共查询到20条相似文献，搜索用时 0 毫秒
1.
对扩展有限元方法(XFEM)的发展及其与其他数值方法的联系进行了综述。该文主要包括以下内容:首先对无网格法的发展背景和历程进行了介绍,并从近似位移场构造的角度对众多的无网格法进行了比较分析;从单位分解理论的形式出发,阐述了XFEM的特点及其与传统有限元法、无网格方法的联系;归纳了关于XFEM的应用研究及其自身理论发展的主要研究方向,并对XFEM的发展进行了展望。 相似文献
2.
Sundararajan Natarajan Stéphane PA Bordas Ean Tat Ooi 《International journal for numerical methods in engineering》2015,104(13):1173-1199
We show both theoretically and numerically a connection between the smoothed finite element method (SFEM) and the virtual element method and use this approach to derive stable, cheap and optimally convergent polyhedral FEM. We show that the stiffness matrix computed with one subcell SFEM is identical to the consistency term of the virtual element method, irrespective of the topology of the element, as long as the shape functions vary linearly on the boundary. Using this connection, we propose a new stable approach to strain smoothing for polygonal/polyhedral elements where, instead of using sub‐triangulations, we are able to use one single polygonal/polyhedral subcell for each element while maintaining stability. For a similar number of degrees of freedom, the proposed approach is more accurate than the conventional SFEM with triangular subcells. The time to compute the stiffness matrix scales with the in case of the conventional polygonal FEM, while it scales as in the proposed approach. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
3.
Thomas‐Peter Fries Ted Belytschko 《International journal for numerical methods in engineering》2010,84(3):253-304
An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented. This method enables the accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non‐smooth features within elements. This is achieved by enriching the polynomial approximation space of the classical finite element method. The GEFM/XFEM has shown its potential in a variety of applications that involve non‐smooth solutions near interfaces: Among them are the simulation of cracks, shear bands, dislocations, solidification, and multi‐field problems. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
4.
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
5.
F. K. F. Radtke A. Simone L. J. Sluys 《International journal for numerical methods in engineering》2010,84(6):708-732
The numerical analysis of large numbers of arbitrarily distributed discrete thin fibres embedded in a continuum is a computationally demanding process. In this contribution, we propose an approach based on the partition of unity property of finite element shape functions that can handle discrete thin fibres in a continuum matrix without meshing them. This is made possible by a special enrichment function that represents the action of each individual fibre on the matrix. Our approach allows to model fibre‐reinforced materials considering matrix, fibres and interfaces between matrix and fibres individually, each with its own elastic constitutive law. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
6.
E. Giner N. Sukumar F. J. Fuenmayor A. Vercher 《International journal for numerical methods in engineering》2008,76(9):1402-1418
In this paper, the numerical modelling of complete sliding contact and its associated singularity is carried out using the partition of unity finite element method. Sliding interfaces in engineering components lead to crack nucleation and growth in the vicinity of the contact zone. To accurately capture the singular stress field at the contact corner, we use the partition of unity framework to enrich the standard displacement‐based finite element approximation by additional (enriched) functions. These enriched functions are derived from the analytical expression of the asymptotic displacement field in the vicinity of the contact corner. To characterize the intensity of the singularity, a domain integral formulation is adopted to compute the generalized stress intensity factor (GSIF). Numerical results on benchmark problems are presented to demonstrate the improved accuracy and benefits of this technique. We conduct an investigation on issues pertaining to the extent of enrichment, accurate numerical integration of weak‐form integrals and the rate of convergence in energy. The use of partition of unity enrichment leads to accurate estimations of the GSIFs on relatively coarse meshes, which is particularly beneficial for modelling non‐linear sliding contacts. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
7.
基于ABAQUS平台的扩展有限元法 总被引：8，自引：1，他引：8
以ABAQUS为平台,提出了一种预设虚节点法,首次在通用有限元程序上嵌入了扩展有限元法的功能。推导了扩展有限元法中的子域积分同Heaviside函数的关系,并改进了一种三角形子域积分算法。对三点弯梁的开裂过程进行了模拟。计算结果表明,扩展有限元法对非连续位移场的表达不依赖于单元边界,是一种模拟裂纹扩展过程等涉及移动非连续问题的有效方法。与通用有限元软件的结合则为应用该方法解决实际复杂问题提供了方便的途径。 相似文献
8.
G. Legrain N. Moës E. Verron 《International journal for numerical methods in engineering》2008,76(10):1471-1488
The aim of the present paper is to study the accuracy and the robustness of the evaluation of Jk‐integrals in linear elastic fracture mechanics using the extended finite element method (X‐FEM) approach. X‐FEM is a numerical method based on the partition of unity framework that allows the representation of discontinuity surfaces such as cracks, material inclusions or holes without meshing them explicitly. The main focus in this contribution is to compare various approaches for the numerical evaluation of the J2‐integral. These approaches have been proposed in the context of both classical and enriched finite elements. However, their convergence and the robustness have not yet been studied, which are the goals of this contribution. It is shown that the approaches that were used previously within the enriched finite element context do not converge numerically and that this convergence can be recovered with an improved strategy that is proposed in this paper. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
9.
A recent approach to fracture modeling has combined the extended finite element method (XFEM) with cohesive zone models. Most studies have used simplified enrichment functions to represent the strong discontinuity but have lacked an analytical basis to represent the displacement gradients in the vicinity of the cohesive crack. In this study enrichment functions based upon an existing analytical investigation of the cohesive crack problem are proposed. These functions have the potential of representing displacement gradients in the vicinity of the cohesive crack and allow the crack to incrementally advance across each element. Key aspects of the corresponding numerical formulation and enrichment functions are discussed. A parameter study for a simple mode I model problem is presented to evaluate if quasi‐static crack propagation can be accurately followed with the proposed formulation. The effects of mesh refinement and mesh orientation are considered. Propagation of the cohesive zone tip and crack tip, time variation of the cohesive zone length, and crack profiles are examined. The analysis results indicate that the analytically based enrichment functions can accurately track the cohesive crack propagation of a mode I crack independent of mesh orientation. A mixed mode example further demonstrates the potential of the formulation. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
10.
Seth Watts Daniel A. Tortorelli 《International journal for numerical methods in engineering》2016,108(12):1498-1524
It is common in solving topology optimization problems to replace an integer‐valued characteristic function design field with the material volume fraction field, a real‐valued approximation of the design field that permits ‘fictitious’ mixtures of materials during intermediate iterations in the optimization process. This is reasonable so long as one can interpolate properties for such materials and so long as the final design is integer valued. For this purpose, we present a method for smoothly thresholding the volume fractions of an arbitrary number of material phases which specify the design. This method is trivial for two‐material design problems, for example, the canonical topology design problem of specifying the presence or absence of a single material within a domain, but it becomes more complex when three or more materials are used, as often occurs in material design problems. We take advantage of the similarity in properties between the volume fractions and the barycentric coordinates on a simplex to derive a thresholding, method which is applicable to an arbitrary number of materials. As we show in a sensitivity analysis, this method has smooth derivatives, allowing it to be used in gradient‐based optimization algorithms. We present results, which show synergistic effects when used with Solid Isotropic Material with Penalty and Rational Approximation of Material Properties material interpolation functions, popular methods of ensuring integerness of solutions. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
11.
G. Legrain R. Allais P. Cartraud 《International journal for numerical methods in engineering》2011,86(6):717-743
This paper describes the use of the extended finite element method in the context of quadtree/octree meshes. Particular attention is paid to the enrichment of hanging nodes that inevitably arise with these meshes. An approach for enforcing displacement continuity along hanging edges and faces is proposed and validated on various numerical examples (holes, material interfaces, and singularities) in both 2D and 3D. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
12.
N. Sukumar N. Moës B. Moran T. Belytschko 《International journal for numerical methods in engineering》2000,48(11):1549-1570
An extended finite element method (X‐FEM) for three‐dimensional crack modelling is described. A discontinuous function and the two‐dimensional asymptotic crack‐tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. This enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces. Computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed. Stress intensity factors (SIFs) for planar three‐dimensional cracks are presented, which are found to be in good agreement with benchmark solutions. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
13.
Fabian Krome Hauke Gravenkamp 《International journal for numerical methods in engineering》2017,109(6):790-808
This work introduces a semi‐analytical formulation for the simulation and modeling of curved structures based on the scaled boundary finite element method (SBFEM). This approach adapts the fundamental idea of the SBFEM concept to scale a boundary to describe a geometry. Until now, scaling in SBFEM has exclusively been performed along a straight coordinate that enlarges, shrinks, or shifts a given boundary. In this novel approach, scaling is based on a polar or cylindrical coordinate system such that a boundary is shifted along a curved scaling direction. The derived formulations are used to compute the static and dynamic stiffness matrices of homogeneous curved structures. The resulting elements can be coupled to general SBFEM or FEM domains. For elastodynamic problems, computations are performed in the frequency domain. Results of this work are validated using the global matrix method and standard finite element analysis. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
14.
X. Y. Liu Q. Z. Xiao B. L. Karihaloo 《International journal for numerical methods in engineering》2004,59(8):1103-1118
The extended finite element method (XFEM) is improved to directly evaluate mixed mode stress intensity factors (SIFs) without extra post‐processing, for homogeneous materials as well as for bimaterials. This is achieved by enriching the finite element (FE) approximation of the nodes surrounding the crack tip with not only the first term but also the higher order terms of the crack tip asymptotic field using a partition of unity method (PUM). The crack faces behind the tip(s) are modelled independently of the mesh by displacement jump functions. The additional coefficients corresponding to the enrichments at the nodes of the elements surrounding the crack tip are forced to be equal by a penalty function method, thus ensuring that the displacement approximations reduce to the actual asymptotic fields adjacent to the crack tip. The numerical results so obtained are in excellent agreement with analytical and numerical results available in the literature. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
15.
16.
M.J. Peake J. Trevelyan G. Coates 《International journal for numerical methods in engineering》2013,93(9):905-918
The BEM is a popular technique for wave scattering problems given its inherent ability to deal with infinite domains. In the last decade, the partition of unity BEM, in which the approximation space is enriched with a linear combination of plane waves, has been developed; this significantly reduces the number of DOFs required per wavelength. It has been shown that the element ends are more susceptible to errors in the approximation than the mid‐element regions. In this paper, the authors propose that this is due to the use of a collocation approach in combination with a reduced order of continuity in the Lagrangian shape function component of the basis functions. It is demonstrated, using numerical examples, that choosing trigonometric shape functions, rather than classical polynomial shape functions (quadratic in this case), provides accuracy benefits. Collocation schemes are investigated; it is found that the somewhat arbitrary choice of collocating at equally spaced points about the surface of a scatterer is better than schemes based on the roots of polynomials or consideration of the Fock domain. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
17.
W. Aquino J. C. Brigham C. J. Earls N. Sukumar 《International journal for numerical methods in engineering》2009,79(7):887-906
A methodology is presented for generating enrichment functions in generalized finite element methods (GFEM) using experimental and/or simulated data. The approach is based on the proper orthogonal decomposition (POD) technique, which is used to generate low‐order representations of data that contain general information about the solution of partial differential equations. One of the main challenges in such enriched finite element methods is knowing how to choose, a priori, enrichment functions that capture the nature of the solution of the governing equations. POD produces low‐order subspaces, that are optimal in some norm, for approximating a given data set. For most problems, since the solution error in Galerkin methods is bounded by the error in the best approximation, it is expected that the optimal approximation properties of POD can be exploited to construct efficient enrichment functions. We demonstrate the potential of this approach through three numerical examples. Best‐approximation studies are conducted that reveal the advantages of using POD modes as enrichment functions in GFEM over a conventional POD basis. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
18.
D. Chen C. Birk C. Song C. Du 《International journal for numerical methods in engineering》2014,97(13):937-959
A high‐order time‐domain approach for wave propagation in bounded and unbounded domains is proposed. It is based on the scaled boundary FEM, which excels in modelling unbounded domains and singularities. The dynamic stiffness matrices of bounded and unbounded domains are expressed as continued‐fraction expansions, which leads to accurate results with only about three terms per wavelength. An improved continued‐fraction approach for bounded domains is proposed, which yields numerically more robust time‐domain formulations. The coefficient matrices of the corresponding continued‐fraction expansion are determined recursively. The resulting solution is suitable for systems with many DOFs as it converges over the whole frequency range, even for high orders of expansion. A scheme for coupling the proposed improved high‐order time‐domain formulation for bounded domains with a high‐order transmitting boundary suggested previously is also proposed. In the time‐domain, the coupled model corresponds to equations of motion with symmetric, banded and frequency‐independent coefficient matrices, which can be solved efficiently using standard time‐integration schemes. Numerical examples for modal and time‐domain analysis are presented to demonstrate the increased robustness, efficiency and accuracy of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
19.
M. Reza Eslami 《International journal for numerical methods in engineering》2011,88(8):715-748
In this paper, the Polytope Finite Element Method is employed to model an embedded interface through the body, independent of the background FEM mesh. The elements that are crossed by the embedded interface are decomposed into new polytope elements which have some nodes on the interface line. The interface introduces discontinuity into the primary variable (strong) or into its derivatives (weak). Both strong and weak discontinuities are studied by the proposed method through different numerical examples including fracture problems with traction‐free and cohesive cracks, and heat conduction problems with Dirichlet and Dirichlet–Neumann types of boundary conditions on the embedded interface. For traction‐free cracks which have tip singularity, the nodes near the crack tip are enriched with the singular functions through the eXtended Finite Element Method. The concept of Natural Element Coordinates (NECs) is invoked to drive shape functions for the produced polytopes. A simple treatment is proposed for concave polytopes produced by a kinked interface and also for locating crack tip inside an element prior to using the singularity enrichment. The proposed method pursues some implementational details of eXtended/Generalized Finite Element Methods for interfaces. But here the additional DOFs are constructed on the interface lines in contrast to X/G‐FEM, which attach enriched DOFs to the previously existed nodes. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
20.
Thu Hang Vu Andrew J. Deeks 《International journal for numerical methods in engineering》2006,65(10):1714-1733
The scaled boundary finite element method is a novel semi‐analytical technique, whose versatility, accuracy and efficiency are not only equal to, but potentially better than the finite element method and the boundary element method for certain problems. This paper investigates the possibility of using higher‐order polynomial functions for the shape functions. Two techniques for generating the higher‐order shape functions are investigated. In the first, the spectral element approach is used with Lagrange interpolation functions. In the second, hierarchical polynomial shape functions are employed to add new degrees of freedom into the domain without changing the existing ones, as in the p‐version of the finite element method. To check the accuracy of the proposed procedures, a plane strain problem for which an exact solution is available is employed. A more complex example involving three scaled boundary subdomains is also addressed. The rates of convergence of these examples under p‐refinement are compared with the corresponding rates of convergence achieved when uniform h‐refinement is used, allowing direct comparison of the computational cost of the two approaches. The results show that it is advantageous to use higher‐order elements, and that higher rates of convergence can be obtained using p‐refinement instead of h‐refinement. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献