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1.
Similar to plane strain, axisymmetric stress problem is also highly kinematics constrained. Standard displacement‐based finite element exhibits volumetric locking issue in simulating nearly/fully incompressible material or isochoric plasticity under axisymmetric loading conditions, which severely underestimates the deformation and overestimates the bearing capacity for structural/geotechnical engineering problems. The aim of this paper is to apply variational multiscale method to produce a stabilized mixed displacement–pressure formulation, which can effectively alleviate the volumetric locking issue for axisymmetric stress problem. Both nearly incompressible elasticity and isochoric J2 elastoplasticity are investigated. First‐order 3‐node triangular and 4‐node quadrilateral elements are tested for locking issues. Several representative simulations are provided to demonstrate the performance of the linear elements, which include the convergence study and comparison with closed‐form solutions. A comparative study with pressure Laplacian stabilized formulation is also presented. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
2.
It is well accepted that severe numerical difficulties arise when using the conventional finite element displacement method to analyse incompressible, or nearly incompressible, solids. These effects are caused by the kinematic constraints imposed on the nodal velocities by the constant volume condition. In elastic-plastic analysis, these effects are due to a conflict between the plastic flow rule and the finite element discretization. Although several methods have been proposed to cope with this problem, none has been based on the appropriate choice of displacement interpolation to minimise the constraints. In this paper, a new displacement interpolation, which is able to reduce the imposed constraints, is adopted. Comparisons of the results with those from a conventional linear displacement interpolation are made for predictions of cylindrical and spherical cavity expansion limit pressures in elastic-plastic solids. This study suggests that the proposed displacement interpolation is preferable to the conventional one in the elastic-plastic finite element analysis of one dimensional-axisymmetric problems which involve nearly incompressible material behaviour. 相似文献
3.
It is well known that the Babuska–Brezzi stability criterion or the Zienkiewicz–Taylor patch test precludes the use of the finite elements with the same low order of interpolation for displacement and pore pressure in the nearly incompressible and undrained cases, unless some stabilization techniques are introduced for dynamic analysis of saturated porous medium where coupling occurs between the displacement of solid skeleton and pore pressure. The numerical manifold method (NMM), where the interpolation of displacement and pressure can be determined independently in an element for the solution of u–p formulation, is derived based on triangular mesh for the requirement of high accurate calculations from practical applications in the dynamic analysis of saturated porous materials. The matrices of equilibrium equations for the second‐order displacement and the first‐order pressure manifold method are given in detail for program coding. By close comparison with widely used finite element method, the NMM presents good stability for the coupling problems, particularly in the nearly incompressible and undrained cases. Numerical examples are given to illustrate the validity and stability of the manifold element developed. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
4.
The displacement formulation of the finite element method is well suited to the analysis of elasto-plasticity problems involving compressible material behaviour, but it is well known that numerical difficulties occur when the material is incompressible or nearly incompressible. The effect of these additional constraints depends on both element formulation and mesh topology. A two-dimensional plane strain finite element formulation suitable for the solution of problems involving large strains and displacements (but small rotations) based on the isoparametric approach is described. The kinematics of deformation are defined in terms of the Eulerian strain rates that are invariably used in small strain analysis; the formulation therefore retains some of the character of small strain theory but includes additional geometrically non-linear terms. The results of a series of plane strain finite element analyses of two cylindrical expansion problems are presented. These results confirm the previously observed trend that as Poisson's ratio approaches 0·5 then the quality of the calculated stress deteriorates. The study also indicates that the solution quality depends increasingly on mesh topology as perfect incompressibility is reached. 相似文献
5.
Many low‐order displacement‐based finite elements with exact integration are not suitable for estimating collapse loads of undrained geotechnical problems, especially for axisymmetric cases. As a result, higher‐order elements have to be used for these situations. In this technical note, the enhanced assumed strain (EAS) finite element method proposed by Simo and Rifai for elasticity problems are extended to plasticity problems to determine collapse loads. The numerical results for the problem of a smooth rigid surface footing on a deep purely cohesive undrained soil layer are given. It is demonstrated that the four‐noded quadrilateral EAS finite element is capable of estimating the collapse loads accurately for both undrained plane strain and axisymmetric problems. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
6.
Displacement and mixed finite element formulations of shear localization in materials are presented. The formulations are based on hypoplastic constitutive laws for soils and the mixed enhanced treatment involving displacement, strain and stress rates as independently varied fields. Included in these formulations are the standard displacement method, the three‐field mixed formulation, the enhanced assumed strain method and the mixed enhanced strain method. Several numerical examples demonstrating the capability and performance of the different finite element formulations are presented. The numerical results are compared with available experimental data for Hostun RF sand and numerical results for Karlsruhe sand on biaxial tests. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
7.
Modelling shear band is an important problem in analysing failure of earth structures in soil mechanics. Shear banding is the result of localization of deformation in soil masses. Most finite element schemes are unable to model discrete shear band formation and propagation due to the difficulties in modelling strain and displacement discontinuities. In this paper, a framework to generate shear band elements automatically and continuously is developed. The propagating shear band is modelled using discrete shear band elements by splitting the original finite element mesh. The location or orientation of the shear band is not predetermined in the original finite element mesh. Based on the elasto‐perfect plasticity with an associated flow rule, empirical bifurcation and location criteria are proposed which make band propagation as realistic as possible. Using the Mohr–Coulomb material model, various results from numerical simulations of biaxial tests and passive earth pressure problems have shown that the proposed framework is able to display actual patterns of shear banding in geomaterials. In the numerical examples, the occurrence of multiple shear bands in biaxial test and in the passive earth pressure problem is confirmed by field and laboratory observations. The effects of mesh density and mesh alignment on the shear band patterns and limit loads are also investigated. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
8.
S. Amir Reza Beyabanaki Ahmad Jafari S. Omid Reza Biabanaki M. Ronald Yeung 《Computers and Geotechnics》2009
This paper presents a new numerical model that can add a finite element mesh into each block of the three-dimensional discontinuous deformation analysis (3-D DDA), originally developed by Gen-hua Shi. The main objectives of this research are to enhance DDA block’s deformability. Formulations of stiffness and force matrices in 3-D DDA with conventional Trilinear (8-node) and Serendipity (20-node) hexahedral isoparametric finite elements meshed block system due to elastic stress, initial stress, point load, body force, displacement constraints, inertia force, normal and shear contact forces are derived in detail for program coding. The program code for the Trilinear and Serendipity hexahedron elements have been developed, and it has been applied to some examples to show the advantages achieved when finite element is associated with 3-D DDA to handle problems under large displacements and deformations. Results calculated for the same models by use of the original 3-D DDA are far from the theoretical solutions while the results of new numerical model are quite good in agreement with theoretical solutions; however, for the Trilinear elements, more number of elements are needed. 相似文献
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10.
Appropriate Uses and Practical Limitations of 2D Numerical Analysis of Tunnels and Tunnel Support Response 总被引：5，自引：3，他引：2
Nicholas Vlachopoulos Mark S. Diederichs 《Geotechnical and Geological Engineering》2014,32(2):469-488
In spite of the gradual development of three-dimensional analysis packages utilizing finite element models or finite difference algorithms for stress–strain calculations, two-dimensional (2D) analysis is still used as the primary engineering tool for practical analysis of tunnel behavior and tunnel support performance for design—particularly at the preliminary stage of a project. The applicability of 2D finite element analysis or analytical convergence confinement solutions to staged support installation depend on the application of an assumed or validated longitudinal displacement profile. Convergence in commonly applied 2D staged models is controlled by boundary displacement or internal pressure relaxation. While there have been developments to improve this methodology, this often assumes independence between the ground reaction curve and the support resistance, independence between the longitudinal displacement profile to support application, and the assumption that non-isotropic stresses and non-circular geometries can be handled in the same way as circular tunnels in isotropic conditions. This paper examines the validity of these assumptions and the error inherent in these extensions to 2D tunnel analysis. Anisotropic stresses and lagged (staged) excavation present a particular problem. Practical solutions are proposed for support longitudinal displacement LDPs in simplified conditions. 相似文献
11.
Rigoberto G. Sanabria Castro Sandra M. C. Malta Abimael F. D. Loula Luiz Landau 《Computational Geosciences》2002,5(4):301-330
A finite element formulation is proposed to approximate a nonlinear system of partial differential equations, composed by an elliptic subsystem for the pressure–velocity and a transport equation (convection–diffusion) for the concentration, which models the incompressible miscible displacement of one fluid by another in a rigid porous media. The pressure is approximated by the classical Galerkin method and the velocity is calculated by a post-processing technique. Then, the concentration is obtained by a Galerkin/least-squares space–time (GLS/ST) finite element method. A numerical analysis is developed for the concentration approximation. Then, stability, convergence and numerical results are presented confirming the a priori error estimates. 相似文献
12.
In geotechnical engineering, numerical analysis of pile capacity is often performed in such a way that piles are modeled using only the geometry of their final position in the ground and simply loaded to failure. In these analyses, the stress changes caused by the pile installation are neglected, irrespective of the installation method. For displacement piles, which are either pushed or hammered into the ground, such an approach is a very crude simplification. To model the entire installation process of displacement piles a number of additional nonlinear effects need to be considered. As the soil adjacent to the pile is displaced significantly, small deformation theory is no longer applicable and a large deformation finite element formulation is required. In addition, the continuously changing interface between the pile and the soil has to be considered. Recently, large deformation frictional contact has been used to model the pile installation and cone penetration processes. However, one significant limitation of the analysis was the use of linear elements, which have proven to be less accurate than higher order elements for nonlinear materials such as soils.
This paper presents a large deformation frictional contact formulation which can be coupled consistently with quadratic solid elements. The formulation uses the so-called mortar-type discretisation of the contact surfaces. The performance of this contact discretisation technique is demonstrated by accurately predicting the stress transfer between the pile and the soil surfaces. 相似文献
13.
利用多次冻融后加筋黏土路堤相关试验参数对其进行有限元计算, 确定了加筋黏土结构各初始因素对其工作性能的影响规律, 并利用ABAQUS有限元计算软件对各种计算条件下的位移和应力进行求解, 确定了冻融循环后位移和应力的最大值. 结果显示: 增加加筋黏土路堤中的格栅层数可以减小冻融后加筋路堤的竖向和水平位移及土体剪应力最大值, 且格栅层数的增加对土体变形的影响强于对土体剪应力值的影响. 土体压实度的增大可以减小加筋路堤的竖向和水平位移, 同时引起土中剪应力数值的增大; 土体初始含水率的减小可以减小加筋路堤的竖向和水平位移, 同时引起土中剪应力数值的减小. 相似文献
14.
By using the lower bound limit analysis in conjunction with finite elements and linear programming, the bearing capacity factors due to cohesion, surcharge and unit weight, respectively, have been computed for a circular footing with different values of ?. The recent axisymmetric formulation proposed by the authors under ?=0 condition, which is based on the concept that the magnitude of the hoop stress (σθ) remains closer to the least compressive normal stress (σ3), is extended for a general c–? soil. The computational results are found to compare quite well with the available numerical results from literature. It is expected that the study will be useful for solving various axisymmetric geotechnical stability problems. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
15.
Rigoberto G. Sanabria Castro Sandra M. C. Malta Abimael F. D. Loula Luiz Landau 《Computational Geosciences》2001,5(4):301-330
A finite element formulation is proposed to approximate a nonlinear system of partial differential equations, composed by an elliptic subsystem for the pressure–velocity and a transport equation (convection–diffusion) for the concentration, which models the incompressible miscible displacement of one fluid by another in a rigid porous media. The pressure is approximated by the classical Galerkin method and the velocity is calculated by a post-processing technique. Then, the concentration is obtained by a Galerkin/least-squares space–time (GLS/ST) finite element method. A numerical analysis is developed for the concentration approximation. Then, stability, convergence and numerical results are presented confirming the a priori error estimates. 相似文献
16.
桩贯入土体产生的挤土效应问题较为复杂。利用ABAQUS软件建立了单桩贯入夹硬层土和均质土的二维轴对称有限元模型,经过分析比较,得出了单桩贯入夹硬层土体所特有的位移场及应力场的变化规律。分析表明：桩贯入夹硬层土过程中,软硬土层交界处土体水平位移变化剧烈;硬土层的存在,会使土体水平及竖向位移受到约束;夹硬层土的水平挤压应力要远大于均质土情况;与水平应力相比,竖向挤压应力在硬土层处明显偏小。 相似文献
17.
In this paper a bifurcation analysis of boreholes in deep rock formations under uniform stress at infinity is presented. Rock is described by the constitutive equations of a deformation theory of plasticity for rigidplastic, incompressible and cohesive-frictional material. The corresponding bifurcation problem is solved numerically by the finite element method. The evidence gained from the numerical solution is utilized to establish a simplified borehole stability analysis that combines Biot's hodograph method with a surface instability analysis. 相似文献
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19.
M. E. Duncan Fama 《国际地质力学数值与分析法杂志》1989,13(3):331-337
It is shown that a finite element calculation which approximates an ‘infinite medium’; problem by a mesh with finite boundaries will yield greater accuracy when stress boundary conditions are applied on the far-field boundary than is obtainable with displacement boundary conditions. In particular, with Poisson's ratio close to 0.5, the accuracy of the latter model is severely impaired, whereas the stress boundary condition model is unaffected for Poisson's ratio of 0.49 and a reasonable mesh. The eight-node quadratic isoparametric element displays superb accuracy for the axisymmetric thick cylinder with either type of boundary condition. 相似文献
20.
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. 相似文献