Showing papers on "Smoothed finite element method published in 2008"
TL;DR: The performance of finite element methods for dynamic crack propagation in brittle materials is studied in this paper, where three methods are considered: the extended finite element method (XFEM), element deletion method and interelement crack method.
Abstract: The performance of finite element methods for dynamic crack propagation in brittle materials is studied. Three methods are considered: the extended finite element method (XFEM), element deletion method and interelement crack method. The extended finite element method is a method for arbitrary crack propagation without remeshing. In element deletion methods, elements that meet a fracture criterion are deleted. In interelement crack methods, the crack is limited to element edges; the separation of these edges is governed by a cohesive law. We show that XFEM and interelement method show similar crack speeds and crack paths. However, both fail to predict a benchmark experiment without adjustment of the energy release rate. The element deletion method performs very poorly for the refinements studied, and is unable to predict crack branching.
361 citations
TL;DR: In this paper, a quadrilateral element with smoothed curvatures for Mindlin-Reissner plates is proposed, where the curvature at each point is obtained by a non-local approximation via a smoothing function.
360 citations
TL;DR: This paper presents a generalized gradient smoothing technique, the corresponding smoothed bilinear forms, and the smoothed Galerkin weakform that is applicable to create a wide class of efficient numerical methods with special properties including the upper bound properties.
Abstract: This paper presents a generalized gradient smoothing technique, the corresponding smoothed bilinear forms, and the smoothed Galerkin weakform that is applicable to create a wide class of efficient numerical methods with special properties including the upper bound properties. A generalized gradient smoothing technique is first presented for computing the smoothed strain fields of displacement functions with discontinuous line segments, by "rudely" enforcing the Green's theorem over the smoothing domain containing these discontinuous segments. A smoothed bilinear form is then introduced for Galerkin formulation using the generalized gradient smoothing technique and smoothing domains constructed in various ways. The numerical methods developed based on this smoothed bilinear form will be spatially stable and convergent and possess three major important properties: (1) it is variationally consistent, if the solution is sought in a Hilbert space; (2) the stiffness of the discretized model will be reduced comp...
350 citations
TL;DR: In this article, the SUPG method, a SOLD method and two types of FEM-FCT methods are compared with a 3D example with nonhomogeneous Dirichlet boundary conditions and homogeneous Neumann boundary conditions.
207 citations
TL;DR: In this article, the authors present an overview and recent progress of the extended finite element method X-FEM in the analysis of crack growth modeling, and summarize the important milestones achieved by the finite element community in the arena of computational fracture mechanics.
200 citations
TL;DR: It is shown that the present explicit finite element scheme is well suited to solution via highly parallel graphics hardware, and that even a midrange GPU allows significant solution speed gains compared with equivalent CPU implementations.
Abstract: The use of biomechanical modelling, especially in conjunction with finite element analysis, has become common in many areas of medical image analysis and surgical simulation. Clinical employment of such techniques is hindered by conflicting requirements for high fidelity in the modelling approach, and fast solution speeds. We report the development of techniques for high-speed nonlinear finite element analysis for surgical simulation. We use a fully nonlinear total Lagrangian explicit finite element formulation which offers significant computational advantages for soft tissue simulation. However, the key contribution of the work is the presentation of a fast graphics processing unit (GPU) solution scheme for the finite element equations. To the best of our knowledge, this represents the first GPU implementation of a nonlinear finite element solver. We show that the present explicit finite element scheme is well suited to solution via highly parallel graphics hardware, and that even a midrange GPU allows significant solution speed gains (up to 16.8 times) compared with equivalent CPU implementations. For the models tested the scheme allows real-time solution of models with up to 16 000 tetrahedral elements. The use of GPUs for such purposes offers a cost-effective high-performance alternative to expensive multi-CPU machines, and may have important applications in medical image analysis and surgical simulation.
187 citations
TL;DR: The FEM in dentistry recently focused on simulation of realistic intra-oral conditions such as the nonlinear stress-strain relationship in the periodontal tissues and the contact phenomena in teeth, which could hardly be solved by the linear static model.
148 citations
TL;DR: In this article, a stabilized conforming nodal integration finite element method based on strain smoothing stabilization is presented, where the integration of the stiffness matrix is performed on the boundaries of the finite elements.
Abstract: A stabilized conforming nodal integration finite element method based on strain smoothing stabilization is presented. The integration of the stiffness matrix is performed on the boundaries of the finite elements. A rigorous variational framework based on the Hu–Washizu assumed strain variational form is developed.
We prove that solutions yielded by the proposed method are in a space bounded by the standard, finite element solution (infinite number of subcells) and a quasi-equilibrium finite element solution (a single subcell). We show elsewhere the equivalence of the one-subcell element with a quasi-equilibrium finite element, leading to a global a posteriori error estimate.
We apply the method to compressible and incompressible linear elasticity problems. The method can always achieve higher accuracy and convergence rates than the standard finite element method, especially in the presence of incompressibility, singularities or distorted meshes, for a slightly smaller computational cost.
It is shown numerically that the one-cell smoothed four-noded quadrilateral finite element has a convergence rate of 2.0 in the energy norm for problems with smooth solutions, which is remarkable. For problems with rough solutions, this element always converges faster than the standard finite element and is free of volumetric locking without any modification of integration scheme. Copyright © 2007 John Wiley & Sons, Ltd.
144 citations
TL;DR: Both uniform convergence and optimal complexity of the adaptive finite element eigenvalue approximation are proved.
Abstract: In this paper, an adaptive finite element method for elliptic eigenvalue problems is studied. Both uniform convergence and optimal complexity of the adaptive finite element eigenvalue approximation are proved. The analysis is based on a certain relationship between the finite element eigenvalue approximation and the associated finite element boundary value approximation which is also established in the paper.
140 citations
TL;DR: In this paper, a smoothed finite element method (SFEM) is presented to analyze linear and geo- metrically nonlinear problems of plates and shells using bilinear quadrilateral elements.
Abstract: A smoothed finite element method (SFEM) is presented to analyze linear and geo- metrically nonlinearproblems of plates and shells using bilinear quadrilateral elements The formu- lationis based on thefirst order shear deformation theory In the present SFEM, the elements are fur- therdividedintosmoothingcells toperform strain smoothingoperation,andthestrainenergy ineach smoothing cell is expressed as an explicit form of the smoothed strain The effect of the number of divisionsofsmoothingcellsinelements isinvesti- gatedindetail Itisfoundthatusingthreesmooth- ing cells for bending strain energy integrationand one smoothing cell for shear strain energy inte- gration achieve most accurate results and hence these numbers recommended for plates and shells in this study In the geometrically nonlinear anal- ysis, the total Lagrangian approach is adopted The arc-length technique in conjunction with the modified Newton-Raphson method is utilized to solve the nonlinear equations The numerical ex- amples demonstrate that the present SFEM pro- vides very stable and most accurate results with the similar computational effort compared to the existing FEM techniques tested in this work
117 citations
13 Jun 2008
TL;DR: The method is described in general terms, the basic formulation is presented, and some issues regarding effective finite element procedures are summarized.
Abstract: The objective of this article is to give an overview of finite element methods that currently are used extensively in academia and industry. The method is described in general terms, the basic formulation is presented, and some issues regarding effective finite element procedures are summarized. Various applications are given briefly to illustrate the current use of the method. Finally, the article concludes with key challenges for the additional development of the method.
Keywords:
finite elements;
reliability and effectiveness;
solids;
structures;
statics and dynamics;
CFD;
CAE;
computer programs
Book•
17 Oct 2008TL;DR: A quick review of numerical methods for PDEs Finite Difference Methods for Parabolic Equations and Finite Element Methods for Electromagnetics.
Abstract: Brief Overview of Partial Differential Equations The parabolic equations The wave equations The elliptic equations Differential equations in broader areas A quick review of numerical methods for PDEs Finite Difference Methods for Parabolic Equations Introduction Theoretical issues: stability, consistence, and convergence 1-D parabolic equations 2-D and 3-D parabolic equations Numerical examples with MATLAB codes Finite Difference Methods for Hyperbolic Equations Introduction Some basic difference schemes Dissipation and dispersion errors Extensions to conservation laws The second-order hyperbolic PDEs Numerical examples with MATLAB codes Finite Difference Methods for Elliptic Equations Introduction Numerical solution of linear systems Error analysis with a maximum principle Some extensions Numerical examples with MATLAB codes High-Order Compact Difference Methods 1-D problems High-dimensional problems Other high-order compact schemes Finite Element Methods: Basic Theory Introduction to 1-D problems Introduction to 2-D problems Abstract finite element theory Examples of conforming finite element spaces Examples of nonconforming finite elements Finite element interpolation theory Finite element analysis of elliptic problems Finite element analysis of time-dependent problems Finite Element Methods: Programming Finite element method mesh generation Forming finite element method equations Calculation of element matrices Assembly and implementation of boundary conditions The MATLAB code for P1 element The MATLAB code for the Q1 element Mixed Finite Element Methods An abstract formulation Mixed methods for elliptic problems Mixed methods for the Stokes problem An example MATLAB code for the Stokes problem Mixed methods for viscous incompressible flows Finite Element Methods for Electromagnetics Introduction to Maxwell's equations The time-domain finite element method The frequency-domain finite element method Maxwell's equations in dispersive media Meshless Methods with Radial Basis Functions Introduction The radial basis functions The MFS-DRM Kansa's method Numerical examples with MATLAB codes Coupling RBF meshless methods with DDM Other Meshless Methods Construction of meshless shape functions The element-free Galerkin method The meshless local Petrov-Galerkin method Answers to Selected Problems Index Bibliographical remarks, Exercises, and References appear at the end of each chapter.
TL;DR: Some strategies are proposed for the enrichment of low order mixed finite element approximations in the incompressible setting and for well chosen enrichment strategies, the finite element convergence rate is preserved and the inf–sup condition is passed.
TL;DR: In this paper, a new concurrent simulation technique was developed to couple the meshfree method with the finite element method (FEM) for the analysis of crack tip fields, which can take advantage of both the mesh-free method and FEM but at the same time can overcome their shortcomings.
TL;DR: In this paper, the authors present a finite element approximation of the scalar hyperbolic wave equation written in mixed form, that is, introducing an auxiliary vector field to transform the problem into a first-order problem in space and time.
TL;DR: It is proved convergence and optimal complexity of an adaptive mixed finite element algorithm, based on the lowest-order Raviart–Thomas finite element space, is proved.
Abstract: We prove convergence and optimal complexity of an adaptive mixed finite element algorithm, based on the lowest-order Raviart–Thomas finite element space. In each step of the algorithm, the local refinement is either performed using simple edge residuals or a data oscillation term, depending on an adaptive marking strategy. The inexact solution of the discrete system is controlled by an adaptive stopping criterion related to the estimator.
TL;DR: In this paper, different combinations of finite difference methods and finite element methods are used to numerically solve the elastodynamic wave equations and the computational advantages and disadvantages of the different numerical algorithms are discussed.
01 Jan 2008
TL;DR: In this paper, the authors consider a body force f acting on a linearly elastic body which occupies a region Ω ⊂ R, with boundary ∂Ω.
Abstract: Here the unknowns σ and u denote the stress and displacement fields caused by a body force f acting on a linearly elastic body which occupies a region Ω ⊂ R, with boundary ∂Ω. Then σ takes values in the space S = Rn×n sym of symmetric n × n matrices and u takes values in V = R. The differential operator ε is the symmetric part of the gradient, (i.e., (εu)ij = (∂ui/∂xj +∂uj/∂xi)/2), div denotes the divergence operator, applied row-wise, and the compliance tensor A = A(x) : S → S is a bounded and symmetric, uniformly positive definite operator reflecting the properties of the material at each point. In the isotropic case, the mapping σ 7→ Aσ has the form
TL;DR: In this paper, the authors present advances in the discrete element modelling of underground excavation processes extending modelling possibilities as well as increasing computational efficiency using techniques of parallel computing and coupling discrete element method with finite element method.
Abstract: The paper presents advances in the discrete element modelling of underground excavation processes extending modelling possibilities as well as increasing computational efficiency. Efficient numerical models have been obtained using techniques of parallel computing and coupling the discrete element method with finite element method. The discrete element algorithm has been applied to simulation of different excavation processes, using different tools, TBMs and roadheaders. Numerical examples of tunnelling process are included in the paper, showing results in the form of rock failure, damage in the material, cutting forces and tool wear. Efficiency of the code for solving large scale geomechanical problems is also shown.
TL;DR: In this article, the authors compared the dynamic responses of finite element analyses and field experiments and showed that the bridge model is more important than the vehicle model in simulating train-bridge interaction problems.
TL;DR: In this paper, a smoothed four-node piezoelectric element is built by incorporating the strain smoothing method of mesh-free conforming nodal integration into the standard 4-node quadrilateral finite element, which allows the field gradients to be directly computed from shape functions.
Abstract: This paper reports a study of linear elastic analysis of two-dimensional piezoelectric structures using a smoothed four-node piezoelectric element. The element is built by incorporating the strain smoothing method of mesh-free conforming nodal integration into the standard four-node quadrilateral piezoelectric finite element. The approximations of mechanical strains and electric potential fields are normalized using a constant smoothing function. This allows the field gradients to be directly computed from shape functions. No mapping or coordinate transformation is necessary so that the element can be used in arbitrary shapes. Through several examples, the simplicity, efficiency and reliability of the element are demonstrated. Numerical results and comparative studies with
other existing solutions in the literature suggest that the present element is robust, computationally inexpensive and easy to implement.
TL;DR: In this paper, the frequency and time-domain finite element analysis of complex antennas and arrays is discussed, and numerical approaches to modeling infinite phased arrays, large finite arrays, and antenna-platform interaction are presented.
Abstract: Various technical issues are addressed in the frequency- and time-domain finite element analysis of complex antennas and arrays that may consist of fine structures and composite materials. The paper starts with the finite element formulation of a generic antenna problem. Formulation for the modeling of general electrically and magnetically dispersive, lossy, and anisotropic materials in the time-domain finite element analysis is presented for the first time. This is followed by discussion of three typical techniques for truncation of the finite element computational domain via the use of absorbing boundary conditions, perfectly matched layers, and boundary integral equations. It then describes the modeling of antenna feeds using a current probe (including an improved model), a voltage gap, and a waveguide port boundary condition. After that, numerical approaches to modeling infinite phased arrays, large finite arrays, and antenna-platform interaction are presented, including two novel domain decomposition algorithms in both the frequency and time domains. Numerical examples are given to demonstrate the capability and application of the finite element analysis of a variety of complex antennas and arrays.
TL;DR: Non‐overlapping domain decomposition techniques are used to solve the finite element equations and to couple them with a boundary element method and it is shown how to choose the parameter defining the augmented local matrices in order to improve the convergence.
Abstract: Non-overlapping domain decomposition techniques are used to solve the finite element equations and to couple them with a boundary element method. A suitable approach dealing with finite element nodes common to more than two subdomains, the so-called cross-points, endows the method with the following advantages. It yields a robust and efficient procedure to solve the equations resulting from the discretization process. Only small size finite element linear systems and a dense linear system related to a simple boundary integral equation are solved at each iteration and each of them can be solved in a stable way. We also show how to choose the parameter defining the augmented local matrices in order to improve the convergence. Several numerical simulations in 2D and 3D validating the treatment of the cross-points and illustrating the strategy to accelerate the iterative procedure are presented.
TL;DR: The FE-LSPIM QUAD4 element as discussed by the authors uses new shape functions that combine the meshfree and finite element shape functions so as to synergize the individual strengths of mesh free and finite elements methods.
01 Jan 2008
TL;DR: The Selective Approach method is a new procedure that combines two diverse methodologies to create an efficient and robust algorithm able to handle concave refinement regions and self-intersecting hex sheets.
Abstract: Hexahedral refinement increases the density of an all-hexahedral mesh in a specified region, improving numerical accuracy. Previous research using solely sheet refinement theory made the implementation computationally expensive and unable to effectively handle concave refinement regions and self-intersecting hex sheets. The Selective Approach method is a new procedure that combines two diverse methodologies to create an efficient and robust algorithm able to handle the above stated problems. These two refinement methods are: 1) element by element refinement and 2) directional refinement. In element by element refinement, the three inherent directions of a Hex are refined in one step using one of seven templates. Because of its computational superiority over directional refinement, but its inability to handle concavities, element by element refinement is used in all areas of the specified region except regions local to concavities. The directional refinement scheme refines the three inherent directions of a hexahedron separately on a hex by hex basis. This differs from sheet refinement which refines hexahedra using hex sheets. Directional refinement is able to correctly handle concave refinement regions. A ranking system and propagation scheme allow directional refinement to work within the confines of the Selective Approach Algorithm.
07 May 2008
TL;DR: In this paper, a three-dimensional finite element method is proposed and used to deal with large-scale nonlinear contact friction problems in deformable rocks, together with the use of the node-to-point contact element strategy.
Abstract: A three-dimensional finite element method is proposed and used to deal with large-scale nonlinear contact friction problems in deformable rocks. Together with the use of the node-to-point contact element strategy, the corresponding three-dimensional finite element algorithm is presented to simulate the nonlinear contact friction behaviour between deformable rock blocks. In order to ensure the correctness and accuracy of the resulting numerical solutions, the proposed finite element formulation for a three-dimensional nonlinear contact friction problem is verified using a benchmark problem, for which the analytical solution is available. As an application example, the proposed three-dimensional finite element method is used to investigate the plate behaviour of a subduction fault model, which simulates a region around Northeast Japan. Due to the general nature of the methodology, the proposed three-dimensional finite element algorithm can be also used to simulate many nonlinear contact friction problems associated with the slope instability process and the sliding failure mechanism between a gravity dam and its foundation in the engineering field.
TL;DR: In this paper, the authors developed a simulation tool for soil-tire interaction analysis, where finite element method and discrete element method (DEM) are coupled together, and which can be realized on a desktop PC.
Abstract: The goal of this study is to develop a practical and fast simulation tool for soil-tire interaction analysis, where finite element method (FEM) and discrete element method (DEM) are coupled together, and which can be realized on a desktop PC. We have extended our formerly proposed dynamic FE-DE method (FE-DEM) to include practical soil-tire system interaction, where not only the vertical sinkage of a tire, but also the travel of a driven tire was considered. Numerical simulation by FE-DEM is stable, and the relationships between variables, such as load-sinkage and sinkage-travel distance, and the gross tractive effort and running resistance characteristics, are obtained. Moreover, the simulation result is accurate enough to predict the maximum drawbar pull for a given tire, once the appropriate parameter values are provided. Therefore, the developed FE-DEM program can be applied with sufficient accuracy to interaction problems in soil-tire systems.