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Showing papers on "Smoothed finite element method published in 1992"


Journal ArticleDOI
TL;DR: The diffuse element method (DEM) as discussed by the authors is a generalization of the finite element approximation (FEM) method, which is used for generating smooth approximations of functions known at given sets of points and for accurately estimating their derivatives.
Abstract: This paper describes the new “diffuse approximation” method, which may be presented as a generalization of the widely used “finite element approximation” method. It removes some of the limitations of the finite element approximation related to the regularity of approximated functions, and to mesh generation requirements. The diffuse approximation method may be used for generating smooth approximations of functions known at given sets of points and for accurately estimating their derivatives. It is useful as well for solving partial differential equations, leading to the so called “diffuse element method” (DEM), which presents several advantages compared to the “finite element method” (FEM), specially for evaluating the derivatives of the unknown functions.

1,951 citations


Journal ArticleDOI
TL;DR: The basic explicit finite element and finite difference methods that are currently used to solve transient, large deformation problems in solid mechanics are reviewed.
Abstract: Explicit finite element and finite difference methods are used to solve a wide variety of transient problems in industry and academia. Unfortunately, explicit methods are rarely discussed in detail in finite element text books. This paper reviews the basic explicit finite element and finite difference methods that are currently used to solve transient, large deformation problems in solid mechanics. A special emphasis has been placed on documenting methods that have not been previously published in journals.

1,218 citations


Journal ArticleDOI
TL;DR: In this article, a general approach to adaptivity for finite element methods is presented and applications to linear elasticity, non-linear elasto-plasticity and nonlinear conservation laws, including numerical results.

331 citations


Book
01 Jan 1992
TL;DR: Solid Modeling--Finite and Boundary Elements Material Modeling Finite elements of a Continuum Special Finite Elements: Plate/Shell Element, Joint Element Boundary Element Methods--Practical Implementation Coupled Boundaries Element/Finite Element Analysis Non-Linear Problems Mesh Design and Error Analysis Computer Aided Pre- and Post-Processing Appendices Index.
Abstract: Solid Modeling--Finite and Boundary Elements Material Modeling Finite Elements of a Continuum Special Finite Elements: Plate/Shell Element, Joint Element Boundary Element Methods--Basic Principles Boundary Element Methods--Practical Implementation Coupled Boundary Element/Finite Element Analysis Non-Linear Problems Mesh Design and Error Analysis Computer Aided Pre- and Post-Processing Appendices Index.

187 citations


Journal ArticleDOI
TL;DR: In this paper, the time-discontinuous Galerkin and least-squares methods for structural dynamics were used to prove a general convergence theorem in a norm stronger than the energy norm.
Abstract: SUMMARY Time finite element methods are developed for the equations of structural dynamics. The approach employs the time-discontinuous Galerkin method and incorporates stabilizing terms having least-squares form. These enable a general convergence theorem to be proved in a norm stronger than the energy norm. Results are presented from finite difference analyses of the time-discontinuous Galerkin and least-squares methods with various temporal interpolations and commonly used finite difference methods for structural dynamics. These results show that, for particular interpolations, the time finite element method exhibits improved accuracy and stability.

157 citations


Journal ArticleDOI
TL;DR: In this article, the effect of a large elastic structure surrounding a weld and the welding operation on the final weld state has been investigated and the results indicate that this coupling effect with the surrounding structure should be included in numerical simulations of welding processes, and that full three-dimensional models are essential in predicting welding distortion.
Abstract: Current simulations of welding distortion and residual stress have considered only the local weld zone. A large elastic structure surrounding a weld, however, can couple with the welding operation to produce a final weld state much different from that resulting when a smaller structure is welded. The effect of this coupling between structure and weld has the potential of dominating the final weld distortion and residual stress state. This paper employs both twoand three-dimensional finite element models of a circular cylinder and stiffening ring structure to investigate the interaction of a large structure on weld parameters such as weld gap clearance (fitup) and fixturing. The finite element simulation considers the full thermo-mechanical problem, uncoupling the thermal from the mechanical analysis. The thermal analysis uses temperaturedependent material properties, including latent heat and nonlinear heat convection and radiation boundary conditions. The mechanical analysis uses a thermal-elasticplastic constitutive model and an element "birth"procedure to simulate the deposition of weld material. The effect of variations of weld gap clearance, fixture positions, and fixture types on residual stress states and distortion are examined. The results of these analyses indicate that this coupling effect with the surrounding structure should be included in numerical simulations of welding processes, and that full three-dimensional models are essential in predicting welding distortion. Elastic coupling with the surrounding structure, weld fitiip, and fixturing are found to control residual stresses, creating substantial variations in highest principal and hydrostatic stresses in the weld region. The position and type of fixture are shown to be primary determinants of weld distortion.

151 citations


Journal ArticleDOI
TL;DR: Different methods are presented for the calculation of torque as a function of rotation angle in an electrical machine, using Maxwell stress tensor, coenergy derivation, Coulomb's virtual work, and the magnetizing current method.
Abstract: Different methods are presented for the calculation of torque as a function of rotation angle in an electrical machine. These methods are integrated in a calculation code by using the finite element method. The movement is taken into account by means of the moving band technique, involving quadrilateral finite elements in the airgap. The torque is calculated during the displacement of the moving part by using the following methods: Maxwell stress tensor, coenergy derivation, Coulomb's virtual work, A. Arkkio's method (1988), and the magnetizing current method. The results obtained by the different methods are compared with experimental data and make it possible to obtain practical information concerning the advantages and limitations of each method. >

142 citations


Book
01 Jun 1992
TL;DR: The Finite Element Method as mentioned in this paper is a method for the specification and assembly of finite element models and vectors for field problems, and it has been used in many applications in the literature.
Abstract: 1. Background And Application. 2. Introduction To The Method. 3. Practical Aspects Of The Finite Element Method - 4. Interpolation Functions And Simplex Elements. 5. Formulation Of The Element Characteristic Matrices And Vectors For Elasticity Problems. 6 Formulation Of The Element Characteristics Matrices And Vectors For Field Problems. 7. Assembly And Solution Of The Finite Element Equations. 8. Higher Order Element Formulations. 9. Practical Aspects Of The Finite Element Method 10. Further Applications Of The Finite Element Method. 11. Practical Aspects Of The Finite Element Method 12. Commercial Finite Element Programs.

136 citations


Journal ArticleDOI
TL;DR: In this paper, the cost of obtaining solutions to problems governed by the Helmholtz equation in both interior and exterior domains by means of boundary element and finite element methods is studied and compared.
Abstract: The cost of obtaining solutions to problems governed by the Helmholtz equation in both interior and exterior domains by means of boundary element and finite element methods is studied and compared. The main emphasis is on the computational effort required to solve the systems of equations emanating from the two methods. Boundary element methods require fewer equations to be solved by virtue of the fact that only boundaries are discretized. These equations, however, are less structured than those of finite element methods and hence cost-effectiveness is not as clear cut as might be expected. Both direct and iterative solution techniques are examined. For interior problems finite element methods are more economical on most practical configurations. Finite elements also appear to possess a certain computational advantage on the exterior problems examined, and, in general, are definitely competitive with boundary element methods. The cost-effectiveness of the two solution strategies is examined. Some issues of equation formation are also addressed.

125 citations


Journal ArticleDOI
TL;DR: In this article, the convergence of mixed finite element approximations to the Reissner-Mindlin plate problem is analyzed, and several known elements fall into the analysis, thus providing a unified approach.
Abstract: In this paper we analyze the convergence of mixed finite element approximations to the solution of the Reissner-Mindlin plate problem. We show that several known elements fall into our analysis, thus providing a unified approach. We also introduce a low-order triangular element which is optimalorder convergent uniformly in the plate thickness.

110 citations


Journal ArticleDOI
TL;DR: A novel transformation, called the parallelepipedic shell transformation, is developed and this transformation and the manner of implementation of these techniques in Flux3d software lead to an efficient tool for modeling an open boundary problem by means of the finite-element method.
Abstract: A finite element method for the computation of open boundary problems using transformations is presented. The principle of the method is presented. A novel transformation, called the parallelepipedic shell transformation, is developed. This transformation and the manner of implementation of these techniques in Flux3d software lead to an efficient tool for modeling an open boundary problem by means of the finite-element method. Validation, results, and application are presented. >

Journal ArticleDOI
TL;DR: A review of the finite element method applied to the problem of supersonic aeroelastic stability of plates and shells is presented in this article, which is limited to linear models.
Abstract: A review of the finite element method applied to the problem of supersonic aeroelastic stability of plates and shells is presented. The review is limited to linear models. Some new contributions in the field are presented and future trends are discussed. 105 refs., 18 figs., 6 tabs.

Journal ArticleDOI
TL;DR: In this article, the mixed finite element method is used to obtain an accurate approximation of the flow quantity u = -A? · (A??) = f. In a variety of problems, it is desirable to obtain a flow quantity approximated by the mixed-finite element method.
Abstract: An important class of problems in mathematical physics involves equations of the form -? · (A??) = f. In a variety of problems it is desirable to obtain an accurate approximation of the flow quantity u = -A??. Such an accurate approximation can be determined by the mixed finite element method. In this article the lowest-order mixed method is discussed in detail. The mixed finite element method results in a large system of linear equations with an indefinite coefficient matrix. This drawback can be circumvented by the hybridization technique, which leads to a symmetric positive-definite system. This system can be solved efficiently by the preconditioned conjugate gradient method. After approximating u by the lowest-order mixed finite element method, streamlines and residence times can be determined easily and accurately by computations at the element level.

01 Jan 1992
TL;DR: In this article, the authors present a table of contents and a list of FIGURES and TABLES for each chapter, including a chapter and a table. But they do not discuss the authorship.
Abstract: i ACKNOWLEDGMENTS iii TABLE OF CONTENTS v LIST OF FIGURES vii LIST OF TABLES ix CHAPTER

Journal ArticleDOI
TL;DR: Very general weak forms may be developed for dynamic systems, the most general being analogous to a Hu-Washizu three-field formulation, thus paralleling well-established weak methods of solid mechanics.
Abstract: Very general weak forms may be developed for dynamic systems, the most general being analogous to a Hu-Washizu three-field formulation, thus paralleling well-established weak methods of solid mechanics. In this work two different formulations are developed: a pure displacement formulation and a two-field mixed formulation. With the objective of developing a thorough understanding of the peculiar features of finite elements in time, the relevant methodologies associated with this approach for dynamics are extensively discussed. After having laid the theoretical bases, the finite element approximation and the linearization of the resulting forms are developed, together with a method for the treatment of holonomic and nonholonomic constraints, thus widening the horizons of applicability over the vast world of multibody system dynamics. With the purpose of enlightening on the peculiar numerical behavior of the different approaches, simple but meaningful examples are illustrated. To this aim, significant parallels with elastostatics are emphasized.

Book
31 Jan 1992
TL;DR: 1. Finite Elements and Structural Dynamics. 2. Element Matrices.
Abstract: 1. Finite Elements and Structural Dynamics. 2. Element Matrices. 3. System Matrices. 4. Solution of System Matrices. 5. Dynamic Response and Advanced Topics. 6. NATVIB -- A Computer Package. Index.

Book ChapterDOI
01 Jan 1992
TL;DR: The finite element method (FEM) as discussed by the authors was originally developed for analysis of complex structural systems, for which there is no simple solution, and it was used to find an approximate solution for a small element of a structural system.
Abstract: The finite element method (FEM) appeared as a need for analysis of complex structural systems, for which there is no simple solution. In the application of the method the structural system is subdivided into elements of finite dimensions, i.e. finite elements. An approximate solution is found for such a small element, and then, by assembling all the elements of the system, a system of algebraic equations is derived. The solution of these equations gives an approximate solution of the complete structural system. In that way a very complex problem is reduced to a solution of simple algebraic equations.

Journal ArticleDOI
TL;DR: This paper presents a new automatic mesh generation method for the finite element analysis of shallow water flow that can be generated so that the element Courant number is nearly constant in the whole domain.
Abstract: This paper presents a new automatic mesh generation method for the finite element analysis of shallow water flow. The key feature of this method is that the finite element mesh can be generated so that the element Courant number is nearly constant in the whole domain. It follows that the numerical stability and accuracy improve automatically. Moreover, the finite element mesh data, including the data of water depth, can be prepared automatically. The three-node triangular element is used for the finite element.

Journal ArticleDOI
TL;DR: In this paper, a numerical technique is described for the analysis of multiple interacting deformable bodies undergoing large displacements and rotations, where each body is considered an individual discrete unit, which is idealized by a finite element model.
Abstract: A numerical technique is described for the analysis of multiple interacting deformable bodies undergoing large displacements and rotations. Each body is considered an individual discrete unit, which is idealized by a finite element model. Discrete finite element models interact with their surroundings through contact stresses, which are continually updated as the elements move and deform. The method of analysis consists of a finite element formulation based on a generalized explicit updated Lagrangian method. This formulation is a general finite element formulation, that permits the large deformation analysis of both continuum and discontinuum systems. Different validations of the proposed method of analysis, including cases that involve very large rotations, as well as some examples that demonstrate the application of the discrete finite element method to problems in rock mechanics are presented and discussed in the paper.

Journal ArticleDOI
TL;DR: In this paper, a temporal finite element based on a mixed form of Hamilton's weak principle is summarized for optimal control problems, and an extension of the formulation to allow for control inequality constraints is also presented.
Abstract: A temporal finite element based on a mixed form of Hamilton's weak principle is summarized for optimal control problems. The resulting weak Hamiltonian finite element method is extended to allow for discontinuities in the states and/or discontinuities in the system equations. An extension of the formulation to allow for control inequality constraints is also presented. The formulation does not require element quadrature, and it produces a sparse system of nonlinear algebraic equations. To evaluate its feasibility for real-time guidance applications, this approach is applied to the trajectory optimization of a four-state, two-stage model with inequality constraints for an advanced launch vehicle. Numerical results for this model are presented and compared to results from a multiple-shooting code. The results show the accuracy and computational efficiency of the finite element method.

Journal ArticleDOI
TL;DR: The iterative methods (conjugate gradient and generalized minimum residual method) are compared with the frontal equation solver for efficiency, and the iterative solvers are found to be economical when a large number of equations are to be solved.
Abstract: Finite element analysis of complex three-dimensional flows requires solution of a large system of algebraic equations. These equations are most often solved using direct methods, i.e., Gauss elimination method. However, for complex problems, direct methods demand prohibitively large CPU times and storage, thus making it difficult to solve these equations economically even on supercomputers. Iterative methods, on the other hand, do not require large storage and CPU times because the global system of equations are not formulated and factorized. These advantages over direct methods have revived the interest in iterative solvers. The element by element solvers using conjugate gradient methods have been used successfully for the solution of problems in fluid and solid mechanics and were shown to be advantageous over direct methods. In this paper we present an element by element algorithm for solution of incompressible flow problems using a penalty finite element model. The iterative methods (conjugate gradient and generalized minimum residual method) are compared with the frontal equation solver for efficiency, and the iterative solvers are found to be economical when a large number of equations are to be solved.

Journal ArticleDOI
TL;DR: In this paper, the authors demonstrate that the stability of the finite element solution also depends on the boundary conditions of the problem and the magnetic characteristics of the moving conductor, and that the upwind finite element scheme can be used to solve the problem whenever numerical oscillation is exhibited.
Abstract: Numerical simulations have been conducted in an attempt to clarify some of the findings of previous work on the necessity of upwinding in the finite element analysis of electromagnetic problems that involve relative motion. The results presented demonstrate that, besides the Peclet number, the stability of the finite element solution also depends on the boundary conditions of the problem and the magnetic characteristics of the moving conductor. When the moving conductor is nonferromagnetic and a periodic boundary condition is imposed, a Galerkin method can model the problem successfully. Whenever numerical oscillation is exhibited, the upwind finite element scheme can be used to solve the problem. In a 3-D model where the biconjugate gradient solver is the most economical, and often the only, choice of solver to use, upwinding may be necessary to ensure convergence. >

Journal ArticleDOI
TL;DR: In this article, the scalar potential in the hybrid finite element (FE) and boundary element (BE) method for electromagnetic problems is used to reduce the number of unknown variables and make it easy to couple the BE region with the FE region.
Abstract: The authors propose a novel boundary element formulation using the scalar potential in the hybrid finite element (FE) and boundary element (BE) method for electromagnetic problems. They adopt the analytical integration as much as possible in this method. This approach has the advantage of reducing the number of unknown variables and makes it easy to couple the BE region with the FE region. A practical application of the proposed method to the three-dimensional eddy current problem is presented. The calculated values agree well with experimental results. >


Journal ArticleDOI
TL;DR: In this paper, a general method to treat internal constraints within the context of mixed finite element methods has been presented in previous work The underlying idea is to constrain the assumed stress and strain fields to satisfy the homogeneous equilibrium equations in a weak sense and satisfy a priori the internal constraints.
Abstract: A general method to treat internal constraints within the context of mixed finite element methods has been presented in previous work The underlying idea is to constrain the assumed stress and strain fields to satisfy the homogeneous equilibrium equations in a weak sense and thus satisfy a priori the internal constraints This method is now applied to generate four-node plane stress/strain elements For these elements, it is proved that locking at the nearly incompressible limit (plane strain) is avoided at the element level The proposed elements are shown to yield excellent results on a set of standard problems Furthermore, excellent stresses are obtained at the element level

Journal ArticleDOI
TL;DR: In this paper, the symmetrization-iteration method (SIM) for coupling of boundary element and finite element methods is presented and the numerical results of two-dimensional elastostatics show that SIM has very high accuracy.

Book ChapterDOI
01 Jan 1992
TL;DR: In this article, the boundary element method is applied to damage problems by introducing convenient inelastic strains which account for strength and/or stiffness decrease, while a damage parameter is not considered explicitly and the material stiffness matrix is maintained constant throughout the domain during the whole load history.
Abstract: The boundary element method is applied to damage problems by introducing convenient inelastic strains which account for strength and/or stiffness decrease. Thus, a damage parameter is not considered explicitly and the material stiffness matrix is maintained constant throughout the domain during the whole load history. As a consequence, the material remains homogeneous and a traditional boundary element approach can be followed, as well as for any other quasi-static inelastic problem (e.g., for elastic-plastic structural analysis). The main features of the technique proposed in the paper are pointed out and numerical examples are given.

01 Sep 1992
TL;DR: This thesis studies some Schwarz algorithms for the p-version finite element method, in which increased accuracy is achieved by increasing the degree p of the elements while the mesh is fixed, and proves a constant bound, independent of thedegree p and the number of elements N, for the condition number of the iteration operator.


Journal ArticleDOI
TL;DR: In this paper, the use of the impedance boundary condition in a finite element formulation is presented for high-frequency axisymmetric problems, and the method has the following advantages: (a) a gain in discretization time; (b) a smaller system to be solved and thus an increase in computer memory; and (c) a total computation time.
Abstract: The use of the impedance boundary condition in a finite element formulation is presented for high-frequency axisymmetric problems. The method has the following advantages: (a) a gain in discretization time; (b) a smaller system to be solved and thus a gain in computer memory; and (c) a gain in total computation time. >