bluuebunny/crossref_metadata_2025_split huggingface dataset:
A numerical method for analysis of bounded metalworking processes
Authors: Sekhon G. S. , Shishodia K. S. , Sharma P. C. 
Published: August 2005

AbstractThis paper describes a numerical procedure for the solution of metalworking problems of a strain‐hardening material. The overall metalworking process is split up into a number of stages and the governing equations for a typical stage are set up in terms of incremental displacements. The incremental deformation occurring in each successive stage is found by an interative numerical procedure based on the concept of piecewise linearization. The ‘composite’ solution yields the distribution of stress and strain in the work material at various stages of the process. Finally, application of the method to finite axisymmetric compression is described.
An accurate method of dynamic substructuring with simplified computation
Authors: Leung Yee‐Tak 
Published: August 2005

AbstractA new dynamic substructuring method is presented. The substructures are identified by their fixed‐interface modes and the condensed stiffness and mass matrices at zero vibration frequency. Physical co‐ordinates are used instead of the modal co‐ordinates to make the condition of compatibility between elements applicable. The dimension of the fundamental matrices is equal to the number of interface co‐ordinates for each substructure. All information needed to formulate the fundamental matrices may be obtained experimentally. Both discrete and continuous parameter models are considered.A number of numerical examples are given and the method is compared with the other methods of dynamic substructure. It is shown that the numerical accuracy lost in the ordinary eigenvalue economization process may be recovered by the present method.
A finite element model for plasma simulation in multipoles
Authors: Hennart J. P. , England R. , Martin J. G. , Melendez L. L. 
Published: August 2005

AbstractA numerical model is proposed to simulate the space‐time behaviour of a low‐density plasma in a linear multipole. Semi‐discrete Galerkin techniques are used in conjunction with triangular finite elements. For both space and time discretizations, special techniques are developed to numerically separate the effect of rapid diffusion along the field lines from the slow perpendicular diffusion. Numerical results are exhibited to show how these techniques succeed in eliminating the problems caused by the strong anisotropy of the diffusion coefficient in the strongly curved and very inhomogeneous multipole configuration.
Reconsiderations on singularity or crack tip elements
Authors: Yamada Y. , Ezawa Y. , Nishiguchi I. , Okabe M. 
Published: August 2005

AbstractVarious singularity finite elements proposed so far are reviewed and their correlations are discussed. The method adopted in the comparative study is based on the singularity mapping or transformation technique. It is suggested that a compact design of computational routines is materialized by using the element which embodies singularity transformation and can be compatible with the notion of using the variable‐number‐nodes element in the general‐purpose computer programs.
Spurious modes in two‐dimensional isoparametric elements
Authors: Bićcanić N. , Hinton E. 
Published: August 2005

AbstractThe reasons for the presence of spurious modes in plane isoparametric elements are examined. Eigenvalue and eigenvector analyses of stiffness matrices for single elements and unconstrained and constrained meshes reveal the types of mechanisms and near‐mechanisms that can be expected when reduced or selective integration techniques are used with quadrilateral elements in the analysis of plane strain problems.
On consistent finite difference formulae for ordinary differential equations
Authors: Miller R. E. 
Published: August 2005

AbstractThis paper presents a finite difference method for two‐point boundary value problems described by fourth‐order ordinary differential equations which results in consistency of truncation errors. It is demonstrated that the order of the formulae used to approximate the boundary conditions must be higher than those used for similar derivative terms in the differential equation. A generalization of the method to differential equations of order n is discussed. The procedure is illustrated with a numerical example.
Automatic local refinement for irregular rectangular meshes
Authors: Simpson R. Bruce 
Published: August 2005

AbstractThe use of local mesh refinements for the generation of meshes for the finite element or finite difference methods is studied. A class of rectangular meshes which admit restricted local refinements, referred to as irregular rectangular meshes, is introduced and its representation discussed. Properties of algorithms for mesh refinements are discussed from the viewpoints of termination with a mesh in the specified class, memory utilization, symmetry and fragmentation of the mesh.
Interpolation by fast Fourier and Chebyshev transforms
Authors: Monro Donlad M. 
Published: August 2005

AbstractTransform methods for the interpolation of regularly spaced data are described, based on fast evaluation using discrete Fourier transforms. For periodic data adequately sampled, the fast Fourier transform (FFT) is used directly. With undersampled or aperiodic data, a Chebyshev interpolating polynomial is evaluated by means of the FFT to provide minimum deviation and distributed ripple. The merits of two kinds of Chebyshev series are compared. All the methods described produce an interpolation passing directly through the given values and are applied easily to the multi‐dimensional case.
Smoothing techniques for certain primitive variable solutions of the Navier–Stokes equations
Authors: Lee Robert L. , Gresho Philip M. , Sani Robert L. 
Published: August 2005

AbstractSeveral types of smoothing technique are considered which generate continuous approximation (i.e. nodal values) for vorticity and pressure from finite element solutions of the Navier–Stokes equations using quadrilateral elements. The simpler schemes are based on combinations of linear extrapolation and/or averaging algorithms which convert elementwise. Gauss point values to nodal point values. More complicated schemes, based on a global smoothing technique which employ the mass matrix (consistent or lumped), are also presented.An initial assessment of the accuracy of the several schemes is obtained by comparing the approximate vorticities with an analytical function. Next, qualitative vorticity comparisons are made from numerical solutions of the steady‐state driven cavity problem. Finally, applications of smoothing techniques to discontinuous pressure fields are demonstrated.
Checking the topological consistency of a finite element mest
Authors: Preiss K. 
Published: August 2005

AbstractAlgorithms are described for checking the topological consistency of two‐ or three‐dimensional meshes. Two‐dimensional meshes may include mixtures of triangles, quadrilaterals and other polygons with optional edge or centre nodes; three‐dimensional meshes may include mixtures of cuboids and tetrahedra with optional edge; sie or internal nodes.
Three‐dimensional computer code for dynamic response of solids to intense impulsive loads
Authors: Johnson Gordon R. , Colby Dwight D. , Vavrick Daniel J. 
Published: August 2005

AbstractEarlier publications demonstrated the capability of the EPIC‐3 code to perform high velocity impact computations in three dimensions.1,2 These capabilities were demonstrated with simplified material and sliding surface models in a core‐contained computer program. This paper presents recent developments which include more comprehensive material and sliding surface formulations, and an expanded computer program which can handle problems of unlimited size by beffering data between disc files and core. The EPIC‐3 code is based on an explicit, finite element, Lagrangian formulation which uses constant strain tetrahedral elements.
On the construction and numerical solution of transmission‐line and lumped network models of Maxwell's equations
Authors: Brewitt‐Taylor C. R. , Johns P. B. 
Published: August 2005

AbstractIt is sometimes convenient to express a numerical algorithm in terms of a network model. The physical picture given can often help the engineer to visualize the properties of the method. In field problems, a lumped network model corresponds to a space discrete field while a transmission‐line model corresponds to a field which is discrete in space and time. In this paper, the relationship is given between the lumped network models and transmission‐line network models used in the steady‐state solution of Maxwell's equations in two and three space dimensions. The use of dual networks is also discussed. An analysis is given for the velocity of waves travelling in any direction across the networks and this is used to compare the accuracy of the models. The use of diakoptics or substructures for the solution of large networks is outlined and this is illustrated by a compound two‐dimensional example.
Transformation of dependent variables and the finite element solution of nonlinear evolution equations
Authors: Čermák Libor , Zlámal Miloš 
Published: August 2005

AbstractTransformation of dependent variables as, for example, the Kirchhoff transformation, is a classical tool for solving nonlinear partial differential equations. This approach is used here in connection with the finite element method and explained first in case of nonlinear heat conduction problems without phase change. The main applications of the method given in the paper concern a nonlinear degenerate parabolic equation for fluid flow through a porous medium and Stefan (moving boundary) problems.
Growth of planar cracks induced by hydraulic fracturing
Authors: Mastrojannis E. N. , Keer L. M. , Mura T. 
Published: August 2005

AbstractA method is proposed for the study of growth, under normal internal pressure, of pre‐existing hydraulically induced planar cracks. The continuous growth process is approximated by a stepwise one, and during each growth step the volume of fluid within the crack cavity is assumed constant. The normal distance through which each point on the crack edge moves outwards is controlled by the level of stress intensity factor KI at each point, and the crack‐resistance characteristics of the material, which can be expressed by some critical level of KI, denoted by KIC. For the present study, that distance was assumed proportional to (KI − KIC)4 for KI > KIC. The evaluation of KI at the crack edge is achieved by utilizing the method discussed by Mastrojannis et al.1 The proposed method was applied to the study of the initial stage of growth of a circular crack under linearly varying normal pressure, and of an elliptical crack under uniform normal pressure.
Finite element analysis of free jet impingement
Authors: Obee Timothy N. , De Witt Kenneth J. 
Published: August 2005

AbstractAn analysis of axisymmetric free jet impingement on to finite disks was performed using the finite element method. The method employed the velocity potential as the dependent variable and six‐node triangle elements to represent the region of flow. The analysis was divided into three parts corresponding to three distinct regions of the flow: (1) In the disk region, the free jet impinged on to a finite disk which was oriented normal to the flow. The jet was subjected to zero or normal gravity and to surface tension effects of varying degrees. (2) Upon leaving the disk region, the jet entered the plume region where it was acted upon internally by surface tension and externally by zero or normal gravity. (3) In the collision region, the flow from the plume region collided symmetrically at some downstream area about the axis of symmetry. The major result achieved from this investigation was the development of techniques to locate the free surface in all three regions for a range of conditions. The velocity profiles along selected lines of constant values of the potential were determined, and a successful comparison was made between the numerical results and existing experimental data.
Finite plane strain deformations of rubberlike materials
Authors: Batra R. C. 
Published: August 2005

AbstractA finite element program capable of analysing finite plane strain deformations of incompressible rubberlike (Mooney–Rivlin) materials has been developed. Two problems, namely a long wall loaded uniformly in two directions and a thick‐wall cylindrical pressure vessel loaded internally, have been solved. The computed values of displacements, strains, stresses and hydrostatic pressure agree very closely with their values obtained analytically.
The evaluation of the error term in some numerical quadrature formulae: An addendum
Authors: Smith H. V. 
Published: August 2005

AbstractIn a previous paper the author deduced a method of evaluating the error term arising in some quadrature formulae. This method depended on the analytic evaluation of a Hilbert transform. The result is now extended to all quadrature formulae used for the calculation of integrals over finite intervals by approximating the Hilbert transform.
The limitations of the patch test
Authors: Stummel F. 
Published: August 2005

AbstractA simple approximation by nonconforming finite elements is presented that passes the patch test of Irons and Strang but does not yield approximate solutions converging to the solution of the given boundary value problem. It is constructed from continuous piecewise linear functions perturbed by step functions. Further, strange convergence properties of such approximations are explained in all details because they may be typical for the behaviour of nonconforming finite elements violating the basic precondition for convergence.
Direct analysis of elastic–plastic structures with ‘overlay’ materials during cyclic loading
Authors: Zarka J. 
Published: August 2005

AbstractSeveral computer codes have incorporated the ‘overlay’ material models: the volume element, which is characteristic of the material, is composed of sub‐elements with different kinematic hardening, perfectly plastic or even viscoplastic flow rules and different elastic properties, these sub‐elements exhibiting all, however, the same total strain.1,2In this paper it is demonstrated how the simple mathematical framework we first proposed for elastic‐plastic structures with kinematic hardening material,3 and we extended to some elastic viscoplastic ones,4 can easily be applied to these particular ‘overlay’ materials.One of the interesting advantages of this approach is a straightforward analysis of structural response under cyclic loadings by applying the linear elastic analysis.
A method for space truss analysis in the post‐buckling range
Authors: Schmidt Lewis C. , Gregg Bernhard M. 
Published: August 2005

AbstractA dual load method of truss analysis is presented that allows highly nonlinear member behaviour to be followed. In particular, a brittle type of strut behaviour is considered. The method assumes that the inelastic strut response is known and that piecewise linearization of the behaviour is acceptable. An example is given to illustrate the type of problem that can be handled. The example involves negative stiffness of the members and consequently attention must be given to the equation solving procedure for the structure. A comparison is made with some observed test results.
An approximate laplace transform inversion using exponential series representation
Authors: Novotný Bohuslav 
Published: August 2005

AbstractA numerical Laplace transform inversion technique is described, which is a modification of the inversion method using an exponential series representation. By adding an auxiliary function and using Erdélyi's inversion formula, the proposed technique provides the inverse approximation with improved accuracy near t = 0. Numerical illustrations shows that this procedure also works in cases when the original method of schapery fails to give satisfactory results.
Eigensolution for large structural systems with substructures
Authors: Arora Jasbir S. , Nguyen D. T. 
Published: August 2005

AbstractA method for calculating natural frequencies and mode shapes of large structural systems with substructures and the subspace iteration is developed. The method uses only substructural stiffness matrices and the mass matrix for each finite element of the system. The mass matrix for the entire structure or any of its substructures need not be computed. However, efficiency of the method is improved when mass matrix for the entire structure is computed and saved in the computer core. No approximating assumptions are made. Thus, natural frequencies and mode shapes for the finite element model employed are the same with or without the substructuring algorithm. This is demonstrated by computing first ten natural frequencies and the corresponding mode shapes for an open truss helicopter tail‐boom structure.
Thermodynamic considerations in the numerical simulation of steady compressible flow
Authors: Thyagaraja A. 
Published: August 2005

AbstractThe notion of thermodynamic consistency of a finite difference scheme is introduced in connection with steady compressible flow simulation. This concept requires that the finite difference scheme must lead to solutions which are consistent with the Second Law of Thermodynamics, whatever the grid sizes employed. Thus, in addition to the usual consistency with the conservation equations of mass, momentum and energy, the solutions of the finite difference equations must satisfy thermodynamic restrictions. The scheme proposed by Singhal and Spalding for the computation of plane, isentropic flow is generalized in a thermodynamically consistent way to handle inviscid, adiabatic but non‐isentropic plane flow. Numerical solutions are obtained for a model problem using both the original and the extended methods. The results are compared with analytical predictions of shock‐expansion theory. The effectiveness and the thermodynamic consistency of the new formulation is demonstrated.
An algorithm for the solution of a third‐order eigenvalue problem
Authors: Schajer G. S. , Mote C. D. 
Published: August 2005

AbstractA simple, rapidly convergent procedure is described for solving a third‐order symmetric eigenvalue problem Au = λ Bu typically arising in vibration analysis. The eigenvalue problem is represented in terms of its variational dual, the Rayleigh quotient, and the eigenosolution is obtained through a topographical search for points of quotient stationarity. The associated computer routine is compact and can easily be incorporated within the calling program. Degenerate eigensolutions cause no difficulty. An example FORTRAN routine is given.
A method for the automatic generation of triangular elements on a surface
Authors: Cohen Howard D. 
Published: August 2005

AbstractAn algorithm is given to discretize a polygon or curved surface into triangular arrays. The method first involves the manual division of the array into quadrilaterals with specified numbers on rows and columns. The individual points are then filled in automatically and elements are automatically generated. A point of particular importance is that the number of columns or rows may be made to change. A subroutine is given to perform this task.
A mesh refinement method for transient heat conduction problems solved by finite elements
Authors: Pammer Z. 
Published: August 2005

AbstractThis paper deals with the finite element calculation of those transient temperature fields which develops in a body, due to a sudden change in temperature of fluid being in contact with the surface. A special co‐ordinate transformation is applied to approach the temporal change of the surface temperature. By analysing the interpolability of the temperature distribution it is proved that the sizes of elements near to the surface are critical in this respect. For the sizes of critical elements situated on the boundaries of the body, criteria formed from dimensionless numbers are determined, by the use of which a subdivision method is described. The application of the method is presented on a two‐dimensional heat conduction problem, and the results are compared with the analytical solution.
Finite element analysis of laminar flow in the entrance region of ducts
Authors: Comini G. , Giudice S. Del , Strada M. 
Published: August 2005

AbstractThis paper presents a generally applicable approach to developing laminar flow problems in straight ducts of arbitrary shape. A three‐level central alogrithm which does not require iterations is used to march ahead with the solution in the axial direction.The calculation procedure can be implemented by utilizing, with minor modifications, any standard finite element code for linear heat conduction.Several illustrative examples demonstrate accuracy and versatility of the proposed technique.
Some novel applications on the Frontal concept
Authors: Abbas Syed F. 
Published: August 2005

AbstractThis paper describes the hitherto unpublicized flexibilities inherent in the longevity‐based Frontal concept of Irons. Diverse applications such as Guyan‐reduced superelement generation, substructuring, matrix storage in Frontal form, Frontal matrix multiplication and Frontal Subspace Iteration method are discussed. It is observed that most of these extensions require only minor modifications to Irons'original program. The first part of the paper reviews the development in the Frontal method so far. Part II describes the experiences related to the largest multi‐algorithm Frontal package reported to date. Suggestions for a simplified Frontal algorithm are also given and would be useful to those who wish to write their own solver, or improve an existing one. An algorithm and a computer program for Frontal multiplication are also provided.
Pressure marching schemes that work
Authors: Richards C. W. , Crane C. M. 
Published: August 2005

AbstractNumerical solutions for two‐dimensional or axisymmetric viscous fluid flow problems are usually based on the stream function/vorticity formulation. Frequently, however, the pressure distribution is of prime interest. Difficulties have been reported in the literature with the use of obvious pressure marching schemes. Consequently, several investigators have preferred to use an iterative method which involves solving a Poisson equation with Neumann boundary conditions. In this paper, the fundamental cause of failure of the marching schemes is investigated. The authors introduce the concept of compatible pressure and vorticity schemes and show that lack of compatibility has been the principal reason for the poor results obtained using marching schemes. Compatible pressure marching methods are developed and shown to give good results. Comparisons are made between the Poisson equation method and the compatible marching method. To make the comparisons meaningful, special test cases with analytical solutions have been used.
An algorithm for defining a single near‐optimum mesh for multiple‐load‐case problems
Authors: Shephard Mark S. 
Published: August 2005

AbstractA method for defining a single near‐optimum finite element discretization for multiple‐load‐case problems is described. An example problem is included to demonstrate the application of the multiple‐load‐case algorithm. A comparison to a fine uniform mesh is also included to indicate the computational efficiencies possible with such a procedure. †Assistant Professor; formerly Research Assistant, Department of Structural Engineering, Cornell University, Ithaca, New York, U.S.A.