Showing papers on "Extended finite element method published in 1977"
TL;DR: In this article, an efficient technique for evaluating stress intensity factors is presented, based on the crack closure integral, which can be used with a constant strain finite element stress analysis and a coarse grid.
2,187 citations
01 Jan 1977
2,004 citations
TL;DR: The finite element method is now recognized as a general approximation process which is applicable to a variety of engineering problems and boundary solution procedures have been introduced as an independent alternative which at times is more economical and possesses certain merits as mentioned in this paper.
Abstract: The finite element method is now recognized as a general approximation process which is applicable to a variety of engineering problems—structural mechanics being only one of these. Boundary solution procedures have been introduced as an independent alternative which at times is more economical and possesses certain merits. In this survey of the field we show how such procedures can be utilized in conventional FEM context.
711 citations
TL;DR: In this paper, a simple and efficient finite element is introduced for plate bending applications, where Bilinear displacement and rotation functions are employed in conjunction with selective reduced integration, and the element is surprisingly accurate.
Abstract: A simple and efficient finite element is introduced for plate bending applications. Bilinear displacement and rotation functions are employed in conjunction with selective reduced integration. Numerical examples indicate that, despite its simplicity, the element is surprisingly accurate.
647 citations
577 citations
TL;DR: In this paper, the linear elastic, stiffness-derivative, finite element technique was generalized to determine the ductile fracture parameter J from elastic-plastic finite element solutions, based on energy comparison of two slightly different crack lengths.
365 citations
TL;DR: In this article, the construction of finite element methods for 2nd order elliptic equations based on a primal hybrid variational principle was studied and the optimal error bounds were proved, as well as a general analysis of nonconforming finite element method.
Abstract: The paper is devoted to the construction of finite element methods for 2nd order elliptic equations based on a primal hybrid variational principle. Optimal error bounds are proved. As a corollary, we obtain a general analysis of nonconforming finite element methods.
322 citations
TL;DR: In this paper, a finite element approximation for a class of singular integral equations of the first kind was discussed. But the convergence rate of the Galerkin method with finite elements as trial functions is not known.
322 citations
Book•
01 Feb 1977
TL;DR: Finite element techniques for fluid flow, Finite element techniques with real-time application, اطلاعات رسانی کشاورزی, £20,000 (US$30,000; €40,000)
Abstract: Finite element techniques for fluid flow , Finite element techniques for fluid flow , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی
226 citations
01 Jan 1977
TL;DR: In this article, the axisymmetric elasticity problem with thermal and rotational loading using the boundary-integral equation method is formulated and the resulting one dimensional numerical model is evaluated for a series of problems, including a problem solved by a finite element model.
Book•
01 Jan 1977
TL;DR: In this paper, the authors consider general linear parabolic equations in a given time dependent domain and describe a general class of Galerkin-type approximations which are continuous with respect to the space variables, but which admit discontinuities in time at each step.
Abstract: We consider general linear parabolic equations in a given time dependent domain and we describe a general class of Galerkin-type approximations which are continuous with respect to the space variables, but which admit discontinuities with respect to time at each step. Unconditional stability is proved and a general error estimate is established. These results are applied to certain finite element methods based on space-time finite elements.
01 Dec 1977
TL;DR: In this article, a simple recursion technique is employed to generate the matrix representing the annular region, where all nodes are eliminated from the external element except those on its inner surface, so that the final matrix is no larger than that required to describe the region of interest.
Abstract: Electric- and magnetic-field problems with boundaries at infinity are treated in finite-element terms by constructing an element to model an extremely large annulus surrounding the region of interest. A simple recursion technique is employed to generate the matrix representing the annular region. All nodes are eliminated from the external element except those on its inner surface, so that the final matrix is no larger than that required to describe the region of interest only. The method is simpler to program and requires less computing effort than boundary-integral techniques. It has been tested by solving several 2-dimensional magnetostatic and electrostatic problems and comparing the results with analytic solutions. The method can be applied to any 2-dimensional field problem bounded by a large empty region in which the field satisfies Laplace's equation.
TL;DR: In this article, a finite element method for the numerical solution of the two-dimensional Stefan problem is described, where at each time step, the free boundary is approximated by a polygonal line whose vertices coincide with triangulation nodes.
TL;DR: In this article, a powerful finite element formulation for plate bending has been developed using a modified version of the variational method of Trefftz, and the notion of a boundary has been generalized to include the interelement boundary.
TL;DR: In this paper, the boundary element formulation of potential problems is presented using weighted residual techniques, and the advantage of using this method in preference to finite elements is discussed in the applications.
TL;DR: In this article, mixed-hybrid finite element approximations are described for second-order elliptic boundary value problems, in which independent approximation methods are used for the solution and its gradient on the interior of an element and the trace of the gradients on the boundary of the element.
TL;DR: In this paper, a finite element formulation is described for problems with solution functions known to have local rλ variation (s), 0<λ<1, and thus singular gradients. But the conditions of continuity, low order solution capability, and accurate numerical integration of the singularity element are discussed with a view towards establishing the general range of applicability.
Abstract: A finite element formulation is described for problems with solution functions known to have local rλ variation (s), 0<λ<1, and thus singular gradients. Special 3-node triangular elements encircle the singularity and focus to share a common node at the singular point. The shape function of each triangle has the appropriate r λ mode and a smooth angular mode expressed in element natural co-ordinates. As with standard elements, the unknowns are the nodal values of the function. Even if the precise angular form of the asymptotic solution is known, the formulation makes no attempt to embed it, but instead piecewise approximates it. This allows assembly of the element coefficient matrix using standard procedures without nodeless variables and bandwidth complications.
The conditions of continuity, low order solution capability, and accurate numerical integration of the singularity element are discussed with a view towards establishing the general range of applicability of the formulation. Numerical applications to the elastic fracture mechanics problems of composite bondline cracking and crack branching are discussed.
TL;DR: It is proved that the iterative method can produce a solution to the equations in O(N) arithmetical operations where N is the number of unknowns.
Abstract: An iterative method of multiple grid type is proposed for solving general finite element systems. It is proved that the method can produce a solution to the equations in O(N) arithmetical operations where N is the number of unknowns.
TL;DR: The steady state impressing velocity of the punch during an impression creep test is calculated by the finite element method based on a single power law constitutive equation for the deformation of each element.
Abstract: The steady state impressing velocity of the punch during an impression creep test is calculated by the finite element method based on a single power law constitutive equation for the deformation of each and every element. The calculated impressing velocities and their stress dependence agree very well with the experimental values on succinonitrile crystals using empirical power laws obtained from unidirectional creep tests.
TL;DR: A number of temporal procedures for solving the long-wave surface water equations using the finite element method in space are presented and analyzed in this article, where the analysis determines the stability of the schemes and the error in wave amplitude and phase that can be expected.
TL;DR: In this paper, finite element schemes for analysis of seepage in porous elastic media, based on different spatial and temporal discretization, were implemented in computer programs and evaluated by comparison with the exact solution for Terzaghi's problem of one-dimensional consolidation.
Abstract: Several finite element schemes for analysis of seepage in porous elastic media, based on different spatial and temporal discretization, were implemented in computer programs. Their numerical performance is evaluated by comparison with the exact solution for Terzaghi's problem of one-dimensional consolidation.
Book•
15 Jan 1977TL;DR: In this paper, the elastohydrodynamic lubrication problem is solved by using a finite element procedure and the Newton method, and the numerical procedure is applied to the point contact problem, in which a thin lubricant film is maintained between two balls loaded together by a high load under conditions of pure rolling.
Abstract: The elastohydrodynamic lubrication problem, in which the lubricant pressure and film thickness are sensitive to surface deformation, is solved by using a finite element procedure and the Newton method. The numerical procedure is applied to the point contact problem, in which a thin lubricant film is maintained between two balls loaded together by a high load under conditions of pure rolling. The present analysis shows that pressure spikes are formed near the outlet region, a result which has been found in the line contact problem and which has been conjectured in the present problem.