Showing papers on "Extended finite element method published in 1980"
TL;DR: In this article, the authors present two families of non-conforming finite elements, built on tetrahedrons or on cubes, which are respectively conforming in the spacesH(curl) and H(div).
Abstract: We present here some new families of non conforming finite elements in ?3. These two families of finite elements, built on tetrahedrons or on cubes are respectively conforming in the spacesH(curl) andH(div). We give some applications of these elements for the approximation of Maxwell's equations and equations of elasticity.
3,049 citations
TL;DR: In this article, the error estimates for a procedure obtained by combining the boundary integral method and the usual finite element method are shown. But they are only for a special case of the problem described in this paper.
Abstract: We prove some error estimates for a procedure obtained by combining the boundary integral method and the usual finite element method.
355 citations
TL;DR: In this article, a general numerical method for convection-diffusion problems is presented, which can be extended to three-dimensional convection diffusion problems and can handle problems in the whole range of Peclet numbers.
Abstract: A general numerical method for convection-diffusion problems is presented The method is formulated for two-dimensional problems, but its key Ideas can be extended to three-dimensional problems The calculation domain is first divided into three-node triangular elements, and then polygonal control volumes are constructed by joining the centroids of the elements to the midpoints of the corresponding sides In each element, the dependent variable is interpolated exponentially in the direction of the element-average velocity vector and linearly in the direction normal to it These interpolation functions respond to an element Peclet number and become linear when it approaches zero The discretization equations are obtained by deriving algebraic approximations to integral conservation equations applied to the polygonal control volumes The proposed method has the conservative property, can handle problems in the whole range of Peclet numbers, and avoids the false-diffusion difficulties that commonly afflict o
345 citations
TL;DR: Problems for the solution of incremental finite element equations in practical nonlinear analysis in static analysis and in dynamic analysis using implicit time integration are described and evaluated.
289 citations
TL;DR: In this paper, a finite element formulation of problems of limit loads in soil mechanics via limit analysis theory is presented, followed by a numerical formulation for both the static and kinematic approaches of the ultimate load.
234 citations
TL;DR: In this article, a displacement-based finite element is presented for linear and geometric and material nonlinear analysis of plates and shells, which can be implemented as a variable-number-nodes element and can also be employed as a fully compatible transition element to model shell intersections.
233 citations
TL;DR: In this article, Petrov-Galerkin nonsymmetric weighting for the convective diffusion equation can be interpreted as an added dissipation, and the addition of an appropriate amount of dissipation can therefore give the same oscillation-free solutions as the "unwinding", Petrov and Galerkin, finite element methods.
Abstract: In one dimension, Petrov—Galerkin nonsymmetric weighting for the convective diffusion equation can be interpreted as an added dissipation. The addition of an appropriate amount of dissipation can therefore give the same oscillation-free solutions as the ‘unwinding’, Petrov—Galerkin, finite element methods. The ‘balancing dissipation’ is optimally chosen so that excessive dissipation does not occur. A scheme is presented for extending this approach to two-dimensional problems, and numerical examples show that the new method can be used with improved computational efficiency.
186 citations
TL;DR: In this article, a boundary-location method for finite element simulation of steady, two-dimensional flows of Newtonian liquid with free boundaries is developed, where boundary shape and position and the velocity and pressure fields are simultaneously determined.
Abstract: A boundary-location method is developed for finite element simulation of steady, two-dimensional flows of Newtonian liquid with free boundaries. In the method, boundary shape and position and the velocity and pressure fields are determined simultaneously. Inertial, viscous, gravitational, and surface tension effects are included in the development. The complete set of nonlinear finite element equations is solved by a modified frontal method combined with Newton-Raphson iteration to speed convergence. The finite element used to illustrate the method approximates the pressure as a piecewise constant function and the velocity and free boundaries as piecewise linear functions. Example calculations for flow from a slit show that the method can be effective.
182 citations
01 Jan 1980
181 citations
01 Jan 1980
TL;DR: In this paper, the convergence results for the semi-discrete finite element Galerkin approximation of the nonstationary Navier-Stokes problem are established for a wide class of so-called conforming and nonconforming elements as described in the literature for modelling incompressible flows.
Abstract: In this note we report some basic convergence results for the semi-discrete finite element Galerkin approximation of the nonstationary Navier-Stokes problem Asymptotic error estimates are established for a wide class of so-called conforming and nonconforming elements as described in the literature for modelling incompressible flows Since the proofs are lengthy and very technical the present contribution concentrates on a precise statement of the results and only gives some of the key ideas of the argument for proving them Complete proofs for the case of conforming finite elements may be found in a joint paper of J Heywood, R Rautmann and the author [5], whereas the nonconforming case will be treated in detail elsewhere
167 citations
TL;DR: In this article, a finite element technique for solving multidimensional flow problems with moving boundaries is developed by means of Galerkin's procedure, which accounts automatically for continuous grid deformation during simulation, and utilizes finite difference techniques in the time domain.
TL;DR: In this article, a finite element model for the prediction of discrete fracture propagation in rock structures loaded in compression is presented, which integrates any one of three theories for mixed-mode fracture initiation; it contains an energy balance algorithm for predicting crack increment length.
Abstract: A finite element model for the prediction of discrete fracture propagation in rock structures loaded in compression is presented. The model integrates any one of three theories for mixed-mode fracture initiation; it contains an energy balance algorithm for predicting crack increment length, and incorporates recent developments in finite element stress-intensity factor computation. The predictions of the model are compared with the observed fracture response of a real rock structure. Results show that the model accurately predicts both stable and unstable fracture progagations observed experimentally.
TL;DR: In this article, a hybrid element was developed to account for notch-tip singularities of type rγ, where γ can be complex and proper normalization of the notch tip element size was used to minimize the oscillation of the assumed function around the boundaries of the element and improve the accuracy of the solution.
Abstract: Special accurate and efficient hybrid elements were developed to account for notch-tip singularities of type rγ, where γ can be complex. Proper normalization of the notch-tip element size was used to minimize the oscillation of the assumed function around the boundaries of the element and to improve the accuracy of the solution. Examples of various notch angles and sizes are presented.
TL;DR: In this article, a finite element method incorporating the method of characteristics for the solution of diffusion-convection equation with variable coefficients in one spatial dimension is developed, which employs spatial-temporal elements with sides joining the nodes at subsequent time levels oriented in particular directions.
TL;DR: In this article, the exact differential equations governing the static behavior of an infinitesimal element are presented for dynamical analysis of helical rods, where the element stiffness and mass matrices are based on exact differential equation governing static behaviour of the element.
TL;DR: A concise and efficient algorithm is presented for deriving finite element shape functions from an arbitrary set of independent functions and a variety of two- and three-dimensional interpolatory schemes are developed which are useful for modelling singular behaviour.
Abstract: A concise and efficient algorithm is presented for deriving finite element shape functions from an arbitrary set of independent functions. Based on special one-dimensional interpolatory schemes derived via the algorithm, a variety of two- and three-dimensional interpolatory schemes are developed which are useful for modelling singular behaviour. The methodology presented is general and may be fruitfully applied to the development of ‘special’ finite element shape functions for a variety of other situations.
01 Jan 1980
TL;DR: In this paper, general variational theorems for the rate problem of classical elastoplasticity at finite strains, in both Updated Lagrangian (UL) and Total Lagrangians (TL) rate forms, and in terms of alternate measures of stress-rate and conjugate strain-rates, are critically studied from the point of view of their application.
Abstract: General variational theorems for the rate problem of classical elastoplasticity at finite strains, in both Updated Lagrangian (UL) and Total Lagrangian (TL) rate forms, and in terms of alternate measures of stress-rate and conjugate strain-rates, are critically studied from the point of view of their application. Attention. is primarily focused on the derivation of consistent complementary energy rate principles which could form the basis of consistent and rational assumed stress-type finite element methods, and two such principles, in both UL and TL forms, are newly stated. Systematic procedures to exploit these new principles in the context of a finite element method are discussed. Also discussed are certain general modified variational theorems which permit an accurate numerical treatment of near incompressible behavior at large plastic strains
TL;DR: In this article, a formula is derived for determining the stress intensity factors from the path independent J-integral which has been formulated in the previous paper as the energy release rate by taking the effect of inertia into account.
TL;DR: In this paper, it was shown that the finite element method is bounded in Lo0, on polygonal domains, by a discrete weak maximum principle of the form 11uhIllL 42.
Abstract: Let Q2 be a polygonal domain in the plane and Shr(92) denote the finite element space of continuous piecewise polynomials of degree 2) defined on a quasi-uniform triangulation of Q2 (with triangles roughly of size h) It is shown that if uh E Sh(n) is a "discrete harmonic function" then an a priori estimate (a weak maximum principle) of the form 11uhIllL 42) This says that (modulo a logarithm for r = 2) the finite element method is bounded in Lo0, on plane polygonal domains 0 Introduction and Statement of Results The purpose of this paper is to discuss some estimates for the finite element method on polygonal domains In particular, we shall consider the validity of (for want of a better terminology) a "discrete weak maximum principle" for discrete harmonic functions and then use this result to discuss the boundedness in Loo of the finite element projection In this part we shall discuss the case of a quasi-uniform mesh In Part II we shall concern ourselves with meshes which are refined near points Let us first formulate the problems we wish to consider and state our results References to other work in the literature which are relevant to our considerations will be given as we go along For simplicity let Q2 be a simply connected (this is not essential) polygonal domain in R2 with boundary 3Q2 and maximal interior angle a, 0 < a < 2ir, where we emphasize that in general Q2 is not convex On Q2 we define a -family of finite element spaces For simplicity of presentation we shall restrict ourselves to a special but important class of piecewise polynomials For each 0 < h < 1, let Th denote a triangulation of Q2 with triangles having straight edges We shall assume that each triangle r is contained in a sphere of radius h and contains a sphere of radius yh for some positive constant y We shall also assume that the family {Tn } of triangulations Received September 19, 1978 AMS (MOS) subject classifications (1970) Primary 65N30, 65N15 *This work was supported in part by the National Science Foundation ? 1980 American Mathematical Society 0025-571 8/80/0000-0004/$0475 77 This content downloaded from 1575539253 on Wed, 08 Jun 2016 05:26:01 UTC All use subject to http://aboutjstororg/terms
TL;DR: In this article, the convergence requirements for a finite element may be written as a set of linear constraints on the stiffness matrix, and then a best possible stiffness matrix is constructed by constructing a stiffness matrix from the constraint equations.
Abstract: It is shown how the convergence requirements for a finite element may be written as a set of linear constraints on the stiffness matrix. It is then attempted to construct a best possible stiffness matrix. The constraint equations restrict the way in which these stiffness terms may be chosen; however, there is normally still room for improving or optimizing an element. It is demonstrated how an element stiffness matrix may be found using rigid body, constant strain and higher order deformation modes. Further, it is shown how the constraint equations may be exploited in deriving an ‘energy orthogonality theorem’. This theorem opens the door to a whole new class of simple finite elements which automatically satisfy the convergence requirements. Examples of deriving plane stress and plate bending elements are given.
TL;DR: In this article, a three dimensional finite element formulation and algorithm for the solution of 3D magnetic fields was developed with applications to determination of local flux densities in a 3D field pattern, as well as global energy calculations of an air cored coil.
Abstract: A three dimensional finite element formulation and algorithm for the solution of 3-d magnetic fields was developed. The method is presented here with applications to determination of local flux densities in a 3-d field pattern, as well as global energy calculations of an air cored coil. The results compare well with closed form solution results. Experimental test data of the coil inductance is in agreement with finite element results. The development represents a new technique which is a potentially very powerful tool in many practical applications.
TL;DR: In this paper, the optimal shape design of plane or axisymmetric structures in order to minimize the stress concentration factor along the boundary is discussed, which is described by straight lines and circles.
Abstract: This paper is concerned with the optimal shape design of plane or axisymmetric structures in order to minimize the stress concentration factor along the boundary. This boundary is described by straight lines and circles. The structure is analysed using the finite element method, and the optimization procedure is based on an extended interior penalty function. Three example problems are reported.
TL;DR: In this paper, a finite element method for kineto-elastodynamic analysis of high speed mechanisms has been presented and the effects of number of divisions have been investigated and it is found that a certain minimum number of division of links is necessary to yield accurate results.