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Field Problem (field + problem)
Selected AbstractsExperimental and numerical studies on dynamic crack growth in layered slate rock under wedge impact loads: part II , non-plane strain problemFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 10 2007M. R. ALAM ABSTRACT Dynamic crack propagation in non-plane strain (or 3D) slate blocks under wedge impact loads was investigated numerically in this part of the paper. A parabolic-shaped crack trajectory was taken into consideration to model the crack propagation in slate blocks for analyzing the impact splitting of layered slate rock. Major and minor axes of the parabola were determined from the condition of equal mode I stress intensity factors (SIFs) along the crack front. Mode I SIFs were determined for experimental breaking loads for each increment of crack growth in a manner similar to that mentioned in part I of this paper. These values were compared with the plane strain material fracture toughness value obtained from experimental studies and very good agreement was obtained between them, for the case of actual load applied on the specimen. Numerical analysis of a field problem, i.e., separation of a large-sized slate slab from the rock strata in a slate quarry using wedge impacting, was also carried out in this paper. It can be observed that a large magnitude of load is required to break large-sized slate blocks; but this load is applied through a number of smaller load-capacity actuators-in-parallel, requiring large power capacity for the hydraulic pumps. However, this required power could be reduced considerably if the load applied on the line of hydraulic actuators is cascaded across the (line of) actuators (starting from centrally placed actuators) with a small time delay (equal to the initial crushing time in slate rock). [source] A new hybrid velocity integration method applied to elastic wave propagationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2008Zhiyun Chen Abstract We present a novel space,time Galerkin method for solutions of second-order time-dependent problems. By introducing the displacement,velocity relationship implicitly, the governing set of equations is reformulated into a first-order single field problem with the unknowns in the velocity field. The resulting equation is in turn solved by a time-discontinuous Galerkin approach (Int. J. Numer. Anal. Meth. Geomech. 2006; 30:1113,1134), in which the continuity between time intervals is weakly enforced by a special upwind flux treatment. After solving the equation for the unknown velocities, the displacement field quantities are computed a posteriori in a post-processing step. Various numerical examples demonstrate the efficiency and reliability of the proposed method. Convergence studies with respect to the h - and p -refinement and different discretization techniques are given. Copyright © 2007 John Wiley & Sons, Ltd. [source] Numerical solution of eddy current problems in ferromagnetic bodies travelling in a transverse magnetic fieldINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2003W. Peterson Abstract Eddy currents are investigated in a ferromagnetic bar travelling in a transverse magnetic field. Such an open boundary field problem is analysed by a hybrid approach based on Galerkin finite element formulation coupled with a separation of variables. A steady state is considered, introducing time-periodic boundary conditions. The resultant system of non-linear equations is solved by an iterative procedure based on Brouwer's fixed-point theorem. Numerical results are presented for a bar of circular cross-section made of cast steel or cast iron. Selected examples of the field distribution and characteristics of eddy-current power losses are enclosed in graphic form. Copyright © 2003 John Wiley & Sons, Ltd. [source] Relaxor-based thin film memories and the depolarizing field problemPHYSICA STATUS SOLIDI (A) APPLICATIONS AND MATERIALS SCIENCE, Issue 6 2007Manuel I. Marqués Abstract A simple model for a thin film memory based on a first neighbor interacting model is studied in detail. We have found that the minimum possible value for the thickness (D) as a function of the lateral size of the memory (L), the screening of the charges at the substrate (S) and the strength of the ferroelectric interaction (J), in order to obtain spontaneous polarization is D = SL /2J. We propose a new mechanism to obtain miniaturization of thin film memories to a single layer based on the use of relaxor ferroelectrics instead of regular ferroelectrics. Under the hypothesis of an internal organization of the random fields inside the nanofilm we show analytically how it should be possible to miniaturize the memory to a width as small as D = 1 for any value of L, J and S. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Theory and Numerics of Rate-Dependent Incremental Variational Formulations in FerroelectricityPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Daniele Rosato This paper is concerned with macroscopic continuous and discrete variational formulations for domain switching effects at small strains, which occur in ferroelectric ceramics. The developed new three,dimensional model is thermodynamically,consistent and determined by two scalar,valued functions: the energy storage function (Helmholtz free energy) and the dissipation function, which is in particular rate,dependent. The constitutive model successfully reproduces the ferroelastic and the ferroelectric hysteresis as well as the butterfly hysteresis for ferroelectric ceramics. The rate,dependent character of the dissipation function allows us also to reproduce the experimentally observed rate dependency of the above mentioned hysteresis phenomena. An important aspect is the numerical implementation of the coupled problem. The discretization of the two,field problem appears, as a consequence of the proposed incremental variational principle, in a symmetric format. The performance of the proposed methods is demonstrated by means of a benchmark problem. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Time,accurate Modular CFD-CSD Coupling for Aeroelastic Rotor SimulationsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003A. Altmikus Dipl.-Ing. This paper addresses the timewise accuracy of different coupling approaches applied to instationary aeroelastic simulations of rotors in forward flight. Two different approaches which are widely discussed in literature are examined: the tight or strong coupling, and the fully integrated or monolithic coupling. Strong coupling means an exchange of fluid loads and structural deformations at each time step which is effectuated in a fully modular manner. We will address aspects of conservativity and time-accuracy, and will present results for a helicopter forward flight scenario. However, objections concerning the correct solution of the global non-linear three field problem , structure, grid deformation, aerodynamics , remain. These objections are normally rejected by the monolithic approach. Here, a common set of partial differential equations is derived and solved in a single code. However, a truly monolithic system of equations is only needed for stability analysis, and it can be decomposed in a three field problem respecting appropriate boundary conditions for each domain. Thus, modularity can be maintained, conceiving a quasi-monolithic procedure, when both domains are simultaneously solved in a common non-linear iteration loop on a per time-step basis. First results will be shown for a 2D flutter testcase. [source] Viscoelastic displacement and gravity changes due to point magmatic intrusions in a gravitational layered solid earthGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2001José Fernández Summary We present a method for the computation of time-dependent geodetic and geophysical signatures (deformation, potential and gravity changes) due to magmatic intrusions in a layered viscoelastic,gravitational medium. This work is an extension of a deformation model previously developed to compute effects due to volcanic loading in an elastic gravitational layered media. The model assumes a planar earth geometry, useful for near field problems, and consists of welded elastic and viscoelastic layers overlying a viscoelastic half-space. Every layer can either be considered elastic or viscoelastic. The intrusion (treated as a point source) can be located at any depth, in any of the layers or in the half-space. Several examples of theoretical computations for different media are also presented. We have found that, in line with previous results obtained by other authors, introducing viscoelastic properties in all or part of the medium can extend the effects (displacements, gravity changes, etc.) considerably and therefore lower pressure increases are required to model given observed effects. The viscoelastic effects seem to depend mainly on the rheological properties of the layer (zone) where the intrusion is located, rather than on the rheology of the whole medium. We apply our model to the 1982,1984 uplift episode at Campi Flegrei, modelling simultaneously the observed vertical displacement and gravity changes. The results clearly show that for a correct interpretation of observed effects it is necessary to include the gravitational field in the anelastic theoretical models. This factor can change the value and pattern of time-dependent deformation as well as the gravity changes, explaining cases of displacement without noticeable gravity changes or vice versa, cases with uplift and incremental gravity values, and other cases. The combination of displacement and gravity changes is found to be especially effective in constraining the possible characteristics of the magmatic intrusion as well as the rheology of the medium surrounding it. [source] An embedded Dirichlet formulation for 3D continuaINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2010A. Gerstenberger Abstract This paper presents a new approach for imposing Dirichlet conditions weakly on non-fitting finite element meshes. Such conditions, also called embedded Dirichlet conditions, are typically, but not exclusively, encountered when prescribing Dirichlet conditions in the context of the eXtended finite element method (XFEM). The method's key idea is the use of an additional stress field as the constraining Lagrange multiplier function. The resulting mixed/hybrid formulation is applicable to 1D, 2D and 3D problems. The method does not require stabilization for the Lagrange multiplier unknowns and allows the complete condensation of these unknowns on the element level. Furthermore, only non-zero diagonal-terms are present in the tangent stiffness, which allows the straightforward application of state-of-the-art iterative solvers, like algebraic multigrid (AMG) techniques. Within this paper, the method is applied to the linear momentum equation of an elastic continuum and to the transient, incompressible Navier,Stokes equations. Steady and unsteady benchmark computations show excellent agreement with reference values. The general formulation presented in this paper can also be applied to other continuous field problems. Copyright © 2009 John Wiley & Sons, Ltd. [source] Essential boundary condition enforcement in meshless methods: boundary flux collocation methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2002Cheng-Kong C. Wu Abstract Element-free Galerkin (EFG) methods are based on a moving least-squares (MLS) approximation, which has the property that shape functions do not satisfy the Kronecker delta function at nodal locations, and for this reason imposition of essential boundary conditions is difficult. In this paper, the relationship between corrected collocation and Lagrange multiplier method is revealed, and a new strategy that is accurate and very simple for enforcement of essential boundary conditions is presented. The accuracy and implementation of this new technique is illustrated for one-dimensional elasticity and two-dimensional potential field problems. Copyright © 2001 John Wiley & Sons, Ltd. [source] Performance of algebraic multi-grid solvers based on unsmoothed and smoothed aggregation schemesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2001R. WebsterArticle first published online: 31 JUL 200 Abstract A comparison is made of the performance of two algebraic multi-grid (AMG0 and AMG1) solvers for the solution of discrete, coupled, elliptic field problems. In AMG0, the basis functions for each coarse grid/level approximation (CGA) are obtained directly by unsmoothed aggregation, an appropriate scaling being applied to each CGA to improve consistency. In AMG1 they are assembled using a smoothed aggregation with a constrained energy optimization method providing the smoothing. Although more costly, smoothed basis functions provide a better (more consistent) CGA. Thus, AMG1 might be viewed as a benchmark for the assessment of the simpler AMG0. Selected test problems for D'Arcy flow in pipe networks, Fick diffusion, plane strain elasticity and Navier,Stokes flow (in a Stokes approximation) are used in making the comparison. They are discretized on the basis of both structured and unstructured finite element meshes. The range of discrete equation sets covers both symmetric positive definite systems and systems that may be non-symmetric and/or indefinite. Both global and local mesh refinements to at least one order of resolving power are examined. Some of these include anisotropic refinements involving elements of large aspect ratio; in some hydrodynamics cases, the anisotropy is extreme, with aspect ratios exceeding two orders. As expected, AMG1 delivers typical multi-grid convergence rates, which for all practical purposes are independent of mesh bandwidth. AMG0 rates are slower. They may also be more discernibly mesh-dependent. However, for the range of mesh bandwidths examined, the overall cost effectiveness of the two solvers is remarkably similar when a full convergence to machine accuracy is demanded. Thus, the shorter solution times for AMG1 do not necessarily compensate for the extra time required for its costly grid generation. This depends on the severity of the problem and the demanded level of convergence. For problems requiring few iterations, where grid generation costs represent a significant penalty, AMG0 has the advantage. For problems requiring a large investment in iterations, AMG1 has the edge. However, for the toughest problems addressed (vector and coupled vector,scalar fields discretized exclusively using finite elements of extreme aspect ratio) AMG1 is more robust: AMG0 has failed on some of these tests. However, but for this deficiency AMG0 would be the preferred linear approximation solver for Navier,Stokes solution algorithms in view of its much lower grid generation costs. Copyright © 2001 John Wiley & Sons, Ltd. [source] The reduced scalar potential in regions with permeable materials: Reasons for loss of accuracy and cancellationINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 4 2007S. Balac Abstract Practical three-dimensional magnetic field problems usually involve regions containing current sources as well as regions with magnetic materials. For computational purposes, the use of the reduced scalar potential (RSP) as unknown has the advantage to transform a problem for a vector field throughout the space into a problem for a scalar function, thus reducing the number of degrees of freedom in the discretization. However, in regions with high magnetic permeability the use of the RSP alone usually results in severe loss in accuracy and it is recommended to use both the RSP and the total scalar potential. Using an asymptotic expansion, we investigate theoretically the underlying reasons for this lack of accuracy in permeable regions when using the RSP as a unique potential. Moreover, this investigation leads to an efficient numerical method to compute the magnetic field in regions with high magnetic permeability. Copyright © 2007 John Wiley & Sons, Ltd. [source] Consistency of quasi-static boundary value problems in electromagnetic modellingINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 6 2006S. Suuriniemi Abstract This paper analyses the possibility to computationally settle consistency of field problems, especially those arising from electromagnetic modelling: the electromagnetic theory is expressed in field-oriented concepts, which allow for formulation of boundary value problems with no solution at all or infinitely many solutions. This possibility of such inconsistent problems decreases the productivity of electromagnetic design software. This paper relates the consistency question to topological aspects of the model domain, and proposes a scheme for routine computation of the relevant topological aspects of electromagnetic models. Copyright © 2006 John Wiley & Sons, Ltd. [source] | ||||||||||