bluuebunny/crossref_metadata_2025_split huggingface dataset:
An integral equation method for the solution of 3‐dimensional, non‐linear, magnetostatic problems
Authors: Loines Janet , Bernal Michael J. M. 
Published: August 2005

AbstractA finite element method for computing the resultant magnetic field arising from a given source field in the presence of a magnetic material of variable permeability is described; in this method finite element approximations to the scalar potential of the resulting field and the magnetic susceptibility, in the region occupied by the magnetic material, are determined from the non‐linear integral equation for the scalar potential and the constitutive susceptibility relation, using a collocation scheme.The method is used to compute the shielding effect of a thin rectangular plate of variable permeability on a given source field. The plate is subdivided uniformly into brick elements; the resulting translational invariance of the integrals required in the calculations is exploited to achieve major computational savings.A consequence of the thinness of the plate is that the calculation of the requisite integrals by analytic methods leads to considerable loss of accuracy by differencing; this difficulty is overcome by using a scheme which combines both analytic and quadrature techniques.The resulting system of non‐linear algebraic equations is solved by Powell's hybrid method; an efficient scheme for calculating an initial approximation to the Jacobian, which utilizes the structure of the equations, is presented.The results of the calculations are discussed.
Application of the finite element–difference method to vibration problems
Authors: Huang Xianrui , Cook Robert D. 
Published: August 2005

AbstractThe so‐called finite element–difference method introduced in References 1 and 2 yields a continuous stress field by finite difference operations and finite element interpolations. In the present paper, applications of the method to vibration problems are discussed. The inverse iteration procedure is modified for this method. Numerical results show that the accuracy of solutions depends strongly on the type of finite difference operator chosen: for reliable and accurate solutions in modal analysis problems, element internal strains must be included in the strain field used to compute nodal forces associated with element deformations.
Discrete Green functions for layered strata
Authors: Lin Hong‐Tsung , Tassoulas John L. 
Published: August 2005

AbstractA finite‐element discretization of a layered stratum is considered. The response to a time‐harmonic load at a single node is calculated. For all practical purposes, the result is obtained in closed form in the case of two dimensions (line load) while the Fast Fourier Transform is employed in the three‐dimensional problem (point load).
Notes on the stability of non‐rectangular space–time finite elements
Authors: Bajer Czesław I. 
Published: August 2005

AbstractThe method of space–time finite elements enables the simple solution of quite new problems. It is possible to assume the arbitrary partition of the structure area in each moment of integration of the motion equation. Instability is caused by a too large time step and too great changes of joint locations in successive time steps. A changeable spatial partition is useful in contact dynamic problems, in the case of a travelling support, generally in problems with movable edges. In this paper a stability problem is described and some investigations for chosen types of non‐rectangular space–time finite elements are carried out. Linear and surface elements which in time space gain an additional time dimension are presented. Some numerical examples prove the efficiency of the described method under determined limitations.
Finite elements in CFD: What lies ahead
Authors: Löhner R. 
Published: August 2005

AbstractThe current state of the art of Finite Element Methods in Computational Fluid Dynamics is reviewed. The aim of this review is to point out what appear currently as the main shortcomings of Finite Element Methods, so as to concentrate the efforts to remove them. The analysis of flows using Finite Elements will only be successful if all steps involved in it are optimized. Therefore, I deem it necessary to describe explicit and implicit flow solvers, unstructured multigrid methods, adaptive refinement schemes, grid generation and graphics in 3‐D, the effective use of supercomputer hardware and memory, as well as the combination of structured and unstructured grids.
A new finite element concurrent computer program architecture
Authors: Farhat Charbel , Wilson Edward 
Published: August 2005

AbstractA new computer program architecture for the solution of finite elemet systems using concurrent processing is presented. The basic approach involves the automatic splitting of an arbitrary spatial domain. Processors are dynamically re‐assigned during the several phases of an analysis. Direct and iterative solution strategies are considered. Computational algorithms for finite element dynamic analysis of large‐scale structural problems that exploit concurrent features of MIMD computers are implemented in modules around the basic architecture. Also, problems with localized non‐linearities are treated. A first implementation on a 32‐processor hypercube achieves efficiency rates of up to 90 per cent.
Calculation of fracture mechanics parameters for an arbitrary three‐dimensional crack, by the ‘equivalent domain integral’ method
Authors: Nikishkov G. P. , Atluri S. N. 
Published: August 2005

AbstractIn this paper, an equivalent domain integral (EDI) method and the attendant numerical algorithms are presented for the computation of a near‐crack‐tip field parameter, the vector Jϵ‐integral, and its variation along the front of an arbitrary three‐dimensional crack in a structural component. Account is taken of possible non‐elastic strains present in the structure; in this case the near‐tip Jϵ‐values may be significantly different from the far‐field values Jf, especially under non‐proportional loading.
Analyses of steady‐state visco‐elastic fluids using the penalty function method
Authors: Shiojima Takeo , Shimazaki Yoji 
Published: August 2005

AbstractThe application of the penalty‐function formulation of the finite element method is made possible for analysing visco‐elastic fluid flows by the method which decouples the momentum and continuity equations from the constitutive equation. An upwind finite element scheme is combined with the method in order to solve the constitutive equation. As visco‐elastic fluid models, Jaumann derivative, upper and lower convected derivatives are considered. The Poiseuille flow and the flow through a plane converging channel are analysed.
Three‐dimensional finite element analysis of open‐die forging
Authors: Shiau Y. C. , Kobayashi S. 
Published: August 2005

AbstractThree‐dimensional finite element analysis is applied to operation sequences in open‐die forging. Flat tools with rounded edges for open‐die forging are geometrically modelled using Bézier curves. With this technique, the problems at the die‐workpiece interface, such as the integration of frictional stress, node touching on dies and node separating from dies, can be handled effectively. It is shown that in solving general symmetric problems computation time can be saved by reducing variables and rearranging them in the stiffness matrix. One‐bite operations and operation sequences for producing two‐size bars and two‐size pipes in several bites are investigated in regard to geometry, load, energy and deformation distribution.
The structure of constitutive equations for finite deformation of elastic–plastic materials involving strain‐induced anisotropy with applications
Authors: Lee E. H. , Agah‐Tehrani A. 
Published: August 2005

AbstractConstitutive relations based on finite‐deformation‐valid analysis require the formulation of coupling effects that were not needed in earlier developments which included small deformation restrictions. However, the feasibility to introduce such coupling effects mathematically requires that the new terms introduced must be in accord with physically based concepts of the phenomena involved. An example came to light in which objectivity of a constitutive relation, considered to be generalized for finite deformation applications involving strain‐induced plastic anisotropy, had been achieved by use of the Jaumann derivative in place of the material derivative for the growth of a tensor variable which expressed the anisotropic characteristics. The spin terms thus added to the infinitesimal displacement analogue were not in accord with a physically based assessment of the underlying micro‐mechanical phenomena and in fact led to the prediction of anomalous stress response. This paper comprises comments on the subsequent development of the theory, including a tensor equation for the evolution of the anisotropy. By solving a sample test problem with different initial conditions both the numerical implementation of the constitutive relation and the response according to the proposed growth law of the anisotropy are described and discussed.
Finite element computation of bulging in continuously cast steel with a viscoplastic model
Authors: Dalin J. B. , Chenot J. L. 
Published: August 2005

AbstractThe bulging of continuously cast steel between the support rolls has been computed using a viscoplastic finite element model. Both two‐dimensional and three‐dimensional models are based on the minimization of the functional associated with the Norton–Hoff law and use the streamlines integration to calculate the bulging. By using industrial data, the influence of both numerical parameters and process parameters on the extent of the calculated bulging values has been investigated. The comparison of our results with experimental measurements confirms the relevance of the hypothesis of viscoplastic behaviour.
Transient analysis of forging operations by the pseudo‐concentration method
Authors: Thompson Erik , Smelser R. E. 
Published: August 2005

AbstractThe pseudo‐concentration method is used to follow the flow of metal during the transient analysis of an axisymmetric forging problem. The technique requires a minimum of user interaction and appears to be ideal for computer aided design of dies. An analysis of an engine disc blocker die is presented and compared with experimental results. The same problem is analysed using a Newtonian fluid which is shown to give good qualitative results which would be acceptable in the initial stages of die design.
Plastic and viscoplastic flow of void‐containing metals. Applications to axisymmetric sheet forming problems
Authors: Oñate E. , Kleiber M. , De Saracibar C. Agelet 
Published: August 2005

AbstractA formal analogy between the equations of pure plastic and viscoplastic flow theory for void‐containing metals and those of standard non‐linear elasticity is presented. The formulation is particularized for the analysis of axisymmetric sheet metal forming problems using simple two node linear finite elements. Details of the treatment of friction and strain hardening phenomena, time increment computation and elastic effects are also given. Examples of the effect of void porosity on the hemispherical stretching of a circular sheet are presented.
A finite element simulation of the sheet metal forming process
Authors: Nakamachi Eiji 
Published: August 2005

AbstractA finite element simulation code of the sheet metal forming process has been developed. This simulation code plays an important role in the computer aided engineering (CAE) system for an automobile parts forming process, which includes the pre‐ and post‐processes. The paper presents the development of an updated Lagrangian type finite element modelling, based on the elastic–plastic (J2 flow law) membrane shell theory. An attempt is made to calculate the strain distribution incurred by peripherally clamped or non‐clamped square plates when impressed by rigid punches. These are the cases of square box‐shape punch drawing and arbitrary shaped panel stretch forming.
Computation of low‐speed compressible flows with time‐marching procedures
Authors: Merkle Charles L. , Choi Yun‐Ho 
Published: August 2005

AbstractThe extension of time‐marching procedures to low Mach number and low Reynolds number conditions is considered. It is shown that the disparate speeds of the acoustic and particle waves prevent convergence at high Reynolds numbers, while the requirement that both the Courant and the von Neumann numbers be of order one prevents convergence in very viscous flows. A perturbation expansion is used to introduce pseudo‐acoustic waves that propagate at speeds similar to the particle speed at high Reynolds numbers and that allows both the inviscid and viscous time step parameters to be of order one at low Reynolds numbers. The resulting algorithm is shown to give convergence rates that are independent of either Mach number or Reynolds number over a range of five orders of magnitude in both parameters. Results are shown for strong heat addition in low‐speed flow encompassing this broad range of variables.
Finite element analysis of turbulent forced convection in lid‐driven rectangular cavities
Authors: Nonino C. , Del Giudice S. 
Published: August 2005

AbstractTurbulent fluid flow and heat transfer in lid‐driven rectangular cavities are analysed by a finite element procedure for the prediction of the turbulent forced convection in two‐dimensional recirculating flows. The (k–ε) model is used to compute effective viscosities and thermal conductivities. The fluid flow and turbulence model parabolic equations are solved sequentially, one after the other. Then, the calculated velocity distribution is used in the solution of the steady state energy equation to yield the temperature field. Aspect ratios e=0·75, 1·0 and 1·5 and Reynolds numbers ranging from 5 × 104 to 4 × 105 are considered in the numerical examples.
Buoyant flow calculations with non‐orthogonal curvilinear co‐ordinates for vertical and horizontal parallelepiped enclosures
Authors: Yang H. Q. , Yang K. T. , Lloyd J. R. 
Published: August 2005

AbstractA control‐volume‐based finite‐difference formulation is developed for heat transfer and fluid flow in arbitrary three‐dimensional parallelepiped enclosures. The governing equations in Cartesian co‐ordinates are first transformed to those in non‐orthogonal curvilinear co‐ordinates by tensor transformations. After introducing the properties of the parallelepiped geometry, equations are obtained in the primitive variables for which all vectors and tensors are based on the curvilinear co‐ordinates. With proper treatment of the heat flux and stress tensor terms, the finite‐difference equations, analogous to those in the Cartesian coordinates, are formed. Examples are utilized to show the validity of the methodology and the results are found to compare well with existing experimental data. The differences in heat transfer and fluid flow inside parallelepiped enclosures and rectangular enclosures are delineated and discussed from a physical point of view.
Coarse‐fine mesh method for heat and mass transfer in locally complex flows
Authors: Kotake Susumu , Kodama Takeshi 
Published: August 2005

AbstractCombined forced and free convective flows having locally complicated geometries or boundary conditions were numerically studied with a finite difference method of coarse and fine meshes. The coarse‐and‐fine mesh method developed can be used for numerical calculations of both unsteady and steady processes of heat and mass transfer in convective and diffusion flows which are strongly influenced by locally fine flows. The method was applied to a numerical calculation of the steady flow field of a CVD (chemical vapour deposition) reactor which has locally complicated flows caused by small inlet nozzles. The results of the calculation showed a considerable contribution of locally fine flows to the overall flow field, which is well predicted with the present method.
Ignition phase transition of a polymer: Convective exposure
Authors: Durbetaki P. , Phuoc T. X. 
Published: August 2005

AbstractThe ignition of a semi‐infinite solid polymer under convective exposure is investigated. A quasi‐steady approximation is used for the gas phase and the transient effect is accounted for in the solid phase only. Both surface and gas phase chemical reactions are included simultaneously. The ignition mechanism is studied in terms of the concurrent heat transfer, mass transfer, mass transfer and chemical processes at the surface as well as in the gas phase. The gas phase governing equations are integrated independently from the solid phase energy equation using the Adams‐Moulton subroutine. Corrections to the iterative procedure are carried out by establishing a set of perturbation equations and using the Newton‐Raphson and least‐squares methods. The results indicate that ignition occurs in the heterogeneous mode within a narrow range of low flow velocities and high temperatures. An ignition phase transition point exists, and within a wide range of high flow velocities, ignition switches to the homogeneous mode.
Non‐linear simulation of dendritic solidification of an undercooled melt
Authors: Sullivan John M. , Lynch Daniel R. 
Published: August 2005

AbstractTwo‐dimensional finite element simulations of solidification for quiescent undercooled pure metals are presented. The full non‐linear, transient heat equation is used with phase front tracking which is subject to local curvature and interfacial kinetics. During early stages of the waveform instability the simulated solutions match the linear stability analysis with fidelity. Beyond the valid range of that analysis the numerical solution continues to demonstrate the physically observed exponential growth behaviour and characteristic spacing between fingers. Whereas the simulations show the sensitivity of dendritic growth to initial conditions, as expected for an unstable process, the overall pattern formation preserves the characteristic spacing. The simulations are terminated after the onset of bifurcation. Thereafter, the numerical model is inappropriate for physical comparison owing to the planar, two‐dimensional limitation.
Transfinite element methodology for non‐liner/linear transient thermal modelling/analysis: Progress and recent advances
Authors: Tamma Kumar K. , Railkar Sudhir B. 
Published: August 2005

AbstractRecent progress and advances in the development and applicability of a novel ‘transfinite element’ computational methodology is presented for general non‐linear/linear transient thermal problems. The proposed methodology and concepts are new and unique, and demonstrate the applicability to general transient non‐linear/linear thermal analysis situations by combining classical Galerkin schemes and transform approaches with contemporary finite element methods to preserve the modelling versatility and numerical features–thereby, a hybrid computational methodology is proposed. Characteristic features and pertinent details of the approach are described for non‐linear/linear transient thermal problems, wherein non‐linearities due temperature dependence of thermophysical properties and/or general non‐linear bound ary conditions to include radiation, effects due to phase change, etc., are considered. In addition, the use of high‐continuity formulations in conjuction with the proposed methodology to furnish accurate temperature distributions and temperature gradients making use of a relatively smaller number of degrees of freedom is also demonstrated. Numerical test cases are presented for a variety of problems to demonstrate the fundamental features and applicability of the proposed formulations. The proposed hybrid transfinite element methodology and concepts offer significant potential for extension to several areas of mathematical physics and engineering and to interdisciplinary research areas.
Monte Carlo method for radiative heat transfer analysis of general gas‐particle enclosures
Authors: Taniguchi Hiroshi , Yang Wen‐Jei , Kudo Kazuhiko , Hayasaka Hiroshi , Fukuchi Takeru , Nakamachi Ichiro 
Published: August 2005

AbstractA new Monte Carlo method is developed to analyse multi‐dimensional radiative heat transfer in an enclosure containing grey gas with anisotropically scattering grey particles. One set of variables, called READ (Radiative Energy Absorption Distribution), is introduced to represent radiative transfer, thus appreciably reducing repeated computations required by the conventional Monte Carlo technique. A 1 m × 1 m square duct is used as the enclosure with the upper and lower walls at different temperatures in the one‐dimensional case and with adiabatic specular or diffuse side walls in the two‐dimensional case. Results agree well with the existing analytical solutions for one‐dimensional, non‐scattering cases. It is concluded that, with anisotropic scattering, an increase in the absorption coefficient and/or single scattering albedo produces adverse effects on radiative heat transfer. Anisotropic scattering effects cannot be simulated by the use of the effective absorption coefficient.
Some novel techniques for the finite element analysis of heat and mass transfer problems
Authors: Lewis R. W. , Sze W. K. , Huang H. C. 
Published: August 2005

AbstractThe coupled heat and mass transfer partial differential equations as derived by Luikov are used to analyse freezing problems in porous media. A numerical model is subsequently developed to depict the frost heave mechanism in a freezing soil system. An example is given of the application of the model and the results are compared with those achieved from field experiments.Also, a novel application of the coincident node technique is presented for the coupled heat and mass transfer problem. This circumvents the numerical problems usually associated with flow through thin layers, in this case a vapour barrier, sandwiched between materials of greater thickness.
Theoretical basis of the finite element iterative method for the eigenvalue problem in stationary cracks
Authors: Barsoum Roshdy S. 
Published: August 2005

AbstractIn a recently published paper a finite element based iterative method was introduced for the solution of the eigenvalue problem of stationary cracks.1 In this paper we give the theoretical basis of this iterative method and we show why it converges and how it could be extended to more complex fracture problems. The cases of cracks at interfaces are illustrated.
Numerical analysis of a generalized plane ‘elastica’ with non‐linear material behaviour
Authors: Coulter Brett A. , Miller Robert E. 
Published: August 2005

AbstractThis article presents a numerical procedure for the analysis of a planar, continuous, flexible member. Large displacements and rotations, non‐linear material behaviour and general cross sections are admitted. A shooting method is utilized along with Newton‐type iteration for improved estimates. The resulting computer program is used to compare with numerical and analytical solutions of problems solved by others, and to present the solution to a problem which brings out very clearly the effects of both geometric and material non‐linearities.
Multi‐grid solutions to the elastic plastic torsion problem in multiply connected domains
Authors: Hoppe Ronald H. W. 
Published: August 2005

AbstractThe elastic plastic torsion problem for an elastic, perfectly plastic cylinder with multiply connected cross section twisted around its longitudinal axis is formulated as an obstacle problem for an associated stress potential, the obstacle being defined in terms of a generalized distance function. Based upon the reformulation of the obstacle problem as an equivalent linear complementarity problem, the latter is discretized by means of finite difference techniques, and a monotonically convergent iterative scheme for its numerical solution is developed. At each step of the iteration the solution of a reduced system of discrete Poisson equations is required which is done by applying multi‐grid techniques with respect to a hierarchy of grid‐point sets. Combined with a suitably chosen nested iteration process this results in a computationally very efficient algorithm for the approximate solution of the elastic plastic torsion problem.