Removal of finite deformation using strain trajectories

A technique is described for removing the effects of finite deformation, given the principal values and orientations of strain at a number of points throughout a deformed body.Using the principal orientations, strain trajectories are constructed for the deformed state. The body is divided into finite elements bounded by these trajectories. Each element is then unstrained without changing its orientation or position. This process creates artificial voids and overlaps, which are minimized by imparting rigid translations and rotations to the elements according to a least squares method.The result is the pattern of strain trajectories for the undeformed state. It is shown that the trajectories for the deformed and undeformed states may be used as reference coordinates in order to map the change in shape of any body as it passes from the deformed to the undeformed state or vice versa. The technique is tested using models of a folded layer and a shear zone. It is suggested that the technique is versatile enough to allow for errors in original strain data. Although the technique has so far been applied to two-dimensional deformations, a similar method should be usable in three dimensions.     

Large strain analysis of some geomechanics problems by the finite element method

This paper presents a rational approach to the finite strain analysis of elastic-plastic materials. An updated incremental finite element technique was applied to problems of shallow foundations of homogeneous as well as multilayer soils. This was based on a variational principle which is suitable for such problems.     

Factorization of finite strains in three dimensions—a computer method

Strain analysis using deformed objects is already well established. The more sophisticated techniques can resolve tectonic strains and indicate the nature of any pre-tectonic fabric. Methods that analyse in two dimensions can produce problems of incomparability when results from three faces of one sample are combined.A method for factorizing finite, non-coaxial strains is presented which overcomes these problems by analysing in three dimensions. Published data from deformed lapilli tuff from the English Lake District have been used to test the method.Results are as valid as those obtained originally from the data, and the technique enables strain analysis to be extended to areas which give imprecise results using existing methods.     

A three-dimensional finite element program for brittle bimodular rock-like materials

The present paper models the behaviour of bimodular materials (materials with different tensile and compressive moduli) by using a three-dimensional finite element method. Since there is no explicit and definite expression for the shear modulus G of bimodular materials, the analysis starts with a 3 × 3 elasticity matrix in the principal stress coordinate system, and then uses a transformation from principal to Cartesian coordinates to obtain the 6 × 6 elasticity matrix. A corresponding iterative technique is proposed, and multiloading sequences in non-proportionate loading—which need more iterations because of the non-linear elastic property—are also discussed. Numerical examples are presented which show good agreement with analytical results.     

A finite element procedure for calculation of strain from interpolated displacements

Second-order universal kriging is proposed as an accurate model for interpolating displacements measured in the field to nodal points of a superimposed finite element mesh. These interpolated displacements are used in a modified finite element procedure to calculate strain. This model is compared to a local trend model to judge superiority. Interpolation models are tested by randomly sampling displacements obtained in a finite element analysis, then applying interpolation in attempts to reconstruct the original results.     

Guidelines for using the finite element method to predict one-dimensional consolidation behaviour

Several finite element schemes, based both on the diffusion and coupled approaches, have been implemented in computer programs and a comparative study carried out to investigate the numerical performance of each scheme. Factors such as stability, convergency, accuracy, computational time and the effects of wide variations in soil parameters (eg laminated soils) have been examined. The study indicates that the numerical performance of each scheme is controlled by a non-dimensional parameter and guidelines have been suggested which allow accurate and economic solutions to be obtained.     

基于有限差分法的抗滑桩计算机辅助设计

基于地基系数“m-m”法、“m-k”法、“k-k”法的原理,考虑桩顶和桩底边界条件以及桩在滑动面处位移、转角、弯矩和剪力的连续条件,可解得桩身各节点的位移和内力,提出了进行抗滑桩全桩内力计算的有限差分法。根据差分方程并用VB6.0编制了实用的计算程序,既可避免繁琐的查表计算,提高计算速度,又可提高计算精度,直观生动,真正实现了人机交互,在界面的引导下,设计人员可完成全部计算,并绘出内力图形和抗滑桩截面配筋图,使设计更方便快捷,该软件可以极大地提高生产效率,降低工程造价,从而实现抗滑桩的优化设计。最后采用上述方法对某滑坡的悬臂抗滑桩进行了设计与计算。     

Assessment of basal stability for braced excavation systems using the finite element method

Conventional methods of predicting the basal stability of braced excavations are unable to take into consideration the stiffness of the retaining wall and the depth of penetration of the wall below the bottom of the excavation. A simple and improved procedure for predicting the stability of strutted excavations using the finite element method is presented. Detailed studies were carried out to assess the effects of the wall properties and soil geometry on the stability of the excavation.     

考虑坡度效应的水平受荷桩应变楔计算方法

由于坡度效应的存在,常规方法并不适用于斜坡上水平受荷桩的计算,首先开展了斜坡上基桩的横向加载破坏试验,以确定斜坡上基桩的破坏模式。在此基础上,沿坡体方向对破坏土楔体进行斜向单元划分,提出了考虑坡度效应的土体应变楔模型,对于其中的关键参数应变楔深度与应变楔土体应变采用迭代求解。迭代过程中,建立基桩横向受荷的桩-土相互作用方程并用有限杆单元法求解,当求解得到的桩身地面处位移与应变楔模型中地面处土体位移之差小于某一允许值时,得到的基桩的水平位移及内力即为最终解答。通过与试验测试数据的对比,验证了该方法的合理性。最后,将土体破坏深度与边坡斜率的比值定义为陡坡效应影响范围,并对其影响因素进行了对比分析。结果表明,陡坡效应的影响范围受土体强度参数及基桩尺寸等多因素影响,其随着桩径的增加而减小,且随土体强度的增强而减小。     

Analysis of three-dimensional, homogeneous, finite strain using ellipsoidal objects

It has been suggested (Oertel, 1971, 1972;Owens, 1974; Shimamoto and Ikeda, 1976) that some methods for analysis of finite homogeneous strain from deformed ellipsoidal objects (Ramsay, 1967; Dunnet, 1969a; Elliott, 1970; Dunnet and Siddans, 1971; Matthews et al., 1974) require sections to be cut in principal planes of the finite strain ellipsoid. A mathematical model is presented which enables the homogeneous deformation of a randomly oriented ellipsoid to be investigated. In particular the elliptical shapes that result on any three mutually perpendicular sections through the ellipsoid, in the deformed state, can be computed, together with the corresponding strain ellipses. The resulting ellipses can be unstrained in the section planes by applying the corresponding reciprocal strain ellipses. It is shown that these restored ellipses are identical with the elliptical shapes that result on planes through the original ellipsoid when the planes are parallel to the unstrained orientation of the section planes.The model is extended to investigate the finite homogeneous deformation of a suite of 100 randomly oriented ellipsoids of constant initial axial ratio. The pattern of elliptical shapes that result on any three mutually perpendicular section planes, in the deformed state, is computed. From this data the two-dimensional strain states in the section planes are estimated by a variety of methods. These are combined to recalculate the three-dimensional finite strain that was imposed on the system. It is thus possible to compare the results of the two- and three-dimensional analyses obtained by the various methods. It is found that providing all six independent combinations of the two-dimensional strain data are used to compute a best finite strain ellipsoid, the methods of Dunnet (1969a), Matthews et al. (1974) and Shimamoto and Ikeda (1976) provide accurate estimates of the three-dimensional finite strain state.It is concluded that measurement of the two-dimensional data on section planes parallel to the principal planes of the finite strain ellipsoid is not necessary and that all six independent combinations of the two-dimensional strain data should always be made and used to compute a best finite strain ellipsoid.     

A large strain finite element formulation for one dimensional membrane elements

A finite element formulation suitable for large strain analysis of one-dimensional membranes is described which has applications to the analysis of problems in soil mechanics involving reinforced earth. The finite element equations, which are derived for a plane strain iso-parametric element of arbitrary order, are cast in the familiar small displacement form, but with a modified material stiffness matrix. In this formulation, full account is taken of element rotations during each load step, an effect which is important when stresses cease to be insignificant when compared with the material modulus. The method is illustrated with reference to a large displacement test problem which has a known closed form solution. An example is included demonstrating the application of the formulation to the analysis of a reinforced unpaved road.     

A method for determination of fine-particle flotability

The modification of a Hallimond tube enabling flotation of very fine particles at low recovery by mechanical entrainment is described. Flotation yields of closely sized fractions of quartz and chalcocite are presented.     

多边形有限单元形函数的几何构造方法

根据非均质材料的细观结构,划分多边形的计算网格。采用多边形单元进行有限元分析,实现了基于材料真实结构的数值模拟。给出了多边形有限单元形函数的几何构造方法,构造了一个辅助多边形,采用散度定理推导出多边形单元形函数的表达式。分析总结了多边形Wachspress插值、Laplace插值和平均值插值的构造方法和性质。     

A novel finite element method for seepage analysis

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.     

Finite volume approach for finite strain consolidation

The paper presents the finite volume formulation and numerical solution of finite strain one‐dimensional consolidation equation. The equation used in this study utilises a nonlinear continuum representation of consolidation with varying compressibility and hydraulic conductivity and thus inherits the material and geometric nonlinearity. Time‐marching explicit scheme has been used to achieve transient solutions. The nonlinear terms have been evaluated with the known previous time step value of the independent variable, that is, void ratio. Three‐point quadratic interpolation function of Lagrangian family has been used to evaluate the face values at discrete control volumes. It has been shown that the numerical solution is stable and convergent for the general practical cases of consolidation. Performance of the numerical scheme has been evaluated by comparing the results with an analytical solution and with the piecewise piecewise‐linear finite difference numerical model. The approach seems to work well and offers excellent potential for simulating finite strain consolidation. Further, the parametric study has been performed on soft organic clays, and the influence of various parameters on the time ate consolidation characteristics of the soil is shown. Copyright © 2015 John Wiley & Sons, Ltd.     

A stabilized assumed deformation gradient finite element formulation for strongly coupled poromechanical simulations at finite strain

An adaptively stabilized finite element scheme is proposed for a strongly coupled hydro‐mechanical problem in fluid‐infiltrating porous solids at finite strain. We first present the derivation of the poromechanics model via mixture theory in large deformation. By exploiting assumed deformation gradient techniques, we develop a numerical procedure capable of simultaneously curing the multiple‐locking phenomena related to shear failure, incompressibility imposed by pore fluid, and/or incompressible solid skeleton and produce solutions that satisfy the inf‐sup condition. The template‐based generic programming and automatic differentiation (AD) techniques used to implement the stabilized model are also highlighted. Finally, numerical examples are given to show the versatility and efficiency of this model. Copyright © 2013 John Wiley & Sons, Ltd.     

Determination of optimum relaxation coefficient using finite difference method for groundwater flow

Solution of Laplace’s equation can be done by iteration methods likes Jacobi, Gauss–Seidel, and successive over-relaxation (SOR). There is no new knowledge about the relaxation coefficient (ω) in SOR method. In this paper, we used SOR for solving Laplace’s differential equation with emphasis to obtaining the optimum (minimum) number of iterations with variations of the relaxation coefficient (ω). For this purpose, a code in FORTRAN language has been written to show the solution of a set of equations and its number of iterations. The results demonstrate that the optimum value of ω with minimum iterations is achieved between 1.7 and 1.9. Also, with increasing β?=??x/?y from 0.25 to 10, the number of iterations reduced and the optimum value is obtained for β?=?2.     

An edge-based strain smoothing particle finite element method for large deformation problems in geotechnical engineering

To solve large deformation geotechnical problems, a novel strain-smoothed particle finite element method (SPFEM) is proposed that incorporates a simple and effective edge-based strain smoothing method within the framework of original PFEM. Compared with the original PFEM, the proposed novel SPFEM can solve the volumetric locking problem like previously developed node-based smoothed PFEM when lower-order triangular element is used. Compared with the node-based smoothed PFEM known as “overly soft” or underestimation property, the proposed SPFEM offers super-convergent and very accurate solutions due to the implementation of edge-based strain smoothing method. To guarantee the computational stability, the proposed SPFEM uses an explicit time integration scheme and adopts an adaptive updating time step. Performance of the proposed SPFEM for geotechnical problems is first examined by four benchmark numerical examples: (a) bar vibrations, (b) large settlement of strip footing, (c) collapse of aluminium bars column, and (d) failure of a homogeneous soil slope. Finally, the progressive failure of slope of sensitive clay is simulated using the proposed SPFEM to show its outstanding performance in solving large deformation geotechnical problems. All results demonstrate that the novel SPFEM is a powerful and easily extensible numerical method for analysing large deformation problems in geotechnical engineering.