Showing papers on "Smoothed finite element method published in 1979"
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
Book•
05 Nov 1979256 citations
236 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.
190 citations
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.
154 citations
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.
131 citations
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.
79 citations
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.
67 citations
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
TL;DR: In this article, the authors presented two finite element models for the prediction of free vibrational natural frequencies of fixed-free beams of general orthotropy, including the transverse shear deformation effect and the rotary inertia effect.
TL;DR: Finite-element methods to approximate both inviscid and viscous incompressible flow problems are presented and it is shown that such a scheme can be extended to viscous flow if the viscosity terms are treated through mixed finite elements.
TL;DR: A finite element method for the solution of viscous incompressible flow problems which incorporates an approximate form of the incompressibility condition automatically into the finite element basis is described.
Abstract: We describe in this paper a finite element method for the solution of viscous incompressible flow problems which incorporates an approximate form of the incompressibility condition automatically into the finite element basis. Several examples of such finite elements are presented and applied to a simple test problem.
TL;DR: In this paper, a 5-level global model is described in which finite element methods are used to describe the variations of fields in the horizontal domain, and three versions of the model are used: two use velocity components as dependent variables but differ in horizontal resolution; the third uses stream function and velocity potential.
Abstract: A 5-level global model is described in which finite element methods are used to describe the variations of fields in the horizontal. Three versions of the model are used: two use velocity components as dependent variables but differ in horizontal resolution; the third uses stream function and velocity potential. The results show that the finite element models are competitive with existing finite difference models but proper comparison is difficult because of the large effect of certain special features of the models, for instance the treatment of the poles. The change in dependent variable has a much greater impact on the results than a change in resolution with no change in formulation.
TL;DR: An overview is presented of the authors' recent theoretical and experimental results on reliable and computationally efficient a - posteriori error bounds for finite element solutions and the design of an experimental finite element system currently under development which incorporates many of these ideas and results.
01 Jan 1979
TL;DR: In this article, a simplified finite element method has been developed for analyzing the acoustic resonances of a prismatic car cavity in one direction (across the width of the car) with a consequent reduction of computing effort.
TL;DR: Finite element methods and the associate collocation methods are considered for solving first-order hyperbolic systems, positive in the sense of Friedrichs as mentioned in this paper, which leads for example to the successfully used box scheme for the heat equation or D.S.N.
Abstract: Finite element methods and the associate collocation methods are considered for solving first-order hyperbolic systems, positive in the sense of Friedrichs. Applied in the case when the meshes are rectangle, those methods lead for example to the successfully used box scheme for the heat equation or D.S.N. scheme for the neutron transport equation. Generalizations of these methods are described here for nonrectangle meshes and (or) noncylindrical domains; stability results and error estimates are derived.
01 Jan 1979
TL;DR: Finite element procedures for analysis of nonlinear dynamic problems in solid and structural mechanics and fluid-structure interaction are surveyed and assessed in this article, and some demonstrative analysis results are given that indicate the present state-of-the-art in non-linear dynamic analysis.
Abstract: Finite element procedures for analysis of nonlinear dynamic problems in solid and structural mechanics and fluid-structure interaction are surveyed and assessed. Effective finite element formulations for highly nonlinear continuum and structural mechanics problems are summarized, modeling considerations for analysis of structural dynamics and wave propagation problems are described, and time integration procedures for the solution of the equations of motion are discussed. Some demonstrative analysis results are given that indicate the present state-of-the-art in nonlinear dynamic analysis.
TL;DR: In this article, a finite element simulation of the equations of momentum and energy transport in fluids has been implemented with triangular elements, and it is shown that the appearance of instability can be delayed by a proper choice of boundary conditions, and its intensity can be reduced through the use of triangular finite elements.
Abstract: A finite element simulation of the equations of momentum and energy transport in fluids has been implemented with triangular elements. An attempt is made to single out the reasons for numerical instabilities reported by other investigators for convection–diffusion transport operations in fluid mechanics when the ratio of the convective to the diffusive terms, measured by the Reynolds and Peclet numbers, is of the order of a hundred. To this end, the equations are solved for several problems to permit a direct comparison with results of other formulations. It is shown that the appearance of instability can be delayed by a proper choice of boundary conditions, and its intensity can be reduced through the use of triangular finite elements. Results agree very well with theoretical solutions for particular test problems including flows with large convection effects, large dissipation effects and fluids with temperature dependent properties.
TL;DR: A SPECIAL difference scheme is presented for solving elliptic problems with a large step of the computing mesh and some ideas of the finite element method are used.
Abstract: A SPECIAL difference scheme is presented for solving elliptic problems with a large step of the computing mesh. Some ideas of the finite element method are used. The possibilities of the scheme are illustrated by examples of calculations of fairly complex solutions with a small number of computing points.
TL;DR: In this article, the authors discuss propagation of sharp signals, problems with different time scales and the effect of boundaries on stability and accuracy of finite element methods for hyperbolic equations.