Showing papers on "Extended finite element method published in 2010"
TL;DR: An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented in this article, which enables accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non-smooth features within elements.
Abstract: 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.
1,228 citations
TL;DR: In this paper, a crack tracking procedure is proposed in detail and implemented in the context of the extended element-free Galerkin method (XEFG) for three-dimensional cracking.
339 citations
TL;DR: The numerical results indicate that for 2D and 3D continuum, locking can be avoided and the principle is extended to partition of unity enrichment to simplify numerical integration of discontinuous approximations in the extended finite element method.
294 citations
TL;DR: In this paper, a comprehensive review on the general methodologies on the damage constitutive modeling by continuum damage mechanics (CDM), the various failure criteria, the damage evolution law simulating the stiffness degradation, and the finite element implementation of progressive failure analysis in terms of the mechanical response for the variable-stiffness composite laminates arising from the continuous failure.
261 citations
TL;DR: It is shown that for isotropic operators, on particular meshes such as triangular meshes with acute angles, the unified method boils down to the well-known efficient two-point flux Finite Volume scheme.
Abstract: We investigate the connections between several recent methods for the discretization of anisotropic heterogeneous diffusion operators on general grids. We prove that the Mimetic Finite Difference scheme, the Hybrid Finite Volume scheme and the Mixed Finite Volume scheme are in fact identical up to some slight generalizations. As a consequence, some of the mathematical results obtained for each of the methods (such as convergence properties or error estimates) may be extended to the unified common framework. We then focus on the relationships between this unified method and nonconforming Finite Element schemes or Mixed Finite Element schemes. We also show that for isotropic operators, on particular meshes such as triangular meshes with acute angles, the unified method boils down to the well-known efficient two-point flux Finite Volume scheme.
245 citations
10 Sep 2010
TL;DR: In this article, the Finite Element Method Finite element analysis of Scalar Fields and Vector Fields has been used in the time domain to estimate boundary conditions in the context of finite element analysis.
Abstract: This chapter contains sections titled: Introduction to the Finite Element Method Finite Element Analysis of Scalar Fields Finite Element Analysis of Vector Fields Finite Element Analysis in the Time Domain Absorbing Boundary Conditions Some Numerical Aspects Summary References Problems
224 citations
TL;DR: This paper presents a method that separates as much as possible the generation and evaluation of the basis functions from the analysis, resulting in a formulation that can be implemented within the traditional structure of a finite element program but that permits the use of arbitrary sets of basis functions that are defined only through the input file.
Abstract: Many of the formulations of cm-rent research interest, including iosogeometric methods and the extended finite element method, use nontraditional basis functions. Some, such as subdivision surfaces, may not have convenient analytical representations. The concept of an element, if appropriate at all, no longer coincides with the traditional definition. Developing a new software for each new class of basis functions is a large research burden, especially, if the problems involve large deformations, non-linear materials, and contact. The objective of this paper is to present a method that separates as much as possible the generation and evaluation of the basis functions from the analysis, resulting in a formulation that can be implemented within the traditional structure of a finite clement program but that permits the use of arbitrary sets of basis functions that are defined only through the input file. Elements ranging from a traditional linear four-node tetrahedron through a higher-order element combining XFEM and isogeometric analysis may be specified entirely through an input file without any additional programming. Examples of this framework to applications with Lagrange elements, isogeometric elements, and XFEM basis functions for fracture are presented.
223 citations
TL;DR: In this article, a review on the numerical manifold method (NMM) is presented, which covers the basic theories of the NMM, such as NMM components, NMM displacement approximation, formulations of the discrete system of equations, integration scheme, imposition of the boundary conditions, treatment of contact problems involved in the nMM, and also the recent developments and applications of NMM.
Abstract: This paper presents a review on the numerical manifold method (NMM), which covers the basic theories of the NMM, such as NMM components, NMM displacement approximation, formulations of the discrete system of equations, integration scheme, imposition of the boundary conditions, treatment of contact problems involved in the NMM, and also the recent developments and applications of the NMM. Modeling the strong discontinuities within the framework of the NMM is specially emphasized. Several examples demonstrating the capability of the NMM in modeling discrete block system, strong discontinuities, as well as weak discontinuities are given. The similarities and distinctions of the NMM with various other numerical methods such as the finite element method (FEM), the extended finite element method (XFEM), the generalized finite element method (GFEM), the discontinuous deformation analysis (DDA), and the distinct element method (DEM) are investigated. Further developments on the NMM are suggested.
200 citations
TL;DR: In this paper, a three-dimensional extended finite element method (X-FEM) coupled with a narrow band fast marching method (FMM) is developed and implemented in the Abaqus finite element package for curvilinear fatigue crack growth and life prediction analysis of metallic structures.
186 citations
TL;DR: In this paper, a method to couple the peridynamic theory and finite element analysis to take advantage of both methods is presented, where peridynamics is used in the regions where failure is expected and the remaining regions are modeled utilizing the finite element method.
Abstract: The finite element method is widely utilized for the numerical solution of structural problems. However, damage prediction using the finite element method can be very cumbersome because the derivatives of displacements are undefined at the discontinuities. In contrast, the peridynamic theory uses displacements rather than displacement derivatives in its formulation. Hence, peridynamic equations are valid everywhere, including discontinuities. Furthermore, the peridynamic theory does not require external criteria for crack initiation and propagation since material failure is invoked through the material response. However, the finite element method is numerically more efficient than the peridynamic theory. Hence, this study presents a method to couple the peridynamic theory and finite element analysis to take advantage of both methods. Peridynamics is used in the regions where failure is expected and the remaining regions are modeled utilizing the finite element method. Then, the present approach is demonstrated through a simple problem and predictions of the present approach are compared against both the peridynamic theory and finite element method. The damage simulation results for the present method are demonstrated by considering a plate with a circular cutout.
TL;DR: A note on the finite element method for the space-fractional advection diffusion equation with non-homogeneous initial-boundary condition is given, where the fractional derivative is in the sense of Caputo.
Abstract: In this paper, a note on the finite element method for the space-fractional advection diffusion equation with non-homogeneous initial-boundary condition is given, where the fractional derivative is in the sense of Caputo. The error estimate is derived, and the numerical results presented support the theoretical results.
TL;DR: The results suggest that combining the X-FEM for structural analysis with the level set based boundary representation is a promising approach for continuum structural optimization.
Abstract: In this paper, we implement the extended finite element method (X-FEM) combined with the level set method to solve structural shape and topology optimization problems. Numerical comparisons with the conventional finite element method in a fixed grid show that the X-FEM leads to more accurate results without increasing the mesh density and the degrees of freedom. Furthermore, the mesh in X-FEM is independent of the physical boundary of the design, so there is no need for remeshing during the optimization process. Numerical examples of mean compliance minimization in 2D are studied in regard to efficiency, convergence and accuracy. The results suggest that combining the X-FEM for structural analysis with the level set based boundary representation is a promising approach for continuum structural optimization.
TL;DR: In this paper, a node-based smoothed finite element method (NS-FEM) using 3-node triangular elements is formulated for static, free vibration and buckling analyses of Reissner-Mindlin plates.
Abstract: In this paper, a node-based smoothed finite element method (NS-FEM) using 3-node triangular elements is formulated for static, free vibration and buckling analyses of Reissner–Mindlin plates. The discrete weak form of the NS-FEM is obtained based on the strain smoothing technique over smoothing domains associated with the nodes of the elements. The discrete shear gap (DSG) method together with a stabilization technique is incorporated into the NS-FEM to eliminate transverse shear locking and to maintain stability of the present formulation. A so-called node-based smoothed stabilized discrete shear gap method (NS-DSG) is then proposed. Several numerical examples are used to illustrate the accuracy and effectiveness of the present method.
TL;DR: In this article, a global bolted joint model (GBJM) is proposed to capture effects such as bolt-hole clearance, bolt-torque, friction between laminates, secondary and tertiary bending in the laminate as well as the load distribution in multi-bolt joints.
Abstract: This paper presents the development and validation of a global bolted joint model (GBJM), a highly efficient modelling strategy for bolted composite joints. Shell elements are used to model the composite laminates and the bolt is represented by a combination of beam elements coupled to rigid contact surfaces. The GBJM can capture effects such as bolt–hole clearance, bolt-torque, friction between laminates, secondary and tertiary bending in the laminates as well as the load distribution in multi-bolt joints. The GBJM is validated using both three-dimensional finite element models and experiments on both single- and multi-bolt joints. The GBJM was found to be robust, accurate and highly efficient, with time savings of up to 97% realised over full three-dimensional finite element models.
TL;DR: In this paper, a multiscale aggregating discontinuity (MAD) method for coarse graining of micro-cracks to the macro-scale was further developed, and three new features were introduced: (1) methods for treating nucleating cracks, (2) the linking of the micro unit cell with the macroelement by the hourglass mode, and (3) methods of recovering macrocracks with variable crack opening.
Abstract: A method for coarse graining of microcrack growth to the macroscale through the multiscale aggregating discontinuity (MAD) method is further developed. Three new features are: (1) methods for treating nucleating cracks, (2) the linking of the micro unit cell with the macroelement by the hourglass mode, and (3) methods for recovering macrocracks with variable crack opening. Unlike in the original MAD method, ellipticity is not retained at the macroscale in the bulk material, but we show that the element stiffness of the bulk material is positive definite. Several examples with comparisons with direct numerical simulations are given to demonstrate the effectiveness of the method. Copyright © 2009 John Wiley & Sons, Ltd.
TL;DR: A volumetric iso‐geometric finite element analysis based on Catmull‐Clark solids is presented, which optimizes the design process and narrows the gap between CAD and CAE.
Abstract: We present a volumetric iso-geometric finite element analysis based on Catmull-Clark solids. This concept allows one to use the same representation for the modeling, the physical simulation, and the visualization, which optimizes the design process and narrows the gap between CAD and CAE. In our method the boundary of the solid model is a Catmull-Clark surface with optional corners and creases to support the modeling phase. The crucial point in the simulation phase is the need to perform efficient integration for the elements. We propose a method similar to the standard subdivision surface evaluation technique, such that numerical quadrature can be used. Experiments show that our approach converges faster than methods based on tri-linear and tri-quadratic elements.However, the topological structure of Catmull-Clark elements is as simple as the structure of linear elements. Furthermore, the Catmull-Clark elements we use are C 2 -continuous on the boundary and in the interior except for irregular vertices and edges.
TL;DR: Numerical results presented for a few benchmark problems in the context of linear elastic fracture mechanics and a multi-material problem show that the proposed integration technique can be easily integrated in any existing code and yields accurate results.
Abstract: Partition of unity methods, such as the extended finite element method, allows discontinuities to be simulated independently of the mesh (Int. J. Numer. Meth. Engng. 1999; 45:601-620). This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome re-meshing,
as the discontinuity evolves. However, to compute the stiffness matrix of the elements intersected by the discontinuity, a subdivision of the elements into quadrature subcells aligned with the discontinuity is commonly adopted. In this paper, we use a simple integration technique, proposed for polygonal domains (Int. J. Nuttier Meth. Engng 2009; 80(1):103-134. DOI: 10.1002/nme.2589) to suppress the need for element subdivision. Numerical results presented for a few benchmark problems in the context of linear elastic fracture mechanics and a multi-material problem show that the proposed method yields accurate results. Owing to its simplicity, the proposed integration technique can be easily integrated in any existing code. Copyright (C) 2010 John Wiley & Sons, Ltd.
TL;DR: The methods key idea is the use of an additional stress field as the constraining Lagrange multiplier function, which allows the straight-forward application of state-of-the-art iterative solvers, like Algebraic Multigrid techniques.
Abstract: This paper presents a new approach for imposing Dirichlet conditions weakly on non-fitting finite element meshes. Such conditions, also called embedded Dirichlet conditions, are typically, but not exclusively, encountered when prescribing Dirichlet conditions in the context of the eXtended Finite Element Method (XFEM). The methods key idea is the use of an additional stress field as the constraining Lagrange multiplier function. The resulting mixed/hybrid formulation is applicable to 1D, 2D and 3D problems. The method does not require stabilization for the Lagrange multiplier unknowns and allows the complete condensation of these unknowns on the element level. Furthermore, only non- zero diagonal-terms are present in the tangent stiffness, which allows the straight-forward application of state-of-the-art iterative solvers, like Algebraic Multigrid (AMG) techniques. Within this paper, the method is applied to the linear momentum equation of an elastic continuum and to the transient, incompressible Navier-Stokes equations. Steady and unsteady benchmark computations show excellent agreement with reference values. The general formulation presented in this paper can also be applied to other continuous field problems.
TL;DR: In this paper, a generalized finite element method (GFEM) based on the solution of interdependent global (structural) and local (crack)-scale problems is proposed, which enables accurate modeling of three-dimensional cracks on meshes with elements that are orders of magnitude larger than the process zone along crack fronts.
Abstract: This paper presents a generalized finite element method (GFEM) based on the solution of interdependent global (structural) and local (crack)-scale problems. The local problems focus on the resolution of fine-scale features of the solution in the vicinity of three-dimensional cracks, while the global problem addresses the macro-scale structural behavior. The local solutions are embedded into the solution space for the global problem using the partition of unity method. The local problems are accurately solved using an hp-GFEM and thus the proposed method does not rely on analytical solutions. The proposed methodology enables accurate modeling of three-dimensional cracks on meshes with elements that are orders of magnitude larger than the process zone along crack fronts. The boundary conditions for the local problems are provided by the coarse global mesh solution and can be of Dirichlet, Neumann or Cauchy type. The effect of the type of local boundary conditions on the performance of the proposed GFEM is analyzed. Several three-dimensional fracture mechanics problems aimed at investigating the accuracy of the method and its computational performance, both in terms of problem size and CPU time, are presented. Copyright © 2009 John Wiley & Sons, Ltd.
TL;DR: In this paper, Gauss-like quadrature rules over arbitrarily-shaped elements in two dimensions without the need for partitioning the finite element are constructed for weakly singular integrands, and a polar transformation is applied to eliminate the singularity so that the integration can be performed efficiently and accurately.
TL;DR: In this paper, a discrete modeling approach is proposed to simulate woven-fabric reinforcement forming via explicit finite element analysis, where the tensile behaviour of yarns is modeled by truss, beam or seatbelt elements, and the shearing behaviour of the fabric is incorporated within shell or membrane elements.
Abstract: A discrete modeling approach is proposed to simulate woven-fabric reinforcement forming via explicit finite element analysis. The tensile behaviour of the yarns is modeled by truss, beam or seatbelt elements, and the shearing behaviour of the fabric is incorporated within shell or membrane elements. This method is easy to set up using the user-defined material subroutine capabilities of explicit finite element programs. In addition, the determination of the material parameters is straightforward from conventional tensile and shear-frame tests. The proposed approach has been implemented in the ABAQUS and LS-DYNA explicit finite element programs. Two types of fabric, a plain-weave and a twill-weave Twintex® (commingled polypropylene and glass fibres) were characterized and used to validate the modeling approach. For this validation, shear-frame and bias-extension tests have been modeled, and the finite element results are compared to experimental data. The determination of experimental shear angle contours was possible via Digital Image Correlation (DIC). The finite element results from ABAQUS and LS-DYNA are similar and agree well with the experimental data. As an example of the capabilities of the method, the deep drawing of a hemisphere is simulated using both finite elements programs.
TL;DR: It is shown that approaches which perform best for simple forms are not tractable for more complicated problems in terms of run-time performance, the time required to generate the code or the size of the generated code.
Abstract: We examine aspects of the computation of finite element matrices and vectors that are made possible by automated code generation. Given a variational form in a syntax that resembles standard mathematical notation, the low-level computer code for building finite element tensors, typically matrices, vectors and scalars, can be generated automatically via a form compiler. In particular, the generation of code for computing finite element matrices using a quadrature approach is addressed. For quadrature representations, a number of optimization strategies which are made possible by automated code generation are presented. The relative performance of two different automatically generated representations of finite element matrices is examined, with a particular emphasis on complicated variational forms. It is shown that approaches which perform best for simple forms are not tractable for more complicated problems in terms of run-time performance, the time required to generate the code or the size of the generated code. The approach and optimizations elaborated here are effective for a range of variational forms.
TL;DR: An approach to improve the geometrical representation of surfaces with the eXtended Finite Element Method is proposed, where surfaces are implicitly represented using the level set method and a new enrichment function is introduced to represent the behavior of curved material interfaces.
TL;DR: In this paper, a stabilized finite element formulation based on the polynomial pressure projection (PPP) technique was used successfully for Stokes equation and for coupled solid deformation-fluid-diffusion using low-order mixed finite elements.
TL;DR: In this paper, the eXtended Finite Element Method (XFEM) is implemented to model the effect of the mechanical and thermal shocks on a body with a stationary crack.
TL;DR: In this paper, an edge-based smoothed finite element method (ES-FEM) using triangular elements was proposed to improve the accuracy and convergence rate of the existing standard FEM for the elastic solid mechanics problems.
Abstract: SUMMARY An edge-based smoothed finite element method (ES-FEM) using triangular elements was recently proposed to improve the accuracy and convergence rate of the existing standard finite element method (FEM) for the elastic solid mechanics problems. In this paper the ES-FEM is further extended to a more general case, n-sided polygonal edge-based smoothed finite element method (nES-FEM), in which the problem domain can be discretized by a set of polygons, each with an arbitrary number of sides. The simple averaging point interpolation method is suggested to construct nES-FEM shape functions. In addition, a novel domain-based selective scheme of a combined nES/NS-FEM model is also proposed to avoid volumetric locking. Several numerical examples are investigated and the results of the nES-FEM are found to agree well with exact solutions and are much better than those of others existing methods. Copyright q 2010 John Wiley & Sons, Ltd.
TL;DR: In this paper, the Lax-Wendroff method (LWM) and the interior-penalty discontinuous Galerkin method (IP-DGM) were investigated for time stepping.
Abstract: SUMMARY
We investigate the stability of some high-order finite element methods, namely the spectral element method and the interior-penalty discontinuous Galerkin method (IP-DGM), for acoustic or elastic wave propagation that have become increasingly popular in the recent past. We consider the Lax-Wendroff method (LWM) for time stepping and show that it allows for a larger time step than the classical leap-frog finite difference method, with higher-order accuracy. In particular the fourth-order LWM allows for a time step 73 per cent larger than that of the leap-frog method; the computational cost is approximately double per time step, but the larger time step partially compensates for this additional cost. Necessary, but not sufficient, stability conditions are given for the mentioned methods for orders up to 10 in space and time. The stability conditions for IP-DGM are approximately 20 and 60 per cent more restrictive than those for SEM in the acoustic and elastic cases, respectively.
TL;DR: In this article, a dual mortar contact formulation is proposed for finite deformation contact of flexible solids embedded in fluid flows, which can capture flow patterns around contacting structures very accurately as well as simulate dry contact between structures.
Abstract: Finite deformation contact of flexible solids embedded in fluid flows occurs in a wide range of engineering scenarios. We propose a novel three-dimensional finite element approach in order to tackle this problem class. The proposed method consists of a dual mortar contact formulation, which is algorithmically integrated into an eXtended finite element method (XFEM) fluid–structure interaction approach. The combined XFEM fluid–structure-contact interaction method (FSCI) allows to compute contact of arbitrarily moving and deforming structures embedded in an arbitrary flow field. In this paper, the fluid is described by instationary incompressible Navier–Stokes equations. An exact fluid–structure interface representation permits to capture flow patterns around contacting structures very accurately as well as to simulate dry contact between structures. No restrictions arise for the structural and the contact formulation. We derive a linearized monolithic system of equations, which contains the fluid formulation, the structural formulation, the contact formulation as well as the coupling conditions at the fluid–structure interface. The linearized system may be solved either by partitioned or by monolithic fluid–structure coupling algorithms. Two numerical examples are presented to illustrate the capability of the proposed fluid–structure-contact interaction approach.
TL;DR: An overview of adaptive discretization methods for linear second-order hyperbolic problems such as the acoustic or the elastic wave equation is given, which also includes variants of the Crank-Nicolson and the Newmark finite difference schemes.
Abstract: Abstract This paper gives an overview of adaptive discretization methods for linear second-order hyperbolic problems such as the acoustic or the elastic wave equation. The emphasis is on Galerkin-type methods for spatial as well as temporal discretization, which also include variants of the Crank-Nicolson and the Newmark finite difference schemes. The adaptive choice of space and time meshes follows the principle of \\goaloriented\" adaptivity which is based on a posteriori error estimation employing the solutions of auxiliary dual problems.