Showing papers on "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: 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: In this paper, the authors developed a computational algorithm for the solution of the uncoupled, quasi-static boundary value problem for a linear viscoelastic solid undergoing thermal and mechanical deformation.
Abstract: SUMMARY This paper is concerned with the development of a computational algorithm for the solution of the uncoupled, quasi-static boundary value problem for a linear viscoelastic solid undergoing thermal and mechanical deformation. The method evolves from a finite element discretization of a stationary value problem, leading to the solution of a system of linear integral equations determining the motion of the solid. An illustrative example is included.
381 citations
TL;DR: In this article, an incremental and piecewise linear finite element theory is developed for the large displacement, large strain regime with particular reference to elastic-plastic behavior in metals, and the resulting equations, though more complex, are in a similar form to those previously developed for large displacement small strain problems, the only additional term being an initial load stiffness matrix which is dependent on current loads.
312 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 article, the authors report on initial numerical experiments for the solution of the nonlinear magnetic field problem by the method of finite elements, a new technique that permits great freedom in prescribing boundary shapes and does not suffer from the deceleration of convergence that plagues the relaxation methods.
Abstract: This paper reports on initial numerical experiments for the solution of the nonlinear magnetic field problem by the method of finite elements, a new technique that permits great freedom in prescribing boundary shapes and does not suffer from the deceleration of convergence that plagues the relaxation methods [9]. The sizes of the triangular elements can be freely chosen so that dense clusters of smaller elements exist in the principal regions of interest (usually the iron parts) and fewer large ones in remote air spaces.
293 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 article, a new iterative approach to steady seepage of ground water with a free surface has been developed using the finite element method, which eliminates a number of difficulties that were inherent in the iterative procedures previously used to solve this problem and rapid convergence is now assured in all cases.
Abstract: A new iterative approach to steady seepage of ground water with a free surface has been developed using the finite element method. This approach eliminates a number of difficulties that were inherent in the iterative procedures previously used to solve this problem and rapid convergence is now assured in all cases. The method is applicable to heterogeneous porous media with complex geometric boundaries and arbitrary degrees of anisotropy. It can handle problems where the free surface is discontinuous and where portions of the free surface are vertical or near vertical. In addition, infiltration or evapotranspiration at the free surface can be handled with ease. Several examples are included to demonstrate the power of this new approach and to show how it can apply to a wider variety of free surface problems than has been possible before.
204 citations
TL;DR: For a plane polygonal domain a and a corresponding general triangulation, the authors define classes of functions pm(x, y) which are polynomials on each triangle and which are in Cm(Q) and also belong to the Sobolev space Wn'"'1(Q).
Abstract: For a plane polygonal domain a and a corresponding (general) triangulation we define classes of functions pm(x, y) which are polynomials on each triangle and which are in Cm)(Q) and also belong to the Sobolev space Wn'"'1(Q). Approximation theoretic properties are proved concerning these functions. These results are then applied to the approximate solution of arbitrary-order elliptic boundary value problems by the Galerkin method. Estimates for the error are given. The case of second-order problems is discussed in conjunction with special choices of approximating polynomials.
196 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.
TL;DR: In this paper, a variational expression of the electromagnetic fields in dielectric loaded waveguides is derived and discretized using the finite element method and an electromagnetic coupling matrix is derived, where no restriction is placed on the shapes of the triangular elements or the order of the polynomial approximation.
Abstract: A variational expression of the electromagnetic fields in dielectric loaded waveguides is derived This expression is discretized using the finite-element method and an electromagnetic coupling matrix is derived and evaluated No restriction is placed on the shapes of the triangular elements or the order of the polynomial approximation A general finite-element computer program is described and dispersion curves and field plots of some dielectric loaded waveguides are presented
TL;DR: In this article, the application of the finite element technique to plane strain consolidation problems, dealing with primary consolidation only, is described, and the main points of a finite element formulation for the consolidation process are summarized.
Abstract: The report describes the application of the finite element technique to plane strain consolidation problems, dealing with primary consolidation only. A description is given of three-dimensional consolidation in order to explain three-dimensional effects in the consolidation process and to discuss similarities in the finite element formulation, Biot's and Terzaghi's formulation. The main points of a finite element formulation for the consolidation process are summarized, and the resulting computer program, CONSOL, is described. The complete element formulation is given in an appendix. An investigation is made on one- and two- dimensional problems, which show the effects discussed in the chapter on consolidation theory. A choice is made of problems which are of practical importance. (Author)
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.
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.
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 paper, the authors treated the plane finite deformations of the models as a series of small incremental deformations and found the velocity fields of the incremental problems using the finite element method.
Abstract: Computer simulation of the time-dependent deformations of layered viscous solids serves as the basis of a study of the mechanics of large-amplitude folds. Several models of a single viscous layer embedded in a less viscous matrix and a model of an infinite stack of layers of alternating viscosity have been studied. This study treats the plane finite deformations of the models as a series of small incremental deformations. The velocity fields of the incremental problems are found using the finite element method. With the single-layer models, the contrast of viscosity between the layer and matrix strongly influences the geometry of folds at the dominant wavelength. Fold geometries vary from concentric for large viscosity contrasts to nearly similar for low contrasts. In each model, the patterns given by directions perpendicular to the principal axes of maximum total compressive strain closely resemble axial-plane foliations in natural folds. Published fabric data for calcite-twin lamellae and quartz-deforma...
TL;DR: In this article, the incremental boundary value problem for elastoplastic workhardening continua, allowing for distributed dislocations, is discussed both in the traditional terms of continuum mechanics and in matrix notation on the basis of finite element discretization.
Abstract: The paper discusses the incremental boundary value problem for elastoplastic workhardening continua, allowing for distributed dislocations. A pair of “dual” extremum theorems reduces the problem to the optimization of convex quadratic forms subject to linear inequalities and equations: the first theorem takes as variables stress and plastic multiplier rates, the latter velocities and plastic multiplier rates. The conclusions reached are specialized to elastic perfectly plastic (nonhardening) cases. The problem is discussed both in the traditional terms of continuum mechanics and in matrix notation on the basis of finite element discretization, using some quadratic programming concepts. Finally a comparison is made with the classical incremental minimum principles of plasticity (Prager-Hodge, Greenberg), which are deduced from the present theorems in a form generalized to the distributed dislocations.
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 elastoplastic analysis of plane-strain and axisymmetric flat punch indentation into a specimen of finite dimensions was made by the finite element method, using an improved finite-element representation.
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, an energy formulation is used in conjunction with the method of finite differences to develop equations leading to buckling loads and vibration frequencies of segmented elastic shells of revolution supported by rings which are treated as discrete elastic structures.
TL;DR: In this paper, the finite element method was used to investigate the natural frequencies and mode shapes of thin circular cylindrical shells with stiffening rings, where each stiffening ring was treated as a discrete element.
TL;DR: In this paper, a unique elasticity finite element program has been implemented which can deal with the general three-dimensional nature of axisym metric composite bodies, which is used to analytically predict the response of unidirectional composite tube specimens to uniaxial tension/compression.
Abstract: To gain needed insight into the effects of thickness to diameter ratio (t/Di), length to diameter ratio (l/Di ), and helical angle (α) on the response of laminated tubes in material characterization tests, a unique new elasticity finite element program has been implemented which can deal with the general three-dimensional nature of axisym metric composite bodies The program, which is utilized here to analytically predict the response of unidirectional composite tube specimens to uniaxial tension/compression, differs from the usual finite element formulations in that it accounts for general anisotropy In particular, it deals with all shear coupling terms and all six com ponents of stress The effects of different gripping methods are also considered Similar studies of torsion and internal pressurization tests will be reported in subsequent notesThis first phase of the study shows that while the response of axial and hoop wrapped tubes (α = 0°, 90°) is essentially indepen dent of length and thickness ra