre‐existing physical discontinuities saturated by a single fluid is presented. The formulation employs discontinuous interpolation functions and enables the reproduction of jumps of displacement and pore pressure associated with a discontinuity inside the element without the need to discretise it. An approximation to estimate the pore pressure in the discontinuity was developed, one which seeks to minimise the influence of refinement. The element's response is verified by comparison with a one‐dimensional analytical solution and simple examples that are simulated using commercial software. Copyright © 2015 John Wiley & Sons, Ltd.     

Use of coupled finite element analysis in unsaturated soil problems

This paper presents a variation of Biot's consolidation theory for analysing problems involving unsaturated soils, and implemented using the finite element method. The numerical method is applied to a few geotechnical problems as examples and the results obtained are compared to some published data. The illustrative examples show how the numerical method can be used to analyse seepage and consolidation problems associated with unsaturated soils and demonstrate the flexibility and applicability of the presented method. Copyright © 2000 John Wiley & Sons, Ltd.     

用无穷边界元分析半无限域问题

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。     

Upper bound limit analysis using linear finite elements and non‐linear programming

A new method for computing rigorous upper bounds on the limit loads for one‐, two‐ and three‐dimensional continua is described. The formulation is based on linear finite elements, permits kinematically admissible velocity discontinuities at all interelement boundaries, and furnishes a kinematically admissible velocity field by solving a non‐linear programming problem. In the latter, the objective function corresponds to the dissipated power (which is minimized) and the unknowns are subject to linear equality constraints as well as linear and non‐linear inequality constraints. Provided the yield surface is convex, the optimization problem generated by the upper bound method is also convex and can be solved efficiently by applying a two‐stage, quasi‐Newton scheme to the corresponding Kuhn–Tucker optimality conditions. A key advantage of this strategy is that its iteration count is largely independent of the mesh size. Since the formulation permits non‐linear constraints on the unknowns, no linearization of the yield surface is necessary and the modelling of three‐dimensional geometries presents no special difficulties. The utility of the proposed upper bound method is illustrated by applying it to a number of two‐ and three‐dimensional boundary value problems. For a variety of two‐dimensional cases, the new scheme is up to two orders of magnitude faster than an equivalent linear programming scheme which uses yield surface linearization. Copyright © 2001 John Wiley & Sons, Ltd.     

考虑强度各向异性的边坡稳定有限元分析

天然沉积的土层总是表现出一定程度的强度各向异性,但现有的边坡稳定有限元分析极少考虑各向异性的影响。对大型有限元软件ABAQUS进行二次开发,使其能够考虑土体黏聚力随大主应力方向的变化,动态更新增量迭代求解过程中边坡不同位置处的抗剪强度,进而提出具备安全系数自动搜索功能的各向异性边坡稳定分析方法。计算结果表明,均匀边坡的有限元解与极限分析上限解相差很小。如果采用土体固结方向的黏聚力并按各向同性评价缓坡的稳定性,可能严重高估安全系数,尤其是在黏聚力较高的情况下。与极限分析不同,建立的强度更新有限元模型能够分析成层边坡的稳定性。     

Numerical and analytical observations on long and infinite slopes

Interest in the mechanics of landslides has led to renewed evaluation of the infinite slope equations, and the need for a more general framework for estimating the factor of safety of long and infinite slopes involving non‐homogeneous soil profiles. The paper describes finite element methods that demonstrate the potential for predicting failure in long slope profiles where the critical mechanism is not necessarily at the base of the soil layer. The influence of slope angle is also examined in long slopes, leading to some counter‐intuitive conclusions about the impact of slope steepness on the factor of safety. Copyright © 2010 John Wiley & Sons, Ltd.     

边坡可靠度分析的非侵入式随机有限元法

提出基于非侵入式随机有限元法的边坡可靠度分析方法,并编写计算程序NISFEM。采用有限元滑面应力法计算边坡安全系数,将Hermite随机多项式展开与SIGMA/W和SLOPE/W模块有机结合实现边坡可靠度非侵入式随机分析。根据随机多项式展开系数,给出边坡安全系数前4阶统计矩（均值、标准差、偏度和峰度）和Sobol指标解析表达式,并采用Sobol指标进行边坡可靠度参数敏感性分析。最后,以均质土坡可靠度问题为例,证明该方法在边坡可靠度分析中的有效性。结果表明,边坡可靠度分析的非侵入式随机有限元法能够有效地考虑边坡变形对边坡可靠度的影响,计算效率远远高于蒙特卡罗模拟方法（MCS）,是解决复杂边坡可靠度问题一种有效地分析手段;黏聚力和内摩擦角变异性对边坡安全系数前四阶统计矩具有明显的影响,重度变异性对安全系数前4阶统计矩几乎没有影响;抗剪强度参数间负相关性对边坡安全系数均值几乎没有影响,但对安全系数标准差、偏度和峰度均有明显的影响。此外,随着抗剪强度参数间负相关性的增加,边坡安全系数由近似正态分布逐渐变为明显的非正态分布。     

极限分析有限元法讲座—— Ⅰ岩土工程极限分析有限元法

经典岩土工程极限分析方法一般采用解析方法，有些还要对滑动面作假设，且不适用于非均质材料，尤其是强度不均的岩石工程，从而使极限分析法的应用受到限制。随着计算技术的发展，极限分析有限元法应运而生，它能通过强度降低或者荷载增加直接算得岩土工程的安全系数和滑动面，十分贴近工程设计。为此，探讨了极限分析有限元法及其在边坡、地基、隧道稳定性计算中的应用，算例表明了此法的可行性，拓宽了该方法的应用范围。随着计算机技术与计算力学的发展，岩土工程极限分析有限元法正在成为一门新的学问，而且有着良好的发展前景。     

多支盘水泥土桩的非线性有限元分析

本文用Ansys分析了多支盘水泥土桩复合地基中的桩体应力、桩间土应力和位移,总结了多支盘水泥土桩的承载特性:设置多支盘,承载力增加约40%,桩侧受力约占90%,第一个支盘受力最大,承载力随盘数、盘径、盘距、桩体弹性模量等产生变化。并分析了多支盘桩的弹性模量、盘数、盘径对复合地基变形的影响。     

节理网络有限元在倾倒斜坡稳定分析中的应用

节理网络有限元是指具有节理网络模拟功能的有限元,它不但能将野外节理统计特征直接输入到模型中,同时允许节理按一定的破坏准则产生屈服,从而较好地模拟边坡的实际结构及破坏特征。论述了倾倒变形边坡的分析方法及存在的问题,介绍了节理网络有限元的功能及参数输入,说明了其在倾倒变形边坡应用中的优势,并以黄河上游茨哈峡电站Ⅰ号倾倒体为例,计算了该倾倒边坡的稳定性及破坏趋势,结果表明,节理网络有限元是倾倒变形边坡稳定分析的一种有效、可靠的方法。     

可调圆弧木模板的三维有限元计算分析

自 20 世纪 90 年代我国开始使用可调圆弧木模板以来,定型圆弧钢模板在建筑中的地位被逐步取代。由于传统的以梁代替面进行的计算,存在着过度简化计算模型的缺陷,造成计算结果与实际相差较大。所以,采用三维有限元对模板 进行计算分析,得到的计算结果经检验与实际能吻合的较好。     

Bearing capacity of non-associative coaxial granular materials by upper bound limit analysis and finite elements

In this paper, an upper bound estimate of the limit load on non-associative coaxial granular materials is presented. The kinematic approach of the upper bound limit analysis has been utilised. The failure mechanism is assumed to coincide with the direction of the shear bands at every point throughout the body. The shear band orientation in non-associative coaxial materials, i.e. those with the same major principal stress and major principal strain increment directions, can be found based on the angle of dilation and the major principal stress direction. Therefore, having known the stress field at limiting equilibrium, the orientation of the shear bands and hence, the failure mechanism can be obtained. In this study, the stress field is first determined by the method of stress characteristics. Then, the finite element interpolation technique is used to interpolate the stress field and to find the orientation of the shear bands at every point within the field. Once the failure mechanism and the stress state at every point along velocity discontinuities have been found, the upper bound limit analysis has been performed to estimate the limit load.     

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.     

Development of an infinite element boundary to model gravity for subsurface civil engineering applications

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.     

Bearing capacity of two interfering strip footings from lower bound finite elements limit analysis

A rigorous lower bound solution, with the usage of the finite elements limit analysis, has been obtained for finding the ultimate bearing capacity of two interfering strip footings placed on a sandy medium. Smooth as well as rough footing–soil interfaces are considered in the analysis. The failure load for an interfering footing becomes always greater than that for a single isolated footing. The effect of the interference on the failure load (i) for rough footings becomes greater than that for smooth footings, (ii) increases with an increase in ?, and (iii) becomes almost negligible beyond S/B > 3. Compared with various theoretical and experimental results reported in literature, the present analysis generally provides the lowest magnitude of the collapse load. Copyright © 2011 John Wiley & Sons, Ltd.     

Iterative analysis of pore‐dynamic models discretized by finite elements

This work proposes an iterative procedure to analyze dynamic linear/nonlinear fully saturated porous media considering time‐domain finite element discretization. In this iterative approach, each phase of the coupled problem is treated separately, uncoupling the governing equations of the model. Thus, simpler, smaller, and better conditioned systems of equations are obtained, rendering more attractive techniques. A relaxation parameter is introduced in order to improve the efficiency and robustness of the iterative solution, and an expression to compute optimal values for the relaxation parameter is discussed. At the end of the paper, numerical examples are presented, illustrating the effectiveness and potentialities of the proposed methodology. Copyright © 2013 John Wiley & Sons, Ltd.