bluuebunny/crossref_metadata_2025_split huggingface dataset:
Numerical modelling of the heat transfer in and around a steel bar during hot rolling
Authors: Visser J. A. , Mathews E. H. 
Published: August 2005

AbstractBy modelling the heat transfer in and around a hot‐rolled steel bar, the temperature distribution in the bar can be predicted at any stage of the hot rolling process. Knowledge of these temperatures is useful when the process is to be optimized. This paper presents a finite difference simulation of the heat transfer and resulting temperature distribution. The numerical procedure accounts for thermal radiation from the bar, convective heat transfer to the atmosphere and cooling water, and conduction between the moving bar and the mill rolls and manipulators. Measured values for convective heat transfer coefficients are used at the boundaries. The following effects are also accounted for in the procedure: deformation of the bar during rolling, tilting the bar between passes through a mill, cropping the bar and contraction resulting from heat losses. Predicted and measured temperatures correlate favourably.
Natural convective heat transfer over inclined short plates
Authors: Chang Keun‐Shik , Han In‐Cheol 
Published: August 2005

AbstractA finite‐difference solution for natural convection over a short flat plate heated on both sides is obtained; the plate has an arbitrary inclination angle. The present numerical method is capable of treating the full flow domain efficiently through the use of a plate/plume‐fitted co‐ordinate system. Correlation between the Nusselt and Rayleigh numbers at intermediate Rayleigh number region, previously obtained only through laborious measurements, is now obtained computationally. Variations of the flow patterns, isotherms and local Nusselt number with the inclination angle and the Rayleigh number are presented Results from a Mach‐Zehnder interferometric study are also presented for comparison.
Parametrized multifield variational principles in elasticity: II. Hybrid functionals and the free formulation
Authors: Felippa Carlos A. 
Published: August 2005

AbstractA one‐parameter family of d‐generalized hybrid/mixed variational principles for linear elasticity is constructed following a domain subdivision. The family includes the d‐generalized Hellinger‐Reissner and potential energy principles as special cases. The parametrized principle is discretized by independently varied internal displacements, stresses and boundary displacements. The resulting finite element equations are studied following a physically motivated decomposition of the stress and internal displacement fields. The free formulation of Bergan and Nygård is shown to be a special case of this element type, and is obtained by assuming a constant internal stress field. The parameter appears as a scale factor of the higher‐order stiffness.
Investigations into the numerical solution of partially saturated, porous‐medium flow
Authors: Dykhuizen R. C. 
Published: August 2005

AbstractThis paper investigates a numerical formulation of the partially saturated, porous‐medium flow equation. It is shown that improper meshing of the region of study may result in nonphysical solutions. These include the nonexistence of any steady solution, unstable steady solutions and even multiple steady solutions. If the mesh size is reduced, each well‐posed problem has only a single steady solution. A limiting value for the numerical cell size, which prevents these nonphysical results, is given. The analysis presented here will be applicable to both the steady flow equation and the transient equation.
First comparisons between numerical modelling and experimental analysis of free convection in a rectangular cavity
Authors: Baggio P. , Bonacina C. , Strada M. 
Published: August 2005

AbstractNatural convection in rectangular cavities has been the subject of numerous studies carried out using numerical methods, and also of some experimental studies. In general, however, the majority of numerical studies lack comparisons with experimental data. In experimental studies, it is generally the total heat flow exchanged across the cavity that is measured; rarely are local measurements of velocities reported.In this study the authors have analysed free convection in a rectangular cavity with an aspect ratio of ∼ 5, in which a preset temperature difference is maintained between two vertical walls, and the other walls are insulated. Numerical analysis was carried out using a penalty finite element method, for different values of the Rayleigh number and different meshes. The numerically predicted velocities are compared with the first experimental data obtained for a rectangular cavity filled with silicone oil.
Direct solution procedure for solution of harmonic problems using complete, non‐singular, Trefftz functions
Authors: Cheung Y. K. , Jin W. G. , Zienkiewicz O. C. 
Published: August 2005

AbstractBoundary approximation solutions using a singular Green function basis have been widely applied to the solution of a variety of linear problems. To avoid the difficulties associated with integration over singularities it is convenient to use sets of non‐singular, complete Trefftz functions, and this procedure has been applied recently with success using an indirect formulation. In the paper we observe that direct formulation is here again possible and that for some problems it performs in a superior way.
A note on a method of solution for convective stability problems
Authors: Kolyshkin A. A. , Vaillancourt Rémi 
Published: August 2005

AbstractA collocation method, based on Chebȳshev polynomials, previously used to solve the spectral Orr‐Sommerfeld problem, is generalized to a system of coupled equations and is applied effectively to the convective stability problem of a viscous flow. Two cases are considered, namely a vertical layer bounded by two parallel planes and a vertical coaxial channel. The number n of interpolation polynomials used as basis functions in the algorithm can be kept practically constant as the Prandtl number varies over a wide interval; thus the algorithm can be used for problems with high Prandtl numbers.
On a finite element method for the calculation of steady cellular interfaces in the one‐sided model of solidification
Authors: Wheeler A. A. , Winters K. H. 
Published: August 2005

AbstractIn this paper we reconsider the work of Ungar and Brown.15 These authors reported calculations of the non‐linear families of steady‐state solutions of the one‐sided model of unidirectional solidification of a binary alloy. They combined a finite element method with a Landau transformation13 to deal with the free boundary, and predicted the non‐linear solutions using numerical continuation and bifurcation techniques. We show that the numerical scheme that they used to calculate these families is mesh‐dependent when the solid‐liquid interface becomes sufficiently deformed.
Finite‐difference solutions of partial differential equations
Authors: Bhattacharya M. C. 
Published: August 2005

AbstractThis paper reports a novel technique of forming improved finite‐difference solutions of partial differential equations. The technique leads to difference solutions which give better performance and accuracy compared with the difference equations in current use. Furthermore, by introducing a technique of subinterval time‐step elimination, the difference equations can be operated for any length of time step with a negligible increase in the computer store requirement. This novel technique enables formulation of finite‐difference equations for problems involving arbitrary geometry. One, two and three‐dimensional formulations involving unequal nodal spacings have been worked out. Estimation of the truncation error has been compared with other methods.
Computation of the eigenfrequencies of acoustic cavities: A new penalty method
Authors: Cifuentes A. , Coppolino R. 
Published: August 2005

AbstractA new penalty method for determining the natural frequencies and normal modes of acoustic cavities is presented. The acoustic medium is described in terms of the displacement field. A new easy‐toimplement penalty function method is employed to enforce the irrotationality condition. This new method has significant advantages when compared to classical penalty function methods since it is more stable with respect to the penalty parameter.
Time‐domain boundary element analysis for linear, viscoelastic problem subject to body force
Authors: Sim Woo Jin , Kwak Byung Man 
Published: August 2005

AbstractA new boundary element formulation in the time domain is presented for the displacement and stress analysis of quasistatic, linear, viscoelastic problems under the action of body forces. The well‐known concept of the particular integral is adopted for an efficient treatment of the volume integral and to improve the numerical accuracy. The stress kernels and particular integrals are derived using the elastic‐viscoelastic correspondence principle. Numerical results are compared with the derived exact solutions to demonstrate the method and its accuracy.
ODE approach to minimum‐weight design of pinned columns in buckling
Authors: Yuan Si 
Published: August 2005

AbstractThe non‐standard ordinary differential equations (ODEs), resulting from minimum‐weight design of pinned columns in buckling, with or without the minimum cross‐section constraints, are converted to an equivalent standard non‐linear ODE system by using trivial ODE and interval mapping techniques. The ODE system is then directly and efficiently solved by the robust ODE code COLSYS. The longitudinal shapes and switching interface points sought are given explicily as part of the solutions with the accuracy satisfying the user pre‐specified error tolerances. Compared with the analytical solutions, the numerical results obtained by this approach can be considered to be numerically exact.
A numerical technique for two‐dimensional transient wave propagation analyses
Authors: Mengi Yalcin , Tanrikulu A. Kamil 
Published: August 2005

AbstractA numerical technique is proposed for solving two‐dimensional transient wave propagation problems. The technique involves the use of the combination of a transform (such as Fourier, sine, cosine) for one space variable and the method of characteristics. Because of its inclusion of the latter method in the analysis, the proposed technique is capable of describing the sharp variations of the disturbances which may occur in the neighbourhood of wave fronts. In the study, an example problem is presented which involves transient waves in an elastic layer generated by out‐ofplane shear stresses acting on its top surface. The formulation of the example problem is kept general in the sense that the variations of the applied shear tractions in the horizontal direction of the layer and in time are kept arbitrary. In the analysis, the Fourier transform is used for the horizontal co‐ordinate. The numerical results are obtained and presented for the uniform strip loading case. The assessment of the proposed technique is made by obtaining the results for the case in which the width of the strip load is very large compared to the height of the layer, and by comparing them with exact ones. It is found that the proposed technique yields the results which compare very well with the exact ones and that it is capable of describing the sharp variations at the wave fronts.
An improved perturbation technique for eigenvalues of continuous systems
Authors: Bickford William B. 
Published: August 2005

AbstractA technique that improves the accuracy of the eigenvalue predictions as computed by a first‐order uniform expansion perturbation scheme for a class of eigenvalue problems associated with linear ordinary and partial differential equations is introduced. As suggested by a comparison with the classical Ritz method, the computational accuracy of a usual perturbation technique such as strained parameters can be effectively increased by simply replacing the usual M‐norms appearing in the denominator of the expressions for the first‐order changes in the eigenvalues by the corresponding MP‐norms, where MP is the perturbed M operator. With increasing sizes of the perturbations of the operators L and M of the class of boundary‐value problems considered, this improved perturbation technique produces results of substantially increased accuracy relative to the usual first‐order uniform expansion perturbation techniques. Numerical examples are presented.
Including bolt bending stiffness in finite‐element analysis of flanged connections
Authors: Tenchev Rosen T. 
Published: August 2005

AbstractThe stiffness matrix of a spring constraint is derived that can restrict only rotation in a mesh of finite elements having no rotation as a degree of freedom. It is connected to two nodes of the structure and does not increase the total number of degrees of freedom. To validate the stiffness matrix, a simple 2‐D numerical example is presented which is in excellent agreement with theoretical results.Integral grey cast iron flanges (BS4504: 1969) are analysed including and not including the bending stiffness of the bolts. The analysis shows that neglecting the bending stiffness of the bolts results in up to 35% error of overestimating the maximum stress in large‐diameter flanges.
A staggered finite‐element solution for water and gas flow in deforming porous media
Authors: Simoni L. , Schrefler B. A. 
Published: August 2005

AbstractA numerical model for the mechanics of partially saturated porous media is presented where the flow of both fluid phases is taken into account. The attention is focused on the choice of the field variables so that the model may easily be extended to deal with the important case when the gaseous phase is at constant reference pressure and with the limiting case of a fully saturated situation. To solve the semi‐discretized governing differential equation system in the time domain a staggered procedure is presented, which also allows for a straightforward solution of the two aforementioned cases. The stability and convergence analyses of the proposed solution scheme are presented for a 3 degree‐of‐freedom model system. In this way it is possible to assess the behaviour of the proposed solution scheme.
A low‐diffusive and oscillation‐free convection scheme
Authors: Zhu J. 
Published: August 2005

AbstractA higher‐resolution and bounded discretization scheme is proposed for calculations of incompressible steady flows with finite‐volume methods. The scheme combines a second‐order upstream‐weighted approximation with the first‐order upwind differencing under the control of a convection boundedness criterion. It is easy to implement for calculations of multi‐dimensional flows, and the resulting finite‐difference coefficient matrix is always diagonally dominant. Applications to three test problems, two linear and one non‐linear, and comparisons with two commonly used schemes, hybrid upwind/central differencing and QUICK, demonstrate the capability of the method in capturing steep gradients while maintaining the boundedness of solutions.
Hybrid adaptive poisson grid generation and grid smoothness
Authors: Roache Patrick J , Salari Kambiz , Steinberg Stanly 
Published: August 2005

AbstractA hybrid technique for adaptive grid generation using a variety of Poisson grid generators is described. The technique ensures that, when adaptivity functions are weak, the adapted grid reverts to an arbitrary specified base grid rather than to the grid produced by the homogeneous elliptic generator. The hybrid technique also serves to expose the weakness of the claim that elliptic grid generators produce smooth grids.
2‐D transient interior flux by time‐domain boundary‐element method
Authors: Israil A. S. M. , Banerjee P. K. 
Published: August 2005

AbstractIn this paper, interior flux calculations for two‐dimensional transient scalar wave propagation are developed and presented for the first time in the BEM literature. There are some severe analytical difficulties in the derivation of these kernels which have been circumvented through physical interpretation. Moreover, an apparent singularity at the wave‐front of these kernels has been reduced to an integrable one through some convenient condensation. These kernels have been implemented in the time‐domain BEM algorithm with linear temporal variation and quadratic spatial variation for the field variables. Some numerical examples are presented to demonstrate the accuracy of the implementation.
Strategies for large scale structural problems on high‐performance computers
Authors: Noor Ahmed K. , Peters Jeanne M. 
Published: August 2005

AbstractNovel computational strategies are presented for the analysis of large and complex structures. The strategies are based on generating the response of the complex structure using large perturbations from that of a simpler model, associated with a simpler structure (or a simpler mathematical/discrete model of the original structure). Numerical examples are presented to demonstrate the effectiveness of the strategies developed.
The extension boundary‐element method for 2‐D potential problems
Authors: Yihua Yan , Huli Shi 
Published: August 2005

AbstractIn the paper, a new BE formulation is introduced so that we can adopt nearby adjacent nodes to improve the trial functions on each boundary element. The extension element approximation is derived and implemented, and the accuracy of the solution is, therefore, raised without increasing the total number of nodes (or the dimension of the system). The proposed method preserves all the advantages of conventional BEM. Furthermore, it may improve the higher‐order variations. Numerical examples demonstrate the validity and prospect of the extension‐BEM (EBEM).
Unified numerical treatment of hyperelastic and rubber‐like constitutive laws
Authors: Gadala M. S. 
Published: August 2005

AbstractA unified numerical treatment for handling various forms of constitutive relations for hyperelastic and rubber‐like materials is presented. A general form for the stress and the constitutive tensors is derived. The form requires the calculation of certain tensors and matrices which are presented. Application examples are given for generalized Mooney–Rivlin, generalized Mooney–Rivlin with modified invariants, Swanson, Blatz‐Ko and Hart‐Smith constitutive models.
Defining residual stresses by applying the fem
Authors: Flašker Joze , Aberšek Boris 
Published: August 2005

AbstractThis paper deals with the influence of residual stresses on the total value of loading for calculation of the stresses of a gear. We develop a computer program RESMET which serves as a pre‐processor, calculates the residual stresses by the application of different FE programs or can be used in simple cases as an independent program. The results obtained by RESMET are in good agreement with those obtained by the experiments.
Grid control for non‐orthogonal elliptic grids
Authors: Vreugdenhil C. B. 
Published: August 2005

AbstractA relation is given between grid properties such as grid angle and aspect ratio and the metric coefficients of the transformation from the physical to the computational domain. A transformation is proposed in which these grid properties occur explicitly, such that the resulting grid will have the required grid angle and aspect ratio. This leads to an elliptic grid‐generation procedure with non‐linear coefficients. Some examples are given which illustrate that the properties can be predicted.
Padé and upwinding finite difference schemes for the quantum mechanical equation of motion
Authors: Kwok Yue‐Kuen , Barthez Daniel 
Published: August 2005

AbstractA systematic approach is presented to search for a two‐level six‐point finite difference of Padé type for the numerical solution of the quantum mechanical equation of motion. A family of second order accurate Pade schemes is obtained and the stability properties are analysed by the von Neumann and matrix methods. Also, a similar stability analysis is also performed for a family of two‐level first order accurate upwinding difference schemes by the von Neumann and matrix methods. Discrepancies between the stability results obtained by the von Neumann and matrix methods are observed.
Numerical methods applicable to laser refraction through a caustic
Authors: Pearson Carl E. , Christiansen Walter H. 
Published: August 2005

AbstractNumerical computation of laser beam refraction may involve difficulties associated with ray paths through a caustic, where first‐order amplitude values become infinite. We choose the special test case of a stratified gas, and compare the results obtained by numerical integration of the ray differential equations with both asymptotic results and direct numerical solution of the exact wave equation. A final section evaluates the numerical solution of a parabolic approximation to the Helmholtz equation, with particular reference to the effect of the caustic. The final conclusion is that, with appropriate safeguards, any of these methods can effectively deal with the presence of a caustic surface.
A subspace iteration for eigenvector derivatives
Authors: Ting T. 
Published: August 2005

AbstractAn iterative procedure for calculating eigenvector derivatives has been developed based on the subspace iteration concept. The basic formulation is derived directly from the first variation of the resulting equations of subspace iteration for solving eigenvalue problems. Since the basic formulation conserves the convergence properties of the original subspace iteration for eigen‐problems, an overrelaxation scheme similar to Bathe's approach is employed to accelerate the subspace iteration process for calculating eigenvector derivatives.
An auxiliary equation method for obtaining superconvergent finite‐element approximations
Authors: Johnson Richard W. , MacKinnon Robert J. 
Published: August 2005

AbstractA finite‐element method is developed which improves accuracy and yields superconvergent approximations to two‐dimensional elliptic boundary‐value problems on a union of square bilinear elements. This method employs an auxiliary equation which is derived using a Taylor series analysis on the discrete formula obtained from a Galerkin finite‐element formulation. Application of the finite‐element method to the auxiliary equation results in O(h4) convergence for problems with constant coefficients and improved accuracy for problems with variable coefficients. Supporting numerical examples are given.
Cubic spline technique for solution of Burgers' equation with a semi‐linear boundary condition
Authors: Jain P. C. , Shankar Rama , Singh T. V. 
Published: August 2005

AbstractBy using the splitting‐up technique and cubic spline method, numerical solutions of Burgers' equation ut = uxx + ϵuux, 0 < x < 1, t > 0 and u(x, 0) known, are obtained constructively by taking either of the two pairs of the semi‐linear boundary conditions: (i) u(0, t) = 0, ux(1, t) = aup(1, t), t > 0; (ii) u(1, t) = 0, ux(0, t), = ‐ aup(0, t), where 0 < p < ∞. The stability analysis of the proposed method is discussed.
Adaptive mesh refinement for faceted shells
Authors: Bonet J. , Pica A. , Peiró J. , Wood R. D. 
Published: August 2005

AbstractThe application of the Zienkiewicz and Zhu error estimator to three‐dimensional faceted shells presents some difficulties which arise from the lack of C1 continuity of the geometry. This paper presents a method to circumvent such difficulties based on the existence of a mapping from a flat reference configuration to the actual shell. This mapping is used not only to enable meshes to be generated in a two‐dimensional space, but also to define a stress measure – similar to the first Piola–Kirchhoff stress used in large deformation mechanics – which can be consistently smoothed over the reference configuration. A preliminary investigation of the method is provided by three simple examples.