bluuebunny/crossref_metadata_2025_split huggingface dataset:
Global existence for one‐dimensional motion of non‐isentropic viscous fluids
Authors: Yanagi Shigenori 
Published: November 2005

AbstractWe study the p‐system with viscosity given by vt − ux = 0, ut + p(v)x = (k(v)ux)x + f(∫ vdx, t), with the initial and the boundary conditions (v(x, 0), u(x,0)) = (v0, u0(x)), u(0,t) = u(X,t) = 0. To describe the motion of the fluid more realistically, many equations of state, namely the function p(v) have been proposed. In this paper, we adopt Planck's equation, which is defined only for v > b(> 0) and not a monotonic function of v, and prove the global existence of the smooth solution. The essential point of the proof is to obtain the bound of v of the form b < h(T) ⩽ v(x, t) ⩽ H(T) < ∞ for some constants h(T) and H(T).
The oxidation process of silicon: Modelling and mathematical treatment
Authors: Merz W. , Strecker N. 
Published: November 2005

AbstractIn this paper we develop a mathematical model describing the oxidation process of silicon. At first we introduce a model with a sharp reaction front between the silicon and the oxide layer. From this we turn over to a phase field model where the reaction front is replaced by an extended reaction zone. The silicon dioxide and the silicon are regarded as components of a reacting mixture, and the oxygen is assumed to be dissolved in it. We formulate a local existence result of that second model in three space dimensions assuming some simplifications concerning the boundary conditions and solve the complete free boundary value problem numerically. For this, it has been implemented into the process simulator DIOS which allows two‐dimensional computations.
Use of characteristics for boundaries in time dependent finite difference analysis of multidimensional gas dynamics
Authors: Porter Robert W. , Coakley James F. 
Published: November 2005

AbstractRelations form the theory of characteristics are used to connect boundary and interior points in the numerical analysis of multidimensional, unsteady gas dynamics.Since specification of all variables on the boundaries does not occur, it is necessary to employ at least some of the differential equations for boundary points. The objective is to avoid the use of non‐central finite differences and the subsequent generation of a pseudo‐boundary layer.Boundaries consisting of a moving shock wave, a solid wall and a surface in a supersonic, downstream region are considered. The numerical procedure for determining variables on boundaries is described in datail for the hypersonic, blunt body problem.
A computational method for optimal structural design. I. Piecewise uniform structures
Authors: Haug E. J. , Pan K. C. , Streeter T. D. 
Published: November 2005

AbstractThis paper presents a technique for the optimal design of a large class of structures arising in civil and mechanical engineering. Constraint conditions on stress level, magnitudes of elastic deformation, natural frequency and buckling load are admitted. A computational method is developed, which takes advantage of special features of the structural optimization problem. Numerical examples are solved to illustrate the applicability of the method. These problems are, in themselves, of engineering interest.
An alphanumeric finite element mesh plotter
Authors: Felippa Carlos A. 
Published: November 2005

AbstractA FORTRAN subroutine name MESHPL is described. This routine generates an alphanumeric image of an arbitrary two‐dimensional finite element mesh on the line printer. This plotting technique can be used for fast on‐line display of nodal points, elements, boundary conditions and loads during the input data preprocessing stage of a finite element analysis.
On the finite deflection of thin viscoelastic beams
Authors: Holden J. T. 
Published: November 2005

AbstractA direct numerical method is presented for the solution of a class of non‐linear integro‐differential equations which arise in the finite deflection of thin viscoelastic beams. The method is not iterative and thus avoids the convergence problems often associated with iterative methods. The analysis and results are given for the deflection of a uniformly loaded cantilever.
A new relaxation method for obtaining the lowest eigenvalue and eigenvector of a matrix equation
Authors: Muda Yoshiaki 
Published: November 2005

AbstractThe matrix eigenvalue problem Hui = λi ui is considered. It is shown that when a new approximate vector v(n+1) to u1 (the eigenvector of the lowest eigenvalue) is computed from the present one v(n) by the relation v(n+1) = (1− αH + βH2) v(n) or v(n+1) = (1− αH + βH2 – γH3) v(n), the convergence rate is at least double that of the gradient method which corresponds to set β = γ = 0. Moreover, by choosing parameters α, β, or γ properly, one can get about three to five times faster convergence rate than that of the latter method, for H having very small γ2–γ1 and very large λN (the largest eigenvalue), further modifications are suggested. The relation with the Richardson method is also discussed.
Sector elements for matrix displacement analysis
Authors: Raju I. S. , Krishnamurty A. V. , Rao A. K. 
Published: November 2005

AbstractThree sector elements, two for plane stress problems (PSL and PSN) and one for plate bending problems (BSN), have been developed. Of the three elements, two are based on the natural mode technique. The elements have been applied to typical problems to test their performance.
A finite element weighted residual solution to one‐dimensional field problems
Authors: Bruch John C. , Zyvoloski George 
Published: November 2005

AbstractThe one‐dimensional diffusion‐convection equation is formulated with the finite element representation employing the Galerkin approach. A linear shape function and two‐dimensional triangular and rectangular elements in space and time were used in solving the problem. The results are compared with finite difference solutions as well as the exact solution. As another example, the convective term is set equal to zero and these techniques are applied to the resulting heat equation and similar comparisons are made.
An efficient method of fluid–structure coupling in the dynamic analysis of structures
Authors: Dungar R. 
Published: November 2005

AbstractA method of fluid‐structure connection is presented for solutions which mainly involve the calculation of the dynamic response of structures by using the method of modal analysis. This connection method is based upon finite element structural and fluid representation and is efficiently employed when used with the inverse iteration procedure for eigenvalue, eigenvector evaluation. The inverse iteration procedure is described in conjunction with the connection method. Also a method of non‐linear structural analysis and a method of frequency domain analysis are discussed with reference to the presented fluid‐structure connection procedure.Applications are considered for both model and prototype situations. Efficient use of the mini computer for solving dynamic problems by the proposed method is also considered.
Numerical integration of the motions of a tethered buoyant platform
Authors: Ashford R. A. , Wood W. L. 
Published: November 2005

AbstractThe motion of a terthered buoyant platform (TBP) in a regular train is investigated numerically using the Zienkiewicz four‐time‐level scheme.5 Wave forces are calculated using Morison's equation7 and linear wave theory. Results are presented for the theoretical response to the periodic forcing function for an optimized method,6 Wood, A.,6 Wilson θ =1.412 and Houbolt13 and compared with the actual computed behaviour of the TBP.
Analysis of nonlinear chemically reactive flow characteristic of high energy laser systems
Authors: Chung T. J. , Karr G. R. 
Published: November 2005

AbstractThis paper is concerned with the mechanics and computation of the performance of a high energy chemical laser of the HF type. The analysis requires solving the‐viscous, compressible supersonic flow equations which are coupled to the chemical and optical characteristics of the flowing gas media. A finite element method is chosen for performing the computation.The physical system simulated in the work consists of the supersonic mixing of the two flows; one flow consists of hydrogen gas where as the second flow is rich in fluorine gas. Perpendicular to the flow, an optical cavity provides for reflection and amplification of radiation characteristic of the output of the HF laser system.The HF system achieves a population inversion of the HF molecule as a result of the chemical reaction between H2 and F. This reaction also provides heat which couples with the fluid mechanics as an influence on the flow field.This paper will discuss the nonlinear nature of the problem, will present the finite element method used to solve the problem, and will compare results with others who have used finite difference methods for solution.
A curvilinear finite element for shells of revolution
Authors: Feijóo Raúl A. , Jospin Reinaldo J. , Bevilacqua Luiz , Taroco Edgardo 
Published: November 2005

AbstractIn this paper a curved finite element for the solution of shells of revolution is presented. The shell geometry in general, is approximated by a third order interpolation function. The displacement field has four components—three displacements and the rotation of the meridional plane of the of the shell. The displacement field is interpolated with cubic and quintic polynomials. The linear system involving the nodal unknowns is obtained from the principle of virtual work, together with the colateral condition relating the rotation to the other components of the displacement field. It is shown that broken generating lines for the shell surface do not limit the convergence of the solution. Finally, for numerical applications for static and dynamical problems presented.
A finite element analysis of generalized Newtonian fluids through spiral mandrel dies
Authors: Fahy E. J. , Gilmour P. W. 
Published: November 2005

AbstractA method is described which calculates the fluid flow pattern for any generalized Newtonian fluid forced through the narrow annular space between two concentric cylindrical surfaces. The inner surface is engraved with a number of identical equally spaced spiral channels of small constant pitch angle but of varying cross‐sectional area. For equal flow into the spiral passages, the pressure distribution along them is described by a quasi‐linear ordinary difference‐differential equation. A finite element approximation is employed to solve this equation for the pressure and resultant flow field. The method is illustrated by calculating and comparing flow patterns through two different spiral geometries.
Combination of finite element and integral transform techniques in a heat conduction quasi‐static problem
Authors: Colin F. , Floquet A. 
Published: November 2005

AbstractA hybrid method, which consists in using the finite element method for fixed bodies and analytical techniques for moving ones, was developed for the thermal analysis of tribological situations. Unlike the well‐known finite element method, the hybrid method gives accurate results even at high sliding speed. From a practical point of view, both computer time and storage requirements are greatly reduced. The method appears as a valuable technique to predict surface temperature in mechanical assemblies.
A temperature‐based finite element solution for phase‐change problems
Authors: Crivelli Luis A. , Idelsohn Sergio R. 
Published: November 2005

AbstractA finite element procedure for solving multidimensional phase change problems is described. The algorithm combines a temperature formulation with a finite element treatment of the differential equation and discontinuous integration within the two‐phase elements to avoid the necessity of regularization. A new criterion for the computation of the iteration matrix is proposed. It is based on a quasi‐Newton correction of the Jacobian matrix for conduction problems without change of phase. A set of test problems with exact solution is analysed and demonstrates that the procedure can accurately evaluate the front position and temperature history with a reasonable computational effort.
Use of incomplete decomposition of the coefficient matrix in solving linear equations
Authors: Chen Dao‐Qi , Tewarson R. P. 
Published: November 2005

AbstractMatrix incomplete decompositions are widely and successfully used in iterative methods for solving systems of linear equations. We have found that one can also solve systems of linear equations directly by using an incomplete LU decomposition of the coefficient matrix. In some special cases, the proposed method not only leads to great savings in storage space but also improves the computational efficiency; for example, when solving large systems of linear equations with banded shifted coefficient matrices. Some interesting tested subroutines are also given.
Differentiating matrices for arbitrarily spaced grid points
Authors: Lakin W. D. 
Published: November 2005

AbstractDifferentiating matrices allow the numerical differentiation of functions defined at points of a discrete grid. Previous derivations of these matrices have been restricted to grids with uniformly spaced points, and the resulting derivative approximations have lacked precision, especially at endpoints. The present work derives differentiating matrices on grids with arbitrarily spaced points. It is shown that high accuracy can be achieved through use of differentiating matrices on non‐uniform grids through the expedient of including ‘near‐ boundary’ points. Use of the differentiating matrix as an operator in the solution of problems involving ordinary differential equations is also considered.
A mesh re‐zoning technique for finite element simulations of metal forming processes
Authors: Cheng Jung‐Ho , Kikuchi Noboru 
Published: November 2005

AbstractBased on some fundamental properties of finite element approximations, a mesh re‐zoning scheme is proposed for finite element simulations of metal forming problems. It is demonstrated that this technique is indispensable in analysing many difficult forming processes, especially when there exist corners or very irregular shapes on the boundaries. The algorithm is tested by a backward extrusion process and direct extrusion through a square die.
Warping torsion in thin‐walled open section beams using the semiloof beam element
Authors: Mottershead John E. 
Published: November 2005

AbstractMany structural members including metallic, reinforced polymer and concrete members must be modelled, in the simplest approximation, as thin‐walled beams whose cross‐sections exhibit significant, out‐of‐plane warping owing to torsion. The elastic capabilities of the semiloof beam element are extended to include warping torsion of thin‐walled open section beams. The performance of the extended element is compared with that of the original formulation.
Evaluation of boundary integrals for plate bending
Authors: Abdel‐Akher Ahmed , Hartley Gilbert A. 
Published: November 2005

AbstractThe alternative to quadrature, as a procedure for dealing with the integrations required in the direct boundary element method (DBEM), is to carry out the integration analytically and code the results directly. The potential benefits are efficient computer programs; the avoidance of numerical instability; and generally, better accuracy. The technique is developed in this paper.Serious problems arise when Gauss quadrature is employed for the integration of functions which contain, or are close to singularities. A numerical integration approach may fail at the first stage of the analysis, that is, during the assembly of the discrete equations; or it may fail at the subsequent stage of computing domain points near the boundary. The severity of the problem is dependent both on the strength of the singularity, and on geometry. These points are illustrated with examples.
A simple stress error estimator for Hybrid‐Trefftz p‐version elements
Authors: Jirousek J. , Venkatesh A. 
Published: November 2005

AbstractAn a posteriori error estimator is presented which allows a good pointwise evaluation of the error in predicted stresses and can easily be implemented in existing FE codes. Although this estimator has especially been developed for and tested on p‐version Hybrid‐Trefftz (HT) elements, it is anticipated that it can also be applied to conventional conforming p‐version elements. The practical efficiency of the estimator is illustrated through the solution of various plate bending problems by using the HT p‐version Kirchhoff plate elements.2
Large deflection elastic–plastic analysis of plate structures by the finite strip method
Authors: Abayakoon S. B. S. , Olson M. D. , Anderson D. L. 
Published: November 2005

AbstractThe finite strip method is applied to the non‐linear analysis of plate structures. Large deflection effects are included via first order non‐linearities in the strain–displacement relations, and material non‐linearities are included via the von Mises yield criterion and associated flow rule. The virtual work equations are integrated numerically using Gauss quadrature, and the resulting non‐linear equations are solved by Newton–Raphson iteration. Numerical results are presented for many applications including uniformly loaded rectangular and I beams, and square plates with either simply supported or clamped ends (or edges). The results are compared with known results from analytical and/or finite element analyses. Finally, a uniformly loaded stiffened panel is analysed and the results are compared with finite element results. In all cases, the results indicate that a single bending mode in the strip direction is sufficient to yield engineering accuracy for design purposes.
Gauss quadrature rules for finite part integrals
Authors: Tsamasphyros George , Dimou George 
Published: November 2005

AbstractWe construct a set of polynomials φn(x,ζ) which are orthogonal with respect to w(x)/(x − ζ)2, where w x is a weight function. These polynomials can be used for the definition of a Gauss quadrature formula for the finite part integral magnified image The process is exactly the same as the one used for the extraction of the classical Gauss formula for the Riemann integrals. Three different methods are derived.The first and most accurate quadrature formula is successfully tested in some numerical examples. The proposed quadrature formulas have many applications in problems of mathematical physics, mechanics, etc.
Numerical analysis of three‐time‐level finite difference schemes for unsteady diffusion–convection problems
Authors: Rigal Alain 
Published: November 2005

AbstractFor the linear diffusion–convection model problem, this paper develops the numerical analysis of two classes of three‐time‐level second order finite difference schemes: weighed schemes similar to two‐step schemes for differential equations and LF schemes based on the classical conservative approximation of the wave equation. As in our paper devoted to two‐level schemes, Fourier Analysis is an essential tool which yields several key properties (stability, dissipation, numerical diffusion and dispersion). It also permits the analysis of parasitic solutions characteristic of three‐level schemes and their control in terms of the starting scheme.The analysis is completed by giving results on the accuracy, positivity and parabolicity of the numerical schemes.The main conclusions are the expected superiority of these schemes over two‐level schemes when the diffusion phenomenon is not negligible (cell Reynolds number less than 1) and the very limited possibilities of obtaining satisfactory numerical results (even with upstream differencing) when convection is strongly predominating.
An exact element method
Authors: Eisenberger Moshe 
Published: November 2005

AbstractThis paper presents a new element based method through a treatment of a one dimensional model problem. The case solved in this work is of a rod with variable cross‐sectional area, supported along its length by variable stiffness elastic foundation, and loaded with variable axial load. The variations of all the quantities are taken as general polynomials. Using this method the exact terms in the stiffness matrix are found using the solution for the differential equation (up to any desired accuracy). The exact solution is obtained using one element for each segment with continuously varying properties, and the displacements and stresses are exact all along the rod.
Non‐diffusive N + 2 degree Petrov‐Galerkin methods for two‐dimensional transient transport computations
Authors: Cantekin M. E. , Westerink J. J. 
Published: November 2005

AbstractA new non‐diffusive Petrov‐Galerkin type finite element method which uses test functions two polynomial degrees higher than the trial functions is developed for the transient convection dominated transport equation in two dimensions. The scheme uses bilinear quadrilateral finite elements for the spatial discretization and Crank‐Nicolson finite differencing for the time integration. The standard product extension of very successful one‐dimensional N + 2 degree upwinding functions to two dimensions is ineffective for general 2‐D flow problems, especially at higher Courant numbers where cross‐derivative truncation terms become important. Therefore effective N + 2 degree test functions are developed through an analysis by which the truncation error terms in the discrete nodal equation are eliminated up to fifth order. The new scheme is very effective for general 2‐D flows over a wide Courant number range and eliminates the troublesome cross‐derivative truncation terms. The scheme is simple and robust in that the upwinding coefficients are readily defined and only dependent on Courant number. Numerical examples illustrate the excellent behaviour of the new scheme.
Towards adaptive mesh refinement: Application of new rectangular hybrid finite elements in 2D elasticity problems
Authors: Perry B. , Bar‐Yoseph P. , Rosenhouse G. 
Published: November 2005

AbstractA modified global approach to choosing stress terms for hybrid finite elements in plane stress problems is based on the known requirement of minimum number of stress parameters. Let nβ be the number of independent β‐stress parameters, nq the number of nodal displacements and nR the number of rigid body degrees of freedom, then the satisfaction of the criterion nβ ≥ nq − nR of the assembled structure instead of the individual element enables the reduction of nβ. New rectangular hybrid transition elements applied in adaptive mesh refinement and a new eight node rectangular invariant element including only 12 β parameters, based on the modified criterion, are presented here.The new elements, which are used in order to analyse the stress singularity of two bonded elastic plates of different materials, yield reliable results compared with results based on classical hybrid elements, displacement elements and the analytic solution.
Monte Carlo simulation of indoor radiant environment
Authors: Omori Toshiaki , Taniguchi Hiroshi , Kudo Kazuhiko 
Published: November 2005

AbstractThis paper describes a numerical method of radiant environment analysis in a complicated enclosure containing human bodies and furniture. An arbitrary configuration expressed in a three‐dimensional co‐ordinate system can be treated by this method. A unique space index and another surface index are proposed to specify the geometry of solid body and surface in the enclosure. The Monte Carlo method is used to determine direct interchange areas, which are then transformed into total exchange areas using the zone method. Energy balance equations accounting for thermal radiation, convection, wall conduction and air ventilation are then formulated for each solid surface segment in the enclosure. A human body model with skin temperatures and clothing is also proposed to simulate its heat release and to predict local thermal sensation around the body. As a practical application, this method is applied to the analysis of the radiant environment in a floor‐heated meeting room with eight people seated around a table.