Showing papers on "Finite element method published in 1987"

Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods

Abstract: Introduction Signorini's problem Minimization methods and their variants Finite element approximations Orderings, Trace Theorems, Green's Formulas and korn's Inequalities Signorini's problem revisited Signorini's problem for incompressible materials Alternate variational principles for Signorini's problem Contact problems for large deflections of elastic plates Some special contact problems with friction Contact problems with nonclassical friction laws Contact problems involving deformations and nonlinear materials Dynamic friction problems Rolling contact problems Concluding comments.

Flows of Materials with Yield

Abstract: Steady, two‐dimensional flows of Bingham fluids are analyzed by means of a modified constitutive relation that applies everywhere in the flow field, in both yielded and practically unyielded regions. The conservation equations and the constitutive relation are solved simultaneously by Galerkin finite element and Newton iteration. This combination eliminates the necessity for tracking yield surfaces in the flow field. The analysis is applied to a one‐dimensional channel flow, a two‐dimensional boundary layer flow, and a two‐dimensional extrusion flow. The finite element predictions compare well with available analytic solutions for limiting cases.

A finite element method for localized failure analysis

Abstract: A method is proposed which aims at enhancing the performance of general classes of elements in problems involving strain localization. The method exploits information concerning the process of localization which is readily available at the element level. A bifurcation analysis is used to determine the geometry of the localized deformation modes. When the onset of localization is detected, suitably defined shape functions are added to the element interpolation which closely reproduce the localized modes. The extra degrees of freedom representing the amplitudes of these modes are eliminated by static condensation. The proposed methodology can be applied to 2-D and 3-D problems involving arbitrary rate-independent material behavior. Numerical examples demonstrate the ability of the method to resolve the geometry of localized failure modes to the highest resolution allowed by the mesh.

Boundary Element Methods in Dynamic Analysis

Abstract: Related Content Customize your page view by dragging and repositioning the boxes below. Related Journal Articles

A new mixed finite element for calculating viscoelastic flow

Abstract: A new mixed finite element has allowed us to calculate flows of Maxwell-B and Oldroyd-B fluids at very high values of the Deborah number, De . The element is divided into several bilinear sub-elements for the stresses, while streamline-upwinding is used for discretizing the constitutive equation. The method is applied to the stick-slip problem, the flow through a tapered contraction and the flow through four-to-one abrupt plane and circular contractions. Important corner vortices develop at high values of De in the circular contraction. We have not encountered upper limits for the Deborah number in our calculations with Oldroyd-B fluids.

Finite Element Flux-Corrected Transport (FEM-FCT) for the Euler and Navier-Stokes equations

Abstract: A high resolution finite element method for the solution of problems involving high speed compressible flows is presented. The method uses the concepts of flux-corrected transport and is presented in a form which is suitable for implementation on completely unstructured triangular or tetrahedral meshes. Transient and steady state examples are solved to illustrate the performance of the algorithm.

Finite element methods with B-splines

Abstract: Preface 1. Introduction 2. Basic finite element concepts 3. B-splines 4. Finite element bases 5. Approximation with weighted splines 6. Boundary value problems 7. Multigrid methods 8. Implementation Appendix Notation and symbols Bibliography Index.

A new finite formulation for computational fluid dynamics: VII. The Stokes problem with various well-posed boundary conditions: symmetric formulations that converge for all velocity/pressure spaces

Abstract: Symmetric finite element formulations are proposed for the primitive-variables form of the Stokes equations and shown to be convergent for any combination of pressure and velocity interpolations. Various boundary conditions, such as pressure, are accommodated.

The Finite Element Method in the Deformation and Consolidation of Porous Media

Abstract: Introduction The Governing Equations of Multiphase Flow in a Deforming Porous Medium Numerical Solutions of the Governing Equations Constitutive Relationships and Variable Permeabilities Validation of Elastic and Elasto-plastic Consolidation Programs Modelling of Subsidence Heat and Fluid Flow in Deforming Porous Media Secondary Consolidation Two- dimensional, Non-linear Thermoelastoplastic Consolidation Program Plascon.

An adaptive finite element scheme for transient problems in CFD

Abstract: An adaptive finite element scheme for transient problems is presented. The classic h-enrichment / coarsening is employed in conjunction with a triangular finite element discretization in two dimensions. A mesh change is performed every n timesteps, depending on the Courant number employed and the number of ‘protective layers’ added ahead of the refined region. In order to simplify the refinement/ coarsening logic and to be as fast as possible, only one level of refinement/coarsening is allowed per mesh change. A high degree of vectorizability has been achieved on the CRAY XMP 12 at NRL. Several examples involving shock-shock interactions and the impact of shocks on structures demonstrate the performance of the method, indicating that considerable savings in CPU time and storage can be realized even for strongly unsteady flows.

A stable finite element solution for two-dimensional magnetotelluric modelling

Abstract: Summary. We report herein on a finite element algorithm for 2-D magnetotelluric modelling which solves directly for secondary variations in the field parallel to strike, plus the subsequent vertical and transverse auxiliary fields, for both transverse electric and transverse magnetic modes. The governing Helmholtz equations for the secondary fields along strike are the same as those for total field algorithms with the addition of source terms involving the primary fields and the conductivity difference between the body and the host. Our approach has overcome a difficulty with numerical accuracy at low frequencies observed in total field solutions with 32-bit arithmetic far the transverse magnetic mode especially, but also for the transverse electric mode. Matrix ill-conditioning, which affects total field solutions, increases with the number of element rows with the square of the maximum element aspect ratio and with the inverse of frequency. In the secondary formulation, the field along strike and the auxiliary fields do not need to be extracted in the face of an approximately computed primary field which increasingly dominates the total field solution towards low frequencies. In addition to low-frequency stability, the absolute accuracy of our algorithm is verified by comparison with the TM and the TE mode analytic responses of a segmented overburden model.

A finite-element approach to control the end-point motion of a single-link flexible robot

Abstract: A structural finite-element technique based on Bernoulli-Euler beam theory is presented which will permit the finding of the torques (or forces) that are necessary to apply at one end of a flexible link to produce a desired motion at the other end. This technique is suitable for the open loop control of the tip motion. It may also provide a good control law for feedback control. The finite-element method is used to discretize the equations of motion. This method has a major advantage in the fact that different material properties and boundary conditions like hubs, tip loads, changes in cross sections, etc., can be handled in a very simple and straightforward manner. The resulting differential equations are integrated via the frequency domain. This allows for the expansion of the desired end motion into its harmonic components and helps to visualize the complex wave propagation nature of the problem. The performance of the proposed technique is illustrated in the solution of a practical example. Results point out the potential that this technique has in the study of the dynamics and control not only of flexible robots, but also of any other flexible mechanisms like those used in biomechanics, where high precision at the tip of very light flexible arms is required.

A new finite element formulation for computational fluid dynamics: VI. Convergence analysis of the generalized SUPG formulation for linear time-dependent multi-dimensional advective-diffusive systems

Abstract: An SUPG-type finite element method for linear symmetric multidimensional advective-diffusive systems is described and analyzed. Optimal and near optimal error estimates are obtained for the complete range of advective-diffusive behavior.

Saltwater intrusion in aquifers: Development and testing of a three-dimensional finite element model

Abstract: A three-dimensional finite element model is developed for the simulation of saltwater intrusion in single and multiple coastal aquifer systems with either a confined or phreatic top aquifer. The model formulation is based on two governing equations, one for fluid flow and the other for salt transport. Density coupling of these equations is accounted for and handled using a Picard sequential solution algorithm with special provisions to enhance convergence of the iterative solution. Flexibility in the formulation allows for either three-dimensional simulations or quasi three-dimensional simulations, where flow and transport in aquitards are treated using one-dimensional analytical and/or numerical approximations. Spatial discretization of three-dimensional regions is performed using a vertical slicing approach designed to accommodate complex geometry with irregular boundaries, layering, and/or lateral discontinuity. This approach is effectively combined with the use of simple linear elements such as rectangular and triangular prisms, and composite hexahedra and pentahedra made up of tetrahedra. For these elements, computation of element matrices can be performed efficiently using influence coefficient formulas that avoid numerical integration. New transport influence coefficient formulas are presented for rectangular and triangular prism elements. Matrix assembly is performed slice by slice, and the matrix solution is achieved using a slice successive relaxation scheme. This permits a fairly large number of nodal unknowns (of the order of five to ten thousand) to be handled conveniently on small or medium-size minicomputers. Flexibility of the formulation and matrix handling procedures also allows two-dimensional and axisymmetric problems to be solved efficiently using single slice representations. Four examples are presented to demonstrate the model verification and utility. These problems represent a fair range of physical conditions. Where possible, simulation results are compared with previously published solutions.

Finite Element Analysis: From Concepts to Applications

Abstract: The emphasis is on theory, programming and appilications to show exactly how Finite Element Method can be applied to quantum mechanics, heat transfer and fluid dynamics. For engineers, physicists and mathematicians with some mathematical sophistication.

Finite element handbook

Abstract: Finite element handbook , Finite element handbook , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

The optimal convergence rate of the p-version of the finite element method

Abstract: Optimal error estimates for the p-version of the finite element method in two dimensions are proven for the case when $u \in H^k (\Omega )$ or u has singularities induced by the corners of the domain. The case of nonhomogenous essential boundary conditions is also analyzed.

A feedback element method with a posteriori error estimation: Part I. The finite element method and some basic properties of the a posteriori error estimator

Abstract: This paper is the first in a series of two in which we discuss some theoretical and practical aspects of a feedback finite element method for solving systems of linear second-order elliptic partial differential equations (with particular interest in classical linear elasticity). In this first part we introduce some nonstandard finite element spaces, which, though based on the usual square bilinear elements, permit local mesh refinement. The algebraic structure of these spaces and their approximation properties are analyzed. An “equivalent estimator” for the H 1 finite element error is developed. In the second paper we shall discuss the asymptotic properties of the estimator and computational experience.

Control Volume Finite-Element Method for Heat Transfer and Fluid Flow Using Colocated Variables— 1. Computational Procedure

Abstract: A novel computational procedure for the prediction of incompressible fluid flow using primitive variables is presented. The formulation retains the geometric flexibility of the finite-element method and derives the governing discrete algebraic equations by using a conservation balance applied to discrete control volumes distributed throughout the domain. A novel method of closure, to relate the control volume surface values to the nodal point values, is introduced whereby a local discrete analog to the governing differential equation is formed at the control volume Surfaces. From this discrete equation analog the control surface values are determined in terms of the nodal values that represent the discrete problem unknowns. The manner in which this discrete equation is formed, solved, and used permits resolution of two longstanding problems in computational fluid dynamics, namely accurate convection modeling and preclusion of pressure field decoupling. A new and general boundary condition specifi...

Realistic Eigenvalue Bounds for the Galerkin Mass Matrix

Abstract: On considere une equation aux derivees partielles d'evolution avec des conditions initiales et aux limites qu'on resout par la methode des elements finis. On etablit des bornes realistes pour les valeurs propres de la matrice des masses de Galerkin

Understanding and implementing the finite element method

Abstract: Preface Part I. The Basic Framework for Stationary Problems: 1. Some model PDEs 2. The weak form of a BVP 3. The Galerkin method 4. Piecewise polynomials and the finite element method 5. Convergence of the finite element method Part II. Data Structures and Implementation: 6. The mesh data structure 7. Programming the finite element method: Linear Lagrange triangles 8. Lagrange triangles of arbitrary degree 9. The finite element method for general BVPs Part III. Solving the Finite Element Equations: 10. Direct solution of sparse linear systems 11. Iterative methods: Conjugate gradients 12. The classical stationary iterations 13. The multigrid method Part IV. Adaptive Methods: 14. Adaptive mesh generation 15. Error estimators and indicators Bibliography Index.