Showing papers on "Finite element method published in 1995"
Book•
26 Jun 1995
TL;DR: The Finite Element Method as mentioned in this paper is a method for linear analysis in solid and structural mechanics, and it has been used in many applications, such as heat transfer, field problems, and Incompressible Fluid Flows.
Abstract: 1. An Introduction to the Use of Finite Element Procedures. 2. Vectors, Matrices and Tensors. 3. Some Basic Concepts of Engineering Analysis and an Introduction to the Finite Element Methods. 4. Formulation of the Finite Element Method -- Linear Analysis in Solid and Structural Mechanics. 5. Formulation and Calculation of Isoparametric Finite Element Matrices. 6. Finite Element Nonlinear Analysis in Solid and Structural Mechanics. 7. Finite Element Analysis of Heat Transfer, Field Problems, and Incompressible Fluid Flows. 8. Solution of Equilibrium Equations in State Analysis. 9. Solution of Equilibrium Equations in Dynamic Analysis. 10. Preliminaries to the Solution of Eigenproblems. 11. Solution Methods for Eigenproblems. 12. Implementation of the Finite Element Method. References. Index.
8,068 citations
Book•
31 Mar 1995
TL;DR: A comparison of Numerical Data with Test Results and Iterative Methods Using Modal Data for Model Updating shows that the former is more accurate than the latter.
Abstract: Preface. 1. Introduction. 2. Finite Element Modelling. 3. Vibration Testing. 4. Comparing Numerical Data with Test Results. 5. Estimation Techniques. 6. Parameters for Model Updating. 7. Direct Methods Using Modal Data. 8. Iterative Methods Using Modal Data. 9. Methods Using Frequency Domain Data. 10. Case Study: an Automobile Body M. Brughmans, J. Leuridan, K. Blauwkamp. 11. Discussion and Recommendations. Index.
2,177 citations
TL;DR: Numerical and theoretical results show the proposed reproducing kernel interpolation functions satisfy the consistency conditions and the critical time step prediction; furthermore, the RKPM provides better stability than Smooth Particle Hydrodynamics (SPH) methods.
Abstract: This paper explores a Reproducing Kernel Particle Method (RKPM) which incorporates several attractive features. The emphasis is away from classical mesh generated elements in favour of a mesh free system which only requires a set of nodes or particles in space. Using a Gaussian function or a cubic spline function, flexible window functions are implemented to provide refinement in the solution process. It also creates the ability to analyse a specific frequency range in dynamic problems reducing the computer time required. This advantage is achieved through an increase in the critical time step when the frequency range is low and a large window is used. The stability of the window function as well as the critical time step formula are investigated to provide insight into RKPMs. The predictions of the theories are confirmed through numerical experiments by performing reconstructions of given functions and solving elastic and elastic–plastic one-dimensional (1-D) bar problems for both small and large deformation as well as three 2-D large deformation non-linear elastic problems. Numerical and theoretical results show the proposed reproducing kernel interpolation functions satisfy the consistency conditions and the critical time step prediction; furthermore, the RKPM provides better stability than Smooth Particle Hydrodynamics (SPH) methods. In contrast with what has been reported in SPH literature, we do not find any tensile instability with RKPMs.
794 citations
TL;DR: It is demonstrated that a variety of boundary conditions stipulated on the Radiative Transfer Equation can be implemented in a FEM approach, as well as the specification of a light source by a Neumann condition rather than an isotropic point source.
Abstract: This paper extends our work on applying the Finite Element Method (FEM) to the propagation of light in tissue. We address herein the topics of boundary conditions and source specification for this method. We demonstrate that a variety of boundary conditions stipulated on the Radiative Transfer Equation can be implemented in a FEM approach, as well as the specification of a light source by a Neumann condition rather than an isotropic point source. We compare results for a number of different combinations of boundary and source conditions under FEM, as well as the corresponding cases in a Monte Carlo model.
642 citations
TL;DR: In this paper, the authors studied the properties of finite element solutions for the Helmholtz equation with piecewise linear approximation. And they showed that the error in H 1 -norm of discrete solutions is polluted when k 2 h is not small, i.e., the relation of the FE-error to the best approximation generally depends on the wavenumber k.
Abstract: The paper addresses the properties of finite element solutions for the Helmholtz equation. The h-version of the finite element method with piecewise linear approximation is applied to a one-dimensional model problem. New results are shown on stability and error estimation of the discrete model. In all propositions, assumptions are made on the magnitude of hk only, where k is the wavelength and h is the stepwidth of the FE-mesh. Previous analytical results had been shown with the assumption that k 2 h is small. For medium and high wavenumber, these results do not cover the meshsizes that are applied in practical applications. The main estimate reveals that the error in H 1 -norm of discrete solutions for the Helmholtz equation is polluted when k 2 h is not small. The error is then not quasioptimal; i.e., the relation of the FE-error to the error of best approximation generally depends on the wavenumber k . It is noted that the pollution term in the relative error is of the same order as the phase lead of the numerical solution. In the result of this analysis, thorough and rigorous understanding of error behavior throughout the range of convergence is gained. Numerical results are presented that show sharpness of the error estimates and highlight some phenomena of the discrete solution behavior. The h - p -version of the FEM is studied in Part II.
606 citations
TL;DR: In this paper, the authors discuss the issues involved in the development of combined finite/discrete element methods, both from a fundamental theoretical viewpoint and some related algorithmic considerations essential for the efficient numerical solution of large scale industrial problems.
Abstract: This paper discusses the issues involved in the development of combined finite/discrete element methods; both from a fundamental theoretical viewpoint and some related algorithmic considerations essential for the efficient numerical solution of large scale industrial problems. The finite element representation of the solid region is combined with progressive fracturing, which leads to the formation of discrete elements, which may be composed of one or more deformable finite elements. The applicability of the approach is demonstrated by the solution of a range of examples relevant to various industrial sections.
586 citations
TL;DR: In this paper, a new numerical framework for solving conservation laws is developed, which differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods.
541 citations
01 Jan 1995
TL;DR: The aim of this chapter is to clarify the role of magnetism in the design of Induction Machines and to provide a procedure for integrating magnetism into the model of the motor.
Abstract: Preface. 1. Introduction to Finite Elements. 2. Nonlinear Problems. 3. Permanent Magnets. 4. Eddy Current Analysis. 5. Computation of Losses, Resistance and Inductance. 6. Calculation of Force and Torque. 7. Synchronous Machines in the Steady State. 8. The Induction Motor in Steady State. 9. Time Domain Modeling of Induction Machines. 10. Air-Gap Elements for Electrical Machines. 11. Axiperiodic Solutions.
541 citations
TL;DR: In this paper, a Lagrangian finite element model of orthogonal high-speed machining is developed, which accounts for dynamic effects, heat conduction, mesh-on-mesh contact with friction, and full thermo-mechanical coupling.
Abstract: A Lagrangian finite element model of orthogonal high-speed machining is developed. Continuous remeshing and adaptive meshing are the principal tools which we employ for sidestepping the difficulties associated with deformation-induced element distortion, and for resolving fine-scale features in the solution. The model accounts for dynamic effects, heat conduction, mesh-on-mesh contact with friction, and full thermo-mechanical coupling. In addition, a fracture model has been implemented which allows for arbitrary crack initiation and propagation in the regime of shear localized chips. The model correctly exhibits the observed transition from continuous to segmented chips with increasing tool speed.
529 citations
Book•
18 Jan 1995
TL;DR: Oriented toward those who will use finite elements (FE) rather than toward theoreticians and computer programmers, this book emphasizes the behavior of FE and how to use the FE method successfully.
Abstract: From the Publisher:
Oriented toward those who will use finite elements (FE) rather than toward theoreticians and computer programmers. Emphasizes the behavior of FE and how to use the FE method successfully. Includes several examples of FE analysis--each one features a critique of the accuracy of the solutions. Contains end-of-chapter exercises and extensive advice about FE modeling.
475 citations
TL;DR: In this article, a new mixed finite element method for computing viscoelastic flows is presented based on the introduction of the rate of deformation tensor as an additional unknown.
Abstract: A new mixed finite element method for computing viscoelastic flows is presented. The mixed formulation is based on the introduction of the rate of deformation tensor as an additional unknown. Contrary to the popular EVSS method [D. Rajagopalan, R.A. Brown and R.C. Armstrong, J. Non-Newtonian Fluid Mech., 36 (1990) 159], no change of variable is performed into the constitutive equation. Hence, the described method can be used to compute solutions of rheological models where the EVSS method does not apply. The numerical strategy uses a decoupled iterative scheme as a preconditioner for the GMRES algorithm. The stability and the robustness of the method are investigated on two benchmark problems: the 4:1 contraction flow problem and the stick-slip flow problem. Numerical results for the PTT [N. Phan-Thien and R.I. Tanner, J. Non-Newtonian Fluid Mech., 2 (1977) 353] and the Grmela [J. Grmela, J. Rheology, 33 (1989) 207] models show that our method is remarkably stable and cheap in computer time and memory.
TL;DR: In this article, a procedure for coupling meshless methods such as the element-free Galerkin method with finite element methods is developed so that continuity and consistency are preserved on the interface elements.
Abstract: A procedure is developed for coupling meshless methods such as the element-free Galerkin method with finite element methods. The coupling is developed so that continuity and consistency are preserved on the interface elements. Results are presented for both elastostatic and elastodynamic problems, including a problem with crack growth.
TL;DR: A physics-based approach to anatomical surface segmentation, reconstruction, and tracking in multidimensional medical images using a dynamic "balloon" model--a spherical thin-plate under tension surface spline which deforms elastically to fit the image data.
TL;DR: In this article, the authors deal with the development of a multiple scale finite element method by combining the asymptotic homogenization theory with Voronoi cell (VCFEM) for microstructural modeling.
TL;DR: A Generalized Finite Element Method (GFEM) for the Helmholtz equation such that the pollution effect is minimal.
TL;DR: A three-field arbitrary Lagrangian-Eulerian (ALE) finite element/volume formulation for coupled transient aeroelastic problems is presented and a rigorous derivation of a geometric conservation law for flow problems with moving boundaries and unstructured deformable meshes is included.
Abstract: A three-field arbitrary Lagrangian-Eulerian (ALE) finite element/volume formulation for coupled transient aeroelastic problems is presented The description includes a rigorous derivation of a geometric conservation law for flow problems with moving boundaries and unstructured deformable meshes The solution of the coupled governing equations with a mixed explicit (fluid)/implicit (structure) staggered procedure is discussed with particular reference to accuracy, stability, distributed computing, I/O transfers, subcycling and parallel processing A general and flexible framework for implementing partitioned solution procedures for coupled aeroelastic problems on heterogeneous and/or parallel computational platforms is described This framework and the explicit/implicit partitioned procedures are demonstrated with the numerical investigation on an iPSC-860 massively parallel processor of the instability of flat panels with infinite aspect ratio in supersonic airstreams
TL;DR: In this paper, the dispersion curves of propagative waves in a free rail are computed by using triangular and quadrilateral finite elements of the cross-section of the waveguide.
TL;DR: This paper presents a method to calculate photon-measurement density functions (PMDF's), which were introduced in Part 1, for near-infrared imaging and spectroscopy in complex and inhomogeneous objects through the use of a finite-element model.
Abstract: This paper presents a method to calculate photon-measurement density functions (PMDF's), which were introduced in Part 1 [Appl. Opt. 34, 7395-7409 (1995), for near-infrared imaging and spectroscopy in complex and inhomogeneous objects through the use of a finite-element model. PMDF's map the sensitivity of a measurement on the surface of an object to the perturbations of the optical parameters within the object. Data are presented for homogeneous and layered circular objects and for a complex two-dimensional model of a head. In particular the influence of the optical parameters on the shape of the PMDF and the distortions caused by boundary layers and complex inhomogeneties are investigated.
TL;DR: The numerical treatment of contact problems involves the formulation of the geometry, the statement of interface laws, the variational formulation and the development of algorithms as mentioned in this paper, and the discretization of a contact problem in time and space has to be chosen with regard to the nature of the contact problem.
Abstract: The numerical treatment of contact problems involves the formulation of the geometry, the statement of interface laws, the variational formulation and the development of algorithms. In this paper we give an overview with regard to the different topics which are involved when contact problems have to be simulated. To be most general we will derive a geometrical model for contact which is valid for large deformations. Furthermore interface laws will be discussed for the normal and tangential stress components in the contact area. Different variational formulations can be applied to treat the variational inequalities due to contact. Several of these different techniques will be presented. Furthermore the discretization of a contact problem in time and space is of great importance and has to be chosen with regard to the nature of the contact problem. Thus the standard discretization schemes will be discussed as well as techiques to search for contact in case of large deformations.
TL;DR: In this article, the stabilization of finite element methods in which essential boundary conditions are approximated by Babuska's method of Lagrange multipliers is discussed and there is a close connection with this technique and a classical method by Nitsche.
TL;DR: In this article, a hierarchical displacement interpolation was proposed for the beam theory of Reissner, which is capable of eliminating both shear and membrane locking phenomena in the finite element beam theory.
TL;DR: In this article, a non-linear shell theory is introduced, which provides a complete three-dimensional state of stress, and is applied to quadrilateral shell elements, which provide only displacement degrees of freedom located at nodes on the outer surfaces and one degree of freedom at the middle surface.
Abstract: The paper introduces a non-linear shell theory, which provides a complete three-dimensional state of stress. Since the theory is derived from simple three-dimensional continuum mechanics, it is very easy to understand. As an example, the theory is applied to quadrilateral shell elements, which provide only displacement degrees of freedom located at nodes on the outer surfaces and one degree of freedom at the middle surface. It is proposed to eliminate this degree of freedom on element level, so that the elements have the same layout as the equivalent brick elements, but have a better behaviour in bending, have stress resultants and are cheaper with respect to computational effort. The advantages with respect to implementation in a finite element program, as well as in special applications, are obvious. However, well-known conditioning problems in thin shell applications must be expected. Therefore emphasis is put on this issue in the example problems. It is shown that the elements can give acceptable answers in engineering applications and offer a potential for material non-linear applications, which will be considered in a forthcoming paper.
TL;DR: A meshless approach to the analysis of arbitrary Kirchhoff plates by the Element-Free Galerkin (EFG) method is presented and it is shown, that high accuracy can be achieved for arbitrary grid geometries, for clamped and simply-supported edge conditions, and for regular and irregular grids.
Abstract: A meshless approach to the analysis of arbitrary Kirchhoff plates by the Element-Free Galerkin (EFG) method is presented. The method is based on moving least squares approximant. The method is meshless, which means that the discretization is independent of the geometric subdivision into “finite elements”. The satisfaction of the C
1 continuity requirements are easily met by EFG since it requires only C
1 weights; therefore, it is not necessary to resort to Mindlin-Reissner theory or to devices such as discrete Kirchhoff theory. The requirements of consistency are met by the use of a quadratic polynomial basis. A subdivision similar to finite elements is used to provide a background mesh for numerical integration. The essential boundary conditions are enforced by Lagrange multipliers. It is shown, that high accuracy can be achieved for arbitrary grid geometries, for clamped and simply-supported edge conditions, and for regular and irregular grids. Numerical studies are presented which show that the optimal support is about 3.9 node spacings, and that high-order quadrature is required.
TL;DR: The use of a large strain constitutive relationship suitable for modeling brain tissue as well as other soft biological tissue is discussed, and the numerical results compare favorably with the experimental data.
Abstract: Finite element modeling of the finite deformation response of soft tissues presents a formidable challenge. This paper discusses the use of a large strain constitutive relationship suitable for modeling brain tissue as well as other soft biological tissue. Available experimental data on the finite deformation response of brain tissue is used to characterize the constitutive properties. Analytical modeling and finite element simulation of the experiment are performed using the proposed constitutive formulation. The numerical results compare favorably with the experimental data.
TL;DR: A posteriori error estimates are proved, corresponding adaptive algorithms are designed, and some numerical results are presented on adaptive finite element methods for parabolic problems to a class of nonlinear scalar problems.
Abstract: We extend our program on adaptive finite element methods for parabolic problems to a class of nonlinear scalar problems. We prove a posteriori error estimates, design corresponding adaptive algorithms, and present some numerical results.
TL;DR: In this article, the phase difference between the exact and the numerical solutions is investigated and discussed in the context of other work directed to this topic, and it is shown that previous error estimates in H1-norm are of nondispersive character but hold for medium or high wavenumber on extremely refined mesh only.
Abstract: When applying numerical methods for the computation of stationary waves from the Helmholtz equation, one obtains ‘numerical waves’ that are dispersive also in non-dispersive media. The numerical wave displays a phase velocity that depends on the parameter k of the Helmholtz equation. In dispersion analysis, the phase difference between the exact and the numerical solutions is investigated. In this paper, the authors' recent result on the phase difference for one-dimensional problems is numerically evaluated and discussed in the context of other work directed to this topic. It is then shown that previous error estimates in H1-norm are of nondispersive character but hold for medium or high wavenumber on extremely refined mesh only. On the other hand, recently proven error estimates for constant resolution contain a pollution term. With certain assumptions on the exact solution, this term is of the order of the phase difference. Thus a link is established between the results of dispersion analysis and the results of numerical analysis. Throughout the paper, the presentation and discussion of theoretical results is accompanied by numerical evaluation of several model problems. Special attention is given to the performance of the Galerkin method with a higher order of polynomial approximation p(h-p-version).
TL;DR: Optimal error estimates are derived for a complete discretization of linear parabolic problems using space–time finite elements based on the orthogonality of the Galerkin procedure and the use of strong stability estimates.
Abstract: Optimal error estimates are derived for a complete discretization of linear parabolic problems using space–time finite elements. The discretization is done first in time using the discontinuous Galerkin method and then in space using the standard Galerkin method. The underlying partitions in time and space need not be quasi uniform and the partition in space may be changed from time step to time step. The error bounds show, in particular, that the error may be controlled globally in time on a given tolerance level by controlling the discretization error on each individual time step on the same (given) level, i.e., without error accumulation effects. The derivation of the estimates is based on the orthogonality of the Galerkin procedure and the use of strong stability estimates. The particular and precise form of these error estimates makes it possible to design efficient adaptive methods with reliable automatic error control for parabolic problems in the norms under consideration.
TL;DR: In this article, a Voronoi cell finite element method is developed to solve small deformation elastic-plasticity problems for arbitrary heterogenous materials, which is based on Dirichlet Tessellation of microstructural representative materials.
TL;DR: The selection of the GLS mesh parameter for two dimensions is considered, and leads to elements that exhibit improved phase accuracy, and an optimal GLS parameter is found which reduces phase error for all possible wave vector orientations over elements.
Abstract: In this paper a Galerkin least-squares (GLS) finite element method, in which residuals in least-squares form are added to the standard Galerkin variational equation, is developed to solve the Helmholtz equation in two dimensions. An important feature of GLS methods is the introduction of a local mesh parameter that may be designed to provide accurate solutions with relatively coarse meshes. Previous work has accomplished this for the one-dimensional Helmholtz equation using dispersion analysis. In this paper, the selection of the GLS mesh parameter for two dimensions is considered, and leads to elements that exhibit improved phase accuracy. For any given direction of wave propagation, an optimal GLS mesh parameter is determined using two-dimensional Fourier analysis. In general problems, the direction of wave propagation will not be known a priori. In this case, an optimal GLS parameter is found which reduces phase error for all possible wave vector orientations over elements. The optimal GLS parameters are derived for both consistent and lumped mass approximations. Several numerical examples are given and the results compared with those obtained from the Galerkin method. The extension of GLS to higher-order quadratic interpolations is also presented.
TL;DR: This study used finite element analyses to model the planar shear bond test and to evaluate the effects of modulus values, bonding agent thickness, and loading conditions on the stress distribution in the dentin adjacent to the bonding agent-dentin interface.