Showing papers on "Finite element method published in 1979"
TL;DR: In this paper, an incremental approach to the solution of buckling and snapping problems is explored, where the authors use the length of the equilibrium path as a control parameter, together with the second order iteration method of Newton.
1,821 citations
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
Book•
10 May 1979TL;DR: The terminology, coordinate systems, and fundamental concepts of structural behavior are defined, laying the foundation for the study of more advanced treatments such as the finite element method.
Abstract: Examines computerized structural analysis methods for buildings, bridges, and other structures, with special emphasis on current practices. Covers the stiffness analysis of frames, the flexibility method, virtual work principles, special analysis procedures, and more. Defines the terminology, coordinate systems, and fundamental concepts of structural behavior, laying the foundation for the study of more advanced treatments such as the finite element method.
454 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
TL;DR: The methods are shown to have improved implementational properties and may be easily coded into many existing implicit computer programs, and techniques for improving the accuracy in the explicit group, without adverseley affecting stability, are described.
289 citations
TL;DR: In this article, three objective methods for the propagation of a crack band of a blunt front are proposed based on the rate of energy release by the crack band and the angle of the crack front.
Abstract: A propagating smeared crack band of blunt front is much simpler to model by finite elements than a sharp interelement crack, especially when the propagation direction is unknown. For concrete or rock, a smeared crack band is also more realistic. A strength criterion is generally used for the propagation, but this is not objective because of a strong spurious dependence of results on the chosen element size, Three objective methods, which avoid the use of singularity elements, are proposed. Method A is based on the rate of energy release by the blunt crack band. In method B, the usual strength criterion is used but an adjustment of the strength value according to the element size is proposed. In method C, the propagation direction and crack advance are determined by fitting the Mode I asymptotic series to nodal displacements around the crack front, using an optimization subroutine. Special merits of each method are analyzed and solutions of example problems are compared with exact ones.
261 citations
TL;DR: In this article, the finite element method is used to solve a second order elliptic boundary value problem on a polygonal domain, and weighted Besov spaces are used to obtain optimal error estimates and inverse theorems.
Abstract: The finite element method is used to solve a second order elliptic boundary value problem on a polygonal domain. Mesh refinements and weighted Besov spaces are used to obtain optimal error estimates and inverse theorems.
TL;DR: In this paper, the J-line integral was used to extract the magnitude of crack tip stress intensity factors from finite element solutions for thermal stress crack problems, and the properties of the J line integral in the presence of thermal stresses were determined.
Abstract: Methods of using the J-line integral to extract the magnitude of crack tip stress intensity factors from finite element solutions for thermal stress crack problems are presented. The properties of the J-line integral in the presence of thermal stresses are determined. From these properties a procedure for calculating crack tip stress intensity factors is developed. Also a superposition method involving crack surface tractions is presented for thermal stress crack problems. In this procedure the J-line integral path must include segments of the crack surface. All methods developed are illustrated by numerical examples.
Book•
01 Jan 1979
TL;DR: The Methode des elements finis Reference Record was created on 2004-09-07 and will be updated on 2016-08-08.
Abstract: Keywords: Methode des elements finis Reference Record created on 2004-09-07, modified on 2016-08-08
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.
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: In this article, the effects of the root radius, the setting angle and the tip mass are incorporated into the finite element model to investigate the vibration frequency of a rotating beam with tip mass.
TL;DR: In this article, the problem of constructing compatible interior and boundary subspaces for finite element methods with Lagrange multipliers to approximately solve Dirichlet problems for second-order elliptic equations was studied.
Abstract: The paper is concerned with the problem of constructing compatible interior and boundary subspaces for finite element methods with Lagrange multipliers to approximately solve Dirichlet problems for secondorder elliptic equations. A new stability condition relating the interior and boundary subspaces is first derived, which is easier to check in practice than the condition known so far. Using the new condition, compatible boundary subspaces are constructed for quasiuniform triangular and rectangular interior meshes in two dimensions. The stability and optimal-order convergence of the finite element methods based on the constructed subspaces are proved.
TL;DR: In this paper, a finite element method and load incremental theory is used to solve non-linear contact problems with irreversibility resulting from stick-slip phenomenon. But the method is not suitable for the case of gear teeth in mesh and shrink-fitted shafts.
Abstract: The use of contacting components such as gear teeth in mesh and shrink-fitted shafts is very common in engineering practice. This paper deals with the development of a theoretical method which gives a solution for non-linear contact problems with irreversibility resulting from stick-slip phenomenon.
The method is based on the finite element method and load incremental theory. The geometrical and the statical boundary conditions on contact surfaces are treated as additional conditions being independent of stiffness equations. As a result, the algorithm of calculation is simplified and only a part of the simultaneous equations related to the contact surfaces is required to be solved instead of the overall stiffness equations at each step. Furthermore, the magnitude of load causing a change in a contact condition of one contact nodepair is taken as a load increment, in analogy with the incremental iterative procedure for elastic-plastic problems. Therefore, the method provides a general and efficient method for analysis and design of such problems.
As illustrative examples, the stick-slip behaviour of turbo-alternator end-bells and other problems are discussed. The calculated results show a reasonable agreement with experimental data and other solutions.
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 article, the major sources of nonlinearities in reinforced concrete structures are discussed and a large number of proposed mathematical models for the material behaviour of concrete and reinforcement and for the interactive behaviour between the two materials.
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: In this article, a variational finite-element algorithm was proposed to solve the problem of time-harmonic electromagnetic scattering by axisymmetric penetrable bodies having arbitrary cross-sectional profiles and continuous inhomogeneous consistency.
Abstract: This investigation is concerned with the numerical solution of time-harmonic electromagnetic scattering by axisymmetric penetrable bodies having arbitrary cross-sectional profiles and even continuously inhomogeneous consistency. The initiation of this effort involved the discovery and development of the coupled azimuthal potential (CAP) formulation, which is valid in generally lossy isotropic inhomogeneous rotationally symmetric media. Electromagnetic fields in such regions can be represented, using the CAP formulation, in terms of two continuous potentials which satisfy a self-adjoint system of partial differential equations or, equivalently, a variational criterion. Using an optimized variational finite-element algorithm in conjunction with a triregional unimoment method, a versatile computer program is described that provides scattering solutions for each of multiple incident fields impinging upon an arbitrarily shaped inhomogeneous penetrable body of revolution. An extensive evaluation of the accuracy and convergence of the algorithm is presented, which includes comparison of scattering computations and experimental measurements at X -band for several solid and hollow plexiglas bodies of revolution with maximum interior dimensions of over 4 wavelengths.
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 paper, a simple method is presented for modeling perforated muffler components, such as concentric resonators and expansion chambers, with one acoustically long dimension, using a segmentation procedure in which each segment is described by a transmission matrix.
Abstract: A simple method is presented for modeling perforated muffler components such as concentric resonators with perforated flow tube, and expansion chambers and reverse flow chambers with perforated inlet and outlet tubes. The theory includes mean flow, but is confined to those configurations having one acoustically long dimension. It is based on a segmentation procedure in which each segment is described by a transmission matrix. The four‐pole parameters of a component are then found from the product of the transmission matrices. The four‐pole parameters for configurations having through flow, cross flow, and reverse flow are presented. Because the product matrices are dimensionally small and because no inversion is needed, computational time is much lower than other methods such as finite element or finite difference. This allows rapid and economical modeling to be performed where iterative solutions are required because of dominating finite amplitude effects, for example.
TL;DR: For a two-point boundary-value problem the existence of a unique optimal mesh distribution is proved and its properties are analyzed, allowing for rather straightforward extensions to more general problems in one dimension as well as to higher-order elements.
Abstract: A theory of a posteriori estimates for the finite element method has been developed. On the basis of this theory, for a two-point boundary-value problem the existence of a unique optimal mesh distribution is proved and its properties are analyzed. This mesh is characterized in terms of certain, easily computable local error indicators which in turn allow for a simple adaptive construction of the mesh and also permit the computation of a very effective a posteriori error bound. While the error estimates are asymptotic in nature, numerical experiments show the results to be excellent already for 10% accuracy. The approaches are not restricted to the model problem considered here only for clarity; in fact, they allow for rather straightforward extensions to more general problems in one dimension as well as to higher-order elements. 11 tables.
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 variational modal interaction scheme was proposed for the use of the acoustic eigenmodes of the liquid in a rigid motionless enclosure and the hydroelastic modes of the enclosure.
Abstract: The finite element method is used for the computation of the variational modes of the system composed of an elastic tank partially filled with a compressible liquied. We propose, on the one hand, a direct approcach based on a three field mixed variational formulation, and, on the other hand, a variational modal interaction scheme allowing the use of the acoustic eigenmodes of the liquid in a rigid motionless enclosure and the hydroelastic modes of the enclosure. Numerical results show the advantage of the second procedure.