bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the finite element solution of an exterior boundary value problem
Authors: Wood Winifred L. 
Published: August 2005

AbstractThis paper compares three methods for dealing with an exterior boundary value problem by the Finite Element Method, one of which involves using an infinite element. The methods are illustrated by application to the problem of ground water flow round a tunnel with permeable invert. The use of a special trial function with a variable parameter in the infinite element gives a particularly efficient method of solution.
Difference schemes for second order hyperbolic equations
Authors: Jain M. K. , Ahuja Raj , Bhattacharyya S. 
Published: August 2005

AbstractImplicit difference methods for the wave equation in two space variables have been discussed with the help of a stability diagram. The difference methods of intermediate accuracy 0(h4+k2) have been determined. A method of order of accuracy 0(h2+k2) with minimum truncation error has also been found.
An iterative technique for fitting exponentials
Authors: Lal M. , Moore E. 
Published: August 2005

AbstractAn interative method to fit the function \documentclass{article}\pagestyle{empty}\begin{document}$\mathop \[y = \sum\nolimits_i^n { = 1} a_i e^{lix}\] $\end{document} to data is considered. The technique used is that of inversion of a linear differential operator with constant coefficients. This method reproduces the parameters for mathematically precise data and gives satisfactory results when the data are affected by random errors.
Effective numerical treatment of boundary integral equations: A formulation for three‐dimensional elastostatics
Authors: Lachat J. C. , Watson J. O. 
Published: August 2005

AbstractThe field equations of three‐dimensional elastostatics are transformed to boundary integral equations. The elastic body is divided into subregions, and the surface and interfaces are represented by quadrilateral and triangular elements with quadratic variation of geometry and linear, quadratic or cubic variation of displacement and traction with respect to intrinsic co‐ordinates. The integral equation is discretized for each subregion, and a system of banded form obtained. For the integration of kernel‐shape function products, Gaussian quadrature formulae are chosen according to upper bounds for error in terms of derivatives of the integrands. Use of the integral formulation is illustrated by the analysis of a prestressed concrete nuclear reactor pressure vessel.
Stiffness matrix for a non‐prismatic beam‐column element
Authors: Chugh Ashok K. , Biggers S. B. 
Published: August 2005

AbstractAn algorithm is presented which generates an element stiffness matrix for non‐prismatic beam‐column members using Newmark's numerical procedure of successive approximations. The resulting element stiffness matrix on element co‐ordinates is fond to be in excellent agreement with those available for limiting cases. An approximate stability analysis conducted on the covergence of the numerical scheme shows that the proposed algorithm is stable. The critical buckling loads for various and conditions are computed as part of the computational scheme. A computer program listing in FORTRAN IV is included which will handle essentially and order and/or kind of non‐prismaticity of beam elements. The results are presented in the conventional and convenient coefficient format.
Computer plotting of stress contours in excavated slopes
Authors: Kalkani E. C. 
Published: August 2005

AbstractThe contouring of stresses in two‐dimensional slopes is done quickly and efficiently by using the computer and an incremental plotter. The computer program developed here interpolates in two directions between centroids of finite elements at which the stresses are given, determines contour line co‐ordinates, and plots the contours. This program can be easily modified to plot stresses produced by other two‐dimensional finite element analysis programs as long as the arrangement of elements in the mesh is similar.
Stress intensity factors in anisotropic plates using singular isoparametric elements
Authors: Foschi Ricardo O. , Barrett J. D. 
Published: August 2005

AbstractA conformable displacement model is presented for the finite element analysis of stress intensity factors in linear elastic fracture mechanics. The method is an extension to anisotropic materials of the one developed by Benzley for isotropic materials. Very good agreement is shown for the case of inclined cracks in an orthotropic plate between finite element results and those obtained by least squares collocation of stress functions.
Computation of rational product approximations
Authors: Henry Jackson N. 
Published: August 2005

AbstractLet F be a continuous real‐valued function defined on [−1, 1] × [−1,1]. For purposes of simplifaction in some numerical processes, one may desire to have an approximation of the function F. We present a known method of approximation called the best rational product approximation. When developing this approximation to F, certain types of discontinuities may arise. We develop a slight variation of a known technique to overcome such discontinuities. With this modified technique, it is then possible to develop a computer program to compute the approximation of F. A brief discussion of this program is presented along with some of the results which we have obtained.
Improved quadratic elements
Authors: Chang Anthony T. 
Published: August 2005

AbstractA general method to formulate improved quadratic elements is presented. Derivation of the method is based on more accurate shape functions that take into account effects of governing differential equations. These new shape functions have the same form as those of the standard eight‐node quadratic element. Therefore, they may be easily adapted into existing programs.The new quadratic element is compared with both standard and standard condensed quadratic elements. To show relative merits of different quadratic elements eigenvalue tests are performed. Several examples ranging from field problems, plane stress and bar vibration are used to demonstrate the applicability of this approach.
The finite element solution of dissipative electromagnetic surface waveguides
Authors: McAulay A. D. 
Published: August 2005

AbstractA finite element method is developed for investigating the propagation of high frequency electromagnetic waves along closed or open (surface) waveguides containing dissipative materials and having a cross section of arbitrary shape. The complex propagation constants and associated complex electromagnetic fields are determined as a function of frequency for possible modes of propagation. The method is verified by applying it to structures of simple shape for which analytical results may be calculated for comparison. Waveguides considered include a waveguide filled with dissipative material, a dissipative dielectric rod, a dielectric coated wire and a conducting wire.
Optimal structural design under dynamic loads
Authors: Feng T‐T. , Arora J. S. , Haug E. J. 
Published: August 2005

AbstractThis paper presents an algorithm for optimal design of elastic structures, subjected to dynamic loads. Finite element, modal analysis and a generalized steepest descent method are employed in developing a computational algorithm. Structural weight is minimized subject to constraints on displacement, stress, structural frequency, and member size. Optimum results for several example problems are presented and compared with those available in the literature.
Triangular quarter‐point elements as elastic and perfectly‐plastic crack tip elements
Authors: Barsoum Roshdy S. 
Published: August 2005

AbstractTriangular and prismatic quadratic isoparametric elements, formed by collapsing one side and placing the mid‐side node near the crack tip at the quarter point, are shown to embody the (1/√r) singularity of elastic fracture mechanics and the (1/r) singularity of perfect plasticity. The procedure of performing the fracture analysis for the case of small scale yielding is discussed, and the finite element results are compared with theoretical results.The proposed elements have wide application in the fracture analysis of structures where ductile fracture is investigated. They permit a determination of the relationship between crack tip field parameters, loading, and geometry. And for a given fracture criterion can be applied to the prediction of fracture in structures such as pressure vessels under in service conditions.
Solution of a complex quadratic eigenvalue problem
Authors: Gignac Donald A. 
Published: August 2005

AbstractA complex quadratic eigenvalue problem of order n (n = 20, 30, 40,…) encountered in an investigation of pipe flow was reduced to that of computing the eigenvalues of either a real or a complex matrix of order 2n, depending on the linearization technique used. To get satisfactory results using the CDC 6000 series computer, double‐precision versions of certain widely used and highly regarded eigenvalue subroutines were required. Although the modified subroutines used for the real matrix computations required less core than those used for the complex matrix, the calculation time was not significantly faster than that for the complex matrix. The use of ‘balancing’ subroutines merits further investigation.
A numerical method of solving Fredholm integral equations applied to current distribution and inductance in parallel conductors
Authors: Deeley E. M. , Okon E. E. 
Published: August 2005

AbstractIf the resistance of a conductor is negligible compared with the reactance and if radiation effects are ignored the inductance and current distribution may be obtained by using perfectly‐conducting models. In this paper the distribution of current in a system of infinitely‐long, perfectly‐conducting straight conductors of arbitrary cross‐section is shown to satisfy an integral equation of Fredholm type and a general digital procedure for solving this equation, and hence for determining inductance, is given.The relative advantages of stepped, piecewise‐linear and piecewise quadratic approximations to the current distribution are studied using arrangements of strip conductors and of isolated rectangular conductors having known current distributions. The advantageous effect of varying the width of the sections used in the computation is also established. It is shown that inductance estimates accurate to within 0·1 per cent can be obtained with a relatively small number of sections and that for a large number of sections the inductance converges on the theoretical value. The paper also examines current distribution and inductance for ‘go‐and return’ systems of rectangular conductors, as well as for two paralleled conductors with remote return, and compares the inductances obtained with previous derivations.
Finite element analysis of non‐linear static and dynamic response
Authors: Mondkar D. P. , Powell G. H. 
Published: August 2005

AbstractThe paper presents the theoretical and computational procedures which have been applied in the design of a general purpose computer code for static and dynamic response analysis of non‐linear structures. A general formulation of the incremental equations of motion for structures undergoing large displacement finite strain deformation is first presented. These equations are based on the Lagrangian frame of reference, in which constitutive models of a variety of types may be introduced. The incremental equations are linearized for computational purposes, and the linearized equations are discretized using isoparametric finite element formulation. Computational techniques, including step‐by‐step and iterative procedures, for the solution of non‐linear equations are discussed, and an acceleration scheme for improving convergence in constant stiffness iteration is reviewed. The equations of motion are integrated using Newmark's generalized operator, and an algorithm with optional iteration is described. A solution strategy defined in terms of a number of solution parameters is implemented in the computer program so that several solution schemes can be obtained by assigning appropriate values to the parameters. The results of analysis of a few non‐linear structures are briefly discussed.
Eccentrically loaded sandwich panels
Authors: Tatsa E. Z. , Levy M. 
Published: August 2005

AbstractThe paper deals with the design of eccentrically loaded sandwich panels in civil engineering structures. A theoretical analysis taking into account the non‐linear stress–strain properties of the materials and the influence of shear deformations is proposed. A computer program based on the described algorithm is used to solve a numerical example. It is found that the Newton–Raphson procedure both in the solution of strains at individual sections and in the step by step procedure over the whole structure converges rapidly. Thus the method is suitable for the evaluation of the critical load due to strength failure or loss of stability.
Application of least square collocation technique in finite element and finite strip formulation
Authors: Kwok W. L. , Cheung Y. K. , Delcourt C. 
Published: August 2005

AbstractA new approach in the formulation of finite elements using the concepts of least squares in conjunction with collocation is developed. No numerical integration is required in the stiffness formulation and the resulting matrix has the advantage of being always symmetrical. This approach has also been applied to the finite strip method and provides a means for rapid and accurate analysis of high order partial differential equations. The accuracy and versatility of the method are demonstrated by several examples.
Substructured macro elements based on locally blended interpolation
Authors: Cavendish James C. , Gordon William J. , Hall Charles A. 
Published: August 2005

AbstractIn this paper we describe a new class of locally refined macro finite elements which are especially amenable to the use of substructuring techniques for the efficient solution of the resulting idealization. The tools and guidelines illustrated by the examples of modelling crack tips, point load singularities and singularities at re‐entrant corners should enable an analyst to construct other such blended macro elements specifically tailored to his particular class of problems. The use of such substructured macro elements in finite element calculations permits substantial reduction in the manual effort of data preparation and the computational cost of numerical solution.
A theoretical study of thermal stress relief in thin shells of revolution
Authors: Cameron I. G. , Pemberton C. S. 
Published: August 2005

AbstractA numerical method is given for examining the effect of uniformly heating thin shells of revolution which have an initial stress state. It is assumed that the yield strength decreases with temperature so that significant plastic flow takes place. The note includes a detailed study of this annealing effect on a finite length cylinder which has been given an initial state of stress by removing a longitudinal strip from it and rejoining the edges. The spread of the plastic regions with increasing temperature is followed and it is shown that the peak stress following a heating and cooling cycle is about 10–20 per cent in excess of the yield strength of the material at the peak temperature attained.
A numerical method for two‐dimensional Navier–Stokes equation by multi‐point finite differences
Authors: Saitoh Takeo 
Published: August 2005

AbstractA numerical scheme with a high degree of accuracy has been developed for the full Navier–Stokes equations. The method utilizes the multi‐mesh points for space and time derivatives in order to improve the truncation error. Whereas the existing numerical method employing the finite difference scheme, e.g. the explicit, pure implicit, Crank–Nicolson, and DuFort–Frankel schemes, has the truncation errors of the order (Δx)2, Δx being the spatial mesh length, the one for the present method is generally of the order (Δx)3. A numerical example is shown for a natural convection flow in a square box and the results are compared with those of Cormack et al. One order of magnitude reduction of the computing time for a constant degree of accuracy was attained for the two‐dimensional problems. Furthermore, a two order of magnitude reduction is to be expected when the method is applied for the three‐dimensional Navier–Stokes equations.
Isoparametric, finite element, variational solution of integral equations for three‐dimensional fields
Authors: Jeng G. , Wexler A. 
Published: August 2005

AbstractAn improved numerical method, based on a variational approach with isoparametric finite elements, is presented for the solution of the boundary integral equation formulation of three‐dimensional fields. The technique provides higher‐order approximation of the unknown function over a bounding surface described by two‐parameter, non‐planar elements. The integral equation is discretized through the Rayleigh–Ritz procedure. Convergence to the solution for operators having a positive‐definite component is guaranteed. Kernel singularities are treated by removing them from the relevant integrals and dealing with them analytically. A successive element iterative process, which produces the solution of the large dense matrix of the complete structure, is described. The discretization and equation solution take place one element at a time resulting in storage and computational savings. Results obtained for classical test models, involving scalar electrostatic potential and vector elastostatic displacement fields, demonstrate the technique for the solution of the Fredholm integral equation of the first kind. Solution of the Fredholm equation of the second kind is to be reported subsequently.
On the approximation of convection problems in fluid dynamics
Authors: Griffiths D. F. 
Published: August 2005

AbstractIt is well‐known that oscillatory result when cerntral difference of finite element approximations are suoght for convective and boundary layer flows unless the grid length is sufficiently small. A priori limits on the grid spacing, bleow which the solutions are oscullation freee, are derived form one‐dimensional idenlizations of these problems and result form boundaryb layer theiry.
Comparative criteria for finite‐difference formulations for problems of fluid flow
Authors: Runchal Akshai K. 
Published: August 2005

AbstractThis paper concerns a technique for providing quantitative and qualitative answers to the questions related to accuracy and stability of finite‐difference schemes. It is applicable to both the unsteady and the steady flows. The application of the technique provides comparative information about the amplitudes and the speeds of propagation of the numerical and analytic solutions. The difference between the two solutions is characterized in terms of a ‘false’ propagation speed and ‘false’ diffusion parameters for the numerical schemes.The technique is applied to a number of commonly used finite‐difference schemes and it is concluded that the use of central differences for the convective terms and/or explicit formulations tends to increase the amplitudes and wave speeds. The opposite effects on the amplitudes and wave speeds are produced by upwind or ‘donor’ cell differences and/or implicit formulations.
Derivatives of eigenvectors of locally modified structures
Authors: Hirai Itio , Kashiwaki Mitsuhiro 
Published: August 2005

AbstractIn this study a method for obtaining the derivatives of eigenvectors of a locally modified structure with respect to a design variable is presented. Eigensolution to the locally modified structure is expressed by equations consisting of the condensed matrices only which refer to the modified part. The analysis presented herein is developed in conjunction with eigensolution to the modified structure, and the derived fundamental equations are also represented by the same type of condensed matrices only. So, advantages are realized both in computational effort and in computer storage, if the modified part is small compared with the unmodified part. To find exact results, complete eigensolution to the unmodified structure needs to be given. Approximate results are obtained from a few lower eigenvectors and eigenvalues. A pin‐jointed truss is solved as a numerical example.
An experimental–numerical hybrid technique for three dimensional stress analysis
Authors: Chandrashekhara K. , Jacob K. Abraham 
Published: August 2005

AbstractThe paper describes a numerical method for determining the stress distribution in the interior of a three‐dimensional body using experimentally determined surface stresses, and the interior displacements from surface displacements. The normal and shear stresses inside the body are obtained by solving Laplace's equation in terms of sum of normal stresses together with the three‐dimensional compatibility equations in terms of stresses, using the finite difference technique, when the stresses on the surface of the body are known. On the other hand if surface displacements are known (from which strain components could be determined) then displacement components in the interior of a body can be determined by solving Laplace's equation in terms of sum of normal strains together with the three‐dimensional equilibrium equations in terms of displacements. It is shown that axi‐symmetric problems can also be solved in an identical way by transforming the equations into cylindrical co‐ordinates. The application of the method has been illustrated through several examples.
A least squares finite element approach to unsteady gas dynamics
Authors: Polk John F. , Lynn Paul P. 
Published: August 2005

AbstractA numerical technique for solving unsteady gas dynamic equations is presented. The technique is based on least squares finite element concepts with elements that are constructed in both space and time. Both linear and quadratic interpolation is used on individual elements. The technique is tested against a problem whose solution is known so that numerical accuracy can be ascertained.
Finite element analysis of steady‐state elasto‐visco‐plastic flow by the initial stress‐rate method
Authors: Dawson Paul R. , Thompson Erik G. 
Published: August 2005

AbstractA viscous approximation for steady creeping flow is extended to include the effect of elastic strains. Two examples are presented which illustrate both the method and the need for including elastic strains in the analysis of steady‐state visco‐plastic flows.
Closed form elastic‐plastic stiffness matrix for axisymmetric finite elements
Authors: Rich T. P. 
Published: August 2005

AbstractThis note presents the closed form equations for the stiffness terms in the elastic‐plastic stiffness matrix for axisymmetric finite elements. The element considered is a triangular ring element characterized by linear displacement relationships and an averaged state of stress. The physical law is modelled by the incremental theory of plasticity utilizing the Prandtl‐Reuss flow rule and von‐Mises Yield Criterion. Results are presented comparing stiffness terms as computed by numerical integration to those computed from the closed form equations. Significant errors in stiffness terms arising from numerical integration are observed for axisymmetric elements located near the line of axial symmetry as a result of the logarithmic nature of some of the stiffness terms.
A finite element formulation for large elastic‐plastic deformation analysis of polycrystals and some numerical considerations on polycrystalline plasticity
Authors: Gotoh M. 
Published: August 2005

AbstractA finite element formulation for large elasto‐plastic deformation of polycrystalline materials is proposed in incremental form. The effect of rotation of crystal axes besides usual element rotaion is taken into account. Some numerical considerations on polycrystalline plasticity (i.e. stress‐strain curves for several proportional loadings, effect of change of loading path on stress‐strain curve, subsequent yield loci for uniaxial and equi‐biaxial loadings and so forth) are given for the case of small deformation by using a plate model which consists of 121 square FCC crystals.