bluuebunny/crossref_metadata_2025 huggingface dataset:
The extrapolation of implicit methods for the constant coefficient diffusion–convection equation
Authors: Twizell E. H.
Published: August 2005

A fully implicit method and a Crank–Nicolson type method are considered for the solution of the constant coefficient diffusion–convection equation. The former method is seen to be first‐order accurate in time and to be L‐stable or L0‐stable depending on the convection parameter, while the latter is seen to be second‐order accurate in time and to be A‐stable or A0‐stable with oscillations in the solution. The accuracy in time of the fully implicit method is improved by extrapolation. The principal part of the local truncation error of the extrapolation method is shown to be slightly inferior to the Crank–Nicholson type method, but the extrapolation method is shown to be L‐stable or L0‐stable with only small oscillations evident in the solution. The computational requirements of the two second‐order methods are seen to be similar.
A flat triangular shell element with improved membrane interpolation
Authors: Carpenter Nicholas , Stolarski Henryk , Belytschko Ted
Published: August 2005

An 18 degrees‐of‐freedom flat triangular shell element is formulated using the DKT bending element and a new membrane stress formulation. The membrane stress formulation is based on a degenerate linear strain triangle utilizing in‐plane rotations at each node. This new formulation is very simple and satisfies the plane stress patch test. Based on the numerical results from a rigorous set of test problems, the new formulation is shown to be an improvement over earlier attempts to improve the membrane stress in the shell element.
Finite deformations of a viscoelastic roll cover contacting a rigid plane surface
Authors: Bapat C. N. , Batra R. C.
Published: August 2005

Steady‐state finite plane strain deformations of a uniformly rotating rubber‐covered roll contacting a rigid plane surface have been studied by the finite element method. The rubberlike material has been modelled by a constitutive relation recently proposed by Christensen. Both the hydrostatic pressure within an element and the nodal displacements are taken as independent variables. For a constant indentation of the roll cover, the effect of the change in the thickness of the rubberlike layer, the speed of rotation and the values of the material moduli on the total load required to cause the indentation are presented.
A generalization of Uzawa's algorithm for the solution of the Navier‐Stokes equations
Authors: Fortin M. , Fortin A.
Published: August 2005

Usawa's algorithm provides an efficient method for solving the divergence‐free Stokes problem. On the other hand, the Newton–Raphson scheme is very popular for the solution of the nonlinear Navier–Stokes equations. We propose here a new method that combines these two algorithms and converges to a divergence‐free solution of the nonlinear Navier–Stokes equations.
Block diagonal scaling for iterative methods in thermal simulation
Authors: Díaz J. C. , Jines W. R. , McDonald A. E. , Steihaug T.
Published: August 2005

Linear equations arising from reservoir simulation are closely coupled at the local‐cell level, and the variables and equations tend to be poorly equilibrated. Scaling by the inverse of the diagonal block has an equilibrating effect. It usually improves the condition of the matrix for solution by linear iteration. The effects of block diagonal scaling are illustrated for a thermal reservoir simulator, where the original matrix may be indefinite. These results illustrate that for difficult problems block diagonal scaling can significantly enhance the convergence rate of the iterative method. It is also illustrated that preconditioned generated by block incomplete LU decomposition (ILU) and block symmetric Gauss Seidel (BSGS) methods are effective preconditioned for use in thermal simulation.
Numerical solution of regular and singular biharmonic problems with the Tau lines method
Authors: El Misiery A. E. M. , Ortiz E. L.
Published: August 2005

The recursive formulation of the Tau method of Ortiz6 is a versatile tool for the numerical solution of linear and nonlinear systems of differential equations. In this paper it is combined with the method of lines to produce a hybrid Tau lines method which has been applied with success in the numerical treatment of partial differential equations. We report here results obtained in the numerical solution of the biharmonic equation and show that the Tau lines technique performs far better than a specially designed finite element method with which it is compared. We also report results obtained in the numerical solution of a singular boundary‐value problem, defined again by the biharmonic equation, which is relevant to fracture mechanics.
A minimum configuration L‐stable fourth‐order non‐autonomous rosenbrock method for stiff differential equations
Authors: Day J. D.
Published: August 2005

One class of methods for solving stiff systems of ordinary differential equations is the so‐called Rosenbrock method. A fourth‐order method which requires the minimum computational work per step is described.
New symmetric finite difference methods for computing eigenvalues of a boundary‐value problem
Authors: Usmani Riaz A. , Agarwal Ravi P.
Published: August 2005

We develop a new finite difference method of order two and its refinement for computing the eigenvalues of a two‐point boundary‐value problem involving a fourth‐order linear ordinary differential equation. Our methods leads to generalized symmetric five‐ and seven‐band matrix eigenvalue problems. To demonstrate the effectiveness of the proposed methods, the numerical evidence is also included.
Analysis of tubular joint with weld toe crack by finite element methods
Authors: Bhuyan G. S. , Arockiasamy M. , Munaswamy K.
Published: August 2005

Finite element methods are used to obtain the through‐thickness and surface stresses for the tubular T‐joint in the presence of a shallow weld toe crack. The crack tip stress intensity factors are obtained by comparing the stresses at the crack front with the theoretical solution. The embedded elliptical crack front is modelled as straight line segments. The region at the vicinity of the crack is discretized using special elements, which produce singular stress fields at the crack front. It is observed that in presence of a shallow weld toe crack, the stress along the chord surface near the weld toe is less than that of a joint without a crack; which is evident from the presence of the free surface of the crack face. But far from the crack, the stress is always greater than that of the uncracked joint.
Ill‐posed design methods for the computation of inviscid flows
Authors: Wirz H. J.
Published: August 2005

It is shown here that the solutions of the governing partial differential equations fail to behave well for three well‐known methods of analysis and design for the computation of inviscid flows in turbomachines and for time‐dependent transonic airflows. The first two examples are related to flows in turbomachines: the so‐called ‘streamline curvature methods’ and the proposition of C. H. Wu to reduce the solution of an essentially three‐dimensional internal flow problem to successive two‐dimensional ones. Finally, time‐dependent compressible and irrotational flows which employ the density and the velocity potential as dependent variables are considered.
The role of a mixed design and analysis method in a turbomachinery blade design system
Authors: Ceder R. D. , Stow P.
Published: August 2005

In this paper the requirements of a design method are considered, with particular emphasis given to the needs of designers of multi‐stage compressors. It is concluded that what is required is a quasi three‐dimensional compatible design and analysis method. The extension of the finite element blade‐to‐blade method FINSUP to include a design calculation compatible with the analysis calculation is presented. In this method, changes to the blade shape are modelled using a surface transpiration model. By displacing every point on the blade surface individually, the relationship between the blade shape and the surface velocity is determined. It is shown that with a Newton–Raphson procedure adopted in the method, a very efficient manner of introducing the design option is possible. As a consequence the resulting program is fast and completely interactive. An example of the method is shown in which a transonic compressor blade with a suction surface shock is redesigned to give a blade with controlled suction surface diffusion.
On the Gaussian quadrature rule for finite‐part integrals with a first‐order singularity
Authors: Ioakimidis N. I.
Published: August 2005

The Gaussian quadrature rule for finite‐part integrals of the form
equation image
, due to Kutt, is reconsidered. Several new results about this rule are proved. The main result is that the orthogonal polynomials associated with the above quadrature rule are of the form P (y) + an P (y), where P (y) are the shifted Legendre polynomials (orthogonal on [0,1]) and an well‐defined constants. The present results will permit the more systematic use of the above quadrature rule in engineering applications (e.g. in the boundary element method), where finite‐part integrals of the type
equation image
are quite frequently encountered (e.g. during the numerical computation of one‐ and two‐dimensional Cauchy type principal value integrals).
A generalized displacement method for finite element analysis of constrained problems
Authors: Xikui Li , Liu Guo Qiang
Published: August 2005

A new approach to deal with the finite element analysis of structures with linear equality constraints is presented in this paper. By imposing the requirement that the displacement variables satisfy the linear constraint equations a priori, a procedure to form the so‐called generalized displacement subspace Ss is given. The constrained variational problem is then transformed into an unconsrained one defined on the subspace. This approach has been successfully used to analyse the incompressible problems1 and to overcome the shear locking phenomena in the thin plate–shell structure analysis2, 3.
Removal of singularities in tresca and mohr–coulomb yield functions
Authors: Sloan S. W. , Booker J. R.
Published: August 2005

The Tresca and Mohr–Coulomb yield functions are used widely in metal and soil plasticity computations. Both of these criteria, however, possess angular vertices at which the gradient with respect to the stresses, and hence the elastoplastic constitutive law, is undefined. This paper describes a modified yield function which may be used to ‘round‐off’ these vertices. When used in conjunction with the parent yield function, the modified yield function results in a yield surface which is continuous and differentiable for all values of the stresses. The modified yield function is used in the vicinity of the vertices and is given in a form suitable for finite element programming.
Communications oriented programming of parallel iterative solutions of sparse linear systems
Authors: Patrick Merrell L. , Pratt Terrence W.
Published: August 2005

Computing systems of the future for large‐scale scientific and engineering computations will consist of many processors and memories working in parallel to solve a single problem. Efficient use and ease of use of these future systems are two basic problems facing potential users. The development of new parallel algorithms and parallel programming environments is essential for progress toward the solution of these problems. In this paper we develop parallel algorithms for a class of scientific computational problems by partitioning the problems into smaller problems which may be solved concurrently. The effectiveness of the resulting parallel solutions are determined by the amount and frequency of communication and synchronization and the extent to which communication can be overlapped with computation. We present three different parallel algorithms for solving the same class of problems and analyse their effectiveness from this point of view. The algorithms are programmed using a new programming environment. Run‐time statistics and experience obtained from the execution of these programs assist in measuring the effectiveness of these algorithms.
Calculation of confined swirling jets
Authors: Chen C. P.
Published: August 2005

Computations of a confined coaxial swirling jet are carried out using a standard two‐equation (k‐ε) model and two modifications of this model based on Richardson number corrections of the length scale (ε) governing equation. To avoid any uncertainty involved in the setting up of inlet boundary conditions, actual measurements are used at the inlet plane of this calculation domain. The results of the numerical investigation indicate that the k‐ε model is inadequate for the predictions of confined swirling flows. Although marginal improvement of the flow predictions can be achieved by these two corrections, both cannot be judged satisfactory.
BEM—condition number of systems obtained when solving mixed boundary value potential problems
Authors: Migeot Jean‐Louis
Published: August 2005

A study of the condition number of matrices appearing in the resolution of mixed boundary value potential problems through the boundary element method (BEM) is presented here. It is shown how this condition number varies with the size of the domain under consideration. An algorithm is provided giving the best scale factor, which is the one leading to the smallest possible condition number.
On the determination of the roots of some classes of transcendental equations
Authors: Mikhailov M. D. , Özişik M. N.
Published: August 2005

A new approach is developed for fast, automatic and accurate computation of the roots of some classes of transcendental equations without the risk of missing any one of the roots. The method permits the calculation of as many eigenvalues as desired or any one of them directly, without the need for computing the previous ones. The computation procedure is based on the count of the number of roots of the transcendental equation lying between zero and some prescribed value in the eigenvalue spectrum. Basic rules in the application of this method are described, and its use for determining the roots of the transcendental equation is illustrated with examples.
Flow in a coiled tube: The effect of mesh pattern on the convergence rate of predicted critical points
Authors: Winters K. H. , Brown T. W.
Published: August 2005

Non‐unique flows are possible in a coiled tube when the axial pressure gradient driving the flow exceeds a critical value. For a tube of square cross‐section, it is shown that the rate of convergence of the critical value with mesh size depends strongly on the mesh pattern. In the particular, the predictions obtained with mesh patterns which respect the symmetry of the problem converge more rapidly as the mesh size is reduced.
Some higher order methods for computing eigenvalues of two‐point boundary value problems
Authors: Usmani Riaz A. , Agarwal Ravi P.
Published: August 2005

We present new finite difference methods of order at most O(h6) for computing eigenvalues of two‐point boundary value problems. Our methods lead to generalized seven‐band matrix eigenvalue problems. Some typical boundary value problems are treated numerically and these numerical results are summarized in order to demonstrate the practical usefulness of our algorithms.
Evaluation of the leading band coefficients of the boundary integral system of equations
Authors: Sofianos A. I.
Published: August 2005

Numerical integration of integrals that are either improper or have logarithmic integrands is required in order to evaluate some of the coefficients of the boundary integral system of equations in two‐dimensional elastostatics. This technique allows for the evaluation of these coefficients numerically with the use of the Gauss–Legendre quadrature formula.
An example of finite element analysis in a multiply connected region
Authors: Bolkowski Stanislaw , Sroka Jan
Published: August 2005

The temperature field of an underground cable line can be analysed in a simply connected region. Axial symmetry of the temperature distribution of the cable interiors enables them to be extracted from the region dealt with by the finite element method. This transforms the region into a multiply connected one. In this paper, the boundary procedure which replaced the cable interiors was derived. This procedure has the form of the boundary condition of the second kind. The only way to take into account the temperature dependence of the heat losses inside the cables in a simply connected region is to use an iterative process, which is time consuming. A multiply connected region is more effective in that respect, since only modification of the boundary procedure to the boundary condition of the third kind is needed for it. The temperature field of a cable line is an unbounded one. Therefore, the authors developed another boundary procedure in uniform earth which was based on the second Green formula. Numerical experiments confirmed that finite element analysis of the cable temperature field in a multiply connected region is more efficient than in a simply connected one.
Weighted Gaussian methods for three‐dimensional boundary element kernel integration
Authors: Aliabadi M. H. , Hall W. S.
Published: August 2005

The evalution of the inverse distance singular integrand which occurs in the three‐dimensional boundary element formulation of potential problems is treated using weighted Gaussian integration. Three methods are investigated. The first involves repeated use of a one‐dimensional Gaussian formula in which the weights are inverse powers. The second involves the inverse distance in the local parameter plane to which the surface elements are transformed. Comparisons with some exact integrals developed over plane parallelograms show that neither of these first two methods performs particularly well, with the second being appropriate only for integration over unit squares.

A third method is developed using an approximation to the real space distance in the weighting. Such a method does take into account the local properties of the surface and gives integrals accurate to the precision of the computer being used for tests on a plane parallelogram. In a further test integrating over a curved element on a sphere, good accuracy is again achieved. Overall, however, in the type of integration test considered, none of these weighted Gaussian methods integrates as accurately as the expansion or transformation methods published elsewhere.
Analysis of the collocation time finite element method for the non‐linear heat transfer equation
Authors: Kujawski J.
Published: August 2005

The method of collocation time finite element is a modification of the well‐known generalized midpoint method. It has an additional free parameter. The method is applied to the one‐dimensional nonlinear heat transfer equation. Numerical results illustrate that the proposed algorithm is capable of improved performance over the standard generalized midpoint method.
A determinant formalism for shape functions
Authors: Ward J. P.
Published: August 2005

The derivation, and analysis, of shape functions of the more commonly used finite elements is presented in a consistent manner using the formalism of determinants. The formulation emphasizes the multinomial variation, within the element, of the function to be interpolated. Furthermore, with this approach, properties required of shape functions are then transparently obvious.
On the effect of natural damping on the stability of a time‐stepping scheme
Authors: Wood W. L.
Published: August 2005

This paper shows that an algorithm which gives unconditional stability for the numerical integration of the dynamic vibration equation with zero natural damping can have only conditional stability with non‐zero natural damping, i.e. natural damping does not always ‘help’ the stability of the algorithm.
The implementation of directional boundary conditions for finite element computations with iterative solvers
Authors: Devloo Philippe
Published: August 2005

A projection technique for imposing directional boundary conditions in the solution of finite element models with iterative solvers is presented. The proposed method is general, easy to implement, and does not require a transformation of the discrete equations at the boundary or the choice of a penalty parameter.
Determination of average time constant for diffusion processes by means of the finite element method
Authors: Brykalski Andrezej
Published: August 2005

In this paper, a computational scheme of determination of the average time constant for diffusion processes by means of the finite element method has been presented. The algorithm is based on the software package for stationary problems and allows analysis of both two‐ and three‐dimensional problems.
An improved semi‐discrete approach for the solution of one‐dimensional linear boundary‐value problems
Authors: Bickford William B. , Rankin Robert L.
Published: August 2005

A semi‐discrete method for solving inhomogeneous boundary‐value problems whose differential equations possess regular singular points is presented. The method is shown to exhibit substantially improved accuracy as compared with previous similar treatments of the same class of problems. Examples illustrating the improvements are presented.
On the computation of weakly separated laminar flows in a smoothly expanding channel
Authors: Szymczak W. G. , Myers G.
Published: August 2005

In Reference 1, a summary of results of numerical solutions to steady‐state laminar flows in an expanding planar channel from 15 research groups was presented. Both vorticity and pressure values computed along a wall of the channel were compared. This paper presents some possible explanations for the wide discrepancies in these computed results.
Geometrical properties in the B‐spline representation of arbitrary domains
Authors: Rozenthal Paulo , Gattass Marcelo
Published: August 2005

This paper presents a new method to compute areas and moments of arbitrary domains bounded by periodic cubic B‐splines. The proposed method gives exact answers, it is very efficient and relies only on the control points co‐ordinates of the B‐spline. One example is presented and compared with analytical results and with previous numerical work.
Multiderivative methods for nonlinear beam problems
Authors: Twizell E. H. , Tirmizi S. I. A.
Published: August 2005

Second, fourth and sixth order methods are developed and analysed for the numerical solution of nonlinear fourth order boundary value problems with boundary conditions given as two function values together with two second order derivatives or two first order derivatives. The methods arise from a five‐point recurrence relation involving exponential terms, these being replaced by Padé approximants. The methods are tested on two problems from the literature.
On the Bergan‐Wang approach for moderately thick plates
Authors: Abdalla Hamed , Hassan Kamal
Published: August 2005

The Bergan‐Wang approach for the transverse shear inclusion in thin and moderately thick plate deformation has led to an energy expression which is a function of the only lateral deflection. The corresponding Euler equation is an eighth‐order partial differential equation. A variety of examples has been analysed. Analytical solutions have been presented for different thickness to span ratios under different boundary conditions. Results show very close resemblance to solutions based on Reissner plate theory.
A study of the influence of the angle condition on plate bending of triangular finite elements
Authors: Hassan K. , Sarigul N.
Published: August 2005

In triangulating a domain to find a finite element approximation for the solution of a specific problem, the so‐called angle condition is essential. In this paper, a study of the effects of this condition on the spectral properties of the stiffness matrix has been performed for two plate bending elements: the constant moment triangle (CMT) and the discrete Kirchhoff triangle (DKT). This has been done on the element level and also for the global system. It is shown that as the smallest, rather than the largest, angle of the elements considered herein decreases, the condition number of the global stiffness matrix increases.
Computation of the velocity field of an excited shear layer
Authors: Nallasamy M.
Published: August 2005

An infinitely thin shear layer emanating from a semi‐infinite flat plate subjected to acoustic excitation is considered. The flow field outside the excited shear layer is computed employing a source distribution approach. Results are given for the region of the velocity field that cannot easily be obtained by analytical approximations.
Extensional universal serendipity elements
Authors: Zhang Lin
Published: August 2005

In this paper, extensional universal serendipity elements (EUSE) are presented. The paper includes not only isoparametric elements with nodes from 2 to 32 having linear, quadratic and cubic node confiurations at their edges in an arbitrary manner, but also a series of transition isoparametric elements which can connect three‐dimensional solid elements, axisymmetric solid elements with shell elements with shell elements and axisymmetric shell elements, respectively. Shape functions and their derivatives for EUSE are expressed in terms of three one‐dimensional basic functions and their derivatives. EUSE is a more systematic, easy to program and ideal element family in the element libraries.
Performance of four numerical schemes for the unconfined flow (nonlinear Boussinesq) problem
Authors: Taigbenu Akpofure
Published: August 2005

Numerical experiments are performed on four schemes of the boundary element method (BEM) for the unconfined flow (nonlinear Boussinesq) problem with a view to determining the scheme that gives the best performance. The performance measure of a scheme for a particular problem reflects the trade‐off between accuracy and the CPU simulation time—a surrogate for computational cost or efficiency. The four schemes are adaptations of the theory earlier proposed by Taigbenu and Liggett.1 Two of the schemes are predictor–corrector or iterative schemes, while the other two employ a linearization about the known initial data. The variety of schemes enhances the versatility of the boundary element theory in the sense that a program user has a greater flexibility in the choice of scheme which best serves his desired objectives.
On problems with boundary conditions of the u= unknown constant
Authors: Mikhailov M. D.
Published: August 2005

The flow problems confronted with boundary conditions of the type u=constant are reformulated in order to be solved directly by any existing finite element codes.
On the development of an algorithm for solving stiff nonlinear dynamic equations based on the Broyden's updating method
Authors: Yuh J. , Holley W. E.
Published: August 2005

This paper describes a numerical procedure for the solution of stiff dynamic system equations which are written in implicit form f(x,ẋ,t)=0. This study, based on the Broyden's updating method, gives a more efficient way to solve the differential/algebraic equations simultaneously. Using a rank‐one inverse Jacobian updating formula, the inverse Jacobian matrix is corrected directly at each iteration. The algorithm is investigated for several dynamic systems.
On the competition between artificial methods and boundary integral methods for the stokes equations in exterior domains
Authors: Guirguis Georges H.
Published: August 2005

We compare the computer implementation and accuracy of the numerical approximation of the exterior Stokes problem in two dimensions.
New methods of determining the strange attractor by generalized cell mapping approach
Authors: Hua Zhu Wen , Tai Wu Qi
Published: August 2005

The generalized cell mapping method used in solving non‐linear dynamical systems is also a powerful means of determining the state volume in which strange attractors reside. Several methods of refining the size of cells are proposed in this paper. With the aid of these methods it is possible to describe the shape of a strange attractor in however much detail is required. Any part of the cell state space can be enlarged by the suggested zoom technique when the finte structure of this strange attractor is going to be studied. By using the limiting probability distribution calculated from the persistent group, the statistical meaning of the attractor is revealed. Results of examples which were computed on an IBM PC computer show the validity and efficiency of the methods.
Guyan reduction
Authors: Chen Su‐Huan , Pan H. H.
Published: August 2005

Because of the cost of generating computer solutions for a dynamic analysis, it is often desirable to reduce the size of the problem by performing a reduction on the mass and stiffness matrices of the governing set of equations of motion. The well‐known reduction proposed by Guyan is the technique used by most of the large structure codes. This paper is concerned with the accuracy in such reduction and the method to improve it. A formula for the estimate of the error induced by Guyan reduction is derived through from perturbation theory. Based on the same principle, an iterative pertubation scheme is developed to improve the solution accuracy by taking the Guyan solution as the starting value. To demonstrate the practical usefulness of the method, two numerical examples are included.
Boundary element study of an anisotropic plate
Authors: Heng Z.
Published: August 2005

An efficient boundary element technique is developed for use in the analysis of composite structures. The boundary element method is modified by an analytical scheme so as to evaluate the boundary integrals in those elements containing singularities. This technique, combined with a special integration quadrature formula for the remaining elements, significantly improves the computing accuracy of the boundary element method.
Solution of electrostatic problems by the p‐version of the finite element method
Authors: Szabó Barna A.
Published: August 2005

The main points of the finite element formulation of electrostatic problems are summarized and illustrated with a two‐dimensional example which is representative of wiring capacitance computations in VLSI circuit design. Quality control procedures in finite element analysis, based proper mesh design, p‐extension and extraction procedures are demonstrated.
A boundary value method for a class of nonlinear singular perturbation problems
Authors: Kadalbajoo Mohan K. , Reddy Y. N.
Published: August 2005

A boundary value method is presented for solving a class of nonlinear, singularly perturbed, two‐point boundary value problems with a boundary layer on the left end of the underlying interval. By constructing a modified problem with a boundary layer correction, the boundary layer is dealt with separately. The method is iterative on the terminal point of the boundary layer. A lower bound for the terminal point of the perturbation parameter and some theoretical results of the method are discussed for linear problems. Finally, some numerical examples are presented to demonstrate the efficiency of the method.
Laplacian smoothing and Delaunay triangulations
Authors: Field David A.
Published: August 2005

In contrast to most triangulation algorithms which implicitly assume that triangulation point locations are fixed, ‘Laplacian’ smoothing focuses on moving point locations to improve triangulation. Laplacian smoothing is attractive for its simplicity but it does require an existing triangulation. In this paper the effect of Laplacian smoothing on Delaunay triangulations is explored. It will become clear that constraining Laplacian smoothing to maintain a Delaunay triangulation measurably improves Laplacian smoothing.
A comparison of solutions for adiabatic shear banding by forward‐difference and Crank‐Nicolson methods
Authors: Batra R. C. , Wright T. W.
Published: August 2005

A set of non‐linear and coupled equations governing the thermomechanical deformations of a viscoplastic body undergoing simple shearing deformations is integrated in time by using the forward‐difference Galerkin finite‐element (FDGFE) method and the Crank‐Nicolson‐Galerkin finite‐element (CNGFE) method. In the latter scheme the number of unknown functions is increased so that the governing equations contain only first‐order spatial derivatives. It is shown that the solutions obtained by the two methods agree qualitatively; however, the CNGFE method seems to introduce some damping into the system for non‐polar materials, but none for dipolar materials.
A shape function codewriter
Authors: Aladjem M. A. , Mikhalov M. D.
Published: August 2005

A unified matrix algorithm is used to formalize the construction of shape functions for two‐dimensional serendipity quadrilateral elements. Listings are presented for two codewriters which automatically generate FORTRAN and PASCAL functions for shape function calculations.
Steady three‐dimensional thermal convection in a vertical rectangular enclosure
Authors: Chikhaoui A. , Maslanik M. K. , Sani R. L.
Published: August 2005

The numerical study of the steady 3D thermal flow regimes in a vertical enclosure with side‐wall heating and cooling is considered; a primitive variable Galerkin finite element method is used for the simulation in the Boussinesq approximation. The model consists of a rectangular box with vertical and horizontal aspect ratios, respectively, of lz = 12 (vertical length to box width) and ly = 8 (horizontal length to box width). The two large vertical plates are maintained at different and constant temperatures, and the remaining walls are assumed to be perfectly conducting. The enclosure is filled with a fluid of Prandtl number Pr=0.71, and the Grashof number Gr, based on the spacing between the large vertical walls, is up to 1.2 × 104. The 3D results presented herein were obtained with a 11 × 9 × 53 node mesh in half of the enclosure by imposing symmetry at the mid‐plane. The solution in the mid‐plane is compared with a 41 × 121 2D solution and laboratory observations at various Gr values. The transition between the monocellular and multicellular natural convective regimes is determined. The 3D aspect of the flow is illustrated and compared with the 2D solution. Near the onset of multicellular flow predicted by linear stability theory, the 2D and 3D simulations exhibit a steady multicellular structure. The calculated flow patterns are compared to visualizations obtained by smoke traces in physical experiments.
On the solution of heat conduction problems involving heat sources via boundary‐fitted grids
Authors: Grandi G. M. , Ferreri J. C.
Published: August 2005

It is shown that codes employing boundary‐fitted grids (BFG) in heat conduction problems involving heat sources must be implemented in strictly numerically conservative form if accurate results are to be obtained. It is demonstrated that, for one‐dimensional problems, non‐conservative form imply errors originated in grid non‐uniformity that cause a spurious increase in the heat source. This in turn leads to significant errors in the computed soution. Therefore the implementation of BFG codes using non‐conservative forms should be avoided. An application to an unsteady, axisymmetric benchmark problem involving a spherical, time‐decaying heat source is presented.
Calculation of interior values by the boundary element method
Authors: Paulsen Keith D. , Lynch Daniel R.
Published: August 2005

The boundary element method (BEM) provides a straightfoward mechanism for calculating interior values once the appropriate boundary values have been determined. However, the interior solution near the boundary can exhibit unusual behaviour resulting in large numerical inaccuracies. This ‘boundary layer’ effect has been noted but is largely unexplored in the BEM literature. In this paper the numerical inaccuracies are shown to stem from the inability of the quadrature to account for the Green's function near‐singularity. A simple scheme, which adds little extra computational effort, is used to remove the numerical inaccuracies at interior points close to the boundary by increasing the quadrature in the nearby boundary elements.
Parallel processing of central difference transient analysis for three‐dimensional nonlinear framed structures
Authors: Hajjar Jerome F. , Abel John F.
Published: August 2005

The central difference algorithm is a simple but effective time integration algorithm suitable for parallel processing. This paper discusses the development and implementation of the method for the fully nonlinear, transient dynamic analysis of three‐dimensional framed structures. A data structure is presented in which only one nearest‐neighbour communication is required per timestep, and potentially little overhead is incurred for the parallel implementation. Because this explicit method is only conditionally stable, the large disparity of natural vibrational frequencies of frame structures indicates that central difference analysis is most useful for applications having short‐duration loading. An example is presented indicating the speed‐up and efficiency of the algorithm when implemented in a distributed‐memory, coarse‐grained parallel processing environment.
A family of predictor‐corrector methods for second‐order hyperbolic equations
Authors: Twizell E. H. , Khaliq A. Q. M.
Published: August 2005

A family of predictor‐corrector methods is used in PECE mode to obtain a numerical solution of a nonlinear second‐order hyperbolic partial differential equation. One particular predictor‐corrector combination is used to solve a problem from the literature.
Advantages of consistent over lumped methods for analysis of beams on elastic foundations
Authors: Griffiths D. V.
Published: August 2005

A simple method for analysing laterally loaded piles is to consider the problem as a beam on an elastic foundation. In this representation, the finite element method is used to solve the governing differential equation, in preference to the more popular finite difference approaches. The pile is modelled using beam elements, and two different methods are compared for introducing the soil stiffness. The ‘consistent’ approach, where the governing differential equation is discretized using a Galerkin formulation, is shown to be considerably more accurate than a ‘lumped’ approach. The improvement is particularly noticeable when the finite element discretization becomes coarser. Some examples are presented to illustrate the differences, and comparisons are made with closed‐form solution.
An accurate five‐point implicit finite difference method for solving the one‐dimensional wave equation
Authors: Noye B. J. , Rankovic M. J.
Published: August 2005

The ‘modified equaivalent equation’ approach has been used to derive a highly accurate implicit finite difference method (FDM) for solving the classical wave equation in one space dimension, using a computational stencil extending over five spatial grid points. This approach involves minimising the error terms of the modified equivalent partial differential equation which corresponds to the finite difference equation (FDE).
3‐D infinite boundary elements and simulation of monolithic dam foundations
Authors: Chuhan Zhang , Chongmin Song , Guanglun Wang , Feng Jin
Published: August 2005

Based on the asymptotic behaviour of the fundamental solution for 3‐D elasticity problems, this paper presents an infinite boundary element model (IBEM) and its interpolation form. By using the analytical solution for half‐space under a vertical loading, excellent accuracy of this model has been verified. As an engineering application, the infinite foundation of a monolithic gravity dam was modelled by IBEM and the dam itself by normal BEM, and the displacement and stress distributions of the dam were analysed. It was concluded that large structure and foundation problems can be solved by this coupling system with the advantage of having fewer degrees of freedom and less data preparations. The results also clearly show the great improvement of the 3‐D model for critical stresses of the dam over the 2‐D plane model for narrow canyons having a width‐height ratio less than 2·4. Thus, a more economical cross‐section for dams can be achieved by 3‐D analysis.
Non‐linear dynamic substructure analysis using direct integration of steady‐state solution
Authors: Lima E. C. P. , Coutinho A. L. G. A. , Alves J. L. D.
Published: August 2005

A reliable and efficient dynamic substructure technique for the determination of the steady‐state response of structures with physical non‐linearities is presented. Although the algorithm is similar to component mode synthesis, enhanced substructure of Lanczos‐‐Ritz vectors are used, to account for the spatial distribution of the external and inertial loads. The steady‐state solution is computed from the transient response over a single excitation cycle. The non‐linear behaviour is accomplished by a purely iterative pseudo‐force method. The numerical results show the potential of such an approach for the analysis of large structures.
Performance of some globally mapped Lagrangian elements
Authors: Nath B.
Published: August 2005

A study of the performance of some globally mapped Lagrangian elements is presented. The objective was to determine whether there were significant advantages to be gained from mapping. Results show that for biquadratic and bicubic elements, the only ones considered, mapping leads to considerably improved performance, in terms of both accuracy and convergence, over their conventional (unmapped) counterparts. On the debit side, however, the presence of ‘parasitic’ terms in the shape function(s) of mapped Lagrangian elements makes them less efficient than their counterparts of the serendipity family. Nevertheless, results offer sufficient incentive for further work on ways in which Lagrangian elements could be made more efficient for practical application.
Solidification of castings in metallic moulds
Authors: Naik H. B. , Dave A. K.
Published: August 2005

A square‐shaped central section of a relatively long aluminium casting in a metallic mould is analysed as a two‐dimensional heat‐transfer problem. The latent‐heat liberation effect and property variation with temperature are accounted for using an integral averaging technique. The experimental air‐gap data available in the literature are made use of. The modified Newton‐Raphson method, along with the Crank‐Nicholson time‐marching scheme, is used for the solution.
On a BEM formulation for an axisymmetric heat‐conduction problem in a transversely isotropic medium
Authors: Ishida R. , Ochiai Y.
Published: August 2005

In this paper we deal with the boundary‐element formulation for the axisymmetric transient heat‐conduction problem of a transversely isotropic medium. The time‐dependent fundamental solution for the axisymmetric problem is used and the time integral is performed analytically. It is shown that the function obtained is separated into steady and transient parts and the singularity at the boundary integral is only in the steady part.
Reducing modal truncation error in the wave response analysis of offshore structures
Authors: Léger P. , Ricles J. M. , Robayo L. J.
Published: August 2005

The response of offshore structures subjected to wave loading is generally dominated by pseudo‐static behaviour which is not efficiently expressed in truncated modal co‐ordinates. In this paper, a new and efficient method has been developed to reduce modal truncation error in the numerical evaluation of transfer functions for the wave response of offshore structures. The solution is based on a transformation to a reduced system of generalized Ritz co‐ordinates using load‐dependent transformation vectors generated by a subspace iteration type of scheme from specified distributions of the dynamic loads. Numerical applications on a simple gravity platform model were used to establish systematic comparisons between the performance of the mode‐displacement, the mode‐acceleration and load‐dependent solutions using various numbers of transformation vectors.
Implicit methods for diffusion–convection equations
Authors: Patrício F.
Published: August 2005

In this work three implicit methods are considered for the solution of the constant‐coefficient diffusion‐convection equation. Two of these methods are seen to be first and second‐order accurate in time and to be L‐stable or L0‐stable, depending on the relation between the convection and diffusion parameters and the step size. The third one is seen to be third‐order accurate in time and is also L‐stable (L0‐stable). However, some oscillations may appear in the solution. To avoid these oscillations some restrictions are presented.
An integration procedure for curved boundary elements
Authors: Abdel‐Akher A. , Hartley G. A.
Published: August 2005

In the direct boundary element method (DBEM) of analysis, much of the numerical computation involves the integrations along a boundary. The integration is usually performed by quadrature, and in recent pevious papers by the authors1,2 it has been shown that integration can in general be carried out analytically, with the results of the integration presented as algebraic functions, and programmed accordingly. These results have, to this time, been presented for straight boundaries, with application to thinplate bending analysis only.

For an arbitrary shaped curved element, the derivation of closed‐form expressions for boundary integrations is not possible. A semi‐analytical‐numerical procedure, based on representing the boundary as piecewise straight is developed in this paper. In this procedure, the boundary shape is considered dependent of the approximation of the boundary variables, and in the sense that each‘quadratic’ boundary element is considered geometrically to be made up of several piecewise cubic functions, the mulation might be termed‘super‐parametric’. Generally, a curved boundary does not necessarily imply need for higher‐order approximation of boundary variables, but does necessitate that the more applicated shape be accurately modelled.

The integration procedure presented in this paper can be applied in other two‐dimensional problems.
The evaluation of domain integrals in the boundary element method
Authors: Pina H. L.
Published: August 2005

In the application of the boundary element method (BEM) source terms give rise to domain integrals. To keep in the spirit of this method these integrals should be transformed into boundary integrals. Infortunately this is possible only in some circumstances. In this paper we develop further an idea of Vijayakumar and Cormack (1987) to obtain other cases where such transformation is possible
Constructing second‐order structural models with specified mass submatrix condition numbers
Authors: Williams T.
Published: August 2005

This paper presents a simple new algorithm for constructing second‐order models for any given flexible structure, with these models satifsfying the constraint that each leading principal submatrix of the mass matrix must have a specified condition number. Now, the effects of rounding errors in practical computation generally increase with increasing condition number, i.e. as the matrix considered approaches singularity. Thus, the new models should prove useful for the systematic testing of the numerical properties of many algorithms in the dynamics and control of flexible structures.
Removal of integral singularities
Authors: Laures J. P.
Published: August 2005

A procedure based on changing of independent variables is proposed. It allows one to reduce one‐dimensional (1D) and two‐dimensional (2D) singular integrals arising in fracture mechanics (in 2D and 3D problems, respectively). The final non‐singular expressions are exact and usually simpler than the original functions. They may therefore simplify analytical developments, and allow significant reduction of the computational time and an increase in the accuracy of numerical applications.