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Element Size (element + size)
Selected AbstractsSignificance of the elastic peak stress evaluated by FE analyses at the point of singularity of sharp V-notched componentsFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 2 2007G. MENEGHETTI ABSTRACT The paper presents an expression useful to estimate the notch stress intensity factor (NSIF) from finite element analyses carried out by using a mesh pattern with a constant element size. The evaluation of the NSIF from a numerical analysis of the local stress field usually requires very refined meshes and then large computational effort. The usefulness of the presented expression is that (i) only the elastic peak stress numerically evaluated at the V-notch tip is needed and no longer the whole stress,distance set of data; (ii) the adopted meshes are rather coarse if compared to those necessary for the evaluation of the whole local stress field. The proposed expression needs the evaluation of a virtual V-notch tip radius, i.e. the radius which would produce the same elastic peak stress than that calculated by FEM at the sharp V-notch tip by means of a given mesh pattern. Once such a radius has been theoretically determined for a given geometry, the expression can be applied in a wide range of notch depths and opening angles. [source] Smeared crack approach: back to the original trackINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2006M. Cervera Abstract This paper briefly reviews the formulations used over the last 40 years for the solution of problems involving tensile cracking, with both the discrete and the smeared crack approaches. The paper focuses on the smeared approach, identifying as its main drawbacks the observed mesh-size and mesh-bias spurious dependence when the method is applied ,straightly'. A simple isotropic local damage constitutive model is considered, and the (exponential) softening modulus is regularized according to the material fracture energy and the element size. The continuum and discrete mechanical problems corresponding to both the weak discontinuity (smeared cracks) and the strong discontinuity (discrete cracks) approaches are analysed and the question of propagation of the strain localization band (crack) is identified as the main difficulty to be overcome in the numerical procedure. A tracking technique is used to ensure stability of the solution, attaining the necessary convergence properties of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is stable and remarkably robust. As a consequence, the results obtained do not suffer from spurious mesh-size or mesh-bias dependence, comparing very favourably with those obtained with other fracture and continuum mechanics approaches. Copyright © 2006 John Wiley & Sons, Ltd. [source] Effect of element size on the static finite element analysis of steep slopesINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2001Scott A. Ashford Abstract The accuracy of the computed stress distribution near the free surface of vertical slopes was evaluated in this study as a function of the element size, including aspect ratio. To accomplish this objective, a parametric study was carried out comparing stresses computed using the finite element method (FEM) to those obtained from a physical model composed of photoelastic material. The results of the study indicate a reasonable agreement between a gelatin model and the FEM model for shear stresses, and an overall good agreement between the two models for the principal stresses. For stresses along the top of the slope, the height of the element tends to be more important than width or aspect ratio, at least for aspect ratios up to 4. In all cases, the greatest difference between the two models occurs in the vicinity of the slope. Specifically, if H is defined as the slope height, an element height of H/10 appears to be adequate for the study of stresses deep within the slope, such as for typical embankment analyses. However, for cases where tensile stresses in the vicinity of the slope face which are critical, such as for the stability analysis of steep slopes, element heights as small as H/32, or higher-order elements, are necessary. Copyright © 2001 John Wiley & Sons, Ltd. [source] Obtaining smooth mesh transitions using vertex optimization,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008M. Brewer Abstract Mesh optimization has proven to be an effective way to improve mesh quality for arbitrary Lagrangian Eulerian (ALE) simulations. To date, however, most of the focus has been on improving the geometric shape of individual elements, and these methods often do not result in smooth transitions in element size or aspect ratio across groups of elements. We present an extension to the mean ratio optimization that addresses this problem and yields smooth transitions within regions and across regions in the ALE simulation. While this method is presented in the context of ALE simulations, it is applicable to a wider set of applications that require mesh improvement, including the mesh generation process. Published in 2007 by John Wiley & Sons, Ltd. [source] Discrete element method for modelling solid and particulate materialsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2007Federico A. Tavarez Abstract The discrete element method (DEM) is developed in this study as a general and robust technique for unified two-dimensional modelling of the mechanical behaviour of solid and particulate materials, including the transition from solid phase to particulate phase. Inter-element parameters (contact stiffnesses and failure criteria) are theoretically established as functions of element size and commonly accepted material parameters including Young's modulus, Poisson's ratio, ultimate tensile strength, and fracture toughness. A main feature of such an approach is that it promises to provide convergence with refinement of a DEM discretization. Regarding contact failure, an energy criterion based on the material's ultimate tensile strength and fracture toughness is developed to limit the maximum contact forces and inter-element relative displacement. This paper also addresses the issue of numerical stability in DEM computations and provides a theoretical method for the determination of a stable time-step. The method developed herein is validated by modelling several test problems having analytic solutions and results show that indeed convergence is obtained. Moreover, a very good agreement with the theoretical results is obtained in both elastic behaviour and fracture. An example application of the method to high-speed penetration of a concrete beam is also given. Copyright © 2006 John Wiley & Sons, Ltd. [source] Dynamic crack propagation with cohesive elements: a methodology to address mesh dependencyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004F. Zhou Abstract In this paper, two brittle fracture problems are numerically simulated: the failure of a ceramic ring under centrifugal loading and crack branching in a PMMA strip. A three-dimensional finite element package in which cohesive elements are dynamically inserted has been developed. The cohesive elements' strength is chosen to follow a modified weakest link Weibull distribution. The probability of introducing a weak cohesive element is set to increase with the cohesive element size. This reflects the physically based effect according to which larger elements are more likely to contain defects. The calculations illustrate how the area dependence of the Weibull model can be used to effectively address mesh dependency. On the other hand, regular Weibull distributions have failed to reduce mesh dependency for the examples shown in this paper. The ceramic ring calculations revealed that two distinct phenomena appear depending on the magnitude of the Weibull modulus. For low Weibull modulus, the fragmentation of the ring is dominated by heterogeneities. Whereas many cracks were generated, few of them could propagate to the outer surface. Monte Carlo simulations revealed that for highly heterogeneous rings, the number of small fragments was large and that few large fragments were generated. For high Weibull modulus, signifying that the ring is close to being homogeneous, the fragmentation process was very different. Monte Carlo simulations highlighted that a larger number of large fragments are generated due to crack branching. Copyright © 2003 John Wiley & Sons, Ltd. [source] An orthotropic damage model for masonry structuresINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2002Luisa Berto Abstract An orthotropic damage model specifically developed for the analysis of brittle masonry subjected to in-plane loading is described. Four independent internal damage parameters, one in compression and one in tension for each of the two natural axes of the masonry, are defined allowing the stiffness recovery at crack closure as well as the different inelastic behaviour along each natural axis to be considered. The damage field of the material is defined in terms of four equivalent stresses and results, in the space of the in-plane effective stresses, in a double pyramid with a rectangular base where the slopes of the faces correspond to the internal friction angle of the material. The equivalent stresses also control the growth of the damage parameters. The returning path from the effective to the damaged stresses is given by multiplication by a fourth-rank damage effect tensor, which is a function of the damage parameters and of the effective stress state. Mesh size regularization is achieved by means of an enhanced local method taking into account the finite element size. Good agreement has been found in the comparison between numerical results and experimental data both for masonry shear panels and for a large-scale masonry holed wall. Copyright © 2002 John Wiley & Sons, Ltd. [source] A combined rh -adaptive scheme based on domain subdivision.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2001Formulation, linear examples Abstract An adaptive scheme is proposed in which the domain is split into two subdomains. One subdomain consists of regions where the discretization is refined with an h -adaptive approach, whereas in the other subdomain node relocation or r -adaptivity is used. Through this subdivision the advantageous properties of both remeshing strategies (accuracy and low computer costs, respectively) can be exploited in greater depth. The subdivision of the domain is based on the formulation of a desired element size, which renders the approach suitable for coupling with various error assessment tools. Two-dimensional linear examples where the analytical solution is known illustrate the approach. It is shown that the combined rh -adaptive approach is superior to its components r - and h -adaptivity, in that higher accuracies can be obtained compared to a purely r -adaptive approach, while the computational costs are lower than that of a purely h -adaptive approach. As such, a more flexible formulation of adaptive strategies is given, in which the relative importance of attaining a pre-set accuracy and speeding-up the computational process can be set by the user. Copyright © 2001 John Wiley & Sons, Ltd. [source] A Petrov,Galerkin finite element model for one-dimensional fully non-linear and weakly dispersive wave propagationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2001Seung-Buhm Woo Abstract A new finite element method is presented to solve one-dimensional depth-integrated equations for fully non-linear and weakly dispersive waves. For spatial integration, the Petrov,Galerkin weighted residual method is used. The weak forms of the governing equations are arranged in such a way that the shape functions can be piecewise linear, while the weighting functions are piecewise cubic with C2 -continuity. For the time integration an implicit predictor,corrector iterative scheme is employed. Within the framework of linear theory, the accuracy of the scheme is discussed by considering the truncation error at a node. The leading truncation error is fourth-order in terms of element size. Numerical stability of the scheme is also investigated. If the Courant number is less than 0.5, the scheme is unconditionally stable. By increasing the number of iterations and/or decreasing the element size, the stability characteristics are improved significantly. Both Dirichlet boundary condition (for incident waves) and Neumann boundary condition (for a reflecting wall) are implemented. Several examples are presented to demonstrate the range of applicabilities and the accuracy of the model. Copyright © 2001 John Wiley & Sons, Ltd. [source] Magnetohydrodynamic mixer of an electrolyte solutionPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 12 2004Svetlana Gorobets Abstract Mixing process was investigated as a function of metal element size, external magnetic field magnitude and distance from metal cylinder surface. Investigation results have shown an application of magnetic field is possible instrument for electrolyte flow parameter change. Magnetohydrodynamic mixer of an electrolytes solution was proposed on investigation results base. The advantages of proposed device are simple construction and absence energy consumption. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Assessment of sensory substitution prosthesis potentialities in minimalist conditions of learningAPPLIED COGNITIVE PSYCHOLOGY, Issue 4 2006Colline Poirier Pattern recognition with a prosthesis substituting vision by audition was investigated. During 15 1-hour sessions, nine blindfolded sighted subjects were trained to recognise 2D patterns by trial and error. In addition to a global assessment, recognition of pattern element nature (vertical bars, horizontal bars,), element size and element spatial arrangement were independently assessed for each pattern. Influence of experimental parameters (complexity level of patterns, exploration number of a pattern) on recognition was studied. Performances improved over sessions. As a rule, patterns element nature was less well recognised than element size and spatial arrangement. Experimental parameters influenced pattern recognition performance. Results are discussed in relation with auditory and visual perception as well as in the perspective to implement a learning protocol for future users of prosthesis. Copyright © 2006 John Wiley & Sons, Ltd. [source] Incorporating spatially variable bottom stress and Coriolis force into 2D, a posteriori, unstructured mesh generation for shallow water modelsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2009D. Michael Parrish Abstract An enhanced version of our localized truncation error analysis with complex derivatives (LTEA,CD ) a posteriori approach to computing target element sizes for tidal, shallow water flow, LTEA+CD , is applied to the Western North Atlantic Tidal model domain. The LTEA + CD method utilizes localized truncation error estimates of the shallow water momentum equations and builds upon LTEA and LTEA,CD-based techniques by including: (1) velocity fields from a nonlinear simulation with complete constituent forcing; (2) spatially variable bottom stress; and (3) Coriolis force. Use of complex derivatives in this case results in a simple truncation error expression, and the ability to compute localized truncation errors using difference equations that employ only seven to eight computational points. The compact difference molecules allow the computation of truncation error estimates and target element sizes throughout the domain, including along the boundary; this fact, along with inclusion of locally variable bottom stress and Coriolis force, constitute significant advancements beyond the capabilities of LTEA. The goal of LTEA + CD is to drive the truncation error to a more uniform, domain-wide value by adjusting element sizes (we apply LTEA + CD by re-meshing the entire domain, not by moving nodes). We find that LTEA + CD can produce a mesh that is comprised of fewer nodes and elements than an initial high-resolution mesh while performing as well as the initial mesh when considering the resynthesized tidal signals (elevations). Copyright © 2008 John Wiley & Sons, Ltd. [source] Negative permeability around 630 nm in nanofabricated vertical meander metamaterialsPHYSICA STATUS SOLIDI (A) APPLICATIONS AND MATERIALS SCIENCE, Issue 11 2007Heinz Schweizer Abstract We demonstrate a new design of a 3-dimensional meander structure that exhibits negative permeability with a broad bandwidth between 550 nm and 665 nm. The structural design allows for full coupling of the magnetic field component at all angles of incidence. We compare our structure with other metamaterial structures with respect to the series capacitance contributions of the different metamaterials. The investigation of optical metamaterials is carried out combining transmission line analysis with numerical simulations of Maxwell's equations. The analysis is demonstrated for typical split ring structures and the novel 3D meander metamaterial structures. Comparing the resulting scattering parameter spectra as well as the retrieved effective material parameters, we find that transmission line description remains valid for metamaterials at optical frequencies. We find in addition that the longitudinal capacitance is the decisive parameter to achieve negative permeability with a broad bandwidth at optical frequencies. For experimental verification we manufactured split-ring resonator structures and meander metamaterial structures with linewidths down to 30 nm, element sizes down to 100 nm, and periods between 200 nm and 350 nm. For meander metamaterial structures a permeability value of ,1 was achieved within a bandwidth of 50 nm centered at 630 nm. The largest absolute value of ,4.5 was achieved at 650 nm. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | |||||||||||||