Showing papers on "Extended finite element method published in 1976"
Book•
01 Jan 1976
TL;DR: In this article, the authors present a computer program for two-dimensional field problems for structural and solid mechanics, including axisymmetric elasticity and Torsion of noncircular sections.
Abstract: BASIC CONCEPTS. One-Dimensional Linear Element. A Finite Element Example. Element Matrices: Galerkin Formulation. Two-Dimensional Elements. Coordinate Systems. FIELD PROBLEMS. Two-Dimensional Field Equation. Torsion of Noncircular Sections. Derivative Boundary Conditions: Point Sources and Sinks. Irrotational Flow. Heat Transfer by Conduction and Convection. Acoustical Vibrations. Axisymmetric Field Problems. Time-Dependent Field Problems: Theoretical Considerations. Time-Dependent Field Problems: Practical Considerations. Computer Program for Two-Dimensional Field Problems. STRUCTURAL AND SOLID MECHANICS. The Axial Force Member. Element Matrices: Potential Energy Formulations. The Truss Element. A Beam Element. A Plane Frame Element. Theory of Elasticity. Two-Dimensional Elasticity. Axisymmetric Elasticity. Computer Programs for Structural and Solid Mechanics. LINEAR AND QUADRATIC ELEMENTS. Element Shape Functions. Element Matrices. Isoparametric Computer Programs. References. Appendices.
1,027 citations
Book•
01 Jan 1976
TL;DR: On Engineering By J T Oden J N Reddy ONLINE SHOPPING for NUMBER InTRODUCTION
Abstract: On Engineering By J T Oden J N Reddy ONLINE SHOPPING FOR NUMBER INTRODUCTION AN INTRODUCTION. MATHEMATICAL LEARNING THEORY R C ATKINSON. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF INVERSE. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF FINITE. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF WAVES. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF INVERSE. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF THE NAVIER. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF VIBRATIONS. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF INVERSE. INTRODUCTION MATHEMATICAL THEORY FINITE ELEMENTS ABEBOOKS. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF WAVES. AN INTRODUCTION TO THE
686 citations
TL;DR: In this paper, a finite element method for a class of contact impact problems is presented, where the basic ideas of contact-impact, the assumptions which define the class of problems we deal with, spatial and temporal discretizations of the bodies involved, special problems concerning the contact of bodies of different dimensions, discrete impact and release conditions, and solution of the nonlinear algebraic problem are discussed.
452 citations
TL;DR: In this paper, the existence of optimal points for calculating accurate stresses within finite element models is discussed and a method for locating such points is proposed and applied to several popular finite elements.
Abstract: The existence of optimal points for calculating accurate stresses within finite element models is discussed. A method for locating such points is proposed and applied to several popular finite elements.
395 citations
TL;DR: In this paper, the general problem of mass lumping and related processes in the finite element method are discussed and examples are presented to show the good accuracy which can be obtained in linear and non-linear dynamic problems using the scheme.
Abstract: The general problem of mass lumping and related processes in the finite element method are discussed.
A mass lumping scheme is presented for parabolic isoparametric elements. Examples are presented to show the good accuracy which can be obtained in linear and non-linear dynamic problems using the scheme.
333 citations
TL;DR: In this paper, a hybrid crack element is constructed to properly account for the crack tip singularity, and the stress intensity factors and energy release rate for cracks in different bi-material continua are then calculated using the finite element method.
Abstract: The stress singularity at the tip of a crack, either lying along or perpendicular to the interface of the two materials, is first investigated by the complex variable method. The order of the singularity is shown to be dependent on both the crack geometry and two parameters α, β which are related to the four elastic constants of the two materials. A hybrid crack element is constructed to properly account for the crack tip singularity. The stress intensity factors and energy release rate for cracks in different bi-material continua are then calculated using the finite element method. The results show that the present finite element analysis makes possible a highly accurate and efficient numerical solution of fracture mechanics problems.
225 citations
TL;DR: In this article, an incremental plasticity finite element formulation is developed for accurate analysis of the complete field problem including the extensively deformed near tip region, the elastic-plastic region, and the remote elastic region.
Abstract: The subject considered is the stress and deformation fields in a cracked elastic-plastic power law hardening material under plane strain tensile loading. An incremental plasticity finite element formulation is developed for accurate analysis of the complete field problem including the extensively deformed near tip region, the elastic-plastic region, and the remote elastic region. The formulation has general applicability and was used to solve the small scale yielding problem for a set of material hardening exponents. Distributions of stress, strain, and crack opening displacement at the crack tip and through the elastic-plastic zone are presented as a function of the elastic stress intensity factor and material properties.
182 citations
TL;DR: In this article, the authors developed a finite element method which gives accurate numerical approximations to magnetotelluric data over two-dimensional conductivity structures, which employs a simple finite element technique to find the field component parallel to the strike of the structure and a new numerical differentiation scheme to find a field component perpendicular to strike.
Abstract: Summary
This paper develops a finite element method which gives accurate numerical approximations to magnetotelluric data over two-dimensional conductivity structures. The method employs a simple finite element technique to find the field component parallel to the strike of the structure and a new numerical differentiation scheme to find the field component perpendicular to strike. Examples show that the new numerical differentiation scheme is a significant improvement over the standard finite element procedure when meshes of poor quality are used. Algorithms for incorporating the differentiation scheme into the finite element matrix equation and for computing partial derivatives of magnetotelluric data with respect to mesh parameters are derived in order to simplify the computation needed to do the inverse problem.
163 citations
TL;DR: An L/sup 1/ estimate of the gradient of the error in the finite element approximation of the Green's function is proved that is optimal for all degrees.
Abstract: Uniform estimates for the error in the finite element method are derived for a model problem on a general triangular mesh in two dimensions. These are optimal if the degree of the piecewise polynomials is greater than one. Similar estimates of the error are also derived in L/sup p/. As an intermediate step, an L/sup 1/ estimate of the gradient of the error in the finite element approximation of the Green's function is proved that is optimal for all degrees.
162 citations
TL;DR: In this article, a twenty node, isoparametric acoustic finite element model is developed for analysing the acoustic modes of irregular shaped cavities, which is first used to analyse a rectangular enclosure.
138 citations
TL;DR: In this paper, a finite element formulation for large amplitude free oscillations of beams and orthotropic circular plates is presented, which does not need the knowledge of longitudinal/inplane forces developed due to large displacements and thus avoids the use of corresponding geometric stiffness matrices.
TL;DR: In this paper, a liquid finite element formulation which includes the potential energy due to compression but neglects the density change has been developed, where both kinetic and potential energy are expressed as functions of nodal displacements.
Abstract: A liquid finite element formulation which includes the potential energy due to compression but neglects the density change has been developed. Both kinetic and potential energy are expressed as functions of nodal displacements. Thus, the formulation is similar to that used for structural elements, with the only differences being that 1) the fluid can possess gravitational potential, and 2) the constitutive equations for fluid contain no Shear coefficients. Using this approach, structural and fluid elements can be used interchangeably in existing efficient sparse matrix structural computer programs such as SPAR. The theoretical development of the element formulations and the relationships of the local and global coordinates are shown. Solutions of fluid slosh, liquid compressibility, and coupled fluid-shell oscillation problems which were completed using a temporary digital computer program are shown. The frequency correlation of the solutions with classical theory is excellent.
TL;DR: In this article, a Fourier series analysis is performed to determine the dissipative and dispersive characteristics of finite difference and finite element methods for solving the convective-dispersive equation.
Abstract: Various finite difference and finite element methods for solving the one-dimensional convective-dispersive equation are investigated. A Fourier series analysis is performed to determine the dissipative and dispersive characteristics of these numerical methods. The analysis indicates that the commonly observed phenomenon of overshoot of a concentration pulse is due to the inability of the numerical schemes to propagate the small wavelengths which are important to the description of the front. Furthermore, the numerical smearing of a sharp front is due to dissipation of these small wavelengths. The finite element method was found to be superior to finite difference methods for solution of the convective-dispersive equation.
TL;DR: In this article, the finite element method is used for the solution of two-dimensional heat and mass-transfer problems in porous media, and the formulation is given in general terms and is not restricted to any particular type of element.
TL;DR: In this article, a vibrational analysis of general planar mechanisms using a finite element approach is presented, which considers both axial and lateral vibrations using a high order hermite polynomial approximation which conserves moment compatibility between elements.
TL;DR: In this paper, large amplitude asymmetric vibrations of shells of revolution are analyzed by using a finite element method and Sanders' non-linear strain displacement relations are used to derive the element stiffness matrix.
TL;DR: In this article, a numerical procedure for the analysis of general two-dimensional flows of viscous, incompressible fluids using the finite element method is developed, where the partial differential equations describing the continuum motion of the fluid are discretized by using an integral energy balance approach in conjunction with a finite element approximation.
TL;DR: This paper considers the use of unorthodox grids where rapid transition from refined zones to coarser zones is effected, thus introducing exposed nodal freedoms at the zone interfaces, and a technique for automated mesh enrichment of finite element discretizations is devised.
TL;DR: In this paper, the displacement formulation of the minimum potential energy can be used with the finite element method to approximate both compressible and incompressible equilibria of linearly elastic, isotropic solids.
02 Jan 1976
TL;DR: The finite strip method as mentioned in this paper consists in breaking down the field studied into rectangular elements called "strip" linked together by means of "nodal" lines The deflection is transformed into series with a limited number of terms on each nodal line.
Abstract: The finite strip method consists in breaking down the field studied into rectangular elements called: "strip" linked together by means of "nodal" lines The deflection is transformed into series with a limited number of terms On each nodal line are two unknown factors: the deflection and the rotation, instead of three as in the finite element method The width of the half-strip of the stiffness matrix in the finite strip method does not depend on the mesh but on the number of terms in the series This method was shown to be more economical than the finite element method It seems to be more efficient and easier for analyzing plates and beams such as in bridges, in particular orthotropic slab bridges, including cantilevered beams /TRRL/
TL;DR: In this paper, an isoparametric quadrilateral plate bending element is introduced and its use for the free vibration analysis of both thick and thin plates is examined and excellent results are obtained.
TL;DR: In this article, the large amplitude flexural vibrations of rectangular plates are studied using a direct finite element formulation, which is based on an appropriate linearisation of strain displacement relations and uses an iterative method of solution.
TL;DR: In this paper, a finite element method is applied to cable structures and a family of nonlinear elements is developed for elastic deformation in single-span cables, which retains all geometric nonlinearities and allows for any elastic deformations.
TL;DR: In this article, a tinite element method of mixed type was proposed to solve the Dirichlet problem of the von Karman equations, and the existence and convergence of the approximate solution were proved.
Abstract: A tinite element method of mixed type is proposed to solve the Dirichlet problem of the von Karman equations. Existence and convergence of the approximate solution are proved.
TL;DR: In this paper, the classical variational principles are formulated for nonlinear problems by considering incremental deformations of a continuum and associated finite element models are derived, adopting the terminology introduced by Pian for classification of linear finite elements models.