Showing papers on "Finite element method published in 1999"

A finite element method for crack growth without remeshing

Abstract: SUMMARY An improvement of a new technique for modelling cracks in the nite element framework is presented. A standard displacement-based approximation is enriched near a crack by incorporating both discontinuous elds and the near tip asymptotic elds through a partition of unity method. A methodology that constructs the enriched approximation from the interaction of the crack geometry with the mesh is developed. This technique allows the entire crack to be represented independently of the mesh, and so remeshing is not necessary to model crack growth. Numerical experiments are provided to demonstrate the utility and robustness of the proposed technique. Copyright ? 1999 John Wiley & Sons, Ltd.

Elastic crack growth in finite elements with minimal remeshing

Abstract: A minimal remeshing finite element method for crack growth is presented. Discontinuous enrichment functions are added to the finite element approximation to account for the presence of the crack. This method allows the crack to be arbitrarily aligned within the mesh. For severely curved cracks, remeshing may be needed but only away from the crack tip where remeshing is much easier. Results are presented for a wide range of two-dimensional crack problems showing excellent accuracy. Copyright © 1999 John Wiley & Sons, Ltd.

Slope stability analysis by finite elements

Abstract: The majority of slope stability analyses performed in practice still use traditional limit equilibrium approaches involving methods of slices that have remained essentially unchanged for decades. This was not the outcome envisaged when Whitman & Bailey (1967) set criteria for the then emerging methods to become readily accessible to all engineers. The finite element method represents a powerful alternative approach for slope stability analysis which is accurate, versatile and requires fewer a priori assumptions, especially, regarding the failure mechanism. Slope failure in the finite element model occurs 'naturally' through the zones in which the shear strength of the soil is insufficient to resist the shear stresses. The paper describes several examples of finite element slope stability analysis with comparison against other solution methods, including the influence of a free surface on slope and dam stability. Graphical output is included to illustrate deformations and mechanisms of failure. It is argue...

Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis

Abstract: SUMMARY We develop a three-dimensional nite-deformation cohesive element and a class of irreversible cohesive laws which enable the accurate and ecient tracking of dynamically growing cracks. The cohesive element governs the separation of the crack anks in accordance with an irreversible cohesive law, eventually leading to the formation of free surfaces, and is compatible with a conventional nite element discretization of the bulk material. The versatility and predictive ability of the method is demonstrated through the simulation of a drop-weight dynamic fracture test similar to those reported by Zehnder and Rosakis. 1 The ability of the method to approximate the experimentally observed crack-tip trajectory is particularly noteworthy. Copyright ? 1999 John Wiley & Sons, Ltd.

Introduction to the spectral element method for three-dimensional seismic wave propagation

Abstract: SUMMARY We present an introduction to the spectral element method, which provides an innovative numerical approach to the calculation of synthetic seismograms in 3-D earth models. The method combines the £exibility of a ¢nite element method with the accuracy of a spectral method. One uses a weak formulation of the equations of motion, which are solved on a mesh of hexahedral elements that is adapted to the free surface and to the main internal discontinuities of the model. The wave¢eld on the elements is discretized using high-degree Lagrange interpolants, and integration over an element is accomplished based upon the Gauss^Lobatto^Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix, which greatly simpli¢es the algorithm. We illustrate the great potential of the method by comparing it to a discrete wavenumber/re£ectivity method for layer-cake models. Both body and surface waves are accurately represented, and the method can handle point force as well as moment tensor sources. For a model with very steep surface topography we successfully benchmark the method against an approximate boundary technique. For a homogeneous medium with strong attenuation we obtain excellent agreement with the analytical solution for a point force.

Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics

Abstract: This definitive introduction to finite element methods was thoroughly updated for this 2007 third edition, which features important material for both research and application of the finite element method. The discussion of saddle-point problems is a highlight of the book and has been elaborated to include many more nonstandard applications. The chapter on applications in elasticity now contains a complete discussion of locking phenomena. The numerical solution of elliptic partial differential equations is an important application of finite elements and the author discusses this subject comprehensively. These equations are treated as variational problems for which the Sobolev spaces are the right framework. Graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite element methods will find this text invaluable. Specifically, the chapter on finite elements in solid mechanics provides a bridge between mathematics and engineering.

Real-time elastic deformations of soft tissues for surgery simulation

Abstract: We describe a novel method for surgery simulation including a volumetric model built from medical images and an elastic modeling of the deformations. The physical model is based on elasticity theory which suitably links the shape of deformable bodies and the forces associated with the deformation. A real time computation of the deformation is possible thanks to a preprocessing of elementary deformations derived from a finite element method. This method has been implemented in a system including a force feedback device and a collision detection algorithm. The simulator works in real time with a high resolution liver model.

P- and hp- finite element methods : theory and applications in solid and fluid mechanics

Abstract: Variational formulation of boundary value problems The Finite Element Method (FEM): definition, basic properties hp- Finite Elements in one dimension hp- Finite Elements in two dimensions Finite Element analysis of saddle point problems, mixed hp-FEM in incompressible fluid flow hp-FEM in the theory of elasticity

The Mortar finite element method with Lagrange multipliers

Abstract: The present paper deals with a variant of a non conforming domain decomposition technique: the mortar finite element method. In the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices (and the edges in 3D) of subdomains. It is shown that, written under primal hybrid formulation, the approximation problem, issued from a discretization of a second order elliptic equation in 2D, is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms. Finally the parallelization advantages consequence of this variant are also addressed.

An adaptive finite element approach to atomic-scale mechanics—the quasicontinuum method

Abstract: Mixed atomistic and continuum methods offer the possibility of carrying out simulations of material properties at both larger length scales and longer times than direct atomistic calculations. The quasicontinuum method links atomistic and continuum models through the device of the finite element method which permits a reduction of the full set of atomistic degrees of freedom. The present paper gives a full description of the quasicontinuum method, with special reference to the ways in which the method may be used to model crystals with more than a single grain. The formulation is validated in terms of a series of calculations on grain boundary structure and energetics. The method is then illustrated in terms of the motion of a stepped twin boundary where a critical stress for the boundary motion is calculated and nanoindentation into a solid containing a subsurface grain boundary to study the interaction of dislocations with grain boundaries.

The nature of mathematical modeling

Abstract: Preface 1. Introduction Part I. Analytical Models: 2. Ordinary differential and difference equations 3. Partial differential equations 4. Variational principles 5. Random systems Part II. Numerical Models: 6. Finite differences: ordinary difference equations 7. Finite differences: partial differential equations 8. Finite elements 9. Cellular automata and lattice gases Part III. Observational Models: 10. Function fitting 11. Transforms 12. Architectures 13. Optimization and search 14. Clustering and density estimation 15. Filtering and state estimation 16. Linear and nonlinear time series Appendix 1. Graphical and mathematical software Appendix 2. Network programming Appendix 3. Benchmarking Appendix 4. Problem solutions Bibliography.

Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients

Abstract: We propose a multiscale finite element method for solving second order elliptic equations with rapidly oscillating coefficients. The main purpose is to design a numerical method which is capable of correctly capturing the large scale components of the solution on a coarse grid without accurately resolving all the small scale features in the solution. This is accomplished by incorporating the local microstructures of the differential operator into the finite element base functions. As a consequence, the base functions are adapted to the local properties of the differential operator. In this paper, we provide a detailed convergence analysis of our method under the assumption that the oscillating coefficient is of two scales and is periodic in the fast scale. While such a simplifying assumption is not required by our method, it allows us to use homogenization theory to obtain a useful asymptotic solution structure. The issue of boundary conditions for the base functions will be discussed. Our numerical experiments demonstrate convincingly that our multiscale method indeed converges to the correct solution, independently of the small scale in the homogenization limit. Application of our method to problems with continuous scales is also considered.

Modeling elastic wave propagation in waveguides with the finite element method

Abstract: This paper reports on the application of guided waves techniques to nondestructively determine the structural integrity of engineering components. Specifically, this research uses a commercial finite element (FE) code to study the propagation characteristics of ultrasonic waves in annular structures. In order to demonstrate the accuracy of the proposed FE technique, the propagation of guided waves in a flat plate is examined first. Next, the propagation of guided waves in thick ring structures is investigated. Finally, these FE results are compared to analytical and experimental results. The results of this study clearly illustrate the effectiveness of using the FE method to model guided wave propagation problems and demonstrate the potential of the FE method for problems when an analytical solution is not possible because of “complicated” component geometry.

Finite element analysis in geotechnical engineering : theory

Abstract: This book aims to provide geotechnical and structural engineering practitioners, researchers and postgraduate students with an insight into the use of finite element methods in geotechnical contexts, in order that they might make good judgements as to the credibility of the numerical results they may obtain or review in the future. The contents of the chapters are geotechnical analysis, finite element theory for linear materials, geotechnical considerations, real soil behaviour, elastic constitutive models, elasto-plastic constitutive models, advanced constitutive models, finite element theory for non-linear materials, seepage and consolidation, three-dimensional finite element analysis, and fourier series aided finite element method. The book is primarily aimed at users of commercial finite element software both in industry and academia.

A progressive Damage Model for Mechanically Fastened Joints in Composite Laminates

Abstract: A three-dimensional finite element model is developed to predict damage progression and strength of mechanically fastened joints in carbon fibre-reinforced plastics that fail in the bearing, tension and shear-out modes. The model is based on a three-dimensional finite element model, on a three-dimensional failure criterion and on a constitutive equation that takes into account the effects of damage on the material elastic properties. This is accomplished using internal state variables that are functions of the type of damage. This formulation is used together with a global failure criterion to predict the ultimate strength of the joint. Experimental results concerning damage progression, joint stiffness and strength are obtained and compared with the predictions. A good agreement between experimental results and numerical predictions is obtained.

Plasticity: Mathematical Theory and Numerical Analysis

Abstract: Preface to the Second Edition.- Preface to the First Edition.-Preliminaries.- Continuum Mechanics and Linearized Elasticity.- Elastoplastic Media.- The Plastic Flow Law in a Convex-Analytic Setting.- Basics of Functional Analysis and Function Spaces.- Variational Equations and Inequalities.- The Primal Variational Problem of Elastoplasticity.- The Dual Variational Problem of Classical Elastoplasticity.- Introduction to Finite Element Analysis.- Approximation of Variational Problems.- Approximations of the Abstract Problem.- Numerical Analysis of the Primal Problem.- References.- Index.-

The nature of mathematical modeling

Abstract: Preface 1. Introduction Part I. Analytical Models: 2. Ordinary differential and difference equations 3. Partial differential equations 4. Variational principles 5. Random systems Part II. Numerical Models: 6. Finite differences: ordinary difference equations 7. Finite differences: partial differential equations 8. Finite elements 9. Cellular automata and lattice gases Part III. Observational Models: 10. Function fitting 11. Transforms 12. Architectures 13. Optimization and search 14. Clustering and density estimation 15. Filtering and state estimation 16. Linear and nonlinear time series Appendix 1. Graphical and mathematical software Appendix 2. Network programming Appendix 3. Benchmarking Appendix 4. Problem solutions Bibliography.

Hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements

Abstract: New vector finite elements are proposed for electromagnetics. The new elements are triangular or tetrahedral edge elements (tangential vector elements) of arbitrary polynomial order. They are hierarchal, so that different orders can be used together in the same mesh and p-adaption is possible. They provide separate representation of the gradient and rotational parts of the vector field. Explicit formulas are presented for generating the basis functions to arbitrary order. The basis functions can be used directly or after a further stage of partial orthogonalization to improve the matrix conditioning. Matrix assembly for the frequency-domain curl-curl equation is conveniently carried out by means of universal matrices. Application of the new elements to the solution of a parallel-plate waveguide problem demonstrates the expected convergence rate of the phase of the reflection coefficient, for tetrahedral elements to order 4. In particular, the full-order elements have only the same asymptotic convergence rate as elements with a reduced gradient space (such as the Whitney element). However, further tests reveal that the optimum balance of the gradient and rotational components is problem-dependent.

Computational Geomechanics with Special Reference to Earthquake Engineering

Abstract: The Basic Equations. Finite Element Discretization. Error Control in Time and Space. Constitutive Relations. Identification of Model Parameters. Static and Quasi--Static Solution. Validation of Prediction by Centrifuge. Prediction Applications and Back Analysis. Multiphase Examples.

Numerical integration of the Galerkin weak form in meshfree methods

Abstract: The numerical integration of Galerkin weak forms for meshfree methods is investigated and some improvements are presented. The character of the shape functions in meshfree methods is reviewed and compared to those used in the Finite Element Method (FEM). Emphasis is placed on the relationship between the supports of the shape functions and the subdomains used to integrate the discrete equations. The construction of quadrature cells without regard to the local supports of the shape functions is shown to result in the possibility of considerable integration error. Numerical studies using the meshfree Element Free Galerkin (EFG) method illustrate the effect of these errors on solutions to elliptic problems. A construct for integration cells which reduces quadrature error is presented. The observations and conclusions apply to all Galerkin methods which use meshfree approximations.

A general framework for the analysis and design of tubular linear permanent magnet machines

Abstract: A general framework for the analysis and design of a class of tubular linear permanent magnet machines is described. The open-circuit and armature reaction magnetic field distributions are established analytically in terms of a magnetic vector potential and cylindrical coordinate formulation, and the results are validated extensively by comparison with finite element analyses. The analytical field solutions allow the prediction of the thrust force, the winding emf, and the self- and mutual-winding inductances in closed forms. These facilitate the characterization of tubular machine topologies and provide a basis for comparative studies, design optimization, and machine dynamic modeling. Some practical issues, such as the effects of slotting and fringing, have also been accounted for and validated by measurements.