bluuebunny/crossref_metadata_2025_split huggingface dataset:
Convergence and accuracy of three finite difference schemes for a two‐dimensional conduction and convection problem
Authors: Runchal A. K. 
Published: August 2005

AbstractThe convergence and accuracy characteristics of two commonly used finite difference schemes, namely the central and the upwind difference, are compared with a scheme recently proposed by Spalding. For a simple two‐dimensional problem with conduction and convection, it is shown that the scheme proposed by Spalding is preferable choice both from the point of view of accuracy and that of the convergence. The extension of the conclusion to a general case must await further substantiation.
Use of the least squares criterion in the finite element formulation
Authors: Lynn Paul P. , Arya Santosh K. 
Published: August 2005

AbstractThis paper presents a new method of formulating the finite element relationships based on the least squares criterion. To overcome the high degree of inter‐element continuity, a method of reducing the original governing differential equation to a set of equivalent system of first‐order differential equations is proposed. The validity of the method is demonstrated by means of several numerical examples. In particular, application of the method to problems with unknown variational functionals is considered.
Finite element solution algorithm for viscous incompressible fluid dynamics
Authors: Baker A. J. 
Published: August 2005

AbstractA numerical solution algorithm employing the finite element concept of solid mechanics is derived for the transient laminar two‐dimensional flow of an incompressible viscous fluid. Through dependent variable transformation, the problem is uniformly recast into the solution of a quasi‐linear elliptic boundary value‐problem, for which the finite element solution theory is established. The algorithm is uniquely user‐oriented in accepting the generalized elliptic boundary condition specification of any non‐coordinate‐surface solution do main closure segment and on employing an arbitrarily irregular computational latticc. Numerical results are presented for several problems in internal flow illustrating solution accuracy, convergence, versatility and the ability to predict imbedded regions of recirculating flow.
The analysis of dislocation systems by the finite element method
Authors: Owen D. R. J. , Prakash A. 
Published: August 2005

AbstractIt is shown how the stress field due to any prescribed continuous distribution of dislocations can be determined. The finite element method is employed giving wide freedom with regard to boundary geometry and material properties. The presentation is limited to situations which conform to either the standard plane or anti‐plane conditions. Some results are obtained for simple dislocation configurations and compared with theoretical expressions available. Solutions are then obtained to problems in which the material behaves elasto‐plastically, a limiting shear stress criterion being employed. Finally the analysis of discrete edge dislocations by use of the slab analogy is presented.
Singularity programming: A numerical technique for determining the effect of singularities in finite difference solutions illustrated by application to plane elastic problems
Authors: Emery A. F. , Segedin C. M. 
Published: August 2005

AbstractThis paper contains a description of a numerical technique designed to overcome the difficulties encountered in the approximate solution of two‐dimensional discretized field problems when there are singularities arising from sharp corners, discontinuities, point sources, etc. The essence of the method is to modify the discretization by incorporating in the numerical computations the known analytical form of the singularities. The method is applicable to a wide variety of linear two‐dimensional field problems, and is illustrated herein with plane elastic problems.
Determination of stress intensity factors in cracked plates by the finite element method
Authors: Yamamoto Yoshiyuki , Tokuda Naoaki 
Published: August 2005

AbstractStress fields near crack tips in an elastic body can be specified by the stress intensity factors which are closely related to the stress singularities arising from the crack tips. These singularities, however, cannot be represented exactly by conventional finite element models. A new method for the analysis of stresses around cracks is proposed in this paper on the basis of the superposition of analytical and finite element solutions. This method is applied to several two‐dimensional problems whose solutions are obtained analytically, and it is shown that their numerical results are in excellent agreement with analytical ones. Sufficiently accurate results can be obtained by the conventional finite element analysis with rather coarse mesh subdivision. Computational efforts are then considerably reduced compared with other methods.
Accuracy of the finite element analysis for the elastic plate with a circular hole
Authors: Radaj D. 
Published: August 2005

AbstractThis paper compares the results obtained by the finite element method with ‘exact’ solutions to a given set of problems. These are the stresses on the boundary of a hole in an infinite plate, the plate being subjected to three different types of loading. Two types of element are used for these plane stress problems, triangular elements with constant strains and tri‐ angular elements with linearly varying strains. The problems are solved for two different meshes and the results shown are stresses along a radial section and the values derived for stress concentrations against the number of unknowns in each mesh.
An integrated sequential solver for large matrix equations
Authors: Vendhan C. P. , Kapoor M. P. , Das Y. C. 
Published: August 2005

AbstractAn integrated sequential computer programme for the solution of large linear algebraic systems encountered in the discrete analysis of complex structures using finite element idealization is described. The programme uses an algorithm based on Gauss elimination for solution and is independent of the possible symmetric nature of the system matrix thus enhancing the applicability of the programme for systems with unsymmetric coefficient matrices. The present programme can handle large band widths and the core memory is used efficiently for all feasible problem sizes. A FORTRAN print‐out of the programme with relevant explanatory comments and a full notation list are appended.
Exponential fitting using integral equations
Authors: Moore Edward 
Published: August 2005

AbstractThe fitting of a function y =\documentclass{article}\pagestyle{empty}\begin{document}$ \sum\nolimits_{i = 1}^n {A_i {\rm{e}}^{\lambda ix}} $\end{document} to experimental data is considered. Integral equations are developed which have the functions \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\nolimits_{i = 1}^n {A_i {\rm{e}}^{\lambda ix}} $\end{document} as their solutions for n = 1, 2, 3, These integral equations are used to find the frequencies λi. Examples are worked out to illustrate the method. The method is shown to be capable of extension to other functions.
Semi‐analytical finite element procedure for conduction in anisotropic axisymmetric solids
Authors: Padovan Joseph 
Published: August 2005

AbstractThrough the use of complex series representations and the properties of adjoint differential operators, a semi‐analytical finite element procedure is developed which can analyse the steady state and transient temperature fields of thermally anisotropic axisymmetric bodies with complete circumferential properties. Due to its generality, the procedure can handle arbitrary laminate construction with possible meridional and radial variations in locally or globally thermally anisotropic materials. In this respect, the procedure developed herein supercedes the classical semi‐analytical treatment which is limited to specially orthotropic materials. Furthermore, in contrast with the classical procedure, the present treatment reveals several important effects of material anisotropy which are entirely missed by the specially orthotropic assumption.
Numerical quadrature used for radiative heat‐transfer computations
Authors: Look D. C. , Love T. J. 
Published: August 2005

AbstractPhysical reasoning makes it possible to use artificial parameters with numerical quadrature in order to obtain approximate solutions for the Fredholm integral equations associated with radiative heat transfer calculations. With the aid of such parameters, decisions can be made concerning the applicability and usefulness of the numerical quadrature technique.
Effect of time‐dependent material properties on dynamic response
Authors: Yamada Y. , Takabatake H. , Sato T. 
Published: August 2005

AbstractBy representing the time‐dependent material properties by mechanical models, i.e. the generalized Maxwell and/or Voigt (or Kelvin) models, it is possible to formulate a consistent procedure to analyse the effect of material damping on dynamic response. As a continuation of the previous work which concerned the creep and relaxation of viscoelastic materials, the present paper applies this representation to the harmonic response analysis. The harmonic solution can be obtained by decomposing the relevant forces and displacements into real and imaginary parts and it is shown that the modal analysis by an appropriate eigensolution procedure is useful for obtaining the dependence of vibration amplitude on frequencies of sinusoidal external excitations.
Local and global smoothing of discontinuous finite element functions using a least squares method
Authors: Hinton E. , Campbell J. S. 
Published: August 2005

AbstractThe concepts and potential advantages of local and global least squares smoothing of discontinuous finite element functions are introduced.The relationship between local smoothing and the ‘reduced’ integration' technique is established.Examples are presented to illustrate the application of the two smoothing techniques to the finite element stresses from several structural analysis problems.The paper concludes with some practical recommendations for discontinuous finite element function smoothing.
Transient two‐dimensional heat conduction problems solved by the finite element method
Authors: Bruch John C. , Zyvoloski George 
Published: August 2005

AbstractA finite element weighted residual process has been used to solve transient linear and non‐linear two‐dimensional heat conduction problems. Rectangular prisms in a space‐time domain were used as the finite elements. The weighting function was equal to the shape function defining the dependent variable approximation. The results are compared in tables with analytical, as well as other numerical data. The finite element method compared favourably with these results. It was found to be stable, convergent to the exact solution, easily programmed, and computationally fast. Finally, the method does not require constant parameters over the entire solution domain.
Finite element solution of non‐linear heat conduction problems with special reference to phase change
Authors: Comini G. , Del Guidice S. , Lewis R. W. , Zienkiewicz O. C. 
Published: August 2005

AbstractThe paper presents a generally applicable approach to transient heat conduction problems with non‐linear physical properties and boundary conditions. An unconditionally stable central algorithm is used which does not require iteration.Several examples involving phase change (where latent heat effects are incorporated as heat capacity variations) and non‐linear radiation boundary conditions are given which show very good accuracy.Simple triangular elements are used throughout but the formulation is generally valid and not restricted to any single type of element.
Automatic triangulation of arbitrary planar domains for the finite element method
Authors: Cavendish James C. 
Published: August 2005

AbstractThe object of this paper is to describe a new algorithm for the semi‐automatic triangulation of arbitrary, multiply connected planar domains. The strategy is based upon a modification of a finite element mesh genration algorithm recently developed. 1 The scheme is designed for maximum flexibility and is capable of generating meshes of triangular elements for the decomposition of virtually any multiply connected planar domain. Moreover, the desired density of elements in various regions of the problem domain is specified by the user, thus allowing him to obtain a mesh decomposition appropriate to the physical loading and/or boundary conditions of the particular problem at hand. Several examples are presented to illustrate the applicability of the algorithm. An extension of the algorithm to the triangulation of shell structures is indicated.
Projective method applied to three‐dimensional elasticity equations
Authors: Schmidt William F. 
Published: August 2005

AbstractIt is shown how the elasticity equations can be formulated in terms of a general procedure of abstract analysis, called the projective method, for constructing an approximate solution. This allows the many studies of convergence and uniqueness of solutions which have been made in modern mathematics to be applied to the elasticity problem. The abstract formulation also suggests an organizational scheme for generating a computer code. A computer code for hollow or solid cylinders of arbitrary cross section was developed and several numerical examples are presented. The procedure is computationally advantageous for the class of problems under consideration because of the relatively small number of equations that must be solved as compared to the finite element method. The results presented demonstrate the accuracy of the method.
A finite element analysis in polar co‐ordinates of the Saint Venant torsion problem
Authors: Heise Ulrich 
Published: August 2005

AbstractA characteristic feature of the variational functionals for several boundary value problems in polar co‐ordinates is the fact that one independent variable occurs explicitly in the denominator. Therefore, the coefficients of the finite element equations for sectors of circular ring shaped elements are not constants but functions of the distance of the elements from the origin of co‐ordinates.1 We name them coefficient functions. In order to show the particular aspects of the calculations in terms of polar co‐ordinates we deal here with the solution of the torsion problem by bilinear and bicubic Hermitian interpolation.The finite element equations are arranged according to Schaefer2 in the form of block which can easily be transformed into ‘stars’3 or molecules4,5 similar to those used in finite difference methods. The origin of co‐ordinates requires a special consideration, firstly because of the coincidence of several nodes at that point and secondly because of the divergent behaviour of some coefficient functions. It turns out to be advantageous for the numerical calculations to expand the coefficient functions in power series. Besides, the expansions are required to deduce the equations for rectangular elements by limiting processes. The twisting moments and shearing stresses calculated for several cross sections illustrate the numerical suitability of the method. The finite element values are compared partly with exact solutions and partly with experimental results obtained by a moiré method using Prandtl's soap film analogy.6 Finally it is shown how the accuracy of the finite element values can be improved by the Richardson extrapolation7.
Elastoplastic analysis of hollow spheres subjected to external pressure loading
Authors: Grant Donald A. 
Published: August 2005

AbstractThe elastoplastic deformation of spherical shells of uniform thickness acted upon by external pressure is investigated in this paper. A deformation theory of plasticity is combined with the classical elasticity equations and a solution is obtained by the method of successive elastic solutions. A logarithmic effective stress‐effective plastic strain diagram is used to determine the volume change for thick polypropylene spheres under the action of external pressure. These results are compared with previously published experimental volume changes in polypropylene spheres. This comparison shows that the predicted volume changes are similar to the experimental results.
Visco‐plasticity—plasticity and creep in elastic solids—a unified numerical solution approach
Authors: Zienkiewicz O. C. , Cormeau I. C. 
Published: August 2005

AbstractThe visco‐plastic model of material behaviour is of much practical interest in its own right and initial strain techniques for its solution have been developed and proved efficient. More important however is the fact that the visco‐plastic model can be used to generate plasticity solutions in a simple manner when stationary conditions are reached and, at the other extreme, can reproduce standard creep phenomena. Used in this sense it allows the treatment of non‐associated plasticity and strain softening situations which present difficulties in conventional plasticity approaches. A standard programme thus allows the treatment of a wide range of materially non‐linear problems.The paper discusses various applications of the new general formulation and introduces certain numerical information on solution stability.
Imperfections in axially loaded plane frames
Authors: Harung H. S. , Millar M. A. , Brotton D. M. 
Published: August 2005

AbstractA finite beam‐column element computer program for the structural failure analysis of proportionally loaded skeletal plane frames is described. The program, which is based on an iterative stiffness approach, provides for non‐linear elastic or plastic‐non‐linear elastic behaviour. Particular attention is given to the incorporation into the analysis of geometrical imperfections, return of elasticity at plastic hinges and negative frame stiffness. The effect of lack‐of‐fit displacements on the load‐deflection path and failure load of frames that carry relatively large axial loads is described in general terms. The theory is developed further through the application of the computer program to two examples which show the necessity for the allowing for the effect of imperfections when designing axially loaded redundant frames.
Least squares finite element analysis of laminar boundary layer flows
Authors: Lynn Paul P. 
Published: August 2005

AbstractBased on the least squares error criterion, a class of finite element is formulated for the numerical analysis of steady state viscous boundary layer flow problems. The method is essentially a discrete element‐wise minimization of square and weighted residuals which arise from the attempts in approximately satisfying boundary layer equations. An iterative linearization scheme is developed to circumvent the mathematical difficulties posed by the non‐linear boundary layer equations. It results in a process of successive least squares minimizations of residual errors arising from satisfying a set of linear differential equations. A mathematical justification for the method is presented. A major feature of the method lies in the linearization approach which renders non‐linear differential equations amenable to linear least squares finite element analysis. Another important feature rests on the proposed finite element formulation which preserves the symmetric nature of finite element matrix equations through the use of the least squares error criterion. Numerical examples of viscous flow along a flat plate are presented to demonstrate the applicability of the method as well as to illuminate discussions on the theoretical aspects of the method.
Eigenproblem solution of damped structural systems
Authors: Gupta K. K. 
Published: August 2005

AbstractThis article presents an efficient numerical algorithm a complete listing of the associated computer program, developed for the eigenproblem solution of discrete damped structures, including spinning ones. The numerically stable procedure is based on a combined Sturm sequence and inverse iteration technique, which fully exploits the banded form of the relevant matrices and proves to be most substantially economical when compared to similar existing softwares. Numerical results are presented for representative structures, solved by the present computer program written in FORTRAN V for the JPL UNIVAC 1108 computer.
Redundant structure concepts in finite element analyses
Authors: Meek J. L. 
Published: August 2005

AbstractThe paper examines two triangular finite elements used in plate bending analyses for which Lagrange multiplier techniques have been used to set up the necessary equations for the solution. These equations involve either equilibrium of the system or the inter‐element compatibility. Starting from only the notions of equilibrium and continuity as used in the analyses of redundant structures, the paper proceeds to solutions of the same problems. It is found that end results are the same when the equations obtained from the minimization techniques are reduced by Gauss‐elimination in partitioned from.
Three dimensional analysis of compressible potential flows with the finite element method
Authors: Periaux J. 
Published: August 2005

AbstractSolutions of elliptic boundary value problems are obtained with variational formulations by minimization of functionals.Conventional tools of the finite element strategy are emphasized; linear or quadratic approximations on triangular elements, curved iso‐parametric elements, Ni shape funtions, Li homogeneous co‐ordinates. High speed of computation of the final assembled matrices require the use of the Formal–FORMAC calculus. Illusrations of the finite element method are chosen in the class of the 2d–3d compressible subsonic irrotational flows in a nozzle and around one or several lifting bodies of arbitary shape.
Finite elements for the vibration of cones and cylinders
Authors: Ross C. T. F. 
Published: August 2005

AbstractElemental mass matrices have been produced for the vibration of conical and cylindrical shells, based on a semi‐analytical approach. Frequencies and modes of vibration have been compared with existing solutions and also with experimental results obtained from other sources. Good agreement has been found between theory and experiment for thin‐walled circular cylinders and cones, a cone‐cylinder combination, and a cooling tower model.A theoretical investigation was also made on the vibration of a circular cylinder when subjected to uniform pressure.
The economical solution of elastic problem for a range of Poisson's ratio
Authors: Booker J. R. , Small J. C. 
Published: August 2005

AbstractIn this paper an economical method for calculating the stress and displacement fields in an elastic body for a range of Poission's ratios is given. The solution is expanded as a power series in Poission's ratio, the coefficients of the series being determined successively. The range of convergence of the solution is examined, and it is shown that the power series converges for values of Poission's ratio in the range zero to a half, provided a suitable point of expansion is chosen. Particular features of the method are firstly that only one effective inversion of the stiffness matrix, for Poission's ratio zero, is required to obtain the solution for all Poission's ratio and secondly that no special formulation for an incompressible material is required.
A comparison of Crandall and Crank–Nicolson methods for solving a transient heat conduction problem
Authors: Moore A. H. , Kaplan B. , Mitchell D. B. 
Published: August 2005

AbstractA comparison is made of the Crandall and Crank–Nicolson methods applied to a transient heat conduction problem with a convective boundary layer on its surface for a range of values of Nusselt modulus and Fourier modulus. A new equation is derived to handle the convective boundary condition. For reasonable accuracy requirements the Crank–Nicolson method gives superior performance with respect to accuracy.