共查询到20条相似文献，搜索用时 15 毫秒
1.
Wanji Chen 《International journal for numerical methods in engineering》2002,53(3):603-619
Variational principles with relaxed inter‐element continuity requirement for non‐conforming element methods in linear and non‐linear analyses are developed. Based on the principles, any non‐conforming element displacement can be used directly to derive the explicit expressions of non‐conforming displacement function, which can ensure the passage of the patch test C for the requirement of convergence Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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Gang‐Won Jang Je Hyun Jeong Yoon Young Kim Dongwoo Sheen Chunjae Park Myoung‐Nyoun Kim 《International journal for numerical methods in engineering》2003,57(12):1717-1735
The objective of the present study is to show that the numerical instability characterized by checkerboard patterns can be completely controlled when non‐conforming four‐node finite elements are employed. Since the convergence of the non‐conforming finite element is independent of the Lamé parameters, the stiffness of the non‐conforming element exhibits correct limiting behaviour, which is desirable in prohibiting the unwanted formation of checkerboards in topology optimization. We employ the homogenization method to show the checkerboard‐free property of the non‐conforming element in topology optimization problems and verify it with three typical optimization examples. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
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Y. X. Zhang Y. K. Cheung 《International journal for numerical methods in engineering》2003,56(15):2387-2408
A refined non‐conforming triangular plate/shell element for geometric non‐linear analysis of plates/shells using the total Lagrangian/updated Lagrangian approach is constructed in this paper based on the refined non‐conforming element method for geometric non‐linear analysis. The Allman's triangular plane element with vertex degrees of freedom and the refined triangular plate‐bending element RT9 are used to construct the present element. Numerical examples demonstrate that the accuracy of the new element is quite high in the geometric non‐linear analysis of plates/shells. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
5.
Fabio I. Zyserman Patricia M. Gauzellino Juan E. Santos 《International journal for numerical methods in engineering》2003,58(9):1381-1395
We investigate the dispersive properties of a non‐conforming finite element method to solve the two‐dimensional Helmholtz and elastodynamics equations. The study is performed by deriving and analysing the dispersion relations and by evaluating the derived quantities, such as the dimensionless phase and group velocities. Also the phase difference between exact and numerical solutions is investigated. The studied method, which yields a linear spatial approximation, is shown to be less dispersive than a conforming bilinear finite element method in the two cases shown herein. Moreover, it almost halves the number of points per wavelength necessary to reach a given accuracy when calculating the mentioned velocities in both cases here presented. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
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Gang‐Won Jang Sangkeun Lee Yoon Young Kim Dongwoo Sheen 《International journal for numerical methods in engineering》2005,63(6):859-875
As in the case of two‐dimensional topology design optimization, numerical instability problems similar to the formation of two‐dimensional checkerboard patterns occur if the standard eight‐node conforming brick element is used. Motivated by the recent success of the two‐dimensional non‐conforming elements in completely eliminating checkerboard patterns, we aim at investigating the performance of three‐dimensional non‐conforming elements in controlling the patterns that are estimated overly stiff by the brick elements. To this end, we will investigate how accurately the non‐conforming elements estimate the stiffness of the patterns. The stiffness estimation is based on the homogenization method by assuming the periodicity of the patterns. To verify the superior performance of the elements, we consider three‐dimensional compliance minimization and compliant mechanism design problems and compare the results by the non‐conforming element and the standard 8‐node conforming brick element. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
7.
A. Portela 《International journal for numerical methods in engineering》2011,86(12):1457-1480
This paper is concerned with the effective numerical implementation of the adaptive dual boundary‐element method (DBEM), for two‐dimensional potential problems. Two boundary integral equations, which are the potential and the flux equations, are applied for collocation along regular and degenerate boundaries, leading always to a single‐region analysis. Taking advantage on the use of non‐conforming parametric boundary‐elements, the method introduces a simple error estimator, based on the discontinuity of the solution across the boundaries between adjacent elements and implements the p, h and mixed versions of the adaptive mesh refinement. Examples of several geometries, which include degenerate boundaries, are analyzed with this new formulation to solve regular and singular problems. The accuracy and efficiency of the implementation described herein make this a reliable formulation of the adaptive DBEM. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
8.
Carsten Carstensen Kerstin Weinberg 《International journal for numerical methods in engineering》2003,56(15):2313-2330
Adaptive algorithms are important tools for efficient finite‐element mesh design. In this paper, an error controlled adaptive mesh‐refining algorithm is proposed for a non‐conforming low‐order finite‐element method for the Reissner–Mindlin plate model. The algorithm is controlled by a reliable and efficient residual‐based a posteriori error estimate, which is robust with respect to the plate's thickness. Numerical evidence for this and the efficiency of the new algorithm is provided in the sense that non‐optimal convergence rates are optimally improved in our numerical experiments. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
9.
Chan Lee Hobeom Kim Seyoung Im 《International journal for numerical methods in engineering》2017,110(11):1069-1100
The node‐based or edge‐based smoothed finite element method is extended to develop polyhedral elements that are allowed to have an arbitrary number of nodes or faces, and so retain a good geometric adaptability. The strain smoothing technique and implicit shape functions based on the linear point interpolation make the element formulation simple and straightforward. The resulting polyhedral elements are free from the excessive zero‐energy modes and yield a robust solution very much insensitive to mesh distortion. Several numerical examples within the framework of linear elasticity demonstrate the accuracy and convergence behavior. The smoothed finite element method‐based polyhedral elements in general yield solutions of better accuracy and faster convergence rate than those of the conventional finite element methods. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
10.
Xianwu Ling Russell G. Keanini H. P. Cherukuri 《International journal for numerical methods in engineering》2003,56(9):1315-1334
A non‐iterative, finite element‐based inverse method for estimating surface heat flux histories on thermally conducting bodies is developed. The technique, which accommodates both linear and non‐linear problems, and which sequentially minimizes the least squares error norm between corresponding sets of measured and computed temperatures, takes advantage of the linearity between computed temperatures and the instantaneous surface heat flux distribution. Explicit minimization of the instantaneous error norm thus leads to a linear system, i.e. a matrix normal equation, in the current set of nodal surface fluxes. The technique is first validated against a simple analytical quenching model. Simulated low‐noise measurements, generated using the analytical model, lead to heat transfer coefficient estimates that are within 1% of actual values. Simulated high‐noise measurements lead to h estimates that oscillate about the low‐noise solution. Extensions of the present method, designed to smooth oscillatory solutions, and based on future time steps or regularization, are briefly described. The method's ability to resolve highly transient, early‐time heat transfer is also examined; it is found that time resolution decreases linearly with distance to the nearest subsurface measurement site. Once validated, the technique is used to investigate surface heat transfer during experimental quenching of cylinders. Comparison with an earlier inverse analysis of a similar experiment shows that the present method provides solutions that are fully consistent with the earlier results. Although the technique is illustrated using a simple one‐dimensional example, the method can be readily extended to multidimensional problems. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
11.
H. T. Banks Malcolm J Birch Mark P Brewin Stephen E Greenwald Shuhua Hu Zackary R Kenz Carola Kruse Matthias Maischak Simon Shaw John R Whiteman 《International journal for numerical methods in engineering》2014,98(2):131-156
We revisit a method originally introduced by Werder et al. (in Comput. Methods Appl. Mech. Engrg., 190:6685–6708, 2001) for temporally discontinuous Galerkin FEMs applied to a parabolic partial differential equation. In that approach, block systems arise because of the coupling of the spatial systems through inner products of the temporal basis functions. If the spatial finite element space is of dimension D and polynomials of degree r are used in time, the block system has dimension (r + 1)D and is usually regarded as being too large when r > 1. Werder et al. found that the space‐time coupling matrices are diagonalizable over for r ?100, and this means that the time‐coupled computations within a time step can actually be decoupled. By using either continuous Galerkin or spectral element methods in space, we apply this DG‐in‐time methodology, for the first time, to second‐order wave equations including elastodynamics with and without Kelvin–Voigt and Maxwell–Zener viscoelasticity. An example set of numerical results is given to demonstrate the favourable effect on error and computational work of the moderately high‐order (up to degree 7) temporal and spatio‐temporal approximations, and we also touch on an application of this method to an ambitious problem related to the diagnosis of coronary artery disease. Copyright © 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd. 相似文献
12.
Patrick Laborde Julien Pommier Yves Renard Michel Salaün 《International journal for numerical methods in engineering》2005,64(3):354-381
The aim of the paper is to study the capabilities of the extended finite element method (XFEM) to achieve accurate computations in non‐smooth situations such as crack problems. Although the XFEM method ensures a weaker error than classical finite element methods, the rate of convergence is not improved when the mesh parameter h is going to zero because of the presence of a singularity. The difficulty can be overcome by modifying the enrichment of the finite element basis with the asymptotic crack tip displacement solutions as well as with the Heaviside function. Numerical simulations show that the modified XFEM method achieves an optimal rate of convergence (i.e. like in a standard finite element method for a smooth problem). Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
13.
M. H. Aliabadi D. Martin 《International journal for numerical methods in engineering》2000,48(7):995-1014
14.
E. Béchet M. Scherzer M. Kuna 《International journal for numerical methods in engineering》2009,77(11):1535-1565
This paper presents an application of the extended finite element method (X‐FEM) to the analysis of fracture in piezoelectric materials. These materials are increasingly used in actuators and sensors. New applications can be found as constituents of smart composites for adaptive electromechanical structures. Under in service loading, phenomena of crack initiation and propagation may occur due to high electromechanical field concentrations. In the past few years, the X‐FEM has been applied mostly to model cracks in structural materials. The present paper focuses at first on the definition of new enrichment functions suitable for cracks in piezoelectric structures. At second, generalized domain integrals are used for the determination of crack tip parameters. The approach is based on specific asymptotic crack tip solutions, derived for piezoelectric materials. We present convergence results in the energy norm and for the stress intensity factors, in various settings. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
15.
Mark Ainsworth Joe Coyle 《International journal for numerical methods in engineering》2003,58(14):2103-2130
The problem of constructing hierarchic bases for finite element discretization of the spaces H1, H ( curl ), H ( div ) and L2 on tetrahedral elements is addressed. A simple and efficient approach to ensuring conformity of the approximations across element interfaces is described. Hierarchic bases of arbitrary polynomial order are presented. It is shown how these may be used to construct finite element approximations of arbitrary, non‐uniform, local order approximation on unstructured meshes of curvilinear tetrahedral elements. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
16.
T. Nguyen‐Thoi G. R. Liu K. Y. Lam G. Y. Zhang 《International journal for numerical methods in engineering》2009,78(3):324-353
This paper presents a novel face‐based smoothed finite element method (FS‐FEM) to improve the accuracy of the finite element method (FEM) for three‐dimensional (3D) problems. The FS‐FEM uses 4‐node tetrahedral elements that can be generated automatically for complicated domains. In the FS‐FEM, the system stiffness matrix is computed using strains smoothed over the smoothing domains associated with the faces of the tetrahedral elements. The results demonstrated that the FS‐FEM is significantly more accurate than the FEM using tetrahedral elements for both linear and geometrically non‐linear solid mechanics problems. In addition, a novel domain‐based selective scheme is proposed leading to a combined FS/NS‐FEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The implementation of the FS‐FEM is straightforward and no penalty parameters or additional degrees of freedom are used. The computational efficiency of the FS‐FEM is found better than that of the FEM. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
17.
O. J. B. Almeida Pereira J. P. Moitinho de Almeida 《International journal for numerical methods in engineering》2001,50(4):885-898
In the assumed displacement, or primal, hybrid finite element method, the requirements of continuity of displacements across the sides are regarded as constraints, imposed using Lagrange multipliers. In this paper, such a formulation for linear elasticity, in which the polynomial approximation functions are not associated with nodes, is presented. Elements with any number of sides may be easily used to create meshes with irregular vertices, when performing a non‐uniform h‐refinement. Meshes of non‐uniform degree may be easily created, when performing an hp‐refinement. The occurrence of spurious static modes in meshes of triangular elements, when compatibility is strongly enforced, is discussed. An algorithm for the automatic selection, based on the topology of a mesh of triangular elements, of the sides in which to decrease the degree of the approximation functions, in order to eliminate all these spurious modes and preserve compatibility, is presented. A similar discussion is presented for the occurrence of spurious static modes in meshes of tetrahedral elements. An algorithm, based on heuristic criteria, that succeeded in eliminating these spurious modes and preserving compatibility in all the meshes of tetrahedral elements of uniform degree that were tested, is also presented. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
18.
Chang‐Koon Choi Tae‐Yeol Lee Keun‐Young Chung 《International journal for numerical methods in engineering》2002,55(12):1463-1476
A unified approach to eliminate the undesirable lockings in distorted meshes for both non‐conforming quadrilateral membrane and hexahedral elements with drilling (or rotational) degrees of freedom is presented. The direct modification scheme is utilized in the formulation of non‐conforming modes to improve the general behaviour of isoparametric‐based elements. It is shown that the direct modification is very effective in eliminating the locking and this improvement of element behaviour may be doubled if the selective integration scheme is used simultaneously. To verify the validity of elements formulated by the proposed schemes and to evaluate their effectiveness, several numerical tests are carried out. The combined use of additional non‐conforming modes with the direct modification method and the selective integration technique plays an important role to improve the behaviour of elements, especially for distorted mesh cases. Test results also show that the results for both non‐conforming quadrilateral membrane and hexahedral elements obtained by the proposed schemes are equally satisfactory. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
19.
Y. X. Zhang Y. K. Cheung W. J. Chen 《International journal for numerical methods in engineering》2000,49(3):355-382
Two refined quadrilateral flat shell elements named RSQ20 and RSQ24 are constructed in this paper based on the refined non‐conforming element method, and the elements can satisfy the displacement compatibility requirement at the interelement of the non‐planar elements by introducing the common displacements suggested by Chen and Cheung. A refined quadrilateral plate element RPQ4 and a plane quadrilateral isoparametric element are combined to obtain the refined quadrilateral flat shell element RSQ20, and a refined quadrilateral flat shell element RSQ24 is constructed on the basis of a RPQ4 element and a quadrilateral isoparametric element with drilling degrees of freedom. The numerical examples show that the present method can improve the accuracy of shell analysis and that the two new refined quadrilateral flat shell elements are efficient and accurate in the linear analysis of some shell structures. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
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J. Garzon P. O'Hara C. A. Duarte W. G. Buttlar 《International journal for numerical methods in engineering》2014,97(4):231-273
This paper presents improvements to three‐dimensional crack propagation simulation capabilities of the generalized finite element method. In particular, it presents new update algorithms suitable for explicit crack surface representations and simulations in which the initial crack surfaces grow significantly in size (one order of magnitude or more). These simulations pose problems in regard to robust crack surface/front representation throughout the propagation analysis. The proposed techniques are appropriate for propagation of highly non‐convex crack fronts and simulations involving significantly different crack front speeds. Furthermore, the algorithms are able to handle computational difficulties arising from the coalescence of non‐planar crack surfaces and their interactions with domain boundaries. An approach based on moving least squares approximations is developed to handle highly non‐convex crack fronts after crack surface coalescence. Several numerical examples are provided, which illustrate the robustness and capabilities of the proposed approaches and some of its potential engineering applications. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献