Showing papers on "Finite element method published in 1982"
Book•
01 Jan 1982
TL;DR: Elements finis Reference Record created on 2004-09-07, modified on 2016-08-08.
Abstract: Keywords: Methode des elements finis ; Mathematique ; Elements finis Reference Record created on 2004-09-07, modified on 2016-08-08
5,049 citations
TL;DR: In this paper, a semidiscrete finite element method for the solution of second order nonlinear parabolic boundary value problems is formulated and analyzed, where the test and trial spaces consist of discontinuous piecewise polynomial functions over quite general meshes with interelement continuity enforced approximately by means of penalties.
Abstract: A new semidiscrete finite element method for the solution of second order nonlinear parabolic boundary value problems is formulated and analyzed. The test and trial spaces consist of discontinuous piecewise polynomial functions over quite general meshes with interelement continuity enforced approximately by means of penalties. Optimal order error estimates in energy and $L^2$-norms are stated in terms of locally expressed quantities. They are proved first for a model problem and then in general.
1,607 citations
TL;DR: In this article, an arbitrary Lagrangian-Eulerian kinematical description of the fluid domain is adopted in which the grid points can be displaced independently of fluid motion.
1,392 citations
Book•
01 Jan 1982
TL;DR: In this paper, the Finite Element Method is used to derive a system equation from a set of finite element vectors and matrices and then to solve the problem of finding the solution.
Abstract: 1. Overview of the Finite Element Method, 2. Discretization of the Domain, 3. Interpolation Models, 4. Higher Order and Isoparametric Elements, 5. Derivation of Element Matrices and Vectors, 6. Assembly of Element Matrices and Vectors and Derivation of System Equations, 7. Numerical Solution of Finite Element Equations, 8. Basic Equations and Solution Procedure, 9. Analysis of Trusses, Beams and Frames, 10. Analysis of Plates, 11. Analysis of Three-Dimensional Problems, 12. Dynamic Analysis, 13. Formulation and Solution Procedure, 14. One-Dimensional Problems, 15. Two-Dimensional Problems, 16. Three-Dimensional Problems, 17. Basic Equations of Fluid Mechanics, 18. Inviscid and Incompressible Flows, 19. Viscous and Non-Newtonian Flows, 20. Solution of Quasi-Harmonic Equations, 21. Solution of Helmhotz Equation, 22. Solution of Reynolds Equation, Appendix-A Green Greass Theorem.
1,247 citations
TL;DR: Second-order error estimates are proven for spatial discretization, using conforming or nonconforming elements, and indicate a fluid-like behavior of the approximations, even in the case of large data, so long as the solution remains regular.
Abstract: This is the first part of a work dealing with the rigorous error analysis of finite element solutions of the nonstationary Navier–Stokes equations. Second-order error estimates are proven for spatial discretization, using conforming or nonconforming elements. The results indicate a fluid-like behavior of the approximations, even in the case of large data, so long as the solution remains regular. The analysis is based on sharp a priori estimates for the solution, particularly reflecting its behavior as$t \to 0$ and as $t \to \infty $. It is shown that the regularity customarily assumed in the error analysis for corresponding parabolic problems cannot be realistically assumed in the case of the Navier–Stokes equations, as it depends on nonlocal compatibility conditions for the data. The results which are presented here are independent of such compatibility conditions, which cannot be verified in practice.
784 citations
TL;DR: An error bound is given that holds also for the Navier-Stokes equations even when the Reynolds number is infinite (Euler equation) and for thePDE in Lagrangian form.
Abstract: This paper deals with an algorithm for the solution of diffusion and/or convection equations where we mixed the method of characteristics and the finite element method. Globally it looks like one does one step of transport plus one step of diffusion (or projection) but the mathematics show that it is also an implicit time discretization of thePDE in Lagrangian form. We give an error bound (h+Δt+h×h/Δt in the interesting case) that holds also for the Navier-Stokes equations even when the Reynolds number is infinite (Euler equation).
697 citations
TL;DR: In this article, an efficient method for finite element modeling of three-layer laminates containing a viscoelastic layer is described, and modal damping ratios are estimated from undamped normal mode results by means of the modal strain energy method.
Abstract: An efficient method is described for finite element modelling of three-layer laminates containing a viscoelastic layer. Modal damping ratios are estimated from undamped normal mode results by means of the modal strain energy method. Comparisons are given between results obtained by the MSE method implemented in NASTRAN, by various exact solutions for approximate governing differential equations, and by experiment. Results are in terms of frequencies, modal damping ratios, and mechanical admittances for simple beams, plates, and rings. Application of the finite element -- MSE method in design of integrally damped structures is discussed.
542 citations
Book•
01 May 1982
TL;DR: An overview of the fundamental concepts and applications of computerized groundwater modeling can be found in this paper, where the authors present an overview of some of the basic concepts and application of groundwater modeling.
Abstract: Introduction to Groundwater Modeling presents an overview of the fundamental concepts and applications of computerized groundwater modeling.
399 citations
369 citations
TL;DR: A comprehensive study of numerical techniques for solving the atmospheric diffusion equation is reported in this article, in which the three-dimensional problem is converted into a sequence of one-dimensional problems, and a Galerkin, linear finite element scheme with a nonlinear filter is found to be computationally superior to other methods tested for the advection-diffusion components.
320 citations
TL;DR: In this paper, a strain field is assumed and then related to nodal displacements by line integration of the strain field along straight line segments between pairs of nodal points, and the result was not an unqualified success in that the element does not pass the patch test for arbitrary shape, even though it eliminates the locking phenomenon observed in some applications of the corresponding reduced shear isoparametric element.
TL;DR: A finite element method for the solution of two-dimensional transient dispersive-convective transport of non-conservative solute species in fractured porous media is presented in this article, where a two-nodal point one-dimensional transport element for fractures is developed which provides a number of advantages relative to conventional fracture representation by 2-dimensional continuum elements.
Abstract: A finite element method for the solution of two-dimensional transient dispersive-convective transport of nonconservative solute species in fractured porous media is presented. A two-nodal point one-dimensional transport element for fractures is developed which provides a number of advantages relative to conventional fracture representation by two-dimensional continuum elements. To eliminate the oscillatory behavior of convective-dominated transport which is a more likely occurrence in fracture, a very efficient one-dimensional upstreaming method along with a two-dimensional method is implemented. Validity of the numerical scheme is established by comparison with existing one- and two-dimensional analytic solutions.
TL;DR: In this article, an analytical expression for the energy release rate has been derived and put in a form suitable for a numerical analysis of an arbitrary 3-D crack configuration, which is valid for general fracture behavior including nonplanar fracture and shear lips.
Abstract: In this paper an analytical expression for the energy release rate has been derived and put in a form suitable for a numerical analysis of an arbitrary 3-D crack configuration. The virtual crack extension method can most conveniently be used for such a derivation. This method was originally developed from finite element considerations and the resulting expressions were, therefore, based on the finite element matrix formulation [1–5]. In this paper the derivation of the energy release rate leads to an expression which is independent of any specific numerical procedure. The formulation is valid for general fracture behavior including nonplanar fracture and shear lips and applies to elastic materials as well as materials following the deformation theory of plasticity. The body force effect is also included. For 3-D fracture problems it is of advantage to use both an average and a local form of the energy release rate and definitions for both forms are suggested. For certain restrictions on the crack geometry it is shown that the energy release rate reduces to the 3-D form of the J-integral.
TL;DR: In this paper, the exact frequencies and mode shapes for rotating beams in which both the flexural rigidity and the mass distribution vary linearly were solved using the Frobenius method.
Abstract: The method of Frobenius is used to solve for the exact frequencies and mode shapes for rotating beams in which both the flexural rigidity and the mass distribution vary linearly. Results are tabulated for a variety of situations including uniform and tapered beams, with root offset and tip mass, and for both hinged root and fixed root boundary conditions. The results obtained for the case of the uniform cantilever beam are compared with other solutions, and the results of a conventional finite-element code.
TL;DR: In this article, a method for predicting the failure strength and failure mode of mechanically fastened fiber reinforced composite laminates is presented, and the method in cludes two steps.
Abstract: A method is presented for predicting the failure strength and failure mode of mechanically fastened fiber reinforced composite laminates. The method in cludes two steps. First, the stress distribut...
TL;DR: In this paper, the exact virtual work equation for finite element analysis of inelastic problems is presented based on the exact (incremental) virtual work equations, and the procedure for integration of the constitutive rate equations to obtain incremental constitutive equations is based on assumption of a constant strain rate (or straight strain path) during the increment of the Newton-Raphson iteration.
TL;DR: In this paper, a brief review of the formulation of the finite element method for structural-acoustic analysis of an enclosed cavity, and illustrations are given of the application of this analytical method at General Motors Corporation to investigate the acoustics of the automobile passenger compartment.
TL;DR: In this paper, the ability of a displacement-type finite element analysis to predict collapse loads accurately is investigated for undrained geotechnical problems, up to and including those with a quartic displacement expansion.
Abstract: In this paper, the ability of a displacement-type finite element analysis to predict collapse loads accurately is investigated. For the usual assumptions of ideal plasticity and infinitesimal deformations, attention is focused on undrained geotechnical problems. The theoretical criterion originally developed by Nagtegaal et al is applied to each member of the serendipidity quadrilateral and triangular family of elements, up to and including those with a quartic displacement expansion. This method of assessing the suitability of a particular type of element is shown to be valid for any constitutive law which attempts to enforce the constant volume condition at failure, such as critical state type soil models. The method is also generalized to permit an assessment, a priori, of the suitability of any given mesh which is composed of a finite number of elements of the same type. It is postulated that the 15-noded, cubic strain triangle is theoretically capable of accurate computations in the fully plastic range for undrained geotechnical situations which involve axial symmetry or plane strain. This prediction is verified by a series of numerical experiments on footing problems. Extending the work of Nagtegaal et al, it is established theoretically that if lower order finite elements are employed rigorously for non-trivial undrained problems with axial symmetry, then it is impossible to predict the exact limit load accurately, regardless of how refined the mesh may be. (Author/TRRL)
TL;DR: In this article, a finite element method is presented for the numerical simulation of time-dependent incompressible viscous flows, based on a fractional step approach to the time integration of the Navier-Stokes equations in which only the incompressibility condition is treated implicitly.
TL;DR: A new, simple and effective finite element procedure is presented for the practical solution of heat transfer conditions with phase changes with a relatively coarse finite element mesh and large time step.
Abstract: A new, simple and effective finite element procedure is presented for the practical solution of heat transfer conditions with phase changes. In this method, a fixed finite element mesh is employed, and a relatively coarse finite element mesh and large time step can be used in the incremental solution. The results of various numerical studies using the algorithm are presented that demonstrate the effectiveness of the procedure.
TL;DR: In this paper, finite elements in conjunction with elasto-plastic theory can give excellent collapse load predictions for footings resting on c-φ soils, and the problem is approached by consider...
Abstract: The Paper shows how finite elements, in conjunction with elasto-plastic theory, can give excellent collapse load predictions for footings resting on c-φ soils. The problem is approached by consider...
TL;DR: In this article, a model of an inextensible elastic rod with equal principal stiffnesses is presented, which permits large deflections and finite rotations and accounts for tension variation along its length.
Abstract: A new three-dimensional finite element model of an inextensible elastic rod with equal principal stiffnesses is presented. The model permits large deflections and finite rotations and accounts for tension variation along its length. Its use in static analysis is described and a time integration method for dynamic analysis is developed. Accuracy of the spatial discretization and stability of the time integration method are demonstrated by comparison of numerical results with exact solutions for certain nonlinear problems.
TL;DR: In this article, a discussion of the conditions necessary for penalty methods to provide a basis for stable and convergent finite element methods is given, and criteria on the order of reduced integration rules sufficient to produce stable and convergence schemes are described.
Abstract: Several different variational formulations of boundary-value problems with constraints are discussed, with particular reference to constrained problems in elasticity. Special attention is given to exterior penalty methods. A discussion of the conditions necessary for penalty methods to provide a basis for stable and convergent finite element methods is given. In particular, the use of reduced integration is discussed and criteria on the order of reduced integration rules sufficient to produce stable and convergent schemes are described. Applications of reduced integration-penalty methods to incompressible elasticity problems and contact problems are described.
TL;DR: A method is proposed to solve eddy-current problems in three dimensions based on a special blend of FEM and BIEM techniques, and can be applied to non-linear situations.
Abstract: A method is proposed to solve eddy-current problems in three dimensions. It is based on a special blend of FEM and BIEM techniques, and can be applied to non-linear situations. It has been implemented in the linear harmonic case and used in particular for studies on non-destructive testing. We first expose the mathematical foundation, next the dicretization technique. The current possibilities of the code are described and illustrated by computer graphic displays.
TL;DR: This note is a first attempt in this direction and deals with basic approximation properties of translates of one box-splines such as stability, degree of approximation etc.
Abstract: : Local support bases for piecewise polynomial spaces are important for applications such as finite element methods, data fitting etc. In (BH sub 1) a general construction principle for such B-splines was described. A special case are the so called box-splines. They have a particularly regular discontinuity pattern and coincide in special cases with standard finite elements. It is hoped that using translates of box-splines will lead, at least in two variables, to a unified theory for piecewise polynomial functions on regular meshes. This note is a first attempt in this direction and deals with basic approximation properties of translates of one box-splines such as stability, degree of approximation etc. (Author)
TL;DR: The convergence rate of the finite element method is a function of the strategy by which the number of degrees-of-freedom are increased as mentioned in this paper, and the convergence rate depends on the strategy used to increase the degree of freedom.
Abstract: The rate of convergence of the finite element method is a function of the strategy by which the number of degrees-of-freedom are increased. Alternative strategies are examined in the light of recent theoretical results and computational experience.
TL;DR: In this article, a method based on the equilibrium of nodal forces is proposed by assuming the deforming metal to be a slightly compressible rigid-plastic material, which is more accurate than that of the simple extension of infinitesimal deformation when dealing with nonsteady problems, and is particularly effective for the processes in which the mode of deformation is sensitively changed by the distribution of flow stress and variation of shape.
TL;DR: In this paper, an efficient procedure for modeling inelastic behavior in three-dimensional beam-column finite elements is presented, where plastic hinge formation, the interaction of element forces at a hinge, and elastic unloading are taken into account.
TL;DR: In this paper, the reliability of the displacement-formulated finite element method in analyzing the edge-stress problem of a composite laminate is investigated, and two well-known elasticity problems, one involving a stress discontinuity and one a singularity, are analyzed.