Showing papers on "Extended finite element method published in 1979"
01 Jan 1979
TL;DR: A mixed finite element method for solving the stokes problem and the time-dependent navier-stokes equations are presented.
Abstract: Mathematical foundation of the stokes problem.- Numerical solution of the stokes problem a classical method.- A mixed finite element method for solving the stokes problem.- The stationary navier-stokes equations.- The time-dependent navier-stokes equations.- Erratum.
1,238 citations
TL;DR: In this article, a review of recent work and new developments for the penalty function/finite element formulation of incompressible viscous flows is presented, in the context of the steady and unsteady Navier-Stokes equations.
548 citations
TL;DR: In this article, a quisi-Nowton method was proposed to solve nonlinear finite element equations, and initial tests of its application to both material and geometric nonlinearities are discussed.
Abstract: An algorithm is described which appears to give an efficient solution of nonlinear finite element equations. It is a quisi-Nowton method, and we compare it with some of the alternatives. Initial tests of its application to both material and geometric nonlinearities are discussed.
537 citations
TL;DR: In this article, a shallow water wave equation is developed from the primitive two-dimensional shallow water equation, and a finite element model based on this equation and the primitive momentum equation are developed.
374 citations
TL;DR: In this article, error estimates for a class of finite element approximation of the Stokes equation are derived from a new Brezzi-type inequality for this kind of mixed formulation, which is true in 2 or 3 dimensions.
Abstract: In this paper we derive error estimates for a class of finite element approximation of the Stokes equation. These elements, popular among engineers, are conforming lagrangian both in velocity and pressure and therefore based on a mixed variational principle. The error estimates are established from a new Brezzi-type inequality for this kind of mixed formulation. The results are true in 2 or 3 dimensions.
334 citations
Book•
05 Nov 1979256 citations
236 citations
TL;DR: A finite element formulation of the equations governing the laminated anisotropic plate theory of Yang, Norris and Stavsky, is presented in this article, which is a generalization of Mindlin's theory for isotropic plates to laminated aisotropic plates and includes shear deformation and rotary inertia effects.
196 citations
TL;DR: In this paper, an effective solution procedure for the finite element analysis of free surface seepage problems is presented, which employs a non-linear permeability description of the material and avoids iteration with finite element mesh.
Abstract: SUMMARY An effective solution procedure for the finite element analysis of free surface seepage problems is presented. The solution algorithm employs a non-linear permeability description of the material and avoids iteration with the finite element mesh. The results and experiences obtained in the analyses of some problems are presented to demonstrate the usefulness of the technique. The phenomena of fluid flow or seepage through porous media is observed in various disciplines of engineering.''2 It appears therefore natural that, as soon as the generality of the finite element method of analysis was recognized, emphasis was directed to develop the finite element method also for analysis of seepage problems in order to obtain a more genera1 analysis tooL3 Apart from being able to consider in an effective manner complex geometries and material properties, emphasis on the development of the finite element analysis pro- cedures is also important because of the potential of the technique for analysis of coupled stress and fluid flow problems.4s5 The current practice using the finite element method in the analysis of free surface fluid flow through porous media is to assume a free surface, discretize the domain below the free surface using finite elements, solve for the flow conditions in the finite element model, and check whether the free surface boundary conditions are satisfied with sufficient accuracy. If the flow conditions at the free surface are not satisfied to a specified tolerance, the free surface is adjusted and the problem is resolved until the free surface flow conditions are met. Depending on the problems considered, some 10 to 30 iterations may be necessary in steady-state analysis, and in transient analysis an iteration is carried out in the time steps of the time response calculation. In the iteration for the free surface, each iteration step represents a new problem, and a new finite element mesh could be established in each step. However, to keep the analysis effort to a minimum, usually the same basic finite element mesh is employed, but the geometric locations of the nodal points (possibly only near the free surface) are adjusted. The disadvantages of this scheme are that the elements can become very distorted, thus introducing severe errors in the analysis, and that a relatively large computational effort is required. These disadvantages are particularly pronounced in three-dimensional analysis. If non-linear stress and flow conditions * Associate Professor. t Research Assistant.
TL;DR: A finite element of the penalization type for the solution of incompressible viscous Navier-Stokes equations using an isoparametric parabolic element is presented in this article.
TL;DR: In this paper, a combination of the two methods for elastostatics appears to be by Osias, lachat, and Lachat-Lachat interpolation functions are used to define the variables along these elements.
TL;DR: An overview is presented of the authors' recent theoretical and experimental results on reliable and computationally efficient a posteriori error estimates for finite element solutions, and how the results can be extended to the nonlinear case without losing their effectivity.
TL;DR: In this article, a simple, efficient and versatile finite element is introduced for shell applications based on a degeneration concept, in which the displacements and rotations of the shell mid-surface are independent variables.
Abstract: A simple, efficient and versatile finite element is introduced for shell applications. The element is developed based on a degeneration concept, in which the displacements and rotations of the shell mid-surface are independent variables. Bilinear functions are employed in conjunction with a reduced integration for the transverse shear energy. Several examples are tested to demonstrate the effectiveness and versatility of the element. The numerical results indicate that the shell element performs accurately for both thick and thin shell situations.
TL;DR: In this paper, a class of equilibrium finite element methods for elasticity problems is considered, where the approximate stresses satisfy the equilibrium equations but the symmetry of the stress tensor is relaxed.
Abstract: We consider a class of equilibrium finite element methods for elasticity problems. The approximate stresses satisfy the equilibrium equations but the symmetry of the stress tensor is relaxed. Optimal error bounds for the stresses and numerical examples are given.
TL;DR: In this article, a finite element analysis technique for an arbitrarily laminated anisotropic plate is described and a superparametric quadratic plate element with five degrees of freedom per node is used in the analysis.
Abstract: A finite element analysis technique for an arbitrarily laminated anisotropic plate is described. A superparametric quadratic plate element with five degrees-of-freedom per node is used in the analysis. A stress-strain relation is derived from a three-dimensional approach to the problem. The volume integration of the stiffness matrix is evaluated by numerical integration using the Gauss quadrature formula with 2 × 2 × 2 sampling points. A variety of laminated plate problems is solved and the results are compared with the exact solutions, which demonstrate the validity of the method.
TL;DR: In this paper, finite element analysis procedures are utilized to provide theoretical calibration curves for the electrical potential crack-monitoring system as applied to single-edge-notch (SEN) and compact tension (CT) fracture specimens.
Abstract: Finite element analysis procedures are utilized to provide theoretical calibration curves for the electrical potential crack-monitoring system as applied to single-edge-notch (SEN) and compact tension (CT) fracture specimens. The results are compared to existing calibrations for such test piece geometries derived using experimental, electrical analog and analytical (conformal mapping) procedures.
TL;DR: In this article, an upstream finite element scheme is presented for overcoming the problem of numerical oscillations associated with the transient transport equation for convective dominated or purely convective flow, where spatial discretization is performed via a general weighted residual technique which employs asymmetric weighting functions and yields upstream weighting of the convective term in the transport equation.
TL;DR: In this paper, two numerical models for simulating three-dimensional, two-phase fluid flow and heat transport in geothermal reservoirs are introduced, one based on a 3D formulation of the governing equations for geothermal reservoir and the other based on partial integration of the 3D equations in the vertical dimension.
Abstract: Two numerical models are introduced for simulating three-dimensional, two-phase fluid flow and heat transport in geothermal reservoirs. The first model is based on a three-dimensional formulation of the governing equations for geothermal reservoirs. Since the resulting two partial differential equations, posed in terms of fluid pressure and enthalpy, are highly nonlinear and inhomogeneous, they require numerical solution. The three-dimensional numerical model uses finite difference approximations, with fully implicit Newton-Raphson treatment of nonlinear terms and a block (vertical slice) successive iterative technique for matrix solution. Newton-Raphson treatment of nonlinear terms permits the use of large time steps, while the robust iterative matrix method reduces computer execution time and storage for large three-dimensional problems. An alternative model is derived by partial integration (in the vertical dimension) of the three-dimensional equations. This second model explicitly assumes vertical equilibrium (gravity segregation) between steam and water and can be applied to reservoirs with good vertical communication. The resulting equations are posed in terms of depth-averaged pressure and enthalpy and are solved by a two-dimensional finite difference model that uses a stable sequential solution technique, direct matrix methods, and Newton-Raphson iteration on accumulation and source terms. The quasi-three-dimensional areal model should be used whenever possible, because it significantly reduces computer execution time and storage and it requires less data preparation. The areal model includes effects of an inclined, variable-thickness reservoir and mass and energy leakage to confining beds. The model works best for thin (<500 m) reservoirs with high permeability. It can also be applied to problems with vertical to horizontal anisotropy when permeability is sufficiently high. Comparisons between finite difference and higher-order finite, element approximations show some advantage in using finite element techniques for single-phase problems. In general, for nonlinear two-phase problems the finite element method requires use of upstream weighting and diagonal lumping of accumulation terms. These lead to lower-order approximations and tend to obviate any advantage of using the finite element method.
TL;DR: In this article, a new mixed finite element approximation of the Stokes' problem in the velocity pressure formulation was proposed, which is based on a new variational principle allowing the use of low order Lagrange elements and leads to optimal order of convergence for the velocity and the pressure.
Abstract: We study in this paper a new mixed finite element approximation of the Stokes' problem in the velocity pressure formulation. This approximation which is based on a new variational principle allows the use of low order Lagrange elements and leads to optimal order of convergence for the velocity and the pressure. Iterative and direct methods for the solution of the approximate problems will be discussed in a forthcoming paper.
TL;DR: A method of introducing general constraint equations into finite element matrix equations is described that requires no reordering or condensation of the equations, no large matrix operations, and no increase in the number of unknowns.
Abstract: A method of introducing general constraint equations into finite element matrix equations is described. The characteristics of the method are that it requires no reordering or condensation of the equations, no large matrix operations, and no increase in the number of unknowns. The method is suitable for application in minicomputer implementations of finite element analysis unless a large number of constraints is to be applied.
TL;DR: In this paper, a method for representing mild geometrically nonlinear static behavior of thin-type structures, within the finite element method, in terms of the solution of a certain eigenvalue problem is described.
TL;DR: A new approach to gain control of the discretization error by increasing the number of degrees of freedom in regions where the initial finite element model is not adequate is demonstrated by applications to two- and three-dimensional elasticity, including singularity problems.
TL;DR: In this article, the elasticity matrix of a general-purpose finite element program, SAPIV, is modified in such a way that it becomes possible to idealize water as a structural finite element with zero shear modulus.
TL;DR: In this paper, a finite element approach is proposed for the static and dynamic nonlinear analysis of cable structures, in which a variational formulation of equilibrium equations is derived in which static and kinematic variables are measured in some previous configuration of the body.
Book•
01 Jan 1979
TL;DR: A practical introduction to finite element analysis is presented and a comparison study of the determinants of infectious disease and infectious diseaseenza is presented.
Abstract: A practical introduction to finite element analysis , A practical introduction to finite element analysis , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی