Showing papers on "Extended finite element method published in 1970"
TL;DR: In this paper, a finite element formulation which includes the piezoelectric or electroelastic effect is given, a strong analogy is exhibited between electric and elastic variables, and a stiffness finite element method is deduced.
Abstract: A finite element formulation which includes the piezoelectric or electroelastic effect is given. A strong analogy is exhibited between electric and elastic variables, and a ‘stiffness’ finite element method is deduced. The dynamical matrix equation of electroelasticity is formulated and found to be reducible in form to the well-known equation of structural dynamics, A tetrahedral finite element is presented, implementing the theorem for application to problems of three-dimensional electroelasticity.
972 citations
TL;DR: The program given here assembles and solves symmetric positive–definite equations as met in finite element applications, more involved than the standard band–matrix algorithms, but more efficient in the important case when two-dimensional or three-dimensional elements have other than corner nodes.
Abstract: The program given here assembles and solves symmetric positive–definite equations as met in finite element applications. The technique is more involved than the standard band–matrix algorithms, but it is more efficient in the important case when two-dimensional or three-dimensional elements have other than corner nodes. Artifices are included to improve efficiency when there are many right hand sides, as in automated design. The organization of the program is described with reference to diagrams, full notation, specimen input data and supplementary comments on the ASA FORTRAN print-out.
884 citations
TL;DR: In this article, the usefulness of the finite element method for the computation of crack tip stress intensity factors is established, and the results are compared not only to the results of other analytical solutions, but additional correlation is made of two different fracture test specimen types.
608 citations
TL;DR: The proposed approach on a model problem — the Dirichlet problem with an interface for Laplace equation with sufficient condition for the smoothnees can be determined, and the boundary of the domain and the interface will be assumed smooth enough.
Abstract: Numerical solutions of boundary value problems for elliptic equations with discontinuous coefficients are of special interest In the case when the interface (ie the surface of the discontinuity of the coefficients) is smooth enough, then also the solution is usually very smooth (except on the interface) To obtain a high order of accuracy presents some difficulty, especially if the interface does not fit with the elements (in the finite element method) In this case the norm of the error in the spaceW1/2 is of the orderh
1/2 (see eg [1]) and on one dimensional case it is easy to see that the accuracy cannot be improved In this paper we shall show an approach which avoids this difficulty The idea is similar to [2] We shall show the proposed approach on a model problem — theDirichlet problem with an interface forLaplace equation; this will avoid pure technical difficulties The boundary of the domain and the interface will be assumed smooth enough The sufficient condition for the smoothnees can be determined
413 citations
TL;DR: Structure of flexural members, analyzing torsional and lateral stability by finite element method and matrix formulation is presented in this article, where the authors propose a finite element-based matrix formulation.
Abstract: Structure of flexural members, analyzing torsional and lateral stability by finite element method and matrix formulation
302 citations
TL;DR: In this paper, the transient field problem of the type encountered in heat conduction problems is formulated in terms of the finite element process using the Galerkin approach and Curved two-dimensional and three-dimensional, isoparametric elements are used in a time-stepping solution.
Abstract: The transient field problem of the type encountered in heat conduction problems is formulated in terms of the finite element process using the Galerkin approach. Curved two-dimensional and three-dimensional, isoparametric elements are used in a time-stepping solution and their advantages illustrated by means of several examples.
206 citations
TL;DR: In this paper, a conforming shallow shell finite element of arbitrary triangular shape is developed and applied to the solution of several static problems, which incorporates 36 generalized coordinates, namely the normal displacement w and its first and second derivatives plus the tangential displacements u and v and their first derivatives at each vertex.
165 citations
140 citations
TL;DR: The paper shows that proper refinement of the elements around the corners leads to the rate of convergence which is the same as it would be on domain with smooth boundary.
Abstract: The rate of convergence of the finite element method is greatly influenced by the existence of corners on the boundary. The paper shows that proper refinement of the elements around the corners leads to the rate of convergence which is the same as it would be on domain with smooth boundary.
131 citations
TL;DR: In this article, a direct method of computation of the stress intensity factor, K, of linear fracture mechanics is discussed, and the accuracy is quite good for a relatively coarse finite element mesh for the example problems presented.
129 citations
TL;DR: In this article, a general procedure for evaluating the stiffness matrix of a cracked element is developed, and numerical results obtained by the simplest elements are compared with those provided by other methods.
Abstract: The calculation of stress intensity factors for complicated crack configurations in finite plates usually presents substantial difficulty. A version of the finite element method solves such problems approximately by means of special cracked elements. A general procedure for evaluating the stiffness matrix of a cracked element is developed, and numerical results obtained by the simplest elements are compared with those provided by other methods.
TL;DR: In this article, the authors proposed a finite element model based on separate assumptions of interior and interelement displacements and on the assumed boundary tractions of each individual element, and the associated variational functional for this model is presented.
Abstract: The proposed finite element model is based on separate assumptions of interior and interelement displacements and on the assumed boundary tractions of each individual element. The associated variational functional for this model is presented. This method has the same merits of the assumed stress method (References 3 and 4) in that a compatible displacement function at the interelement boundary can be easily constructed, while it can easily be used for shells with distributed loads.
TL;DR: In this article, a numerical method is presented for the determination of lower bounds on the yield-point load of plane stress problems, where a finite element technique is used to construct a parametric family of piecewise quadratic, equilibrium stress fields.
Abstract: A numerical method is presented for the determination of lower bounds on the yield-point load of plane stress problems. In this method, a finite element technique is used to construct a parametric family of piecewise quadratic, equilibrium stress fields. The best lower bound is then found by maximizing the load, subject to the yield constraints, by means of the sequential unconstrained minimization technique. Because all conditions of the Lower Bound theorem are met exactly, the resulting solutions are true bounds. Results are given for square slabs with various cutouts and compared to upper bounds and complete elastic plastic finite element solutions.
TL;DR: Finite element method applicaions to finite axisymmetric deformations of incompressible elastic solids of revolution have been studied in this article, where the finite element method has been applied to deformations in the case of elastic soliders of revolution.
TL;DR: In this paper, a technique of differential displacements is presented whereby problems involving elastic contact are solved by the finite element method, applied to axisymmetric situations in which statically indeterminate conditions occur and provided a means for resolving these conditions in terms of contact stresses.
Abstract: A technique of differential displacements is presented whereby problems involving elastic contact are solved by the finite element method. The technique is applied to axisymmetric situations in which statically indeterminate conditions occur and is shown to provide a means for resolving these conditions in terms of contact stresses. Three typical engineering problems are analysed to demonstrate the technique in cases where body forces, thermal gradients and external applied forces are acting.
TL;DR: The stiffness and consistent mass matrices and their derivation for a thinwalled beam element of open cross-section with non-collinear shear center and centroid are given in this article.
TL;DR: In this paper, an equivalent variational principle to the governing partial differential equations of motion is given, and a finite element solution is developed requiring only approximations in the space domain.
Abstract: The one-dimensional diffusion-convection equation has been widely used to describe approximately the transient motion of a subset of particles in river flow or porous media flow. An equivalent variational principle to the governing partial differential equations of motion is given, and a finite element solution is developed requiring only approximations in the space domain. The solution is applicable to a wide variety of field problems because it can account for a variety of boundary conditions. Additionally, the solution is not dependent upon constant parameters of motion over the entire domain of interest.
TL;DR: In this paper, the two-dimensional diffusion-convection equation, with an assumed set of auxiliary conditions, is converted to a variational principle for systems that do not involve mixed partials.
Abstract: The two-dimensional diffusion-convection equation, together with the appropriate auxiliary conditions, is used to describe approximately the motion of dissolved constituents in porous media flow, dispersion of pollutants in streams and estuaries, energy transfer in reservoirs, and other natural transport processes. The two-dimensional diffusion-convection equation, with an assumed set of auxiliary conditions, is converted to a variational principle for systems that do not involve mixed partials. The variational principle is in turn solved by the Ritz procedure by dividing the domain of interest into an arbitrary number of finite triangular elements. Within each element the unknown function states are represented by a first order space polynomial. The resulting system of first order linear equations is then solved by numerical differentiation using the Adams-Moulton multistep predictor-corrector method.
TL;DR: In this article, a computational procedure based on gradient iterative techniques is proposed for the solution of large problems to which the finite element method is applicable, which can be used either for solving the set of algebraic equations or for the complete inversion of the matrix of coefficients.
Abstract: A computational procedure based on gradient iterative techniques is proposed for the solution of large problems to which the finite element method is applicable. In linear problems the procedure can be used either for solving the set of algebraic equations or for the complete inversion of the matrix of coefficients. Special attention is focused on the practical aspects of the procedure concerning its realization on the digital computer.
TL;DR: In this paper, finite element solution procedures are developed for an elastica problem of inextensible beams using Galerkin's method, and the element stiffness matrices are obtained by using the finite element method.
Abstract: In this study, finite element solution procedures are developed for an elastica problem of inextensible beams. The element stiffness matrices are obtained by using Galerkin's method. Results of a numerical example compare reasonably well with those obtained by using the elliptical integral.
Extensions of this research are currently being made to include membrane effects of beams and to develop plate element stiffness matrices for elastica problems of plate structures.
TL;DR: In this paper, a finite element procedure of the second order of accuracy for solving second order boundary value problems is presented and justified and numerical results are given, where the second-order boundary value problem is formulated as a set of finite element problems.
Abstract: A finite element procedure of the second order of accuracy for solving second order boundary value problems is presented and justified and numerical results are given.
TL;DR: In this article, the finite element equations describing a discrete model of compressible and incompressible Stokesian fluids are derived from a finite element model, and the ideas presented represent extensions and elaborations of a similar procedure described elsewhere.
Abstract: The purpose of this note is to present brief derivations of the finite element equations describing a discrete model of compressible and incompressible Stokesian fluids. The ideas presented represent extensions and elaborations of a similar procedure described elsewhere.
Journal Article•
TL;DR: Some of the basic ideas involved in the development of an automatic generator for finite element stiffness and mass matrices are analyzed and two different programs are presented.