Showing papers on "Smoothed finite element method published in 1984"

An Introduction to the Finite Element Method

Abstract: 1 Introduction 2 Mathematical Preliminaries, Integral Formulations, and Variational Methods 3 Second-order Differential Equations in One Dimension: Finite Element Models 4 Second-order Differential Equations in One Dimension: Applications 5 Beams and Frames 6 Eigenvalue and Time-Dependent Problems 7 Computer Implementation 8 Single-Variable Problems in Two Dimensions 9 Interpolation Functions, Numerical Integration, and Modeling Considerations 10 Flows of Viscous Incompressible Fluids 11 Plane Elasticity 12 Bending of Elastic Plates 13 Computer Implementation of Two-Dimensional Problems 14 Prelude to Advanced Topics

The finite element method displayed

Abstract: Simplifies the teaching of the finite element method. Topics covered include: the approximation of continuous functions over sub-domains in terms of nodal values; interpolation functions for classical elements in one, two, and three dimensions; fundamental element vectors and matrices and assembly techniques; numerical methods of integration; matrix Eigenvalue and Eigenvector problems; and Fortran programming techniques. Contains tables of formulas and constants for constructing codes.

Time Finite Element Discretization of Hamilton's Law of Varying Action

Abstract: Hamilton's Law of Varying Action is used as a variational source for the derivation of finite element discretization procedure in the time domain. Three different versions of the proposed algorithms are presented and verified for accuracy and stability. [The first one is the high-precision, finite time element, analogous to the standard finite elements, with cutoff frequency; the second version is the step by step, one-time element from which the unconditionally stable, with slightly altered accuracy, third algorithm is derived. ] The new operator, connected with the proposed algorithms, bears attractive properties of much greater accuracy than other existing stable methods, and easy computer implementation. Thus, the work herein shows that the reservations expressed against the use of finite elements in time domain seem unjustified.

Finite element and boundary element methods for extrusion computations

Abstract: The present paper reports some new finite element and boundary element results for the expansion of a plane jet of Maxwell fluid. Finite element results for the axisymmetric problem are also presented. The boundary element method represents a new method of solving this problem. The Maxwell stresses are evaluated by integrating along the streamlines; these are then incorporated in the boundary element formulation. The new results are compared with existing finite element solutions of this problem. Although all sets of results predict the same overall behaviour, there is still little agreement on the exact behaviour

Beam on Elastic Foundation Finite Element

Abstract: A stiffness matrix for a beam on elastic foundation finite element and element load vectors due to concentrated forces, concentrated moments, and linearly distributed forces are developed for plane frame analysis. This element stiffness matrix can be readily adopted for the conventional displacement method. For the force method, an element flexibility matrix and element displacement vectors due to the aforementioned loads are also presented. Whereas most other analyses of a beam on elastic foundation finite element approximate the foundation by discrete springs or by cubic hermitian polynomials, the present stiffness and flexibility matrices are derived from the exact solution of the differential equation. Thus, results of this finite element analysis are exact for Navier and Winkler assumptions. Numerical examples are given to demonstrate the efficiency and simplicity of the element.

Surface integral finite element hybrid (SIFEH) method for fracture mechanics

Abstract: An effective surface integral and finite element hybrid (SIFEH) method has been developed to model fracture problems in finite plane domains. This hybridization by (incrementally) linear superposition combines the best features of both component methods. Finite elements are used to model the finite domain (and eventually nonlinearity), while continuous distributions of dislocations (resulting in surface integral equations) are used to model the fracture (i.e. displacement discontinuity). This method has been implemented in a computer program and results of representative problems are presented: these compare very well with known solutions and they demonstrate the computational advantages of SIFEH over other numerical methods (including the individual components).

On the efficiency and accuracy of the boundary element method and the finite element method

Abstract: The efficiency and computational accuracy of the boundary element and finite element methods are compared in this paper. This comparison is carried out by employing different degrees of mesh refinement to solve a specific illustrative problem by the two methods.

Numerical models for casting solidification: Part II. Application of the boundary element method to solidification problems

Abstract: A new numerical model, which is based on the boundary element method, was proposed for the simulation of solidification problems, and its application was demonstrated for solidification of metals in metal and sand molds Comparisons were made between results from this model and those from the explicit finite difference method Temperature recovery method was successfully adopted to estimate the liberation of latent heat of freezing in the boundary element method A coupling method was proposed for problems in which the boundary condition of the interface consisting of inhomogeneous bodies is governed by Newton’s law of cooling in the boundary element method It was concluded that the boundary element method which has several advantages, such as the wide variety of element shapes, simplicity of data preparation, and small CPU times, will find wide application as an alternative for finite difference or finite element methods, in the fields of solidification problems, especially for complex, three-dimensional geometries

Incremental finite element analysis of geometrically altered structures

Abstract: A conceptually simple, general method is described for the finite element simulation of multi-stage construction and excavation processes, including recognition of nonlinear material behaviour. Anomalous results reported in the literature for simulation of excavation of elastic media are examined, and shown to result from the inconsistent determination of nodal excavation forces from element boundary stresses.

Finite element approximation of a nonlinear eigenvalue problem related to MHD equilibria

Abstract: This paper presents numerical analysis of finite element approximation to a nonlinear eigenvalue problem: −Δu=λu + in Ω,u=−1 on Γ=∂Ω, where Ω is a bounded domain inR n (n=1, 2, 3). This problem arises in MHD (magnetohydrodynamics) equilibria and some other important physical phenomena. We consider a simple finite element scheme, and perform its error analysis. We also discuss a lumped finite element scheme, which is introduced to simplify the computations of the original scheme. Some numerical results are illustrated to show the validity of the analysis.

An improved accelerated initial stress procedure for elasto-plastic finite element analysis

Abstract: The most flexible and generally applicable methods for elasto-plastic analysis are those based on an incremental-iterative form of the initial stress approach, but such methods often exhibit slow convergence. The acceleration procedure known as the alpha-constant stiffness method is reconsidered and some modifications are proposed. The principal difference in the present approach lies in the use of a single acceleration parameter, rather than a diagonal matrix of acceleration coefficients. The new scheme shows a significant improvement in numerical stability and converges three times faster than the standard initial stress method. Some practical aspects associated with the method are discussed and a number of applications are presented.

The finite element method for flow and heat transfer analysis

Abstract: The finite element method (FEM) is discussed and a specific formulation for flow problems is outlined that can encompass non-Newtonian inelastic and viscoelastic fluids. A temperature formulation is also considered that can be applied for nonisothermal analyses of fluid flow. Some illustrative examples of the application of the method in polymer processing are also presented.

Modelling of continuous media methodology and computer-aided design of finite element programs

Abstract: In this paper we explain how the EXPERT-SYSTEM technique can be used in the finite element method in order to build an adaptable system able to solve a large class of partial differential equations. The equations to be solved can be described conversationally with the help of a generator program which reduces to a few hours the time necessary to build a new finite element package. The knowledge representation used is described in detail and the general solving strategy is analyzed. Such a system has been compared to industrial programs, and its cost is close to that of the classic method. Some examples of equation description in the fields of magnetics, hydraulics and heat-transfer are given. Some examples of the utilization of these programs are presented.

An axisymmetric finite element analysis of the mechanical function of the meniscus

Abstract: • A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.

Isothermal, multiphase, multicomponent fluid flow in permeable media

Abstract: The authors consider finite difference and finite element approximations to the solution of the multiphase, multicomponent problems. They also consider the problem of efficient integration, by means of system integrators, of the resulting semidiscrete finite difference or finite element systems for a certain class of flows. Techniques which incorporate adaptive timestep control are utilized. In this way they are able to adaptively control the integration process for problems in which the system stiffness may vary markedly. Representative examples in one and two dimensions corresponding to an enhanced oil recovery process (micellar-polymer flooding) are computed. Numerical results obtained using finite difference and finite element methods are presented in the one-dimensional case. Some new ideas related to adaptive upwinding in the finite element computations are used to control oscillatory overshoot. Both streamline finite difference and general two-dimensional finite difference schemes are described and applied in flow simulations.

Finite element seepage flow nets

Abstract: A variational principle and the corresponding finite element equations for determination of the stream function for soil seepage problems is given using the standard finite element potential solution as data. The procedure is very simple and independent of the element type employed. Generalization of the method to multiply connected domains is included.

Finite Element Mesh Generation for Use with Solid Modeling and Adaptive Analysis

Abstract: The automatic generation of finite element models from solid models is discussed. A fully automatic finite element mesh generator based on a modified octree approach is presented. Its possible integration with self-adaptive analysis procedures to form an automated finite element processor is also discussed.

Comparison of Finite Difference and Finite Element Methods

Abstract: A paper which purports to make a comparison between finite difference and finite element methods is doomed to be met with much criticism. The reason for this inevitable fate is that a study such as this must contain a high degree of subjectivity which many readers will have cause to disagree with. Issues such as ulterior motives of the author, the proficiency of a computer programmer, the blurring of features which distinguish finite element from finite difference methods and the reader’s own biases or preferences make presentation of a satisfactorily complete and inoffensive comparison of these two numerical techniques virtually impossible.