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Showing papers on "Finite element method published in 1980"


Journal ArticleDOI
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



Journal ArticleDOI
TL;DR: The FIDAM code as discussed by the authors is a system of computer programs designed for the solution of two-dimensional, linear and nonlinear, elliptic problems and three-dimensional parabolic problems.

670 citations


Journal ArticleDOI
TL;DR: In this paper, a new iteration procedure is introduced to solve the full matrix equations resulting from spectral approximations to nonconstant coefficient boundary-value problems in complex geometries, and the work required to solve these spectral equations exceeds that of solving the lowest-order finite-difference approximation to the same problem by only O(N log N).

668 citations



Journal ArticleDOI
TL;DR: In this article, a detailed formulation for simulating the injection-molding filling of thin cavities of arbitrary planar geometry is presented, in terms of generalized Hele-Shaw flow for an inelastic, non-Newtonian fluid under non-isothermal conditions.
Abstract: A detailed formulation is presented for simulating the injection-molding filling of thin cavities of arbitrary planar geometry. The modelling is in terms of generalized Hele-Shaw flow for an inelastic, non-Newtonian fluid under non-isothermal conditions. A hybrid numerical scheme is employed in which the planar coordinates are described in terms of finite elements and the gapwise and time derivatives are expressed in terms of finite differences. The simulation is applied to the filling of a two-gated plate mold having an intentionally unbalanced runner system. Good agreement is obtained with experimental results in terms of short-shot sequences, weldline formation and pressure traces at prescribed points in the cavity.

474 citations


Journal ArticleDOI
TL;DR: In this paper, a reduced basis technique and a computational algorithm are presented for predicting the nonlinear static response of structures, where a total Lagrangian formulation is used and the structure is discretized by using displacement finite element models.
Abstract: A reduced basis technique and a computational' algorithm are presented for predicting the nonlinear static response of structures. A total Lagrangian formulation is used and the structure is discretized by using displacement finite element models. The nodal displacement vector is expressed as a linear combination of a small number of basis vectors and a Rayleigh-Ritz technique is used to approximate the finite element equations by a reduced system of nonlinear equations. The Rayleigh-Ritz approximation functions (basis vectors) are chosen to be those commonly used in the static perturbation technique namely, a nonlinear solution and a number of its path derivatives. A procedure is outlined for automatically selecting the load (or displacement) step size and monitoring the solution accuracy. The high accuracy and effectiveness of the proposed approach is demonstrated by means of numerical examples.

414 citations


Journal ArticleDOI
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


Journal ArticleDOI
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


Journal ArticleDOI
TL;DR: In this article, the extension to non-Newtonian viscous incompressible fluid flows of a finite-element method using a nine-node isoparametric Langrangian element with a penalty approach for the continuity equation is studied.

310 citations


Journal ArticleDOI
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.


Journal ArticleDOI
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.

Journal ArticleDOI
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.

Journal ArticleDOI
TL;DR: In this paper, a consistent method for computing stress-intensity factors from three-dimensional quarter-point element nodal displacements is presented, which is generalized to permit functional evaluation of stress intensity factors along the crack front.
Abstract: A consistent method for computing stress-intensity factors from three-dimensional quarter-point element nodal displacements is presented. The method is generalized to permit functional evaluation of stress-intensity factors along the crack front. Embedded, surface, and corner crack problems are solved using the proposed technique. Results are compared to previous finite element and boundary element solutions. The comparison shows that use of the functional evaluation technique allows a dramatic decrease in problem size while still maintaining engineering accuracy. Next, a three-dimensional stress-intensity factor calibration of an unusual specimen configuration is presented. By taking advantage of the proposed technique, the calibration was performed with little difference in cost over the more usual two-dimensional approach. Moreover, the three-dimensional solution revealed intersting behaviour that would have been undetected by a two-dimensional solution. Finally, the results of a study on optimum size of the quarter-point element are presented. Surprisingly, Poisson ratio is shown to have marked effect on optimum element size.

Journal ArticleDOI
TL;DR: In this article, a matrix perturbation method is proposed to calculate the Jacobian matrix and to compute the new eigendata for the parameter estimation procedure, which allows the use of other measurements such as modal forces, kinetic energy distribution, and strain energy distributions in the estimation procedure.
Abstract: A matrix perturbation method is proposed to calculate the Jacobian matrix and to compute the new eigendata for the parameter estimation procedure. The advantages of the method are the applicability to large complex structures without knowing the analytical expressions for the mass and stiffness matrices, and a cost effective approach for the recomputation of the eigendata. This method also allows the use of other measurements such as modal forces, kinetic energy distribution, and strain energy distributions in the estimation procedure. A realistic sample problem is presented to demonstrate the effectiveness of the proposed method.

Journal ArticleDOI
TL;DR: A new approach to the analysis of mixed methods for the approximate solution of 4th order elliptic boundary value problems is presented, in this approach one introduces a pair of mesh dependent norms and proves the approximation method is stable with respect to these norms.
Abstract: : This paper presents a new approach to the analysis of mixed methods for the approximate solution of 4th order elliptic boundary value problems. In this approach one introduces a pair of mesh dependent norms and proves the approximation method is stable with respect to these norms. The error estimates then follow in a direct manner. In a mixed method, one introduces an auxiliary variable, usually representing another physically important quantity, and writes the differential equation as a lower order system. One then considers Ritz-Galerkin approximation schemes based on a variational formulation of this lower order system, thereby obtaining direct approximations to both the original and auxiliary variables. Three particular mixed methods for the approximate solution of the biharmonic problem are examined in detail.

Journal ArticleDOI
TL;DR: In this article, a C degrees finite element is developed for the equations governing the heterogeneous laminated plate theory of Yang, Norris and Stavsky, which is a generalization of Mindlin's theory for homogeneous, isotropic plates to arbitrarily laminated anisotropic plates.
Abstract: : A C degrees (penalty) finite element is developed for the equations governing the heterogeneous laminated plate theory of Yang, Norris and Stavsky. The YNS theory is a generalization of Mindlin's theory for homogeneous, isotropic plates to arbitrarily laminated anisotropic plates and includes shear deformation and rotary inertia effects. The present element can also be used in the analysis of thin plates by appropriately specifying the penalty parameter. A variety of problems are solved, including those for which solutions are not available in the literature, to show the material effects and the parametric effects of plate aspect ratio, length-to-thickness ratio, lamination scheme, number of layers and lamination angle on the deflections, stresses, and vibration frequencies. Despite its simplicity, the present element gives very accurate results. (Author)

Journal ArticleDOI
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.

Journal ArticleDOI
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.


Journal ArticleDOI
TL;DR: In this article, the shapes of drops of given volume and density in contact with an inclined plate over a circular wetted area are found from the Young-Laplace equation by means of the finite element method.

Book
01 Jan 1980
TL;DR: In this article, the dynamics of blood glucose and its regulating hormones are developed into a new model, building on the many previous attempts in this area, and the electrical and mechanical activity of the heart is modelled in the following chapter.
Abstract: whilst both the electrical and mechanical activity of the heart is modelled in the following chapter. The dynamics of blood glucose and its regulating hormones is developed into a new model, building on the many previous attempts in this area. As a contrast, the electrical rythms of the gastro-intestinal tract, which have received little attention to date, are dealt with in chapter six. The lungs, and mechanical properties of the respiratory system, have frequently been modelled, but in this section both mathematical and electronic descriptions are evolved which incorporate adaptive trackers, and results are presented from clinical applications of the techniques. Serious consideration is given to modelling circadian and related biological rhythms, with many of the proposed interconnected oscillator systems discussed, and finally a chapter is devoted to the concept of catastrophe theory applied to psychological modelling, with a detailed analysis of anorexia nervosa, the obsessive fasting by slimmers. Those interested in modelling biological systems will find this book very useful, since the references to each chapter are very thorough: however, the problems with the vast complexity of the human body, and the engineering problems of obtaining measurements, ensure that this is a field just opening up for research. PETER WATTS, Medical Engineering Unit, UMIST.

Book ChapterDOI
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

Journal ArticleDOI
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.

Journal ArticleDOI
TL;DR: In this article, a finite element analysis of the geometrically nonlinear behaviour of plates using a Mindlin formulation with the assumption of small rotations is presented, and a comparison of the performance of Linear, Serendipity, Lagrangian and Heterosis elements is given for square, skew, circular and elliptical plates subjected to distributed and point loading.

Journal ArticleDOI
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.

Journal ArticleDOI
F. Ghahremani1
TL;DR: In this article, the effect of grain boundary sliding on anelasticity of polycrystalline materials is analyzed by using the finite element method and a self-consistent theory.

Journal ArticleDOI
TL;DR: In this paper, a very simple and convenient method of analysis for studying two-dimensional mixed-mode crack problems in rectilinear anisotropic solids is presented, where the analysis is formulated on the basis of conservation laws of the elasticity and fundamental relationships in fracture mechanics.
Abstract: A very simple and convenient method of analysis for studying two-dimensional mixed-mode crack problems in rectilinear anisotropic solids is presented. The analysis is formulated on the basis of conservation laws of anisotropic elasticity and of fundamental relationships in anisotropic fracture mechanics. The problem is reduced to a system of linear algebraic equations in mixed-mode stress intensity factors. One of the salient features of the present approach is that it can determine directly the mixed-mode stress intensity solutions from the conservation integrals evaluated along a path removed from the crack-tip region without the need of solving the corresponding complex near-field boundary value problem. Several examples with solutions available in the literature are solved to ensure the accuracy of the current analysis. This method is further demonstrated to be superior to other approaches in its numerical simplicity and computational efficiency. Solutions of more complicated and practical engineering problems dealing with the crack emanating from a circular hole in composites are presented also to illustrate the capacity of this method.

Journal Article
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, and incorporates recent developments in finite element stress-intensity factor computation.
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 propagations observed experimentally. (a) (TRRL)