bluuebunny/crossref_metadata_2025 huggingface dataset:
Transient analysis by Laplace transform and combined finite and boundary element methods for convective diffusion problem
Authors: Okamoto Naotaka , Sawami Hideo
Published: November 2005

A numerical method for solving the problem of transient convective diffusion with a first‐order chemical reaction is presented in this paper. The method is applicable over an infinite region. For steady problems the combined method of finite and boundary elements is recognized as a successful numerical technique for dealing with an infinite region. The present method is also useful in transient problems. In order to formulate the combined method for transient problems, we have developed a new method. In this paper the Laplace transform method incorporating the combined finite and boundary element methods will be considered. This transformation, holding complex values, transforms the transient problem into a steady state form. We also consider the present numerical solution which is obtained by using the numerical inverse Laplace transform as presented by Hosono. In numerical experiments the present method gives us an extremely accurate solution.
Visualization of flows by FEM using six‐node triangular element: Free surfaces and flow patterns of an extrusion process
Authors: Shimazaki Yoji
Published: November 2005

A simple extrusion process for Newtonian and power‐law fluids is analysed. Marker particles are introduced to analyse the fluid flow motions. Area co‐ordinates of six‐node triangular element are used to determine the marker position in the element. With this element, the solution algorithm becomes simple compared with the one using the linear triangular element. The differences in flow and swell patterns between the two fluids are described.
Massively parallel finite element analysis of coupled, incompressible flows: A benchmark computation of baroclinic annulus waves
Authors: Xiao Qiang , Salinger Andrew G. , Zhou Yuming , Derby Jeffrey J.
Published: November 2005

Coupled, three‐dimensional, time‐dependent, incompressible flows in a differentially heated, rotating annulus are simulated using a parallel implementation of the Galerkin finite element method on the Connection Machine 5 (CM‐5) supercomputer. The development of baroclinic annulus waves is computed and found to be consistent with previous experimental reseults. The implementation of a repeated spectral bisection element‐partitioning technique significantly increases the computation speed over a strategy which randomly maps elements to processors, yielding sustained calculation rates of 8.1 GFLOPS on 512 processors of the CM‐5.
Spurious numerical refraction
Authors: Cathers B. , Bates S.
Published: November 2005

The purpose of this paper is to investigate the effect of a non‐uniform mesh in two dimensions (2D). A change in mesh size will, in general, result in spurious refraction (and reflection) which is entirely numerical (rather than physical) in origin. To facilitate the analysis, the mesh geometry has been highly simplified in that only a single change in mesh size is considered. The analysis is based on a finite element wave model.

The domain consists of two conterminous regions discernible only by their different nodal spacings in the x‐direction. The interface between the two regions is internal to the mesh and is a straight line. The model is based upon the Crank‐Nicolson linear finite element scheme applied to the second order wave equation. The results of the analysis are confirmed by numerical experiments. It is shown that under particular numerical conditions total internal reflection may occur and when this is the case, the transmitted wave is evanescent. An analysis of the energy flux associated with the incident, reflected and trasmitted waves shows that energy is conserved across the interface between the two regions.
A segregated implicit solution algorithm for 2D and 3D laminar incompressible flows
Authors: Giannakoglou K. C. , Politis E. S.
Published: November 2005

A segregated algorithm for the solution of laminar incompressible, two‐ and three‐dimensional flow problems is presented. This algorithm employs the successive solution of the momentum and continuity equations by means of a decoupled implicit solution method. The inversion of the coefficient matrix which is common for all momentum equations is carried out through an approximate factorization in upper and lower triangular matrices. The divergence‐free velocity constraint is satisfied by formulating and solving a pressure correction equation. For the latter a combined application of a preconditioning technique and a Krylov subspace method is employed and proved more effecient than the approximate factorization method. The method exhibits a monotonic convergence, it is not costly in CPU time per iteration and provides accurate solutions which are independent of the underrelaxation parameter used in the momentum equations. Results are presented in two‐ and three‐dimensional flow problems.
Numerical simulation of transient planar flow of a viscoelastic material with two moving free surfaces
Authors: Mao Wenqun , Khayat Roger E.
Published: November 2005

In this study, we examine the numerical simulation of transient viscoelastic flows with two moving free surfaces. A modified Galerkin finite element method is implemented to the two‐dimensional non‐steady motion of the fluid of the Oldroyd‐B type. The fluid is initially placed between two parallel plates and bounded by two straight free boundaries. In this Lagrangian finite element method, the spatial mesh deforms in time along with the moving free boundaries. The unknown shape of the free surfaces is determined with the flow field u, v, τ, p by the deformable finite element method, combined with a predictor‐corrector scheme in an uncoupled fashion. The moving free surfaces and fluid motion of both Newtonian and non‐Newtonian flows are investigated. The results include the influence of surface tension, fluid inertia and elasticity.
Extension of the volume‐of‐fluid method for analysis of free surface viscous flow in an ideal gas
Authors: McKibben John F. , Aidun Cyrus K.
Published: November 2005

The volume‐of‐fluid (VOF) method is a simple and robust technique for simulating free surface flows with large deformations and intersecting free surfaces. Earlier implementations used Laplace's formula for the normal stress boundary condition at the interface between the liquid and vapour phases. We have expanded the interfacial boundary conditions to include the viscous component of the normal stress in the liquid phase and, in a limited manner, to allow the pressure in the vapour phase to vary. Included are sample computations that show the accuracy of added third‐order‐accurate differencing schemes for the convective terms in the Navier‐Stokes equation (NSE), the viscous terms in the normal stress at the interface and the solution of potential flow in the vapour phase coupled with the solution of the NSE in the liquid phase. With these modifications we show that the VOF method can accurately predict the instability of a thin viscous sheet flowing through a stagnant vapour phase.
Labeled Schwann cell transplantation: Cell loss, host Schwann cell replacement, and strategies to enhance survival
Authors: Hill Caitlin E. , Moon Lawrence D.F. , Wood Patrick M. , Bunge Mary Bartlett
Published: November 2005

Although transplanted Schwann cells (SCs) can promote axon regeneration and remyelination and improve recovery in models of spinal cord injury, little is known about their survival and how they interact with host tissue. Using labeled SCs from transgenic rats expressing human placental alkaline phosphatase (PLAP), SC survival in a spinal cord contusion lesion was assessed. Few PLAP SCs survived at 2 weeks after acute transplantation. They died early due to necrosis and apoptosis. Delaying transplantation until 7 days after injury improved survival. A second wave of cell death occurred after surviving cells had integrated into the spinal cord. Survival of PLAP SCs was enhanced by immunosuppression with cyclosporin; delayed transplantation in conjunction with immunosuppression resulted in the best survival. In all cases, transplantation of SCs resulted in extensive infiltration of endogenous p75+ cells into the injury site, suggesting that endogenous SCs may play an important role in the repair observed after SC transplantation. © 2005 Wiley‐Liss, Inc.
Nuclear phosphoinositide kinases and inositol phospholipids
Authors: Gonzales Michael L. , Anderson Richard A.
Published: November 2005

The presence of inositol phospholipids in the nuclei of mammalian cells has by now been well established, as has the presence of the enzymes responsible for their metabolism. However, our understanding of the role of these nuclear phosphoinositides in regulating cellular events has lagged far behind that for its cytosolic counterpart. It is clear, though, that the nuclear phosphoinositide pool is independent of the cytosolic pool and is, therefore, likely to be regulating a unique set of cellular events. As with its cytosolic phosphoinositides, many nuclear phosphoinositides and their metabolic enzymes are located at distinct sub‐cellular structures. This arrangement spatially limits the production and activity of inositol phospholipids and is believed to be a major mechanism for regulating their function. Here, we will introduce the components of nuclear inositol phospholipid signal transduction and discuss how their spatial arrangement may dictate which nuclear functions they are modulating. © 2005 Wiley‐Liss, Inc.
What determines African bilateral aid receipts?
Authors: McGillivray Mark
Published: November 2005

This paper empirically models aid allocation to four African countries—Egypt, Kenya, Morocco and Tanzania—using 1968–1999 time series data. The econometric method employed allows for the joint determination of aid to these countries and for recipient‐specific coefficients. It is hypothesised that aid to these countries has been determined by a diverse set of determinants, ranging from their developmental needs or requirements through to donor commercial, political and strategic interests. A special interest of the paper is whether policy regimes have impacted on the amounts of aid received by these countries. Results indicate that they have for all four countries, although the direction of influence differs among them. Copyright © 2005 John Wiley & Sons, Ltd.
Application of cross‐linked β‐cyclodextrin polymer for adsorption of aromatic amino acids
Authors: Tang Shouwan , Kong Liang , Ou Junjie , Liu Yueqi , Li Xin , Zou Hanfa
Published: November 2005

β‐Cyclodextrin (β‐CyD) was cross‐linked by hexamethylene diisocyanate and the polymer was investigated for adsorption of aromatic amino acids (AAA) from phosphate buffer. High adsorption rates were observed at the beginning and the adsorption equilibrium was then gradually achieved in about 45 min. The adsorption of AAA decreased with the increase of initial concentration and also temperature. Under the same conditions, the adsorption efficiencies of AAA were in the order of L‐tryptophan (L‐Trp) > L‐phenylalanine (L‐Phe) > L‐tyrosine (L‐Tyr). Much higher adsorption values, up to 52.4 and 43.0 mg/g for L‐Trp and L‐Phe, respectively, at 50 mmol/L and 3.2 mg/g for L‐Tyr at 2 mmol/L, were obtained with the β‐CyD polymer at 37 °C. It was shown that the adsorption of AAA on the β‐CyD polymer was consistent with the Freundlich isotherm equation. The adsorption of mixed aromatic amino acids and branched‐chain amino acids (BCAA) showed that AAA were preferentially adsorbed with adsorption efficiencies 10–24%, while those of BCAA were lower than 2%. It seems that the structure and hydrophobicity of amino acid molecules are responsible for the difference in adsorption, by influencing the strength of interactions between amino acid molecule and the polymer. Copyright © 2005 John Wiley & Sons, Ltd.
Interactions of cationic porphyrins with double‐stranded oligodeoxynucleotides: a study by electrospray ionisation mass spectrometry
Authors: Ramos Catarina I. V. , Barros Cristina M. , Fernandes Ana M. , Santana‐Marques M. G. , Correia A. J. Ferrer , Tomé João P. C. , Carrilho Maria do Carmo T. , Faustino Maria Amparo F. , Tomé Augusto C. , Neves M. G. P. M. S. , Cavaleiro J. A. S.
Published: November 2005

Electrospray ionisation mass spectrometry (ESI‐MS), electrospray ionisation tandem mass spectrometry (ESI‐MS/MS) and Ultraviolet‐visible (UV–vis) spectroscopy were used to investigate the non‐covalent interactions between small oligonucleotide duplexes with the GC motif and a group of cationic meso(N‐methylpyridynium‐4‐yl)porphyrins (four free bases with one to four positive charges, and the zinc complex of the tetracationic free base).

The results obtained point to outside binding of the porphyrins, with the binding strength increasing with the number of positive charges. Fragmentations involving losses from both chains were observed for the porphyrins with N‐methylpyridinium‐4‐yl groups in opposite meso positions. Copyright © 2005 John Wiley & Sons, Ltd.
Synergistic interaction between 17‐AAG and phosphatidylinositol 3‐kinase inhibition in human malignant glioma cells
Authors: Premkumar Daniel R. , Arnold Beth , Jane Esther P. , Pollack Ian F.
Published: November 2005

The phosphatidylinositol 3′‐kinase (PI3K)/Akt pathway is often constitutively activated in malignant glioma cells, in many cases as a result of mutation of phosphatase and tensin homologue deleted on chromosome ten (PTEN), an endogenous inhibitor of Akt, which renders tumor cells resistant to cytotoxic insults, including those related to anticancer drugs. Pharmacological inhibition of this pathway may potentially restore or augment the effectiveness of conventional chemotherapy or other signaling‐targeted agents. Because the heat shock protein (HSP) is involved in the conformational maturation of a number of signaling proteins critical to the proliferation of malignant glioma cells, we hypothesized that the combination of the PI3K inhibitor LY294002 and the HSP90 inhibitor 17‐allyl‐aminogeldanamycin (17‐AAG) would promote glioma cytotoxicity by decreasing both the activation status and levels of Akt, as well as downregulating the levels of other relevant signaling effectors. We, therefore, examined the effects of LY294002 and 17‐AAG, alone and in combination, on signal transduction and apoptosis in a series of malignant glioma cell lines. Simultaneous exposure to these inhibitors significantly induced cell death, and irreversibly inhibited proliferative activity and colony forming ability of the glioma cell lines. Quantitative analysis revealed that enhancement by LY294002 of 17‐AAG‐induced cytotoxicity was synergistic, leading to a pronounced increase in active caspase‐3 and poly (adenosine diphophate‐ribose) polymerase (PARP) cleavage together with the release of cytochrome c and apoptosis inducing factor (AIF). No significant growth inhibition or caspase activation was seen in control cells. The enhanced cytotoxicity of this combination was associated with diminished Akt activation and a significant downregulation of epidermal growth factor receptor (EGFR), Raf‐1, and mitogen activated protein kinase. Combination of 17‐AAG and LY294002 did not modify phospho‐JNK/SPK and phospho‐p38. Cells exposed to 17‐AAG and LY294002 displayed a significant reduction in cell‐cycle regulatory proteins, such as retinoblastoma (Rb), cyclin dependent kinase (CDK)4, CDK6, cyclin D1, and cyclin D3. Taken together, these findings suggest that the PI3K/Akt pathway plays a critical role in regulating the apoptotic response to 17‐AAG and that targeting this pathway could provide a potent strategy to treat patients with malignant gliomas. © 2005 Wiley‐Liss, Inc.
A study of a non‐linear kinetic model for an ionized gas
Authors: Arlotti Luisa , Bassi Laura , Gamba Patrizia
Published: November 2005

A non‐linear one‐dimensional kinetic model for an ionized gas is considered. In this model the collisions between charged and neutral particies and the field generated by the charges are taken into account. The Cauchy problem for the resulting system of equations is examined. An existence and uniqueness theorem of a global in time solution is proved.
Long‐time behaviour of absorbing boundary conditions
Authors: Engquist B. , Halpern L.
Published: November 2005

A new class of computational far‐field boundary conditions for hyperbolic partial differential equations was recently introduced by the authors. These boundary conditions combine properties of absorbing conditions for transient solutions and properties of far‐field conditions for steady states. This paper analyses the properties of the wave equation coupled with these new boundary conditions: well‐posedness, dissipativity and convergence in time.
Inversion of the exponential X‐ray transform. II: Numerics
Authors: Hazou Irene A. , Solmon Donald C.
Published: November 2005

The exponential X‐ray transform arises in single photon emission computed tomography and is defined on functions on the plane by 𝒫μf(φ,x) = ∫f (x + tφ)eμt where μ is a constant. In [MMAS(10), 561–574, 1988], we derived analytical formulae for filters K corresponding to a general point spread function E that can be used to invert the exponential X‐ray transform via a filtered backprojection algorithm. Here, we use those formulae to derive expressions suitable for numerical computation of the filters corresponding to a specific family of bandlimited point spread functions and give the results of reconstructions of a mathematical phantom using these filters. Also included is an analogue of the Shepp–Logan ellipse theorem, [IEEE Trans. Nucl. Sci. (21), 21–43, 1974], for the exponential X‐ray transform.
Global existence for one‐dimensional motion of non‐isentropic viscous fluids
Authors: Yanagi Shigenori
Published: November 2005

We 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

In 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

Relations 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

This 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

A 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

A 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 mixed finite element model for use in potential flow problems
Authors: Meissner Udo
Published: November 2005

A generalized variational principle is presented, which leads to a modified finite element approach for three‐dimensional field problems. Both, potential function and velocity field, are approximated by expansions which are continuous across the inter‐element boundaries. The rapid convergence of this mixed model is shown by two examples.
A new relaxation method for obtaining the lowest eigenvalue and eigenvector of a matrix equation
Authors: Muda Yoshiaki
Published: November 2005

The 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

Three 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

The 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

A 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

The 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

This 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

In 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

A 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

A 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

A 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

Matrix 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

Differentiating 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

Based 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

Many 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

The 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

An 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

The 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

We 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

For 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

This 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

A 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

A 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

This 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.
Mathematical modelling of LPG tanks subjected to full and partial fire engulfment
Authors: Hadjisophocleous G. V. , Sousa A. C. M. , Venart J. E. S.
Published: November 2005

This paper describes the use of field and zone modelling techniques in studying the behaviour of LPG tanks when subjected to accidental fire conditions. The field modelling approach is used to determine the free convective flows and heat transfer in both the vapour and the liquid regions, and also the heat transfer through the tank wall. Zone modelling techniques are employed to calculate the fire heat flux and the radiation heat transfer from the vapour wetted wall to the liquid/vapour interface. The model is verified by comparing predicted results with full scale experimental data obtained by the Health and Safety Executive, U.K.1 The comparisons indicate that the model can accurately predict the tank pressure and time to first valve opening. The model is used to investigate the effect of fire exposure level on the tank behaviour.
Multi‐grid solution of two coupled Stefan equations arising in induction heating of large steel slabs
Authors: Hoppe Ronald H. W. , Kornhuber Ralf
Published: November 2005

Induction heating of large steel slabs can be described by a coupled system of non‐linear evolution equations of Stefan type represnting the temporal and spatial distribution of the induced magnetic field and the generated temperature within the slab. Discretizing these equations implicitly in time and by finite differences in space, at each time step the solution of a system of difference inclusions is required. For the solution of that system two multi‐grid algorithms are given which, combined with a nested iteration type continuation strategy to proceed in time, result in computationally highly efficient schemes for the numerical simulation of the induction heating process.
A numerical study of three‐dimensional natural convection during freezing of water
Authors: Yeoh G. H. , Behnia M. , Davis G. de Vahl , Leonardi E.
Published: November 2005

A numerical study of three‐dimensional natural convection with phase change in a rectangular parallelepiped is described. The fluid has temperature‐dependent variable properties. The governing equations are approximated by finite differences, second order in space and first order in time. A boundary‐fitted co‐ordinate system is implemented to predict the shape and the movement of the solid‐liquid interface. Preliminary results have been obtained for freezing of water in a cube for Rayleigh numbers in the range of about 105–106.
Hermitian cubic boundary elements for two‐dimensional potential problems
Authors: Durodola J. F. , Fenner R. T.
Published: November 2005

A hermite interpolation based formulation is presented for the boundary element analysis of two‐dimensional potential problems. Two three‐noded Hermitian Cubic Elements (HCE) are introduced for the modelling of corners or points with non‐unique tangents on the boundary. These elements, along with the usual two‐noded HCE, are used in numerical examples. The results obtained show that faster convergence can be achieved using HCE compared with using Lagrange interpolation type Quadratic Elements (QE), for about the same amount of computing resources.
A mixed‐penalty finite element formulation of the linear biphasic theory for soft tissues
Authors: Spilker Robert L. , Maxian Tina A.
Published: November 2005

Hydrated soft tissues of the human musculoskeletal system can be represented by a continuum theory of mixtures involving intrinsically incompressible solid and incompressible inviscid fluid phases. This paper describes the development of a mixed‐penalty formulation for this biphasic system and the application of the formulation to the development of an axisymmetric, six‐node, triangular finite element. In this formulation, the continuity equation of the mixture is replaced by a penalty form of this equation which is introduced along with the momentum equation and mechanical boundary condition for each phase into a weighted residual form. The resulting weak form is expressed in terms of the solid phase displacements (and velocities), fluid phase velocities and pressure. After interpolation, the pressure unknowns can be eliminated at the element level, and a first order coupled system of equations is obtained for the motion of the solid and fluid phases. The formulation is applied to a six‐node isoparametric element with a linear pressure field. The element performance is compared with that of the direct penalty form of the six‐node biphasic element in which the pressure is eliminated in the governing equations prior to construction of the weak form, and selective reduced integration is used on the penalty term. The mixed‐penalty formulation is found to be superior in terms of tendency to lock and sensitivity to mesh distortion. A number of example problems for which analytic solutions exist are used to validate the performance of the element.
Solution of Helmholtz equation by Trefftz method
Authors: Cheung Y. K. , Jin W. G. , Zienkiewicz O. C.
Published: November 2005

The application of the Trefftz method for calculating wave forces on offshore structures is presented. Indirect and direct formulations using complete and non‐singular systems of Trefftz functions for the Helmholtz equation are posed in this paper. An effective technique using different interpolation functions for the velocity potential and wave force are suggested to improve the computational accuracy of the wave force. The numerical examples show that the present method is highly efficient and accurate.
Some computational issues in strain localization problems for rate independent solids
Authors: Perić D. , Mitchell G. P. , Owen D. R. J.
Published: November 2005

Issues related to the constitutive modelling and computational treatment of strain localization are examined for the class of rate independent solids. The significance of the constitutive description in localization problems is emphasized and constitutive models currently employed are briefly reviewed. Difficulties faced in finite element analysis, fundamentally associated with the loss of ellipticity of the related boundary value problem, and present trends in the computational treatment are discussed and illustrated by numerical examples.