Showing papers on "Extended finite element method published in 1975"
TL;DR: The finite element method (FEM) is a numerical technique used to perform finite element analysis of any given physical phenomenon as discussed by the authors, such as structural or fluid behavior, thermal transport, wave propagation, and the growth of biological cells.
Abstract: Introduction to finite element analysis: 1.1 What is ... The finite element method (FEM) is a numerical technique used to perform finite element analysis of any given physical phenomenon. It is necessary to use mathematics to comprehensively understand and quantify any physical phenomena, such as structural or fluid behavior, thermal transport, wave propagation, and the growth of biological cells.
1,811 citations
Book•
01 Jan 1975
TL;DR: The Finite Element Method as discussed by the authors is a method to meet the Finite Elements Method of Linear Elasticity Theory (LETI) and is used in many of the problems of mesh generation.
Abstract: PART I. Meet the Finite Element Method. The Direct Approach: A Physical Interpretation. The Mathematical Approach: A Variational Interpretation. The Mathematical Approach: A Generalized Interpretation. Elements and Interpolation Functions. PART II. Elasticity Problems. General Field Problems. Heat Transfer Problems. Fluid Mechanics Problems. Boundary Conditions, Mesh Generation, and Other Practical Considerations. Appendix A: Matrices. Appendix B: Variational Calculus. Appendix C: Basic Equations from Linear Elasticity Theory. Appendix D: Basic Equations from Fluid Mechanics. Appendix E: Basic Equations from Heat Transfer. References. Index.
1,497 citations
TL;DR: In this article, an Eulerian finite element formulation for large elastic-plastic flow is presented, based on Hill's variational principle for incremental deformations, and is suited to isotropically hardening Prandtl-Reuss materials.
724 citations
TL;DR: In this paper, a set of nonlinear partial differential equations that describe the movement of the saltwater front in a coastal aquifer is solved by the Galerkin-finite element method.
Abstract: The set of nonlinear partial differential equations that describe the movement of the saltwater front in a coastal aquifer is solved by the Galerkin-finite element method. Pressure and velocities are obtained simultaneously in order to guarantee continuity of velocities between elements. A layered aquifer is modeled either with a functional representation of permeability or by a constant value of permeability over each element.
236 citations
TL;DR: Using numerical integration in the formation of the finite element mass matrix and placing the movable nodes at integration points causes it to become lumped or diagonal (block diagonal) with the optimal rate of energy convergence retained.
149 citations
01 Oct 1975
TL;DR: An application for a one-dimensional long period shallow water wave using he method of Galerkin an the four-step Runge-Kuta method is described in this article. But the application is limited to a single wave.
Abstract: An application for a one-dimensional long period shallow water wave using he method of Galerkin an the four-step Runge-Kuta method.
147 citations
TL;DR: In this article, the authors presented a finite element model with nodal degrees of freedom which can satisfy all the forced and natural boundary conditions of a Timoshenko beam, and the mass and stiffness matrices of the element were derived from kinetic and strain energies by assigning polynomial expressions for total deflection and bending slope.
143 citations
TL;DR: In this article, the authors investigated the achievable accuracy of various time-stepping algorithms and how this can be improved if noise is artificially damped to an acceptable level, and concluded that the Crank-Nicolson scheme with a simple averaging process is superior to the other methods investigated.
Abstract: This paper investigates the phenomenon of ‘noise’ which is common in most time-dependent problems. The emphasis is on the achievable accuracy that is obtained with various time-stepping algorithms and how this can be improved if noise is artificially damped to an acceptable level. A series of experiments are made where the space domain is discretized using the finite element method and the variation with time is approximated by several finite difference methods. The conclusion is reached that the Crank–Nicolson scheme with a simple averaging process is superior to the other methods investigated.
130 citations
Book•
01 Jan 1975
TL;DR: In this article, the authors present a structural analysis of a Continuum Mechanics Problem with Finite Element Analysis of Harmonic Problems and finite element analysis of Biharmonic Problems.
Abstract: Introduction and Structural Analysis Continuum Mechanics Problems Finite Element Analysis of Harmonic Problems Finite Element Meshes Some Harmonic Problems Finite Element Analysis of Biharmonic Problems Some Biharmonic Problems Further Applications.
108 citations
TL;DR: In this article, it was shown that the technique introduced in Berger, Scott and Strang [2] can achieve optimal accuracy if the approximating functions interpolate boundary conditions at the Lobatto quadrature points for each element edge on the boundary.
Abstract: This paper shows that the technique introduced in Berger, Scott and Strang [2] can achieve optimal accuracy if the approximating functions interpolate boundary conditions at the Lobatto quadrature points for each element edge on the boundary. No modification of the energy form is required. Estimates are derived in lower norms as well as in the energy norm. A numerical integration scheme is presented that yields optimal accuracy for piecewise quadratics.
TL;DR: In this article, first-order triangular finite elements are derived for the nonlinear diffusion equation in the general form which includes both time-dependent and notional terms, and applied to a simplified model of a single-sided linear induction motor, for which the finite element equations are solved by an implicit method in time and iteratively in space.
Abstract: Following the Galerkin projective technique, first-order triangular finite elements are derived for the nonlinear diffusion equation-in the general form which includes both time-dependent and notional terms. The method is applied to a simplified model of a single-sided linear induction motor, for which the finite element equations are solved by an implicit method in time, and iteratively in space. The results suggest that the screening effect of eddy currents in the iron is quite strong.
TL;DR: In this paper, a generalization is made of a previous phase-space finite element approximation of the second-order form of the one-group, two-dimensional neutron transport equation in x-y geometry.
Abstract: A generalization is made of a previous phase-space finite element approximation of the second-order form of the one-group, two-dimensional neutron transport equation in x-y geometry. Three angular ...
TL;DR: In this paper, the Adams-Moulton multi-step predictor corrector process, the trapezoidal finite difference integration scheme, and the finite element in time were used to predict long wave forms in rectangular channels.
TL;DR: In this paper, a finite element approximation of the minimal surface problem for a strictly convex bounded plane domain Q2 is considered, and the approximating functions are continuous and piecewise linear on a triangulation of Q2.
Abstract: A finite element approximation of the minimal surface problem for a strictly convex bounded plane domain Q2 is considered. The approximating functions are continuous and piecewise linear on a triangulation of Q2. Error estimates of the form 0(h) in the H1 norm and 0(h 2) in the Lp-norm (p < 2) are proved,where h denotes the maximal side in the triangulation.
TL;DR: In this paper, a curved-shell finite element of triangular shape is described which is based on conventional shell theory expressed in terms of surface coordinates and displacements Each of the three surface displacement components is independently represented by a two-dimensional polynomial of constrained-quintic order giving the element a total of 54 degrees of freedom.
TL;DR: In this paper, the Laplace-Young equation was used to solve the problem of finding the height of rise and meniscus curvatures of parallel vertical cylinders in a large array.
TL;DR: In this article, the finite element method was applied to the radially symmetric case of the hydrogen atom, which has computational advantages over the finite difference and Rayleigh−Ritz methods.
Abstract: The finite element method, which in other fields has replaced finite difference and variational methods, is applied to the radially symmetric case of the hydrogen atom. The method is shown to have computational advantages over the finite difference and Rayleigh−Ritz methods. (AIP)
TL;DR: The initial-boundary value problem for a linear parabolic equation in an infinite cylinder under the Dirichlet boundary condition is solved by applying the finite element discretization in the space dimension and A0-stable multistep discretizations in time.
Abstract: The initial-boundary value problem for a linear parabolic equation in an infinite cylinder under the Dirichlet boundary condition is solved by applying the finite element discretization in the space dimension and A0-stable multistep discretizations in time. No restriction on the ratio of the time and space increments is imposed. The methods are analyzed and bounds for the discretization error in the L2-norm are given.
Proceedings Article•
01 Jan 1975
01 Jan 1975
TL;DR: A study of the constraint of incompressibility in the finite element method for plane strain through the use of a Lagrange multiplier and its two approaches from the point of view of rate of convergence and computer time is presented.
Abstract: The constraint of incompressibility is incorporated into the finite element method for plane strain through the use of a Lagrange multiplier. Depending on the approximating function chosen for this multiplier, the constraint condition can be satisfied everywhere within the element or only in an average sense for the entire element. A study of these two approaches from the point of view of rate of convergence and computer time is presented.
TL;DR: In this article, a higher order beam finite element is derived and shown to be very efficient in solving the transient dynamic problem of elastic impact and impact with permanent indentations, and the finite element solutions are found in good agreement with some existing solutions.
TL;DR: In this article, the dispersive properties of elastic waveguides of arbitrary cross-section were analyzed using the finite element theory for the analysis of frequency spectra of fiber reinforced composite.
TL;DR: A review of developments in the finite element field can be found in this article, where the concept of stiffness analysis is introduced and a review of recent developments in finite element fields is presented.
Abstract: Basic concepts The concept of stiffness analysis Bar finite elements Finite elements of continua Triangular finite element for plane elasticity Rectangular finite element for plane elasticity Rectangular finite element for plate flexure Analysis of folded-plate, box-girder and shell structures using rectangular elements Axially symmetric continua Programming Triangular finite element for plate fixture A review of developments in the finite element field Appendices.
TL;DR: In this article, finite element methods are used to solve hydrodynamic lubrication problems involving compressible lubricants and porous bearing solids, and the particular calculation scheme permits solution at high compressibility numbers (Λ > 100) to be obtained without any numerical difficulty.
Abstract: Finite element methods are used to solve hydrodynamic lubrication problems involving compressible lubricants and porous bearing solids. The particular calculation scheme permits solution at high compressibility numbers (Λ > 100) to be obtained without any numerical difficulty. Finite element and finite difference results for the porous, gas lubricated journal bearing are presented and compared.
TL;DR: In this paper, differential equation descriptions for specific three-dimensional environmental hydrodynamical flowfields are established and a finite element numerical solution algorithm is established for each of these developed systems including complete nonlinearity and tensor turbulent transport phenomena.
Abstract: Differential equation descriptions for specific three-dimensional environmental hydrodynamical flowfields are established. The parabolic Navier-Stokes system is applicable to predominant direction steady flowfields. An integral transform formulation of the transient Navier-Stokes system is applicable to recirculating flowfields in lakes, rivers, and tide water regions. A finite element numerical solution algorithm is established for each of these developed systems including complete nonlinearity and tensor turbulent transport phenomena. The algorithm directly utilizes nonuniform computational meshes and nonregular solution domain closures, upon which boundary condition constraints may be readily applied.