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Element Solution (element + solution)
Kinds of Element Solution Selected AbstractsIntegration of General Sparse Matrix and Parallel Computing Technologies for Large,Scale Structural AnalysisCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 6 2002Hsien Hsieh, Shang Both general sparse matrix and parallel computing technologies are integrated in this study as a finite element solution of large,scale structural problems in a PC cluster environment. The general sparse matrix technique is first employed to reduce execution time and storage requirements for solving the simultaneous equilibrium equations in finite element analysis. To further reduce the time required for large,scale structural analyses, two parallel processing approaches for sharing computational workloads among collaborating processors are then investigated. One approach adopts a publicly available parallel equation solver, called SPOOLES, to directly solve the sparse finite element equations, while the other employs a parallel substructure method for the finite element solution. This work focuses more on integrating the general sparse matrix technique and the parallel substructure method for large,scale finite element solutions. Additionally, numerical studies have been conducted on several large,scale structural analyses using a PC cluster to investigate the effectiveness of the general sparse matrix and parallel computing technologies in reducing time and storage requirements in large,scale finite element structural analyses. [source] Load-displacement and bearing capacity of foundations on granular soils using a multi-surface kinematic constitutive soil modelINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2006M. Banimahd Abstract A finite element approach based on an advanced multi-surface kinematic constitutive model is used to evaluate the bearing capacity of footings resting on granular soils. Unlike simple elastic-perfectly plastic models, often applied to granular foundation problems, the present model realistically accounts for stress dependency of the friction angle, strain softening,hardening and non-associativity. After the model and its implementation into a finite element code are briefly discussed, the numerical difficulty due to the singularity at the footing edge is addressed. The bearing capacity factor N, is then calculated for different granular materials. The effect of footing size, shape, relative density and roughness on the ultimate bearing capacity are studied and the computed results compare very favourably with the general experimental trends. In addition, it is shown that the finite element solution can clearly represent counteracting mechanisms of progressive failure which have an important effect on the bearing capacity of granular foundations. Copyright © 2006 John Wiley & Sons, Ltd. [source] Development of a technique for modelling clay liner desiccationINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2003Y. Zhou Abstract This paper presents a model for the analysis of clay liner desiccation in a landfill barrier system due to temperature effects. The model incorporates consideration of fully coupled heat-moisture-air flow, a non-linear constitutive relationship, the dependence of void ratio and volumetric water content on stress, capillary pressure and temperature, and the effect of mechanical deformation on all governing equations. Mass conservative numerical schemes are proposed to improve the accuracy of the finite element solution to the governing equations. The application of the model is then demonstrated by examining three test problems, including isothermal infiltration, heat conduction and non-isothermal water and heat transport. Comparisons are made with results from literature, and good agreement is observed. Copyright © 2003 John Wiley & Sons, Ltd. [source] Conserving Galerkin weak formulations for computational fracture mechanicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2002Shaofan Li Abstract In this paper, a notion of invariant Galerkin-variational weak forms is proposed. Two specific invariant variational weak forms, the J-invariant and the L-invariant, are constructed based on the corresponding conservation laws in elasticity, one of which is the conservation of Eshelby's energy-momentum (Eshelby. Philos. Trans. Roy. Soc. 1951; 87: 12; In Solid State Physics, Setitz F, Turnbull D (eds). Academic Press: New York, 1956; 331; Rice, J. Appl. Mech. 1968; 35: 379). It is shown that the finite element solution obtained from the invariant Galerkin weak formulations proposed here can conserve the value of J-integral, or L-integral exactly. In other words, the J and L integrals of the Galerkin finite element solutions are path independent in the discrete sense. It is argued that by using the J-invariant Galerkin weak form to compute near crack-tip field in an elastic solid, one may accurately calculate the crack extension energy release rate and subsequently the stress intensity factors in numerical computations, because the flux of the energy-momentum is conserved in discrete computations. This may provide an alternative means to accurately simulate crack growth and propagation. Copyright © 2002 John Wiley & Sons, Ltd. [source] A fast, one-equation integration algorithm for the Lemaitre ductile damage modelINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2002E. A. de Souza NetoArticle first published online: 3 MAY 200 Abstract This paper introduces an elastic predictor/return mapping integration algorithm for a simplified version of the Lemaitre ductile damage model, whose return mapping stage requires the solution of only one scalar non-linear equation. The simplified damage model differs from its original counterpart only in that it excludes kinematic hardening. It can be used to predict ductile damage growth whenever load reversal is absent or negligible,a condition met in a vast number of practical engineering applications. The one-equation integration scheme proves highly efficient in the finite element solution of typical boundary value problems, requiring computation times comparable to those observed in classical von Mises implementations. This is in sharp contrast to the previously proposed implementations of the original model whose return mapping may require, in the most general case, the solution of a system of 14 coupled algebraic equations. For completeness, a closed formula for the corresponding consistent tangent operator is presented. The performance of the algorithm is illustrated by means of a numerical example. Copyright © 2002 John Wiley & Sons, Ltd. [source] Smooth finite element methods: Convergence, accuracy and propertiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2008Hung Nguyen-Xuan Abstract A stabilized conforming nodal integration finite element method based on strain smoothing stabilization is presented. The integration of the stiffness matrix is performed on the boundaries of the finite elements. A rigorous variational framework based on the Hu,Washizu assumed strain variational form is developed. We prove that solutions yielded by the proposed method are in a space bounded by the standard, finite element solution (infinite number of subcells) and a quasi-equilibrium finite element solution (a single subcell). We show elsewhere the equivalence of the one-subcell element with a quasi-equilibrium finite element, leading to a global a posteriori error estimate. We apply the method to compressible and incompressible linear elasticity problems. The method can always achieve higher accuracy and convergence rates than the standard finite element method, especially in the presence of incompressibility, singularities or distorted meshes, for a slightly smaller computational cost. It is shown numerically that the one-cell smoothed four-noded quadrilateral finite element has a convergence rate of 2.0 in the energy norm for problems with smooth solutions, which is remarkable. For problems with rough solutions, this element always converges faster than the standard finite element and is free of volumetric locking without any modification of integration scheme. Copyright © 2007 John Wiley & Sons, Ltd. [source] Numerical accuracy of a Padé-type non-reflecting boundary condition for the finite element solution of acoustic scattering problems at high-frequencyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2005R. Kechroud Abstract The present text deals with the numerical solution of two-dimensional high-frequency acoustic scattering problems using a new high-order and asymptotic Padé-type artificial boundary condition. The Padé-type condition is easy-to-implement in a Galerkin least-squares (iterative) finite element solver for arbitrarily convex-shaped boundaries. The method accuracy is investigated for different model problems and for the scattering problem by a submarine-shaped scatterer. As a result, relatively small computational domains, optimized according to the shape of the scatterer, can be considered while yielding accurate computations for high-frequencies. Copyright © 2005 John Wiley & Sons, Ltd. [source] Generalization of robustness test procedure for error estimators.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2005Part I: formulation for patches near kinked boundaries Abstract In this part of paper we shall extend the formulation proposed by Babu,ka and co-workers for robustness patch test, for quality assessment of error estimators, to more general cases of patch locations especially in three-dimensional problems. This is performed first by finding an asymptotic finite element solution at interior parts of a problem with assumed smooth exact solution and then adding a correction part to obtain the solution near a kinked boundary irrespective of other boundary conditions at far ends of the domain. It has been shown that the solution corresponding to the correction part may be obtained in a spectral form by assuming a suitable proportionality relation between the nodal values of a mesh with repeatable pattern of macro-patches. Having found the asymptotic finite element solution, the performance of error estimators may be examined. Although in this paper we focus on the asymptotic behaviour of error estimators, the method described in this part may be used to obtain finite element solution for two/three-dimensional unbounded heat/elasticity problems with homogeneous differential equations. Some numerical results are presented to show the validity and performance of the proposed method. Copyright © 2005 John Wiley & Sons, Ltd. [source] Generalization of robustness test procedure for error estimators.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2005Part II: test results for error estimators using SPR Abstract In this part of the paper we shall use the formulation given in the first part to assess the quality of recovery-based error estimators using two recovery methods, i.e. superconvergent patch recovery (SPR) and recovery by equilibrium in patches (REP). The recovery methods have been shown to be asymptotically robust and superconvergent when applied to two-dimensional problems. In this study we shall examine the behaviour of the recovery methods on several three-dimensional mesh patterns for patches located either inside or at boundaries. This is performed by first finding an asymptotic finite element solution, irrespective of boundary conditions at far ends of the domain, and then applying the recovery methods. The test procedure near kinked boundaries is explained in a step-by-step manner. The results are given in a series of tables and figures for various cases of three-dimensional mesh patterns. It has been experienced that the full superconvergent property is generally lost due to presence of boundary layer solution and the definition of the recoveries near boundaries though the results of the robustness test is still within an acceptable range. Copyright © 2005 John Wiley & Sons, Ltd. [source] A finite element solution of acoustic propagation in rigid porous mediaINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2005A. Bermúdez Abstract This paper deals with the acoustical behaviour of a rigid porous material. A finite element method to compute both the response to an harmonic excitation and the free vibrations of a three-dimensional finite multilayer system consisting of a free fluid and a rigid porous material is considered. The finite element used is the lowest order face element introduced by Raviart and Thomas, that eliminates the spurious or circulation modes with no physical meaning. For the porous medium a Darcy's like model and the Allard,Champoux model are taken into account. The numerical results show that the finite element method allows us to compute the response curve for the coupled system and the complex eigenfrequencies. Some of them have a small imaginary part but there are also overdamped modes. Copyright © 2004 John Wiley & Sons, Ltd. [source] An efficient diagonal preconditioner for finite element solution of Biot's consolidation equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2002K. K. Phoon Abstract Finite element simulations of very large-scale soil,structure interaction problems (e.g. excavations, tunnelling, pile-rafts, etc.) typically involve the solution of a very large, ill-conditioned, and indefinite Biot system of equations. The traditional preconditioned conjugate gradient solver coupled with the standard Jacobi (SJ) preconditioner can be very inefficient for this class of problems. This paper presents a robust generalized Jacobi (GJ) preconditioner that is extremely effective for solving very large-scale Biot's finite element equations using the symmetric quasi-minimal residual method. The GJ preconditioner can be formed, inverted, and implemented within an ,element-by-element' framework as readily as the SJ preconditioner. It was derived as a diagonal approximation to a theoretical form, which can be proven mathematically to possess an attractive eigenvalue clustering property. The effectiveness of the GJ preconditioner over a wide range of soil stiffness and permeability was demonstrated numerically using a simple three-dimensional footing problem. This paper casts a new perspective on the potentialities of the simple diagonal preconditioner, which has been commonly perceived as being useful only in situations where it can serve as an approximate inverse to a diagonally dominant coefficient matrix. Copyright © 2002 John Wiley & Sons, Ltd. [source] A domain decomposition technique for finite element based parametric sweep and tolerance analyses of microwave passive devicesINTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 3 2009Giacomo Guarnieri Abstract A domain decomposition approach is here applied to the finite element solution of a multiport waveguide passive device. The approach allows separating the problem in multiple, coupled subproblems which can be solved individually. By appropriately defining one of these subdomains as containing all the possible variations to be studied it is hence possible to restrict the tolerance analysis to this latter, smaller domain. Numerical results showing the gain in computing time are presented. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009. [source] Efficiency-based h - and hp -refinement strategies for finite element methodsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2-3 2008H. De Sterck Abstract Two efficiency-based grid refinement strategies are investigated for adaptive finite element solution of partial differential equations. In each refinement step, the elements are ordered in terms of decreasing local error, and the optimal fraction of elements to be refined is determined based on efficiency measures that take both error reduction and work into account. The goal is to reach a pre-specified bound on the global error with minimal amount of work. Two efficiency measures are discussed, ,work times error' and ,accuracy per computational cost'. The resulting refinement strategies are first compared for a one-dimensional (1D) model problem that may have a singularity. Modified versions of the efficiency strategies are proposed for the singular case, and the resulting adaptive methods are compared with a threshold-based refinement strategy. Next, the efficiency strategies are applied to the case of hp -refinement for the 1D model problem. The use of the efficiency-based refinement strategies is then explored for problems with spatial dimension greater than one. The ,work times error' strategy is inefficient when the spatial dimension, d, is larger than the finite element order, p, but the ,accuracy per computational cost' strategy provides an efficient refinement mechanism for any combination of d and p. Copyright © 2008 John Wiley & Sons, Ltd. [source] A dual-reciprocity boundary element solution of a generalized nonlinear Schrödinger equationNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2004Whye-Teong Ang Abstract A time-stepping dual-reciprocity boundary element method is presented for the numerical solution of an initial-boundary value problem governed by a generalized non-linear Schrödinger equation. To test the method, two specific problems with known exact solutions are solved. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20, 2004. [source] Lagrange interpolation and finite element superconvergence,NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2004Bo Li Abstract We consider the finite element approximation of the Laplacian operator with the homogeneous Dirichlet boundary condition, and study the corresponding Lagrange interpolation in the context of finite element superconvergence. For d -dimensional Qk -type elements with d , 1 and k , 1, we prove that the interpolation points must be the Lobatto points if the Lagrange interpolation and the finite element solution are superclose in H1 norm. For d -dimensional Pk -type elements, we consider the standard Lagrange interpolation,the Lagrange interpolation with interpolation points being the principle lattice points of simplicial elements. We prove for d , 2 and k , d + 1 that such interpolation and the finite element solution are not superclose in both H1 and L2 norms and that not all such interpolation points are superconvergence points for the finite element approximation. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 33,59, 2004. [source] Lp error estimates and superconvergence for covolume or finite volume element methodsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2003So-Hsiang Chou Abstract We consider convergence of the covolume or finite volume element solution to linear elliptic and parabolic problems. Error estimates and superconvergence results in the Lp norm, 2 , p , ,, are derived. We also show second-order convergence in the Lp norm between the covolume and the corresponding finite element solutions and between their gradients. The main tools used in this article are an extension of the "supercloseness" results in Chou and Li [Math Comp 69(229) (2000), 103,120] to the Lp based spaces, duality arguments, and the discrete Green's function method. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 463,486, 2003 [source] Integration of General Sparse Matrix and Parallel Computing Technologies for Large,Scale Structural AnalysisCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 6 2002Hsien Hsieh, Shang Both general sparse matrix and parallel computing technologies are integrated in this study as a finite element solution of large,scale structural problems in a PC cluster environment. The general sparse matrix technique is first employed to reduce execution time and storage requirements for solving the simultaneous equilibrium equations in finite element analysis. To further reduce the time required for large,scale structural analyses, two parallel processing approaches for sharing computational workloads among collaborating processors are then investigated. One approach adopts a publicly available parallel equation solver, called SPOOLES, to directly solve the sparse finite element equations, while the other employs a parallel substructure method for the finite element solution. This work focuses more on integrating the general sparse matrix technique and the parallel substructure method for large,scale finite element solutions. Additionally, numerical studies have been conducted on several large,scale structural analyses using a PC cluster to investigate the effectiveness of the general sparse matrix and parallel computing technologies in reducing time and storage requirements in large,scale finite element structural analyses. [source] Rapid Exponential Convergence of Finite Element Estimates of the Effective Properties of Heterogeneous MaterialsADVANCED ENGINEERING MATERIALS, Issue 11 2007A. Gusev We develop and validate a general-purpose error estimator for the finite element solutions for the effective properties of heterogeneous materials. We show that the error should decrease exponentially upon increasing order of the polynomial interpolation. We use this finding to demonstrate the practical feasibility of reliable property predictions for a majority of particulate-morphology heterogeneous materials. [source] Fatigue of shot peened 7075-T7351 SENB specimen , A 3-D analysisFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 6 2006T. HONDA ABSTRACT As-received or shot peened 7075-T7351 single-edged notch bend (SENB) specimens, 8.1-mm thick, were fatigued at a constant maximum load and at stress ratios of R= 0.1 and 0.8 to predetermined numbers of fatigue cycles or to failure. The SENB specimens were then fractured by overload and the tunnelling crack profiles were recorded. The crack-growth rate, da/dN, after crack initiation at the notch was determined by crack-profile measurement and fractography at various fatigue cycles. The shot peened surface topography and roughness was also evaluated by three-dimensional (3-D) laser scanning microscopy. Residual stresses in the as-received specimens and those generated by shot peening at Almen scales of 0.004A, 0.008A, 0.012A and 0.016A, were measured by an X-ray diffraction stress analyser with an X-ray target, CrK, every 0.1 mm to a depth of 1 mm. The 3-D stress intensity factor of the curved crack front was determined by the superposition of the 3-D finite element solutions of the stress intensity factor of the loaded SENB specimen without the residual stress and the stress intensity factor of the unloaded SENB specimen with a prescribed residual stress distribution. da/dN versus the resultant stress intensity factor amplitude, ,KI, plots showed that while the residual stress locally retarded the crack-growth rate it had no effect on the overall crack-propagation rate. [source] Theoretical fatigue,effective notch stresses at spot weldsFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 5 2001D. Radaj Notch stress formulae are derived for the application of a notch stress approach to the fatigue assessment of spot welds. A keyhole notch is assumed to describe the edge of the weld spot between the overlapping plates. The stress fields at the keyhole notch under ,singular' and ,non-singular' in-plane loading modes inclusive of the stress concentration factors Kt are derived from the relevant Airy stress functions. The formulae are applied to typical loading cases of spot welds and compared with finite element solutions. Fatigue-effective notch stresses inclusive of fatigue notch factors Kf are calculated by applying the microstructural support hypothesis of Neuber. The notch stresses at the keyhole are also derived for out-of-plane shear loading based on the relevant harmonic stress functions. The multiaxial notch stresses at the weld spot edge are thus completely described. [source] Direct Current Plasma Emission Spectrometric Determination of Major, Minor and Trace Elements in Microwave Oven Acid Leachates of Powdered Whole Coal SamplesGEOSTANDARDS & GEOANALYTICAL RESEARCH, Issue 1 2005Sandro Fadda DCP-AES; échantillons de charbon; four à micro-ondes; éléments facilement ionisables; effets de matrice. Major concentrations of Al2O3, Fe2O3, MgO, CaO, Na2O and K2O, minor levels of TiO2, P2O5 and thirty petrologically, geochemically and environmentally significant trace elements have been determined in microwave oven acid leachates of whole powdered coal samples by direct current plasma-atomic emission spectrometry (DCP-AES). A single sample preparation procedure was suitable for all the determinations with no additional dilution step for major elements solution. Dried samples (0.5 g) were treated in low-pressure PFA digestion vessels with HF/HCl/HNO3/HClO4 acids to quantitatively extract the analytes from the bulk material, while leaving the major part of organic matrix as a residue. The major constituents of geological samples, in particular the easily ionised elements (EIEs) such as alkali and alkaline earths, may complicate the instrumental determinations in DCP-AES because of differential enhancements of elemental emission intensities and stray light interferences. Taking account of these factors, the coal matrix is considered to have very low major oxide totals as compared to many other common geo-environmental and related materials (rocks, sediments, soil, ashes etc.). The sample size employed here, while yielding a relatively concentrated solution to cover a wide range of elemental determinations, provided a sample matrix that significantly diminished interferences for DCP measurements. The need for closely matching the unknowns and calibrators was eliminated except for overall acidity and an excess quantity of caesium for EIE buffering. Calibration of the spectrometer was accomplished by simple aqueous single element solutions as high concentration calibrators in addition to a reagent blank as a low concentration calibrator. Two point working curves were established to allow for the maximum concentrations of each element expected in the unknowns. The precision of determinations under routine conditions as well as the reproducibility of the leaching and precision of instrumental measurements have been evaluated. Relative standard deviations (RSD) were of 1,2% for those elements whose concentrations in solid samples were well above the limits of quantification. Method detection limits in the buffered solutions were also evaluated. To evaluate the accuracy of the microwave oven-DCP method a suite of eight certified coal reference materials of differing rank, were analysed with good agreement with the certified and/or available published data. Results are presented for the uncertified major oxides in the AR series reference materials. Les concentrations en éléments majeurs: Al2O3, Fe2O3, MgO, CaO, Na2O et K2O, en éléments mineurs TiO2, P2O5 et en 30 éléments en trace dont le comportement est important en Pétrologie, en Géochimie et en Environnement, ont été analysées par spectrométrie d'émission atomique à plasma à courant direct (DCP-AES), dans des lessivages acides effectués dans un four à micro-ondes sur des échantillons de charbon mis en poudre. Ce mode préparatoire unique est adaptéà toutes les déterminations sans qu'il soit nécessaire d'effectuer une dilution supplémentaire pour l'analyse des éléments majeurs. Les échantillons préalablement desséchés (0.5 g) sont traités dans les pots de PFA de basse pression, avec un mélange d'acides HF/HCl/HNO3/HClO4, afin d'extraire quantitativement les analytes du matériel géologique, tout en laissant la plus grande part de la matrice organique sous forme résiduelle. Les constituants majeurs de ces échantillons géologiques, en particulier les éléments facilement ionisables (EIEs) tels que les alcalins et les alcalino-terreux, peuvent compliquer l'analyse en DCP-AES à cause des rendements variables des intensités d'émission élémentaires et des interférences de raies de lumière. Mais là dessus, la matrice de charbon se révèle être bien plus pauvre en oxydes majeurs que les autres matériaux géologiques, environnementaux ou de type proche (roches, sédiments, sols, cendres). La taille d'échantillon retenue ici, tout en fournissant une solution relativement concentrée qui permet la détermination de beaucoup d'éléments, fournit une matrice qui diminue significativement les interférences lors de la mesure par DCP-AES. Le besoin d'avoir les solutions d'échantillons et les solutions de calibration avec des matrices très proches est donc éliminé, mis à part pour l'acidité totale et la quantité excessive de Césium pour tamponner les EIE. La calibration du spectromètre est faite avec des solutions mono- élémentaires aqueuses, pour déterminer les points de concentrations élevées et avec le blanc de réactifs pour le point de concentration basse. Les courbes de calibrations sont déterminées avec 2 points, pour autoriser l'analyse de concentrations maximales pour chaque élément dans les échantillons inconnus. La précision des déterminations en conditions de routine ainsi que la reproductibilité de l'opération de lessivage et la précision instrumentale des analyses ont étéévaluées. Les déviations standards relatives (RSD) sont de 1,2% pour tout élément dont les concentrations dans le solide sont au dessus des limites de quantification. Les limites de détection de la méthode dans les solutions tamponnées ont aussi étéévaluées. Enfin, pour évaluer la justesse de cette méthode "micro-ondes - DCP" huit charbons certifiés matériaux de référence de différents types ont été analysés, et sont en bon accord avec les données certifiées ou seulement disponibles publiées. Les données sur un certain nombre d'oxydes d'éléments majeurs actuellement non certifiés sont présentées pour les matériaux de référence AR. [source] Multilayer Analytic Element Modeling of Radial Collector WellsGROUND WATER, Issue 6 2005Mark Bakker A new multilayer approach is presented for the modeling of ground water flow to radial collector wells. The approach allows for the inclusion of all aspects of the unique boundary condition along the lateral arms of a collector well, including skin effect and internal friction losses due to flow in the arms. The hydraulic conductivity may differ between horizontal layers within the aquifer, and vertical anisotropy can be taken into account. The approach is based on the multilayer analytic element method, such that regional flow and local three-dimensional detail may be simulated simultaneously and accurately within one regional model. Horizontal flow inside a layer is computed analytically, while vertical flow is approximated with a standard finite-difference scheme. Results obtained with the proposed approach compare well to results obtained with three-dimensional analytic element solutions for flow in unconfined aquifers. The presented approach may be applied to predict the yield of a collector well in a regional setting and to compute the origin and residence time, and thus the quality, of water pumped by the collector well. As an example, the addition of three lateral arms to a collector well that already has three laterals is investigated. The new arms are added at an elevation of 2 m above the existing laterals. The yield increase of the collector well is computed as a function of the lengths of the three new arms. [source] Modelling of contaminant transport through landfill liners using EFGMINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2010R. Praveen Kumar Abstract Modelling of contaminant transport through landfill liners and natural soil deposits is an important area of research activity in geoenvironmental engineering. Conventional mesh-based numerical methods depend on mesh/grid size and element connectivity and possess some difficulties when dealing with advection-dominant transport problems. In the present investigation, an attempt has been made to provide a simple but sufficiently accurate methodology for numerical simulation of the two-dimensional contaminant transport through the saturated homogeneous porous media and landfill liners using element-free Galerkin method (EFGM). In the EFGM, an approximate solution is constructed entirely in terms of a set of nodes and no characterization of the interrelationship of the nodes is needed. The EFGM employs moving least-square approximants to approximate the function and uses the Lagrange multiplier method for imposing essential boundary conditions. The results of the EFGM are validated using experimental results. Analytical and finite element solutions are also used to compare the results of the EFGM. In order to test the practical applicability and performance of the EFGM, three case studies of contaminant transport through the landfill liners are presented. A good agreement is obtained between the results of the EFGM and the field investigation data. Copyright © 2009 John Wiley & Sons, Ltd. [source] A multiscale modeling of damage and time-dependent behavior of cohesive rocksINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2009A. Abou-Chakra Guéry Abstract The present paper deals with a micromechanical approach to modeling the time-dependent mechanical behavior of a class of cohesive geomaterials. The considered material is Callovo-Oxfordian argillite, which is mainly composed of three constituents: an elastoviscoplastic clay matrix, elastic quartz minerals, and elastic damaged calcite grains. The macroscopic constitutive law is obtained by adapting the incremental method proposed by Hill (J. Mech. Phys. Solids 1965; 13:89,101). Its unified formulation allows a description of not only the time-dependent behavior of the argillite but also its elastoplastic damage response. The developed model is first validated by comparison with finite element solutions and then it is applied to the prediction of argillites' macroscopic responses in connection with their mineralogical compositions. The validity of the model is checked through comparisons between the model's predictions and experimental data. Copyright © 2008 John Wiley & Sons, Ltd. [source] Elastoplastic medium for foundation settlements and monotonic soil,structure interaction under combined loadingsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2007Dawn E. Conniff Abstract Foundation settlements and soil,structure interaction are important problems to structural and geotechnical engineers. This study introduces a novel elastoplastic three-degree-of-freedom medium which models foundations settlements under combined loadings. A soil,structure interaction problem can then be solved by replacing the soil mass with this three-degree-of-freedom elastoplastic medium, thus reducing significantly the size of the problem. The model was developed by extending the classical plasticity concepts to the force-deformation level. Its ability to predict foundation deformations was evaluated using finite element solutions of a typical shallow foundation problem and was found reasonably accurate while producing significant time savings. Copyright © 2006 John Wiley & Sons, Ltd. [source] Inclined load capacity of suction caissonsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2003C. P. Aubeny Abstract A simplified method of analysis for estimating lateral load capacity of suction caisson anchors based on an upper bound plasticity formulation is presented. The simplification restricts the analysis to caissons in uniform and linearly varying undrained strength profiles; nevertheless, its computational efficiency permits quick evaluation of a number of parameters affecting load capacity. The validity and limitations of the simplified formulation are demonstrated through comparisons to more rigorous finite element solutions. A series of sensitivity studies demonstrate the effects of various soil conditions and loading parameters. Copyright © 2003 John Wiley & Sons, Ltd. [source] Solution of the unsaturated soil moisture equation using repeated transformsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2001S. G. Fityus Abstract An alternative method of solution for the linearized ,theta-based' form of the Richards equation of unsaturated flow is developed in two spatial dimensions. The Laplace and Fourier transformations are employed to reduce the Richards equation to an ordinary differential equation in terms of a transformed moisture content and the transform variables, s and ,. Separate analytic solutions to the transformed equation are developed for initial states which are either in equilibrium or dis-equilibrium. The solutions are assembled into a finite layer formulation satisfying continuity of soil suction, thereby facilitating the analysis of horizontally stratified soil profiles. Solution techniques are outlined for various boundary conditions including prescribed constant moisture content, prescribed constant flux and flux as a function of moisture change. Example solutions are compared with linearized finite element solutions. The agreement is found to be good. An adaptation of the method for treating the quasilinearized Richards equation with variable diffusivity is also described. Comparisons of quasilinear solutions with some earlier semi-analytical, finite element and finite difference results are also favourable. Copyright © 2001 John Wiley & Sons, Ltd. [source] Hamiltonian-based error computationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2006Y. L. Kuo Abstract This paper presents two sets of the Hamiltonian for checking errors of approximated solutions. The first set can be applied to those problems having any number of independent and dependent variables. This set of the Hamiltonian can effectively indicate the errors of approximated solutions when requiring a high accuracy. The second set of the Hamiltonian has the invariant property when the Lagrangian is not an explicit function of time, even for non-conservative systems. Both sets can be formulated as error indicators to check errors of approximated solutions. Three illustrative examples demonstrate the error analyses of finite element solutions. Copyright © 2005 John Wiley & Sons, Ltd. [source] Conserving Galerkin weak formulations for computational fracture mechanicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2002Shaofan Li Abstract In this paper, a notion of invariant Galerkin-variational weak forms is proposed. Two specific invariant variational weak forms, the J-invariant and the L-invariant, are constructed based on the corresponding conservation laws in elasticity, one of which is the conservation of Eshelby's energy-momentum (Eshelby. Philos. Trans. Roy. Soc. 1951; 87: 12; In Solid State Physics, Setitz F, Turnbull D (eds). Academic Press: New York, 1956; 331; Rice, J. Appl. Mech. 1968; 35: 379). It is shown that the finite element solution obtained from the invariant Galerkin weak formulations proposed here can conserve the value of J-integral, or L-integral exactly. In other words, the J and L integrals of the Galerkin finite element solutions are path independent in the discrete sense. It is argued that by using the J-invariant Galerkin weak form to compute near crack-tip field in an elastic solid, one may accurately calculate the crack extension energy release rate and subsequently the stress intensity factors in numerical computations, because the flux of the energy-momentum is conserved in discrete computations. This may provide an alternative means to accurately simulate crack growth and propagation. Copyright © 2002 John Wiley & Sons, Ltd. [source] A methodology for fast finite element modeling of electrostatically actuated MEMSINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2009Prasad S. Sumant Abstract In this paper, a methodology is proposed for expediting the coupled electro-mechanical finite element modeling of electrostatically actuated MEMS. The proposed methodology eliminates the need for repeated finite element meshing and subsequent electrostatic modeling of the device during mechanical deformation. We achieve this by using an approximation of the charge density on the movable electrode in the deformed geometry in terms of the charge density in the non-deformed geometry and displacements of the movable electrode. The electrostatic problem has to be solved only once and thus this method speeds up the coupled electro-mechanical simulation process. The proposed methodology is demonstrated through its application to the modeling of four MEMS devices with varying length-to-gap ratios, multiple dielectrics and complicated geometries. Its accuracy is assessed through comparisons of its results with results obtained using both analytical solutions and finite element solutions obtained using ANSYS. Copyright © 2008 John Wiley & Sons, Ltd. [source] | ||||||||||||||||