Showing papers on "Finite element method published in 1975"

Finite-Element Analysis

Abstract: Introduction to finite element analysis: 1.1 What is ... The finite element method (FEM) is a numerical technique used to perform finite element analysis of any given physical phenomenon. It is necessary to use mathematics to comprehensively understand and quantify any physical phenomena, such as structural or fluid behavior, thermal transport, wave propagation, and the growth of biological cells.

The finite element method for engineers

Abstract: PART I. Meet the Finite Element Method. The Direct Approach: A Physical Interpretation. The Mathematical Approach: A Variational Interpretation. The Mathematical Approach: A Generalized Interpretation. Elements and Interpolation Functions. PART II. Elasticity Problems. General Field Problems. Heat Transfer Problems. Fluid Mechanics Problems. Boundary Conditions, Mesh Generation, and Other Practical Considerations. Appendix A: Matrices. Appendix B: Variational Calculus. Appendix C: Basic Equations from Linear Elasticity Theory. Appendix D: Basic Equations from Fluid Mechanics. Appendix E: Basic Equations from Heat Transfer. References. Index.

Approximation by finite element functions using local regularization

Abstract: The aim ofthis paper is to give an elementary proof of a theorem of approximation of Sobolev spaces H(Q) by fimte éléments without to use classical interpolation The construction which we give hère allows us in some cases to fit boundary conditions

Crack tip finite elements are unnecessary

Abstract: It is shown that a singularity occurs in isoparametric finite elements if the mid-side nodes are moved sufficiently from their normal position. By choosing the mid-side node positions on standard isoparametric elements so that the singularity occurs exactly at the corner of an element it is possible to obtain quite accurate solutions to the problem of determining the stress intensity at the tip of a crack. The solutions compare favourably with those obtained using some types of special crack tip elements, but are not as accurate as those given by a crack tip element based on the hybrid principle. However, the hybrid elements are more difficult to use.

Splines and Variational Methods

Abstract: Introductory ideas Lagrangian interpolates Hermitian interpolates polynomial splines and generalizations approximating functions of several variables fundamentals for variational methods the finite element method the method of collocation.

Finite element formulations for large deformation dynamic analysis

Abstract: SUMMARY Starting from continuum mechanics principles, finite element incremental formulations for non-linear static and dynamic analysis are reviewed and derived. The aim in this paper is a consistent summary, comparison, and evaluation of the formulations which have been implemented in the search for the most effective procedure. The general formulations include large displacements, large strains and material non-linearities. For specific static and dynamic analyses in this paper, elastic, hyperelastic (rubber-like) and hypoelastic elastic-plastic materials are considered. The numerical solution of the continuum mechanics equations is achieved using isoparametric finite element discretization. The specific matrices which need be calculated in the formulations are presented and discussed. To demonstrate the applicability and the important differences in the formulations, the solution of static and dynamic problems involving large displacements and large strains are presented.

Three-dimensional finite element analysis of vertically loaded pile groups

Abstract: The finite element method has been applied to study the behaviour of vertically loaded single piles and pile groups in a homogeneous linearly elastic medium. Three-dimensional and axisymmetric ele-...

Nonlinear Analysis of RC Shells of General Form

Abstract: A general finite element method of analysis is developed to analyze reinforced concrete shells of general form and slabs of arbitrary geometry under dead load and monotonically increasing live loads. The method can be used to trace the load-deformation response and crack propagation through the elastic, inelastic, and ultimate ranges. The nonlinear analysis includes cracking with a tension stiffening effect and the elastoplastic behavior of the concrete and steel reinforcement. The coupling between the membrane action and the bending action due to material asymmetry is also included. Validity of the method is studied by comparing analytical results with experimental data. It is found that the tension stiffening effect has a significant influence on the post-cracking response of underreinforced concrete structures. The importance of the failure criteria and flow rules is also studied.

Some nonconforming finite elements for the plate bending problem

Abstract: We consider various non-conforming finite element methods to solve the plate bending problem. We show thaï all the éléments pass the ''Patch test", a pratical condition for convergence. Using gênerai results, we dérive in each case the error bounds for both strains and displacements. 1 INTRODUCTION We shall study the convergence and accuracy of the approximate solutions of the plate bending problem obtained with finite element methods using some nonconforming éléments. These éléments are the quadratic triangular element of Morley [15], two cubic triangular éléments recently introduced by Fraeijs de Veubeke [9], the rectangular element of Adini [1] and the triangular element of Zienkiewicz [3], To obtain the corresponding error estimâtes, the keystone is the patch test of Irons [10]. The first three éléments pass the patch test for polynomials of degree less than or equal to 2 whatever the mesh geometry. Zienkiewicz's triangle passes it only if the mesh is generated by three sets of parallel lines. Adini's rectangle passes it for polynomials with degree less than or equal to 2, whatever are the dimensions of the rectangles and it passes a "super" patch test — so called by Strang [19] when ail rectangles are equal. (1) Commissariat à l'énergie atomique Centre d'Etudes de Limeil Villeneuve-Saint-Georges — France Revue Française d'Automatique, Informatique et Recherche Opérationnelle n° avril 1975, R-l. 10 P. LASCAUX ; P. LESAINT The main results are the following : Let u be the exact solution, let un be the approximate solution that one gets on a mesh of order h (the supremum of the element side length), then : \\U-Uh\\ g) = | ƒ (x,y) g (x,y) dx dy and the corresponding norrn by : Given an integer m > 0, we consider the usual Sobolev space : # " ( « ) {v,vez, (n) , bveL (n), | a | < m } , with the norm and semi norm || \\m ^ and | \m ^ defined by : ""Un =C I liav||0>n) , I ot | = m where a is a multiindex such that a ~ (at , a 2 ) , â . > 0 ,

A New Measuring Method of Residual Stresses with the Aid of Finite Element Method and Reliability of Estimated Values

Abstract: In estimation of residual stresses, the existing methods are mainly based on the idea that variation of strains on the surface of the object is measured by sectioning continuously until there is no variation of the measured strains, which corresponds to the residual stresses. In this kind of method, some definite mathematical relation between the variation of stresses and the released surface force is required. This kind of relation was obtained for the cases where the geometry, boundary condition, and pattern of residual stress distribution are simple. This difficulty is solved when numerical analytical methods, such as the finite element method, etc. are applied.In this paper, a general theory is developed based on the finite element method. With this method, three dimensional residual stresses can be measured. Furthermore, reliability of estimated values, of residual stresses by this method is mathematically studied when error is contained in the measured strains.

Dynamic Analysis of Footings on Layered Media

Abstract: A finite element formulation for the dynamic analysis of circular footings resting on or embedded in layered soil strata is presented The formulation provides excellent results, accurately reproducing the lateral radiation effects through a consistent energy transmitting boundary, which is an extension of that suggested by Waas and Lysmer for two-dimensional problems Because the boundary can be placed directly at the edge of the footing without loss of accuracy, it also provides savings in storage requirements and time of computation over other solutions The analysis must be performed in the frequency domain; arbitrary transient loading conditions are then handled using fast Fourier transformation techniques

The finite element methods

Abstract: An application for a one-dimensional long period shallow water wave using he method of Galerkin an the four-step Runge-Kuta method.

A comparison of time marching schemes for the transient heat conduction equation

Abstract: This paper investigates the phenomenon of ‘noise’ which is common in most time-dependent problems. The emphasis is on the achievable accuracy that is obtained with various time-stepping algorithms and how this can be improved if noise is artificially damped to an acceptable level. A series of experiments are made where the space domain is discretized using the finite element method and the variation with time is approximated by several finite difference methods. The conclusion is reached that the Crank–Nicolson scheme with a simple averaging process is superior to the other methods investigated.

An assumed displacement hybrid finite element model for linear fracture mechanics

Abstract: This paper deals with a procedure to calculate the elastic stress intensity factors for arbitrary-shaped cracks in plane stress and plane strain problems. An assumed displacement hybrid finite element model is employed wherein the unknowns in the final algebraic system of equations are the nodal displacements and the elastic stress intensity factors. Special elements, which contain proper singular displacement and stress fields, are used in a fixed region near the crack tip; and the interelement displacement compatibility is satisfied through the use of a Lagrangean multiplier technique. Numerical examples presented include: central as well as edge cracks in tension plates and a quarter-circular crack in a tension plate. Excellent correlations were obtained with available solutions in all the cases. A discussion on the convergence of the present solution is also included.

Distribution of plastic strain and negative pressure in necked steel and copper bars

Abstract: The distributions of plastic strain and negative pressure (hydrostatic tensile stress) have been computed both by an approximate method based on an extension of the Bridgman development and by a finite element analysis in inhomogeneously deforming bars after necking. The computations have been made for both initially smooth bars as well as bars having machined initial natural neck profiles, for two types of stress-strain behavior, modelling a spheroidized 1045 steel and a fully aged Cu-0.5 pct Cr alloy. The results of the finite element analysis show that the approximate method based on an extension of the Bridgman development is good only for slightly necked bars. In more acutely necked bars the Bridgman development is good only near the center of the neck. Some experimental results on strain distribution and on neck profiles are also presented.

Bridge deck analysis

Abstract: The book presents the theory and applications of the analytical techniques used in finding stresses in highway and other bridge decks. Current trends in bridge design and construction are discussed and are followed by the various analytical methods. The plate method is dealt with, initially by the basic derivation and solution of the plate equation. A chapter is devoted to the determination of the equivalent plate rigidities of various representative types of bridge deck. An approximate method of determination of bending moments for initial design is described. Various special applications of orthotropic plate theory are covered and the finite difference method for plates is described, including a summary of the dynamic relaxation method. The last four chapters deal with the stiffness method and its application: grillage and space frame analysis, the folded plate method, the finite element method, and the finite strip method. The book is intended for use by bridge designers and students with a particular interest in bridge engineering. /TRRL/

Prediction of transmission loss in mufflers by the finite−element method

Abstract: A numerical technique based on the finite−element method has been developed for analyzing the performance of systems of acoustic elements including expansion chambers in mufflers. The theories developed are, firstly, the variational formulation of the acoustic field existing in the system and, secondly, the finite−element approximate solutions of the variational problems. The predictions of transmission loss are then made by forming the equivalent acoustic four−terminal transmission network in which the acoustic four−pole constants are calculated from the finite−element method. As used, the finite−element approach is perfectly general and may be applied to any system component with arbitrary boundary geometry provided this may be realized by an assembly of rectangular elements. The method is applied to simple expansion chamber models because the results are tractable and theoretical results from acoustic filter theory are available for comparison purposes. The comparison brings out an important fact: the accuracy of the prediction of transmission loss implies that the variational formulation and finite−element approximations are adequately applicable to a number of practical applications.Subject Classification: 50.40; 20.40.

Finite Element Models for Ocean Circulation Problems

Abstract: In this paper a finite element model is presented for a limited region ocean circulation problem. Stability and aliasing error analysis are given as well as the conservation laws that are intrinsic to the finite element scheme.

On Lp- Lr Estimates for the Wave-Equation

Abstract: The purpose of this note is to present a short proof of some of the results announced by Littman [4], and in particular to obtain a fundamental Lp-Lp , estimate for a class of evolution equations with constant coefficients, in particular containing the stimate for the wave-equation due to Strichartz [-7, 8]. The method used here is particularly apt to deal with approximations to the wave-equation, such as those obtained by finite element or finite difference methods. Details of such applications will appear elsewhere.

Calculation of Microstrip Discontinuity Inductances

Abstract: Inductive components of microstrip discontinuity equivalent circuits are calculated by the Galerkin method. The formulation and method of calculation are discussed and a large number of numerical results for symmetric corners, T junctions, and steps changes are presented. These results compare well with experiment.