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Mesh Distortion (mesh + distortion)
Selected AbstractsSimultaneous untangling and smoothing of moving gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2008Ezequiel J. López Abstract In this work, a technique for simultaneous untangling and smoothing of meshes is presented. It is based on an extension of an earlier mesh smoothing strategy developed to solve the computational mesh dynamics stage in fluid,structure interaction problems. In moving grid problems, mesh untangling is necessary when element inversion happens as a result of a moving domain boundary. The smoothing strategy, formerly published by the authors, is defined in terms of the minimization of a functional associated with the mesh distortion by using a geometric indicator of the element quality. This functional becomes discontinuous when an element has null volume, making it impossible to obtain a valid mesh from an invalid one. To circumvent this drawback, the functional proposed is transformed in order to guarantee its continuity for the whole space of nodal coordinates, thus achieving the untangling technique. This regularization depends on one parameter, making the recovery of the original functional possible as this parameter tends to 0. This feature is very important: consequently, it is necessary to regularize the functional in order to make the mesh valid; then, it is advisable to use the original functional to make the smoothing optimal. Finally, the simultaneous untangling and smoothing technique is applied to several test cases, including 2D and 3D meshes with simplicial elements. As an additional example, the application of this technique to a mesh generation case is presented. Copyright © 2008 John Wiley & Sons, Ltd. [source] Modelling of paste flows subject to liquid phase migrationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2007M. J. Patel Abstract Particulate pastes undergoing extrusion can exhibit differential velocities between the solid and liquid phases, termed liquid phase migration (LPM). This is observed experimentally but understanding and predictive capacity for paste and extruder design is limited. Most models for LPM feature one-dimensional analyses. Here, a two-dimensional finite element model based on soil mechanics approaches (modified Cam-Clay) was developed where the liquid and the solids skeleton are treated separately. Adaptive remeshing routines were developed to overcome the significant mesh distortion arising from the large strains inherent in extrusion. Material data to evaluate the model's behaviour were taken from the literature. The predictive capacity of the model is evaluated for different ram velocities and die entry angles (smooth walls). Results are compared with experimental findings in the literature and good qualitative agreement is found. Key results are plots of pressure contributions and extrudate liquid fraction against ram displacement, and maps of permeability, liquid velocity and voids ratio. Pore liquid pressure always dominates extrusion pressure. The relationship between extrusion geometry, ram speed and LPM is complex. Overall, for a given geometry, higher ram speeds give less migration. Pastes flowing into conical entry dies give different voids ratio distributions and do not feature static zones. Copyright © 2007 John Wiley & Sons, Ltd. [source] Finite-element analysis of a combined fine-blanking and extrusion processINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2006P. F. Zheng Abstract This paper presents the characteristics of the combined fine-blanking and extrusion process and gives a detailed analysis of the process with the finite-element method. To carry out the simulation step by step and avoid the tendency to diverge in the calculations, the remeshing, tracing and golden section methods were developed and introduced into the finite-element program. Different boundary conditions were used in the simulation; the mesh distortion, field of material flow, and the stress and strain distributions were obtained. From the simulated results, the deformation characteristics under different boundary conditions were revealed. An experiment was also carried out to verify the simulated results. A large strain analysis technique was chosen to determine the effective strain distribution based on the experiment. The effective strain distributions from the simulation are in accordance with the effective strain distributions and the hardness distributions from the experiment. Copyright © 2005 John Wiley & Sons, Ltd. [source] Application of the quadrilateral area co-ordinate method: a new element for Mindlin,Reissner plateINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2006Song Cen Abstract The quadrilateral area co-ordinate method is used to formulate a new quadrilateral element for Mindlin,Reissner plate bending problem. Firstly, an independent shear field is assumed based on the locking-free Timoshenko's beam formulae; secondly, a fourth-order deflection field is assumed by introducing some generalized conforming conditions; thirdly, the rotation field is determined by the strain,displacement relations. Furthermore, a hybrid post-processing procedure is suggested to improve the stress/internal force solutions. Following this procedure, a new 4-node, 12-dof quadrilateral element, named AC-MQ4, is successfully constructed. Since all formulations are expressed by the area co-ordinates, element AC-MQ4 presents some different, but beneficial characters when compared with other usual models. Numerical examples show the new element is free of shear locking, insensitive to mesh distortion, and possesses excellent accuracy in the analysis of both thick and thin plates. It has also been demonstrated that the area co-ordinate method, the generalized conforming condition method, and the hybrid post-processing procedure are efficient tools for developing simple, effective and reliable finite element models. Copyright © 2005 John Wiley & Sons, Ltd. [source] Generalized nodes and high-performance elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2005Rong Tian Abstract The paper concerns the development of robust and high accuracy finite elements with only corner nodes using a partition-of-unity-based finite-element approximation. Construction of the partition-of-unity-based approximation is accomplished by a physically defined local function of displacements. A 4-node quadratic tetrahedral element and a 3-node quadratic triangular element are developed. Eigenvalue analysis shows that linear dependencies in the partition-of-unity-based finite-element approximation constructed for the new elements are eliminable. Numerical calculations demonstrate that the new elements are robust, insensitive to mesh distortion, and offer quadratic accuracy, while also keeping mesh generation extremely simple. Copyright © 2005 John Wiley & Sons, Ltd. [source] Two simple and efficient displacement-based quadrilateral elements for the analysis of composite laminated platesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2004Y. X. Zhang Abstract Two simple 4-node 20-DOF and 4-node 24-DOF displacement-based quadrilateral elements named RDKQ-L20 and RDKQ-L24 are developed in this paper based on the first-order shear deformation theory (FSDT) for linear analysis of thin to moderately thick laminates. The deflection and rotation functions of the element sides are obtained from Timoshenko's laminated composite beam functions. Linear displacement interpolation functions of the standard 4-node quadrilateral isoparametric plane element and displacement functions of a quadrilateral plane element with drilling degrees of freedom are taken as in-plane displacements of the proposed elements RDKQ-L20 and RDKQ-L24, respectively. Due to the application of Timoshenko's laminated composite beam functions, convergence can be ensured theoretically for very thin laminates. The elements are simple in formulation, and shear-locking free for extremely thin laminates even with full integration. A hybrid-enhanced procedure is employed to improve the accuracy of stress analysis, especially for transverse shear stresses. Numerical tests show that the new elements are convergent, not sensitive to mesh distortion, accurate and efficient for analysis of thin to moderately thick laminates. Copyright © 2004 John Wiley & Sons, Ltd. [source] Computational form-finding of tension membrane structures,Non-finite element approaches: Part 1.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2003Use of cubic splines in finding minimal surface membranes Abstract This paper, presented in three parts, discusses a computational methodology for form-finding of tension membrane structures (TMS), or fabric structures, used as roofing forms. The term ,form-finding' describes a process of finding the shape of a TMS under its initial tension. Such a shape is neither known a priori, nor can it be described by a simple mathematical function. The work is motivated by the need to provide an efficient numerical tool, which will allow a better integration of the design/analysis/manufacture of TMS. A particular category of structural forms is considered, known as minimal surface membranes (such as can be reproduced by soap films). The numerical method adopted throughout is dynamic relaxation (DR) with kinetic damping. Part 1 describes a new form-finding approach, based on the Laplace,Young equation and cubic spline fitting to give a full, piecewise, analytical description of a minimal surface. The advantages arising from the approach, particularly with regard to manufacture of cutting patterns for a membrane, are highlighted. Part 2 describes an alternative and novel form-finding approach, based on a constant tension field and faceted (triangular mesh) representation of the minimal surface. It presents techniques for controlling mesh distortion and discusses effects of mesh control on the accuracy and computational efficiency of the solution, as well as on the subsequent stages in design. Part 3 gives a comparison of the performance of the initial method (Part 1) and the faceted approximations (Part 2). Functional relations, which encapsulate the numerical efficiency of each method, are presented. Copyright © 2002 John Wiley & Sons, Ltd. [source] Computational form-finding of tension membrane structures,Non-finite element approaches: Part 2.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2003Triangular mesh discretization, control of mesh distortion in modelling minimal surface membranes Abstract This paper, presented in three parts, discusses a computational methodology for form-finding of tension membrane structures (TMS), or fabric structures, used as roofing forms. The term ,form-finding' describes a process of finding the shape of a TMS under its initial tension. Such a shape is neither known a priori, nor can it be described by a simple mathematical function. The work is motivated by the need to provide an efficient numerical tool, which will allow a better integration of the design/analysis/manufacture of TMS. A particular category of structural forms is considered, known as minimal surface membranes (such as can be reproduced by soap films). The numerical method adopted throughout is dynamic relaxation (DR) with kinetic damping. Part 1 gave a background to the problem of TMS design, described the DR method, and presented a new form-finding methodology, based on the Laplace,Young equation and cubic spline fitting to give a full, piecewise, analytical description of the surface. Part 2 describes an alternative and novel form-finding method, based on a constant tension field and faceted (triangular mesh) representation of the minimal surface. Techniques for controlling mesh distortion are presented, and their effects on the accuracy and computational efficiency of the solution, as well as on the subsequent stages in design, are examined. Part 3 gives a comparison of the performance of the initial method (Part 1) and the faceted approximations (Part 2). Functional relations, which encapsulate the numerical efficiency of each method, are presented. Copyright © 2002 John Wiley & Sons, Ltd. [source] Iterative correction to enhance the mesh distortion tolerance of isoparametric QUAD8 elementINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2005S. Rajendran Abstract An iterative correction method is proposed to enhance the otherwise poor performance of QUAD8 element in the presence of mesh distortions. The method is based on the idea of applying corrective nodal loads iteratively in order to reduce the malicious effects of mesh distortions. The effectiveness of the method is demonstrated for typical illustrative problems using meshes having different types of mesh distortions of varying degree. The mathematical condition for convergence is discussed. Copyright © 2005 John Wiley & Sons, Ltd. [source] An accurate hybrid macro-element with linear displacementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2005Xiao-Ping Xie Abstract A hybrid stress quadrilateral macro-element HQM is proposed. Compatible linear displacements are used on its two triangular sub-domains, and a 5-parameter incomplete linear stress mode is suggested. Equivalence to another quadrilateral element HQ4 with compatible isoparametric bilinear displacements is proven. Due to elimination of stress parameters at the element level, the computational cost of HQM/HQ4 is as same as that of Q4. Numerical tests show that the element is accurate, insensitive to mesh distortions, and free from Poisson locking. Copyright © 2004 John Wiley & Sons, Ltd. [source] On the numerical treatment of initial strains in biological soft tissuesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2006E. Peña Abstract In this paper, different methodologies to enforce initial stresses or strains in finite strain problems are compared. Since our main interest relies on the simulation of living tissues, an orthotropic hyperelastic constitutive model has been used to describe their passive material behaviour. Different methods are presented and discussed. Firstly, the initial strain distribution is obtained after deformation from a previously assumed to be known stress-free state using an appropriate finite element approach. This approach usually involves important mesh distortions. The second method consists on imposing the initial strain field from the definition of an initial incompatible ,deformation gradient' field obtained from experimental data. This incompatible tensor field can be imposed in two ways, depending on the origin of the experimental tests. In some cases as ligaments, the experiment is carried out from the stress-free configuration, while in blood vessels the starting point is usually the load-free configuration with residual stresses. So the strain energy function would remain the same for the whole simulation or redefined from the new origin of the experiment. Some validation and realistic examples are presented to show the performance of the strategies and to quantify the errors appearing in each of them. Copyright © 2006 John Wiley & Sons, Ltd. [source] Exponential finite elements for diffusion,advection problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2005Abbas El-Zein Abstract A new finite element method for the solution of the diffusion,advection equation is proposed. The method uses non-isoparametric exponentially-varying interpolation functions, based on exact, one- and two-dimensional solutions of the Laplace-transformed differential equation. Two eight-noded elements are developed and tested for convergence, stability, Peclet number limit, anisotropy, material heterogeneity, Dirichlet and Neumann boundary conditions and tolerance for mesh distortions. Their performance is compared to that of conventional, eight- and 12-noded polynomial elements. The exponential element based on two-dimensional analytical solutions fails basic tests of convergence. The one based on one-dimensional solutions performs particularly well. It reduces by about 75% the number of elements and degrees of freedom required for convergence, yielding an error that is one order of magnitude smaller than that of the eight-noded polynomial element. The exponential element is stable and robust under relatively high degrees of heterogeneity, anisotropy and mesh distortions. Copyright © 2005 John Wiley & Sons, Ltd. [source] On solving large strain hyperelastic problems with the natural element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2005B. Calvo Abstract In this paper, an extension of the natural element method (NEM) is presented to solve finite deformation problems. Since NEM is a meshless method, its implementation does not require an explicit connectivity definition. Consequently, it is quite adequate to simulate large strain problems with important mesh distortions, reducing the need for remeshing and projection of results (extremely important in three-dimensional problems). NEM has important advantages over other meshless methods, such as the interpolant character of its shape functions and the ability of exactly reproducing essential boundary conditions along convex boundaries. The ,-NEM extension generalizes this behaviour to non-convex boundaries. A total Lagrangian formulation has been employed to solve different problems with large strains, considering hyperelastic behaviour. Several examples are presented in two and three dimensions, comparing the results with the ones of the finite element method. NEM performs better showing its important capabilities in this kind of applications. Copyright © 2004 John Wiley & Sons, Ltd. [source] 2D nearly orthogonal mesh generationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2004Yaoxin Zhang Abstract The Ryskin and Leal (RL) system is the most widely used mesh generation system for the orthogonal mapping. However, when this system is used in domains with complex geometry, particularly in those with sharp corners and strong curvatures, serious distortion or overlapping of mesh lines may occur and an acceptable solution may not be possible. In the present study, two methods are proposed to generate nearly orthogonal meshes with the smoothness control. In the first method, the original RL system is modified by introducing smoothness control functions, which are formulated through the blending of the conformal mapping and the orthogonal mapping; while in the second method, the RL system is modified by introducing the contribution factors. A hybrid system of both methods is also developed. The proposed methods are illustrated by several test examples. Applications of these methods in a natural river channel are demonstrated. It is shown that the modified RL systems are capable of producing meshes with an adequate balance between the orthogonality and the smoothness for complex computational domains without mesh distortions and overlapping. Copyright © 2004 John Wiley & Sons, Ltd. [source] | ||||||||||