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1.
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   

2.
A method is presented for coupling cubic‐order quadrilateral finite elements with the finite side of a new coordinate ascent hierarchical infinite element. At a common side shared by a hierarchical infinite element and an arbitrary number of finite elements, the displacements are minimized in the least square sense with respect to the degrees‐of‐freedom of the finite elements. This leads to a set of equations that relate the degrees‐of‐freedom of the finite and hierarchical infinite elements on the shared side. The method is applied to a non‐homogeneous cross‐anisotropic half‐space subjected to a non‐uniform circular loading with Young's and shear moduli varying with depth according to the power law. A constant mesh constructed from coupled finite and hierarchical infinite elements is used and convergence is sought simply by increasing the degree of the interpolating polynomial. The displacements and stresses produced by conical and parabolic circular loads applied on the surface are obtained. The efficiency of the proposed method is demonstrated through convergence and comparison studies. New results produced by a frusto‐conical circular load applied on the surface of a half‐space made up of heavily consolidated London clay are provided. The non‐homogeneity parameter and degree of anisotropy are shown to influence the soil response. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

3.
A constitutive model that captures the material behavior under a wide range of loading conditions is essential for simulating complex boundary value problems. In recent years, some attempts have been made to develop constitutive models for finite element analysis using self‐learning simulation (SelfSim). Self‐learning simulation is an inverse analysis technique that extracts material behavior from some boundary measurements (eg, load and displacement). In the heart of the self‐learning framework is a neural network which is used to train and develop a constitutive model that represents the material behavior. It is generally known that neural networks suffer from a number of drawbacks. This paper utilizes evolutionary polynomial regression (EPR) in the framework of SelfSim within an automation process which is coded in Matlab environment. EPR is a hybrid data mining technique that uses a combination of a genetic algorithm and the least square method to search for mathematical equations to represent the behavior of a system. Two strategies of material modeling have been considered in the SelfSim‐based finite element analysis. These include a total stress‐strain strategy applied to analysis of a truss structure using synthetic measurement data and an incremental stress‐strain strategy applied to simulation of triaxial tests using experimental data. The results show that effective and accurate constitutive models can be developed from the proposed EPR‐based self‐learning finite element method. The EPR‐based self‐learning FEM can provide accurate predictions to engineering problems. The main advantages of using EPR over neural network are highlighted.  相似文献   

4.
By using a complete set of poroelastodynamic spherical wave potentials (SWPs) representing a fast compressional wave PI, a slow compressional wave PII, and a shear wave S with 3 vectorial potentials (not all are independent), a solution scheme based on the method of fundamental solution (MFS) is devised to solve 3‐D wave scattering and dynamic stress concentration problems due to inhomogeneous inclusions and cavities embedded in an infinite poroelastic domain. The method is verified by comparing the result with the elastic analytical solution, which is a degenerated case, as well as with poroelastic solution obtained using other numerical methods. The accuracy and stability of the SWP‐MFS are also demonstrated. The displacement, hoop stress, and fluid pore pressure around spherical cavity and poroelastic inclusion with permeable and impermeable boundary are investigated for incident plane PI and SV waves. The scattering characteristics are examined for a range of material properties, such as porosity and shear modulus contrast, over a range of frequency. Compared with other boundary‐based numerical strategy, such as the boundary element method and the indirect boundary integral equation method, the current SWP‐MFS is a meshless method that does not need elements to approximate the geometry and is free from the treatment of singularities. The SWP‐MFS is a highly accurate and efficient solution methodology for wave scattering problems of arbitrary geometry, particularly when a part of the domain extends to infinity.  相似文献   

5.
A challenging computational problem arises when a discrete structure (e.g. foundation) interacts with an unbounded medium (e.g. deep soil deposit), particularly if general loading conditions and non‐linear material behaviour is assumed. In this paper, a novel method for dealing with such a problem is formulated by combining conventional three‐dimensional finite‐elements with the recently developed scaled boundary finite‐element method. The scaled boundary finite‐element method is a semi‐analytical technique based on finite‐elements that obtains a symmetric stiffness matrix with respect to degrees of freedom on a discretized boundary. The method is particularly well suited to modelling unbounded domains as analytical solutions are found in a radial co‐ordinate direction, but, unlike the boundary‐element method, no complex fundamental solution is required. A technique for coupling the stiffness matrix of bounded three‐dimensional finite‐element domain with the stiffness matrix of the unbounded scaled boundary finite‐element domain, which uses a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co‐ordinate system, is described. The accuracy and computational efficiency of the new formulation is demonstrated through the linear elastic analysis of rigid circular and square footings. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

6.
This paper presents a three‐dimensional energy‐based solution for the time‐dependent response of a deeply embedded and unsupported semi‐infinite tunnel of circular cross‐section. The tunnel is taken to be excavated quasi‐instantaneously from an infinite rock body that initially exhibits an isotropic stress state and that is made up of a homogeneous, isotropic and viscoelastic material. The viscoelastic behaviour is modelled by means of Burger's model, and the rock is taken to behave volumetrically linear elastic and to exhibit exclusively deviatoric creep. This viscoelastic problem is transformed into the Laplace domain, where it represents a quasi‐elastic problem. The displacement fields in the new solution are taken to be the products of independent functions that vary in the radial and longitudinal directions. The differential equations governing the displacements of the system and appropriate boundary conditions are obtained using the principle of minimum potential energy. The solutions for these governing equations in the Laplace domain are then obtained analytically and numerically using a one‐dimensional finite difference technique. The results are then transformed back into the time domain using an efficient numerical scheme. The accuracy of the new solution is comparable with that of a finite element analysis but requires much less computation effort. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

7.
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   

8.
Practical civil engineering problems are usually formulated in an infinite half-space domain, and a selected finite domain is required to analyze the dynamic responses of a fluid-saturated porous medium by the finite element method (FEM). Devising a method to deal with the boundaries of the finite domain is the key issue for this open system. In this paper, a two-dimensional spring–dashpot artificial boundary (SDAB) for transient analysis in a fluid-saturated porous media is developed. Based on Biot’s dynamic theory of fluid-saturated porous media, the normal and tangential boundary stress formulae are deduced for out-going cylindrical body waves. The boundary stress is proportional to displacement and velocity, thus continuously distributed dashpots and springs can be placed on the artificial boundaries in the normal and tangential directions to simulate the energy absorption of the infinite media outside of the finite domain for the interior distributed source problems. In this paper, the input seismic motion can be realized by applying an equivalent load on the SDAB for the seismic scattering problems of exterior distributed sources. Numerical examples are given and the analyzed results show that the SDAB and the method of wave motion input have good stability and acceptable accuracy.  相似文献   

9.
In this paper a micro‐polar continuum approach is proposed to model the essential properties of cohesionless granular materials like sand. The model takes into account the influence of particle rotations, the mean grain size, the void ratio, the stresses and couple stresses. The constitutive equations for the stresses and couple stresses are incrementally non‐linear and based on the concept of hypoplasticity. For plane strain problems the implementation of the model in a finite element program is described. Numerical studies of the evolution of micro‐polar effects within a granular strip under plane shearing are presented. It is shown that the location and evolution of shear localization is strongly influenced by the initial state and the micro‐polar boundary conditions. For large shearing the state quantities tend towards a stationary state for which a certain coupling between the norm of the stress deviator and the norm of the couple stress tensor can be derived. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

10.
A new mixed displacement‐pressure element for solving solid–pore fluid interaction problems is presented. In the resulting coupled system of equations, the balance of momentum equation remains unaltered, while the mass balance equation for the pore fluid is stabilized with the inclusion of higher‐order terms multiplied by arbitrary dimensions in space, following the finite calculus (FIC) procedure. The stabilized FIC‐FEM formulation can be applied to any kind of interpolation for the displacements and the pressure, but in this work, we have used linear elements of equal order interpolation for both set of unknowns. Examples in 2D and 3D are presented to illustrate the accuracy of the stabilized formulation for solid–pore fluid interaction problems. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

11.
The scaled boundary finite‐element method, a semi‐analytical computational scheme primarily developed for dynamic stiffness of unbounded domains, is applied to the analysis of unsteady seepage flow problems. This method is based on the finite‐element technology and gains the advantages of the boundary element method as well. Only boundary of the domain is discretized, no fundamental solution is required and singularity problems can be modeled rigorously. Anisotropic and non‐homogeneous materials satisfying similarity are modeled with no additional efforts. In this study, firstly, formulation of the method for the transient seepage flow problems is derived followed by its solution procedures. The accuracy, simplicity and applicability of the method are demonstrated via four numerical examples of transient seepage flow – three of them are available in the literature. Homogenous, non‐homogenous, isotropic and anisotropic material properties are considered to show the versatility of the technique. Excellent agreement with the finite‐element method is observed. The method out‐performs the finite‐element method in modeling singularity points. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

12.
The main objective of this work is to develop a novel moving‐mesh finite‐volume method capable of solving the seepage problem in domains with arbitrary geometries. One major difficulty in analysing the seepage problem is the position of phreatic boundary which is unknown at the beginning of solution. In the current algorithm, we first choose an arbitrary solution domain with a hypothetical phreatic boundary and distribute the finite volumes therein. Then, we derive the conservative statement on a curvilinear co‐ordinate system for each cell and implement the known boundary conditions all over the solution domain. Defining a consistency factor, the inconsistency between the hypothesis boundary and the known boundary conditions is measured at the phreatic boundary. Subsequently, the preceding mesh is suitably deformed so that its upper boundary matches the new location of the phreatic surface. This tactic results in a moving‐mesh procedure which is continued until the nonlinear boundary conditions are fully satisfied at the phreatic boundary. To validate the developed algorithm, a number of seepage models, which have been previously targeted by the other investigators, are solved. Comparisons between the current results and those of other numerical methods as well as the experimental data show that the current moving‐grid finite‐volume method is highly robust and it provides sufficient accuracy and reliability. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

13.
黄耀英  王润富  吴中如 《岩土力学》2009,30(12):3682-3688
根据两个合理的判断依据,对弹性力学中的楔形体、半平面体、圆锥体和半空间体等经典解答进行了比较分析,发现了半无限平面应变问题和半空间体问题解答之间的关系;通过对解答之间的关系进行研究分析指出,弹性力学中的半无限平面体的符拉芒解答和半空间体的布希涅斯克解答存在局限性。对半无限地基、底部完全位移约束的有限深地基和底部光滑刚性支承的有限深地基在水平表面作用无限均布压力时的应力和位移分量进行了比较分析,认为底部完全位移约束的有限深地基模型较其他两种地基模型更合理些。  相似文献   

14.
An analytical investigation of a half‐space containing transversely isotropic material under forced vertical and horizontal displacements applied on a rectangular rigid foundation is presented in this paper. With the goal of a rigorous solution to the shape‐ and rigidity‐ induced singular mixed boundary value problem, the formulation employs scalar potential representation, the Fourier expansion and the Hankel integral transforms method to obtain the surface arbitrary point‐load solution in cylindrical coordinate system. The obtained Green's functions are rewritten in rectangular coordinate system, allowing the response of the half‐space because of an arbitrary distributed load on a rectangular surface area be given in terms of a double integral. The numerical evaluations of stresses are done with the use of an element, which is singular at the edge and the corner of the rectangle. Upon the imposition of the rigidity displacement boundary condition for a rigid foundation and the use of a set of two‐dimensional adaptive‐gradient elements, which can capture the singular behavior in the contact stress effectively, a set of new numerical results are presented to illustrate the effect of transverse isotropy on the foundation response. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

15.
An efficient finite–discrete element method applicable for the analysis of quasi‐static nonlinear soil–structure interaction problems involving large deformations in three‐dimensional space was presented in this paper. The present method differs from previous approaches in that the use of very fine mesh and small time steps was not needed to stabilize the calculation. The domain involving the large displacement was modeled using discrete elements, whereas the rest of the domain was modeled using finite elements. Forces acting on the discrete and finite elements were related by introducing interface elements at the boundary of the two domains. To improve the stability of the developed method, we used explicit time integration with different damping schemes applied to each domain to relax the system and to reach stability condition. With appropriate damping schemes, a relatively coarse finite element mesh can be used, resulting in significant savings in the computation time. The proposed algorithm was validated using three different benchmark problems, and the numerical results were compared with existing analytical and numerical solutions. The algorithm performance in solving practical soil–structure interaction problems was also investigated by simulating a large‐scale soft ground tunneling problem involving soil loss near an existing lining. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

16.
It is shown that the property of the scale invariance of the eigenvalues and eigenmodes of a finite element can be used as a basis to calculate good approximations to the analytical magnitudes of eigenvalues. This requires the subdivision of the element into a mesh of small elements with the same shape as the large element, the enforcement of the modal boundary displacements of the large element to the mesh of small elements and finally the application of the conditions of both the nodal equilibrium and the equality of the nodal work at both scales. Due to the self‐similarity of the elements at all scales the authors propose to call this method the fractal approach. The method is applied to calculate the hour‐glass eigenvalue of a plane square 4‐node quad for isotropic linear elastic material. The resulting hour‐glass eigenvalue is shown to be a good approximation of the analytical magnitude as derived in a companion paper. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

17.
The scaled boundary finite‐element method is derived for elastostatic problems involving an axisymmetric domain subjected to a general load, using a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co‐ordinate system. The method is particularly well suited to modelling unbounded problems, and the formulation allows a power‐law variation of Young's modulus with depth. The efficiency and accuracy of the method is demonstrated through a study showing the convergence of the computed solutions to analytical solutions for the vertical, horizontal, moment and torsion loading of a rigid circular footing on the surface of a homogeneous elastic half‐space. Computed solutions for the vertical and moment loading of a smooth rigid circular footing on a non‐homogeneous half‐space are compared to analytical ones, demonstrating the method's ability to accurately model a variation of Young's modulus with depth. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

18.
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.  相似文献   

19.
The present paper investigates bifurcation analysis based on the second‐order work criterion, in the framework of rate‐independent constitutive models and rate‐independent boundary‐value problems. The approach applies mainly to nonassociated materials such as soils, rocks, and concretes. The bifurcation analysis usually performed at the material point level is extended to quasi‐static boundary‐value problems, by considering the stiffness matrix arising from finite element discretization. Lyapunov's definition of stability (Annales de la faculté des sciences de Toulouse 1907; 9 :203–274), as well as definitions of bifurcation criteria (Rice's localization criterion (Theoretical and Applied Mechanics. Fourteenth IUTAM Congress, Amsterdam, 1976; 207–220) and the plasticity limit criterion are revived in order to clarify the application field of the second‐order work criterion and to contrast these criteria. The first part of this paper analyses the second‐order work criterion at the material point level. The bifurcation domain is presented in the 3D stress space as well as 3D cones of unstable loading directions for an incrementally nonlinear constitutive model. The relevance of this criterion, when the nonlinear constitutive model is expressed in the classical form (dσ = Mdε) or in the dual form (dε = Ndσ), is discussed. In the second part, the analysis is extended to the boundary‐value problems in quasi‐static conditions. Nonlinear finite element computations are performed and the global tangent stiffness matrix is analyzed. For several examples, the eigenvector associated with the first vanishing eigenvalue of the symmetrical part of the stiffness matrix gives an accurate estimation of the failure mode in the homogeneous and nonhomogeneous boundary‐value problem. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

20.
Strain localization developing inside soft rock specimens is examined through experimental observation and numerical simulation. In the experimental study, soft rock specimens are sheared at different strain rates under plane strain conditions and deformation and strain localization characteristics are analysed. Transition of localization mode from highly localized mode for higher strain rate to distributed and diffused mode of strain localization for lower strain rates was observed. In the numerical study, simulations of plane strain compression tests are carried out at different strain rates by using an overstressed‐type elasto‐viscoplastic model in finite element computations. The role of strain rates on setting gradients of strain fields across shear band is clarified. The probable mechanism for transition of localization mode is discussed. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

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