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Quadrilateral Elements (quadrilateral + element)

Distribution by Scientific Domains

Engineering	95%

Selected Abstracts

LayTracks: a new approach to automated geometry adaptive quadrilateral mesh generation using medial axis transform

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2004
W. R. Quadros
Abstract A new mesh generation algorithm called ,LayTracks', to automatically generate an all quad mesh that is adapted to the variation of geometric feature size in the domain is described. LayTracks combines the merits of two popular direct techniques for quadrilateral mesh generation,quad meshing by decomposition and advancing front quad meshing. While the MAT has been used for the domain decomposition before, this is the first attempt to use the MAT, for the robust subdivision of a complex domain into a well defined sub-domain called ,Tracks', for terminating the advancing front of the mesh elements without complex interference checks and to use radius function for providing sizing function for adaptive meshing. The process of subdivision of a domain is analogous to, formation of railway tracks by laying rails on the ground. Each rail starts from a node on the boundary and propagates towards the medial axis (MA) and then from the MA towards the boundary. Quadrilateral elements are then obtained by placing nodes on these rails and connecting them inside each track, formed by adjacent rails. The algorithm has been implemented and tested on some typical geometries and the quality of the output mesh obtained are presented. Extension of this technique to all hexahedral meshing is discussed. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Study on the degeneration of quadrilateral element to triangular element

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2004
L.-X. Li
Abstract In this paper, the problems involved in the process of degeneration of quadrilateral element into triangular element are thoroughly analysed. The contents include the formulation of the geometry mapping induced by collapsing one side of the quadrilateral element and the construction of the shape functions. The study focuses first on a 4-node bilinear quadrilateral (Q4) element to 3-node constant strain triangular (CST) element, and then on a 8-node serendipity (Q8) element to 6-node triangular element (T6). In the analysis, the quadrilateral element and degenerate triangular element are assumed to be enclosed by straight edges. The theoretical results show that there is another better approach to realize the degeneration, and that even for conventional approach of degeneration we can give more reasonable explanation to the unclear problems like the CST property in degenerate CST element and the necessity of the additional terms in degenerate T6 element. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Two-scale method for shear bands: thermal effects and variable bandwidth

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2007
Pedro M. A. Areias
Abstract A method for the analysis of shear bands using local partition of unity is developed in the framework of the extended finite element method (XFEM). Enrichments are introduced for both the displacement field and the thermal field. The shear band width is determined by minimizing the plastic work. A coupled finite strain thermo-elastoplastic constitutive law is used. The enrichment is injected into the mesh when the material law becomes unstable. The criterion based on a complete stability analysis for materials in the finite strain regime including heat conduction, strain hardening, strain rate hardening and thermal softening is presented. A mixed continuous quadrilateral element is employed. The method is applied to the Nesterenko experiments, which exhibit multiple propagating shear bands and other problems. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Application of the quadrilateral area co-ordinate method: a new element for Mindlin,Reissner plate

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2006
Song 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]

Fast and accurate 4-node quadrilateral

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2004
Magnus Fredriksson
Abstract An accurate and variationally consistent 4-node quadrilateral element is introduced where high coarse mesh accuracy and low mesh distortion sensitivity are characteristic qualities, even when incompressibility is approached for plane strain. One-point quadrature integration procedure is adopted and a new improved stabilization technique is developed. Orthogonality conditions are utilized so that the patch test is satisfied for arbitrary quadrilaterals. Several numerical examples including a convergence rate study are presented which confirm the excellent performance of this element. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Application of piece-wise linear weight functions for 2D 8-node quadrilateral element in contact problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2004
Chouping Luo
Abstract The present study is a continuation of our previous work with the aim to reduce problems caused by standard higher order elements in contact problems. The difficulties can be attributed to the inherent property of the Galerkin method which gives uneven distributions of nodal forces resulting in oscillating contact pressures. The proposed remedy is use of piece-wise linear weight functions. The methods to establish stiffness and/or mass matrix for 8-node quadrilateral element in 2D are presented, i.e. the condensing and direct procedures. The energy and nodal displacement error norms are also checked to establish the convergence ratio. Interpretation of calculated contact pressures is discussed. Two new 2D 8-node quadrilateral elements, QUAD8C and QUAD8D, are derived and tested in many examples, which show their good performance in contact problems. Copyright © 2004 John Wiley & Sons, Ltd. [source]

A vertically moving grid finite-element modelling of tidal flow in the Changjiang Estuary, China

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2003
Z. Shi
Abstract An estuarine two-dimensional vertical finite-element model of tidal flow has been established by laterally integrating Navier,Stokes equation. To this end, a moving grid finite-element method has been used. An arbitrarily shaped quadrilateral element has been selected. This model has been validated by using field data from two monitoring stations at the North Passage of the Changjiang Estuary. Using this numerical model, two types of modelled results were obtained: (1) vertical distributions of tidal current velocities at the North Passage of the Changjiang Estuary; (2) longitudinal distributions of tidal current velocities at maximum flood tide, at high slack water, at maximum ebb tide and at low slack water tide at the North Passage of the Changjiang Estuary. The conclusion is that the model provides a reasonable agreement with observed data. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Simulating the hydraulic characteristics of the lower Yellow River by the finite-volume technique

HYDROLOGICAL PROCESSES, Issue 14 2002
Qing Wan
Abstract The finite-volume technique is used to solve the two-dimensional shallow-water equations on unstructured mesh consisting of quadrilateral elements. In this paper the algorithm of the finite-volume method is discussed in detail and particular attention is paid to accurately representing the complex irregular computational domain. The lower Yellow River reach from Huayuankou to Jiahetan is a typical meandering river. The generation of the computational mesh, which is used to simulate the flood, is affected by the distribution of water works in the river channel. The spatial information about the two Yellow River levee, the protecting dykes, and those roads that are obviously higher than the ground, need to be used to generate the computational mesh. As a result these dykes and roads locate the element interfaces of the computational mesh. In the model the finite-volume method is used to solve the shallow-wave equations, and the Osher scheme of the empirical function is used to calculate the flux through the interface between the neighbouring elements. The finite-volume method has the advantage of using computational domain with complex geometry, and the Osher scheme is a method based on characteristic theory and is a monotone upwind numerical scheme with high resolution. The flood event with peak discharge of 15 300 m3/s, occurring in the period from 30 July to 10 August 1982, is simulated. The estimated result indicates that the simulation method is good for routing the flood in a region with complex geometry. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Rank deficiency in superconvergent patch recovery techniques with 4-node quadrilateral elements

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2007
Z. Yue
Abstract The linear systems of equations generated by the Superconvergent Patch Recovery technique (Int. J. Numer. Methods Eng. 1992; 33:1331,1382; Comput. Methods Appl. Mech. Eng. 1992; 101:207,224) can exhibit rank deficiency under certain purely geometric conditions. The rank deficiency problem can be corrected simply and efficiently by utilizing a local rotated co-ordinate system. This rotated SPR procedure is easily automated and adds robustness to automatic adaptive solution methods. Copyright © 2006 John Wiley & Sons, Ltd. [source]

An advanced boundary element method for solving 2D and 3D static problems in Mindlin's strain-gradient theory of elasticity

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2010
G. F. Karlis
Abstract An advanced boundary element method (BEM) for solving two- (2D) and three-dimensional (3D) problems in materials with microstructural effects is presented. The analysis is performed in the context of Mindlin's Form-II gradient elastic theory. The fundamental solution of the equilibrium partial differential equation is explicitly derived. The integral representation of the problem, consisting of two boundary integral equations, one for displacements and the other for its normal derivative, is developed. The global boundary of the analyzed domain is discretized into quadratic line and quadrilateral elements for 2D and 3D problems, respectively. Representative 2D and 3D numerical examples are presented to illustrate the method, demonstrate its accuracy and efficiency and assess the gradient effect on the response. The importance of satisfying the correct boundary conditions in gradient elastic problems is illustrated with the solution of simple 2D problems. Copyright © 2010 John Wiley & Sons, Ltd. [source]

Two simple and efficient displacement-based quadrilateral elements for the analysis of composite laminated plates

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2004
Y. 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]

Application of piece-wise linear weight functions for 2D 8-node quadrilateral element in contact problems

Stabilized finite element methods with reduced integration techniques for miscible displacements in porous media

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2004
C. M. Dias
Abstract The objective of this work is to study some techniques to increase computational performance of stabilized finite element simulations of miscible displacements. We propose the use of a reduced integration technique for bilinear quadrilateral elements in the determination of the pressure and concentration fields. We also study the evaluation of pressure gradient (Darcy's velocity) by differentiation at super-convergent points. Numerical examples are shown to validate our approach, accessing its efficiency and accuracy. Copyright © 2003 John Wiley & Sons, Ltd. [source]

A comparative study of GLS finite elements with velocity and pressure equally interpolated for solving incompressible viscous flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2009
Yongtao Wei
Abstract A comparative study of the bi-linear and bi-quadratic quadrilateral elements and the quadratic triangular element for solving incompressible viscous flows is presented. These elements make use of the stabilized finite element formulation of the Galerkin/least-squares method to simulate the flows, with the pressure and velocity fields interpolated with equal orders. The tangent matrices are explicitly derived and the Newton,Raphson algorithm is employed to solve the resulting nonlinear equations. The numerical solutions of the classical lid-driven cavity flow problem are obtained for Reynolds numbers between 1000 and 20 000 and the accuracy and converging rate of the different elements are compared. The influence on the numerical solution of the least square of incompressible condition is also studied. The numerical example shows that the quadratic triangular element exhibits a better compromise between accuracy and converging rate than the other two elements. Copyright © 2008 John Wiley & Sons, Ltd. [source]

An approximate projection method for incompressible flow

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2002
David E. Stevens
This paper presents an approximate projection method for incompressible flows. This method is derived from Galerkin orthogonality conditions using equal-order piecewise linear elements for both velocity and pressure, hereafter Q1Q1. By combining an approximate projection for the velocities with a variational discretization of the continuum pressure Poisson equation, one eliminates the need to filter either the velocity or pressure fields as is often needed with equal-order element formulations. This variational approach extends to multiple types of elements; examples and results for triangular and quadrilateral elements are provided. This method is related to the method of Almgren et al. (SIAM J. Sci. Comput. 2000; 22: 1139,1159) and the PISO method of Issa (J. Comput. Phys. 1985; 62: 40,65). These methods use a combination of two elliptic solves, one to reduce the divergence of the velocities and another to approximate the pressure Poisson equation. Both Q1Q1 and the method of Almgren et al. solve the second Poisson equation with a weak error tolerance to achieve more computational efficiency. A Fourier analysis of Q1Q1 shows that a consistent mass matrix has a positive effect on both accuracy and mass conservation. A numerical comparison with the widely used Q1Q0 (piecewise linear velocities, piecewise constant pressures) on a periodic test case with an analytic solution verifies this analysis. Q1Q1 is shown to have comparable accuracy as Q1Q0 and good agreement with experiment for flow over an isolated cubic obstacle and dispersion of a point source in its wake. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Adaptive numerical solution of thick plates using first-order shear deformation theory.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2003
Part I: Error estimates
Abstract A posteriori error estimation employing both a residual based estimator and a recovery based estimator is discussed. Interest is focused upon the application to Reissner-Mindlin type thick plates modeled using first-order shear deformation theory, and our investigation is limited to uniform meshes of bilinear quadrilateral elements. Numerical results for selected test problems are presented for the resulting error estimators and discussed. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 44,66, 2003 [source]

Micromechanically motivated finite element model for ferroelectric ceramics

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009
Jayabal K.
Ferroelectric ceramics exhibit significant coupled electromechanical phenomena that have been widely employed in sensor and actuator applications. In regular finite element models dealing with electromechanical plane problems, each grain needs to be subdiscretized by many triangular or quadrilateral elements for required accuracy. This problem can be overcome by a polygonal finite element approach where each grain is modelled by a single finite element without compromising on the results. In this paper, a polygonal finite element approach has been employed to understand the anisotropic response of the ferroelectric ceramics in their piezoelectric region. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]