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1.
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
2.
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。 相似文献
3.
Explicit time integration schemes provide an efficient solution to non-linear dynamic finite element analyses of geotechnical problems especially when high frequency response is important. Such explicit time integration schemes require one of two distinct transmitting boundary formulations to overcome the problem of radiation damping. These are the superposition boundary approach, which involves the cancellation of the reflected waves by combining the solutions of two different boundary conditions and the viscous boundary approach, which involves the absorption of incident wave energy by frequency independent viscous dashpots. The theoretical justification of these two approaches and their means of implementation are reviewed. The solutions obtained using the two different boundary approaches to the problem of a rigid massless circular footing vibrating on an elastic half-space are compared with an independent theoretical solution. The performance of the boundaries for problems involving step loading is also examined and the implications for any loading pattern with a non-zero time average are discussed. 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.
A comprehensive numerical study on finite element implementation of hypoplastic models is presented. Two crucial aspects, local integration of the constitutive equations (the local problem) and forming tangent operators for Newton–Raphson iteration (the global problem), are investigated. For solving the local problem, different integration algorithms, including explicit and implicit methods, are examined using tri-axial compression tests and incremental stress response envelopes, as well as typical boundary value problems. For solving global problems, three different ways of generating the tangent operator are compared. The numerical evidences indicate that, in terms of accuracy, efficiency and robustness, explicit methods with substepping and error control are the best choices for constitutive integration of hypoplastic models while the so-called continuum tangent operators have certain advantages over two other types of numerically-generated consistent tangent operators. 相似文献
6.
极限分析方法是土边坡稳定性分析的重要方法之一。刚体有限元上限法是其中的一类,此类方法仍旧存在一些关键问题需要完善。由于单元的刚性假设,系统的塑性变形内能耗散仅发生在单元间的界面上,故此类方法的性能主要取决于界面的布局,即采用非结构化三角形单元计算往往精度较差。为此,提出了基于滑动面摄动的刚体有限元上限法及临界滑动面的搜索方法。首先,在考虑刚体转动的基础上构造刚体有限元上限法的二阶锥规划模型,用于确定在给定试滑动面条件下的运动许可速度场。其次,将试滑动面的控制参数视为决策变量,建立搜索临界滑动面的非线性非凸优化问题模型,并采用非线性单纯形方法和粒子群方法求解此优化问题找出临界滑动面。通过经典边坡稳定问题的分析求解,验证了所提出的新方法,进一步证实了网格类型（即界面的布局）是影响刚体有限元上限法计算精度的主要因素。经过计算结果的对比发现,在刚体有限元上限法中考虑刚体转动是非常必要的,不仅可以提高刚体有限元上限法的计算精度,还可以克服此方法对界面布局的依赖性。 相似文献
7.
B. Nath 《国际地质力学数值与分析法杂志》1981,5(2):139-163
A novel finite element method has been proposed in this paper for the solution of seepage problems economically and accurately. In this method the governing equation and the prescribed boundary conditions are transformed so that they refer to a suitable logarithmically condensed ‘image’ space; the physical problem domain is also mapped into the image space. The transformed equation is then solved in the image space using standard finite elements, subject to the transformed boundary conditions. Because physical space is logarithmically condensed in the image space, the proposed method is capable of dealing with large or very large aspect ratio seepage problems economically and accurately. The validity of the method has been demonstrated by means of a number of examples including anisotropy and non-linearity. In all cases an excellent degree of accuracy was achieved, efficiently and economically. 相似文献
8.
Investigation of a hybrid polygonal finite element formulation for confined and unconfined seepage 
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下载免费PDF全文 This study presents a formulation for field problems using hybrid polygonal finite elements, taking steady state seepage through a porous material as the focus. We make comparisons with a conventional finite element formulation based on a single primary variable, focussing on the advantages of the hybrid formulation in terms of flux field accuracy and extension to convex polygonal shaped elements. For the unconfined case, we adopt a head dependent hydraulic conductivity that does not require remeshing. The performance of the hybrid polygonal element formulation is demonstrated through a series of numerical examples. The results show a sensitivity of the location of the free surface in unconfined seepage to mesh configuration for hybrid quadrilateral meshes with various aspect ratios, but not for hybrid polygonal meshes with various orientations and irregularity. Examination of the free surface location results for several conforming shape function options shows an insensitivity to choice of interpolation function, provided that it conforms with the assumptions in the formulation. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
9.
A coupling scheme for boundary and finite elements using joint elements is proposed which includes the consideration of body forces. In this scheme the boundary and joint elements are formulated in a similar way as finite elements (i.e., the equivalent FE procedure). These joint elements are efficiently used to combine different BE regions. For the evaluation of a body forces, two methods are compared on computational efficiency and it is found that the method using Galerkin tensor is more efficient than the method dividing the problem domain into several internal cells. Two main geotechnical problems considering self weight are numerically examined using this coupling procedure. 相似文献
10.
A hybrid boundary element formulation for the steady state analysis of piles and pile groups embedded in a soil stratum in which the modulus increases linearly with depth is presented. The piles are represented by compressible columns or flexible beams and the soil as a hysteretic, layered medium. The explicit Green's function corresponding to dynamic loads in the interior of a layered stratum, developed earlier by Kausel is used in the study. The governing differential equations for the pile domain are solved for a distributed periodic loading intensity and those for the soil domain by a system of boundary elements at the pile-soil interface. These are then assembled into a system of algebraic equations by satisfying interface equilibrium and compatibility. The results of the analysis have been compared against those from alternative formulations, e.g. finite elements, and confirm the accuracy of the proposed formulation. Representative results for single piles and pile groups are presented. 相似文献
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An implicit material point method (MPM), a variant of the finite element method (FEM), is presented in this paper. The key feature of MPM is that the spatial discretisation uses a set of material points, which are allowed to move freely through the background mesh. All history-dependent variables are tracked on the material points and these material points are used as integration points similar to the Gaussian points. A mapping and re-mapping algorithm is employed, to allow the state variables and other information to be mapped back and forth between the material points and background mesh nodes during an analysis. In contrast to an explicit time integration scheme utilised by most researchers, an implicit time integration scheme has been utilised here. The advantages of such an approach are twofold: firstly, it addresses the limitation of the time step size inherent in explicit integration schemes, thereby potentially saving significant computational costs for certain types of problems; secondly, it enables an improved algorithm accuracy, which is important for some constitutive behaviours, such as elasto-plasticity. The main purpose of this paper is to provide a unified MPM framework, in which both quasi-static and dynamic analyses can be solved, and to demonstrate the model behaviour. The implementation closely follows standard FEM approaches, where possible, to allow easy conversion of other FEM codes. Newton’s method is used to solve the equation of motion for both cases, while the formation of the mass matrix and the required updating of the kinematic variables are unique to the dynamic analysis. Comparisons with an Updated Lagrangian FEM and an explicit MPM code are made with respect to the algorithmic accuracy and time step size in a couple of representative examples, which helps to illustrate the relative performance and advantages of the implicit MPM. A geotechnical application is then considered, illustrating the capabilities of the proposed method when applied in the geotechnical field. 相似文献
13.
SummaryThe Application of Finite Elements to Heat Conduction Problems Involving Latent Heat A finite element method is developed for the solution of heat conduction problems which involve latent heat. The method is superior to other wellknown approaches to these problems in that it allows a wider range of material properties and boundary conditions to be dealt with, such as are encountered in complex engineering operations like ground freezing. The method is applied to simple triangular finite elements in this paper, although it could be extended to other types of element including three-dimensional ones. Several example problems are discussed and illustrated, and comparisons are made with other approaches where these can also be used. 相似文献
14.
针对传统算法效率低的问题,将隐式双时间步法应用于求解二维浅水方程,建立了非结构网格下高效的有限体积模型。在应用双时间步法时,虚拟时间层中的定常问题采用高效的隐式LU-SGS（Lower-Upper Symmetric Gauss-Seidel）方法进行迭代求解。通过模拟计算4个典型算例以及与传统显式算法进行比较,对模型精度、效率及处理实际问题能力进行检验,分析了时间步长、内迭代次数对模型性能的影响。结果表明,双时间步法放宽了稳定性对时间步长的限制,时间步长可取到显式格式10倍以上,计算耗时减少了50%以上,模型具有良好精度与适应性,具有较好的推广应用价值。 相似文献
15.
刚性块体极限分析上限法常应用于岩土工程稳定性研究,然而应用时需假定刚性块体破坏模式并递推繁琐的几何关系。为此,提出一种适应性更广的基于非线性规划模型的刚体平动运动单元上限有限元法,并解决了其优化模型初始值的确定问题。通过引入有限单元思想,将计算区域离散成刚体单元,同时以单元速度和节点坐标作为决策变量,由上限定理建立非线性规划模型获得上限解。利用编制的上限有限元程序进行边坡和浅埋隧道稳定性算例验证,表明运动单元上限有限元法能调整速度间断线至较优方位,所得破坏模式特征鲜明,上限解精度高,可广泛应用于边坡、隧道等稳定性分析研究。 相似文献
16.
Since the attenulation of propagating waves through soil/rock is related to the localized material properties as well as the strain developed, the commonly used Rayleigh-type damping model and its variations are not suitable for dynamic finite element analysis of such materials. A linear viscoelastic material model based on the concept of the relaxation spectrum is manipualted in place of the damping model in this paper. The method proposed by Day and Minster11 to transform the convolutional form of the stress–strain relationship to a set of differential operators using the Pade approximant method is generalized to non-scalar waves and implemented for transient finite element analyses. A time-marching scheme is also proposed to incorporate the resultant differential operators into the governing equation of motion. The accuracy related to the Pade approximant method and the time-marching scheme is investigated by critically analysing some scalar wave propagation problems. The proposed technique is further verified using two one-dimensional stress wave propagation problems and a two-dimensional transient propagating wave through an unbounded linear viscoelastic medium. Some encouraging results have been obtained using the proposed technique and guidelines for using this technique are also presented. Comparisons of analytical solutions obtained by Fourier synthesis and numerical results have been provided. 相似文献
17.
Wave propagation problems, such as blasting for excavation of a new tunnel oriented perpendicular to an existing tunnel, are truly three dimensional in nature. Dynamic finite element analysis with three-dimensional elements is, however, very expensive. The cheaper and simpler alternative would be to model the problem approximately in two dimensions. This paper shows that dynamic finite element analysis of such problems using conventional two-dimensional plane strain elements produces responses which are erroneously excessive. This is accredited to the inability to the inability of the two-dimensional elements to correctly model the rapid attenuation of the amplitudes of the outward propagating waves. To overcome this problem, a pseudo-plane strain concept is introduced and has been found to be a viable alternative. Numerical results are presented to demonstrate the application of the concept. 相似文献
18.
This work addresses an enrichment technique for the three-dimensional (3D) finite element (FE) analysis of a vertical drain foundation because (1) 1D and 2D simulations are insufficient to integrally describe the consolidation behaviour and (2) drains are small both in spacing and size, resulting in enormous computational costs for a traditional 3D FE analysis. Based on the idea of the semi-analytical finite element method (FEM), which combines general FEM with the high accuracy of a closed-form solution, a new spatial element that contains a drain well and its neighbouring smear zone is presented. This new combined element is depicted by eight global independent nodes and two local dependent nodes, and a classical analytical theory is introduced to set up the relationship between the two kinds of nodes. Because permeability diversity between the drain and the smear zone is considered, both the effects of smearing and well resistance are taken into account with the composite element method (CEM). A detailed derivation of the CEM is performed using the weighted residual method. The accuracy of the proposed method is validated with a totally penetrating, single-drain ground analysis for seven calculation conditions. Additionally, the proposed CEM saves 1/4–1/2 mesh elements and helps to avoid slender elements for the FEM analysis of the drained foundation. 相似文献
19.
An algorithm based on the finite element method is developed to analyze the dynamic response of multiple, jointed concrete pavements to moving aircraft loads. In the finite element idealization, the pavement-subgrade system is idealized by thin plate finite elements resting on Winkler-type viscoelastic foundation represented by a series of distributed springs and dashpots. The dowel bars at the transverse joints are represented by beam elements. It i assumed that the dowel bar is fully embedded into the pavement thus neglecting dowel-pavement interaction effects. The longitudinal keyed or aggregate interlock joints are modeled by vertical spring elements. The dynamic aircraft-pavement interaction effects are considered in the analysis by modeling the aircraft by masses supported by spring-dashpot systems representing the landing gear of the aircraft. It is assumed that the aircraft travels along a straight line with a specific initial velocity and acceleration. The aircraft-pavement interaction takes the form of two sets of coupled equations which result ina non-symmetric stiffness matrix. An approximate mixed iteration-direct elimination scheme is used to solve for the dynamic equations. The accuracy of the computer code is verified by the available experimental and analytical solutions. A parametric study is conducted to investigate the effects of various parameters on the dynamic response of pavements. 相似文献
20.
In this paper, a large deformation finite element (LDFE) approach termed ‘remeshing and interpolation technique with small strain (RITSS)’ is extended from static to dynamic soil-structure interaction applications. In addition, a technique termed ‘element addition’ is developed to improve the computational efficiency of both static and dynamic LDFE analyses that involve moving boundaries. The RITSS approach is based on frequent mesh generation to avoid element distortion. In dynamic RITSS, the field variables mapped from the old to the new mesh involve not only the stresses and material properties, but also the nodal velocities and accelerations. Using the element addition technique, new soil elements are attached to the domain boundaries periodically when the soil near the boundaries becomes affected by large displacements of the structure. The procedures of this Abaqus-based dynamic LDFE analysis and element addition technique are detailed, and the robustness of the techniques is validated and assessed through three example analyses: penetration of a flat footing into a half-space and movement of rigid and deformable landslides down slopes. 相似文献