bluuebunny/crossref_metadata_2025 huggingface dataset:
A viscous–inviscid coupling method for the design of low Reynolds number aerofoil sections
Authors: Hassan Ahmed A.
Published: August 2005

An interactive numerical coupling procedure has been developed for the design of aerofoil sections with an allowance for viscous effects, provided that the boundary layer is fully attached over the aerofoil. Special emphasis is given to the design of natural laminar flow (NLF) aerofoils. The method described combines, in an iterative process, an inviscid hodograph‐based inverse‐design algorithm (IDA) developed by the author, the inviscid‐analysis algorithm (FLO6) by Jameson, and the boundary layer algorithm (LTBLCEQL) by Miner, Anderson and Lewis. In the physical plane, the inviscid computational results define an aerofoil configuration (or displacement surface) having a preset trailing edge gap. Viscous effects are then incorporated in the design procedure via the displacement surface concept. As expected, the numerical results suggest that aerofoils having long runs of NLF are easily obtained, provided that the proper choice of the gradients of the prescribed input pressure distribution is made.
High order difference group explicit (HODGE) methods
Authors: Yousif W. S. , Evans D. J.
Published: August 2005

Point iterative methods at which, at any one time, only a single equation of the linear system is treated are well known. However, in recent times block (or line) iterative methods, in which a group of equations (or points on the grid mesh) are treated implicity and solved directly by a specialized algorithm, have become the standard techniques for solving the sparse linear systems derived from the finite difference/element discretization of a self‐adjoint elliptic partial differential equation on a two‐dimensional grid. The main concern of this paper is to construct new groupings of the mesh points of the network into four and nine points using the high order accurate nine‐point finite difference equations and to investigate their advantages when used explicity in the standard iterative methods4,5,6.
On computing eigenvalues of two‐point boundary value problems
Authors: Usmani Riaz A.
Published: August 2005

This paper presents some new finite difference methods for computing eigenvalues of two‐point boundary value problems of the form y″ + λq(x)y = 0, y(a) = y(b) = 0. The approximations Λ for λ are computed from a generalized seven‐band symmetric matrix eigenvalue problem resulting from a suitable discretization of this boundary value problem. The numerical approximations are 0(h4)‐convergent. It is shown that the accuracy of the numerical results can be pushed to 0(h5) and 0(h6), provided that the function q(x) vanishes at x = a and b. Some numerical evidence is included to demonstrate the practical usefulness of the algorithms.
On the numerical solution of the Riccati algebraic matrix equation
Authors: El‐Gindy T. M. , Salim M. S. , Farghaly M. S.
Published: August 2005

The Riccati equation arises in various problems, particularly in practical engineering problems. It is required to solve the resulting Riccati algebraic matrix equation instead of solving the time‐invariant optimal control problem in one of its standard forms. In this paper an unconstrained minimization technique referred to as the Davidon–Fletcher–Powell (DFP) method is used in solving such an equation by minimizing its norm. The positive‐definite solution of the equation is also obtained, which is desirable in most engineering problems.
Improvement of the runtime behaviour of a frontal solution code
Authors: Gloos D. , Hoehn W. , Spellucci P.
Published: August 2005

The frontal solution method for finite element linear systems is well known to be especially useful for small and medium‐sized computing equipment. Even memory sizes from 1 to 8 MB, which are now possible, put severe space limitations on three‐dimensional calculations run on a time‐sharing system. This paper describes a programming technique which greatly increases the applicability of the frontal solution method without using the automatic paging of modern operating systems, which would result in extreme inefficiency.
OAHM: A fortran subroutine for solving a class of unsymmetric linear systems of equations
Authors: Makinson G. J. , Shah A. A.
Published: August 2005

The discretization, by means of the usual 5‐point difference formulae, of an elliptic partial differential equation can give rise to an unsymmetric and sparse linear system of equations in which the matrix A of coefficients is an M‐matrix such that each element in the upper/lower triangular part is greater than or equal to the respective element in the lower/upper triangular part. In other applications, dense matrices with the same property can arise. A FORTRAN subroutine called OAHM is presented for the solution of such systems which can be easily modified to deal efficiently with the sparse case. The OAHM subroutine uses a regular splitting and the convergence is therefore guaranteed.
An explicit form of the plastic matrix for a Mohr–Coulomb material
Authors: Griffiths D. V. , Willson S. M.
Published: August 2005

An explicit from of the plastic matrix for a Mohr–Coulomb material in two dimensions is presented. The derivation, which assumes elastic–perfectly plastic behaviour is obtained by direct differentiation of a non‐invariant expression for the Mohr–Coulomb yield function. A FORTRAN 77 subroutine is also provided.
Finite element simulation of recirculating flows with heat transfer
Authors: Polansky G. F. , Lamb J. P. , Klein D. E.
Published: August 2005

The finite element method was investigated as a means of simulating incompressible laminar and turbulent flow with heat transfer. Governing equations include the complete, two‐dimensional Navier–Stokes equations expressed in terms of primitive variables. The turbulent viscosity is determined by a two‐equation (k‐ϵ) model of turbulence. Both high Reynolds' number and low Reynolds' number forms of the two‐equations model were considered. The formulation was first tested in laminar recirculating flows as well as in a fully developed turbulent channel flow. The code was then applied successfully to flow past a confined backward facing step and to a backward facing ramp. Although the high Reynolds' number turbulence model was found to be incompatible with the current numerical scheme, good results were obtained using the low Reynolds' number model. Results of the current calculations are compared with experimental data and a variety of other computational results.
Numerical treatment of boundary conditions at points connecting more than two electrically distinct regions
Authors: Paulsen Keith D. , Lynch Daniel R. , Strohbehn John W.
Published: August 2005

Points of intersection of three or more lossy dielectric regions (i.e. tissues) often occur in anatomical cross‐sections of the human body obtained with CT‐scans. The boundary conditions for the electric and magnetic fields require special attention at these points, in contrast to points of connectin of only two tissues, thus posing a problems for numerical methods involved with calculating the electromagnetic fields in tissue. In this paper, a simple theoretical analysis, which exposes the dominant analytic behaviour near such points, is followed. The derived analytic behaviour is numerically enforced via a special basis function which is compatible with the finite element method. Results are shown which indicate that the special basis preserves the analytic behaviour while maintaining grid resolution that is typical of the overall mesh.
A simple wave envelope element example
Authors: Bettess Peter
Published: August 2005

The wave envelop element method, due to Astley,1 is applied to a simple one‐dimensional example problem. It is shown that the method yields the exact answer and it is concluded that the method has a number of profound advantages.
A simple method to form interface elements in the heat transfer analysis
Authors: Karjalainen Jussi A.
Published: August 2005

A technique of creating matrices of interface elements for a heat transfer analysis by the finite element method (FEM) is presented. The method utilizes general convection matrices in the formation of an interface element matrix.
Concurrent iterative solution of large finite element systems
Authors: Farhat Charbel , Wilson Edward
Published: August 2005

A general iterative algorithm for the solution of large finite element systems of arbitrary domain geometry is designed to operate efficiently on modern computers with concurrent processors. The domain is recursively and automatically subdivided into the same number of subdomains as available processors. Convergence is ensured because of the Gauss–Seidel type of iterations operated on each subdomain and corresponding interface. This subdomain iterative solution approach is compatible with the other phases of a complete concurrent finite element analysis (concurrent stiffness formation and assembly and concurrent element post‐processing), from both the data structure and computation points of view. Implementation of the resulting stratagem on MIMD computers is presented. Several examples are run on a hypercube multiprocessor to validate the proposed algorithm and assess its performance. An efficiency of 91 per cent is achieved for a problem with 16,000 degrees‐of‐freedom.
p‐adaptive boundary elements for three‐dimensional potential problems
Authors: Cerrolaza Miguel , Alarcón Enrique
Published: August 2005

This paper deals with the boundary element method (BEM) p‐convergence approach applied to three‐dimensional problems governed by Laplace's equation. The advantages derived from the boundary discretization and hierarchical interpolation functions are collated in order to minimize human effort in preparation of input data and improve numerical results.
Adaptive grid refinement methods for time‐dependent flow problems
Authors: Ewing Richard E.
Published: August 2005

In the multi‐dimensional numerical simulation of certain multi‐phase fluid flow processes, many phenomena are sufficiently localized and transient that self‐adaptive local grid refinement techniques are necessary to resolve the local physical behaviour. For large‐scale simulation problems, efficiency is the key to the choice of specific adaptive strategies. Several different types of self‐adaptive methods will be discussed and briefly compared. The differences in complexity of the data structure and efficiency of the solution techniques will be explained. Concepts for incorporating these methods in existing large‐scale simulators will also be presented. Man man‐years have been invested in developing large‐scale numerical simulators which do an excellent job of resolving most of the larger length‐scale phenomena in our production processes. Although adaptive local refinement methods are critical for many applications, most techniques which have been developed to date either cannot be incorporated in our codes or are so computationally complex that they destroy the efficiency of existing simulators. Recently, new preconditioning techniques have been developed which allow grid refinement methods to be used efficiently in exisiting codes without disrupting the basic solution process. These techniques are highly amenable to vectorization and parallelization of the algorithms. They are also a first step in allowing complex well models to be incorporated into large field‐scale codes and applications.
A geometrically nonlinear finite element analysis of wrinkled membrane surfaces by a no‐compression material model
Authors: Contri P. , Schrefler B. A.
Published: August 2005

A total Lagrangian formulation and a continuum approach are used in a geometrically nonlinear finite element analysis of wrinkled regions in membranes. The analysis makes use of a no‐compression material model together with large out‐of‐plane displacements of the elements to simulate a problem which is in fact due to the lack of flexural stiffness. This model simulates the stress state in surface areas with distributed wrinkles better than a model where the tendency of the membrane to avoid compressive stresses is simulated only by large out‐of‐plane displacements of the elements. A distinction between single folds and wrinkled regions is introduced.
An efficient method for determining eigenvalues in vibratory systems
Authors: Zimoch Zdzislaw
Published: August 2005

In this paper the method of eigenvalues computation of mechanical linear systems is presented. The method has a general character and applies to conservative as well as non‐conservative systems. It is especially useful for complex structures with a large number of degrees‐of‐freedom.
Use of quasi‐Newton methods for large strain elastic‐plastic finite element computations
Authors: Gelin J. C. , Picart P.
Published: August 2005

In this paper, quasi‐Newton methods are used to solve large strain elastic‐plastic problems. The governing nonlinear equations are derived from the principle of virtual work written in an updated Lagrangian manner. The constitutive equations result directly from the definition of free energy and plastic potential that involve a convex functional form. A mixed algorithm is proposed that combines the Newton‐Raphson method and modified Newton‐;Raphson method with symmetric quasi‐Newton update. The efficiency of the algorithm, measured in terms of rate of convergence and computation time is studied on numerical tests. The procedure has a very wide field of application in nonlinear elastic‐plastic analysis.
On the folding of numerically generated grids: Use of a reference grid
Authors: Castillo José E. , Steinberg Stanly , Roache Patrick J.
Published: August 2005

When variational grid generation techniques are used to produce grids suitable for solving numerical partial differential equations in irregular geometries, a reference grid can be used to determine the properties of the desired grid. Grid folding is a major problem in all methods of numerical grid generation; this paper studies the use of a reference grid, in variational smoothing methods, to prevent such foldings. The effects of various types of reference grid are compared and natural reference grids are shown to prevent foldings in the examples studied. The analysis is performed for a model problem with only one free point, and is then applied for finer grids. In addition, a short description of a discrete variational method is given. The reference grid concept applies to this discrete formulation.
Free surface flow — exposing the hidden nonlinearity
Authors: Liggett James A.
Published: August 2005

Most calculations of free surface flow use an inconsistent equation. The inconsistency comes about through the need to apply the boundary conditions on the known boundary instead of on an unknown (advanced time step) boundary. That condition represents a nonlinearity and its treatment should be made consonant with that of the other nonlinearities. Although algebraically difficult, that nonlinearity can be treated in a rational manner with the result that the accuracy is improved.
Upwind and downwind effects of numerical approximations to wave equations
Authors: Pearson Carl E.
Published: August 2005

A wave equation such as ut + cux = 0 propagates effects downwind only, but upwind effects resulting from a numerical approximation to the equation can be equally strong. Several common numerical approximations are considered, and asymptotic effects for small timesteps are evaluated. An extension to vector equations in several variables (related to the Euler equations of computational fluid mechanics) is made.
A restarted version of a generalized preconditioned conjugate gradient method
Authors: Axelsson O.
Published: August 2005

A generalized preconditioned conjugate gradient method for the iterative solution of a preconditioned linear system Bx = b was recently derived and analysed by the author. Here is presented a special version of it which is efficient in cases where the matrix‐vector multiplication with the given matrix is costly, as in various substructuring methods, where the matrix is usually not present in explicit form but the action of it can be computed.

For a restarted version, it is shown that the residuals decrease monotonically for any nonsingular matrix B except when a certain inner product is zero. It is shown why it is advantageous to let the maximal number of search directions in each cycle be not smaller than the number of clusters of eigenvalues of B in the complex plane. An upper bound is derived for the rate of convergence of the algorithm when the clusters can be transformed to an ellipse by a polynomial mapping.
Transformation of incremental plasticity relation from defining space to general Cartesian stress space
Authors: Chan A. H. C. , Zienkiewicz O. C. , Pastor M.
Published: August 2005

Incremental plasticity relations are frequently defined in terms of stress invariants and their related strain quantities, and in computation need to be transformed to a Cartesian co‐ordinate system. This paper indicates how much transformation can be implemented simply and consistently without redefining yield and plastic potential. Indeed, the procedure developed is applicable to the transformation between any two stress spaces.
A simple procedure for reducing numerical integration errors near singularities
Authors: Manno Vincent P.
Published: August 2005

Numerical integration of functions near singularity points presents a challenge to even advanced quadrature algorithms. Often it would be advantageous to have a simple technique with which to test the accuracy of these estimates. One such technique is described. It consists of subtracting an integrable complementary function from the original integrand, which reduces the curvature of the function to be integrated. This allows simpler numerical integration techniques to be employed for verification. In addition, the technique can be used directly to improve the accuracy of the baseline quadrature. The method provides a means of estimating the order of the functional singularity, which may be unknown.
FEM‐FCT: Combining unstructured grids with high resolution
Authors: Löhner R. , Morgan K. , Vahdati M. , Boris J. P. , Book D. L.
Published: August 2005

We present the extension of flux‐corrected transport (FCT) schemes to unstructured grids. The spatial discretization is performed via finite elements. In particular, we have chosen triangular elements in two dimensions. The limiting procedure is based on Zalesak's extension to more than one dimension of the FCT schemes developed by Boris and Book. The resulting scheme, FEM‐FCT, is capable of resolving moving and stationary shocks within two elements, and several examples are given that demonstrate the accuracy attainable, even for complicated geometries.
Numerical calculation of profiles corresponding to given pressure distributions
Authors: Meyer J. P. , Mathews E. H. , Van Zyl G. P.
Published: August 2005

The pressure distribution over the profile of a body in fluid flow influences the forces, moments and flow separation on it. It is therefore often advantageous to design a profile in such a way that a predetermined pressure distribution is obtained over the final profile. In this paper a numerical procedure is proposed for calculating the profile corresponding to a given pressure distribution. The procedure employs a transformed version of the potential flow equation for the stream function, which makes the method very effective. Predicted profiles are verified against an analytical solution and against the profile of a NACA 0015 aerofoil. The measured pressure distribution on a calculated axisymmetrical profile is also found to compare favourably with its prescribed pressure distribution.
A new generalized conforming triangular element for thin plates
Authors: Yuqiu Long , Junqing Zhao
Published: August 2005

The concept of a generalized conforming element14 is used to introduce a generalized compatibility condition under constant moment, and a new version of the generalized conforming triangular element for thin plate with nine degrees of freedom is developed. The formulation is as simple as for the conventional non‐conforming element, and it can be implemented in a routine manner. By satisfying the generalized compatibility condition under constant moments, the present element can always pass the patch test, and convergence towards an exact solution is guaranteed. The element gives highly accurate results, requires fewer degrees of freedom, and is not sensitive to geometrical distortion.
A point concerning quadratic elements in two‐dimensional boundary element methods
Authors: Deb Anindya , Wang Hui‐Ching
Published: August 2005

In two‐dimensional boundary element methods, the use of quadratic elements for modelling geometric shape and interpolating boundary variables is quite common. For straight boundaries, an interesting indeterminancy of the normal at an end‐node may occur in the usual numerical strategy if the intermediate node lies at a distance of a quarter of the element length from that node. Inaccuracies in the values of nodal boundary stresses caused by errors in the direction cosines of normals are most easily avoided by choosing the intermediate node to lie sufficiently far away from the one‐quarter point from either end‐node.
On the imposition of a flowrate by an augmented Lagrangian method
Authors: Fortin André
Published: August 2005

This paper introduces an augmented Lagrangian method for the imposition of a given flowrate in the numerical simulation of problems where no a priori knowledge of the velocity profile at the inlet of the domain is availble. This method can be seen as a convenient way to generate boundary conditions consistent with the Navier‐Stokes equations when only the flowrate is known. The theoretical formulation of the problem and a numerical algorithm are presented. The efficiency of the proposed method is verified by numerical simulations.
Inviscid transonic flow over a wavy wall decaying downstream
Authors: Park Jeong‐Joo , Chang Keun‐Shik
Published: August 2005

Inviscid transonic flow over a wavy wall with either subsonic or supersonic freestream speeds is studied by solving the Euler equations numerically. The streamwise flow development through a series of shock waves and entropy production are investigated in depth. In the case of supersonic freestream, isentropy contours of both horseshoe and staircase forms are found. The limitations and validity of this inviscid rotational flow model are discussed by comparing the results with those for viscous turbulent flow calculated previously.
A consistent mass EBE algorithm for linear parabolic systems
Authors: Gladwell I. , Smith I. M. , Gilvary B. , Wong S. W.
Published: August 2005

To date, EBE algorithms for parabolic systems have assumed that the mass or capacity matrix may be lumped (diagonalized). An algorithm is presented in which this lumping process is not necessary. The practical implications of these alternatives are discussed.
Two‐level finite element method for plane cracks
Authors: Leung A. Y. T. , Wong S. C.
Published: August 2005

A new method to evaluate the stress intensity factors for plates of arbitary shape by conventional finite elements is introduced. The problems of the large number of unknowns and the round‐off errors associated with fine meshes are eliminated by means of global interpolation functions. These global interpolation functions are actually the analytical solutions of the displacement patterns near the crack tips. While the analytical solutions do not satisfy the boundary conditions in general, the present method considers the boundary conditions by master nodes. Very few unknowns can predict accurate results and no unconventional finite elements are required. The stress intensity factors can be calculated from the nodal displacements of the super‐element in one go. Plates with single and double notch edges and centre crack are taken as examples. The method can be generalized to other crack problems without difficulty.
A new boundary element method coupled with FEM packages
Authors: Gangming Luo
Published: August 2005

The asymmetry of the stiffness matrix in the boundary element method makes the coupling of the boundary and finite element methods difficult. In the paper, the author presents a new boundary element method model in which the stiffness matrix in the model is close to symmetry. After symmetrization, the stiffness matrix can be used as an ordinary finite element type element stiffness matrix to be assembled in the total stiffness matrix. Compared with the directly symmetrized model,1,2 the model in the paper has higher accuracy.
Finite element computations for second‐order hyperbolic equations with non‐smooth solutions
Authors: Bales L. A.
Published: August 2005

Computed discrete negative norm errors for the approximate solution of second‐order hyperbolic equations with non‐smooth solutions are presented. The numerical approximations are based on a finite element discretization in the space variable and a two‐step cosine method in the time variable. The approximate solution develops large oscillations when, for example, the solution has jump discontinuities. The error in some negative norms is small and this suggests that good accuracy may be obtained (where the solution is smooth) if smoothing operators are applied to the approximate solution. The results of applying several smoothing operators are presented.
The control of spurious modes in the 20‐noded solid isoparametric element
Authors: Kelen P.
Published: August 2005

The 20‐noded solid isoparametric element can be over‐stiff if a standard integration rule (such as 13, 3 × 3 × 3 or more Gauss points) is used to evaluate the stiffness matrix. Reduced integration (2 × 2 × 2 Gauss points) of the stiffness matrix often gives improved flexibility. Unfortunately, reduced integration can also predict spurious low‐energy modes in certain cases. A simple control method is suggested for the restraint of spurious modes which gives good results with the majority of practical meshes.
Convergence studies of least‐squares finite elements for first‐order systems
Authors: Carey G. F. , Shen Y.
Published: August 2005

A least‐squares finite element method for first‐order systems describing two‐point boundary‐value problems is constructed. Comparison studies are made with the corresponding mixed Galerkin formulation for the same system. Numerical experiments on representative test problems reveal that the least‐squares method has superior convergence behaviour to the mixed method. Some superconvergence properties of the least‐squares method are identified.
A finite element algebraic closure model for turbulent separated‐reattaching flows
Authors: Olson M. D. , Zhong Qin
Published: August 2005

The Baldwin‐Lomax algebraic turbulence model has been modified for two‐dimensional incompressible separated‐reattaching flows. The finite element method and the modified turbulence model are combined in a new program. The streamline upwind technique is adopted to eliminate solution oscillations due to coarse element grids. A new computational procedure is adopted to reach high Reynolds numbers efficiently. Preliminary results with experimental comparisons are presented for a turbulent blockage flow problem.
An algorithm for the computation of the Tustin bilinear transformation
Authors: Westreich D.
Published: August 2005

This note presents a simple algorithm for computing the Tustin bilinear transformation of a continuous transfer function.
A procedure for calcualting vorticity boundary conditions in the stream‐function–vorticity method
Authors: Mackinnon R. J. , Carey G. F. , Murray P.
Published: August 2005

A new superconvergent projection formula for determining vorticity boundary data in the stream‐function‐vorticity method is constructed.
The use of network theory in the finite‐element analysis of coupled thermo‐electric fields
Authors: de Alwis A. A. P. , Fryer P. J.
Published: August 2005

A possible alternative to the conventional way of modelling heat generation in the solution of coupled electric and thermal fields is presented. The numerical method presented uses a resistance network analogy and results in a 7% saving in computing time. An analytical formulation presented saves a further 4%. This will be important in the solution of large problems.
BEM for general anisotropic 2D elasticity using particular integrals
Authors: Deb A. , Banerjee P. K.
Published: August 2005

In the context of the direct boundary‐element method (DBEM) for most general two‐dimensional elastostatics, new particular integrals are presented in this paper to account for inertial and centrifugal body forces, as well as for those cases of three‐dimensional behaviour where the assumption of plane strain (or stress) may remain approximately valid despite the presence of non‐zero strain (or stress) in the out‐ofplane direction. These integrals have been implemented in a general‐purpose multi‐region boundary‐element code (namely, GPBEST) and tested via examples.
On fast determining eigenvalues in vibration
Authors: Zimoch R. Z.
Published: August 2005

A method for fast determining eigenvalues in real vibratory systems is demonstrated. The method applies to systems with distinct eigenvalues. Examples to illustrate the solution procedure are presented.
Sloshing in two‐dimensional container with inclined side walls—boundary‐element approach
Authors: Kamiya N. , Miyazawa H.
Published: August 2005

Non‐linear wave motion on the free water surface in a two‐dimensional container subjected to external periodical excitation is considered in this paper. In order to analyse the problem for arbitrary container geometries, a solution scheme using free surface Lagrangean particles is employed. Fluid motion is assumed to be governed by the Laplace equation in terms of the velocity potential with a non‐linear pressure equation on the surface. The boundary element method with explicit time marching is used by the fluid region boundary discretization alone at each time increment. Various containers with an inclined side wall are analysed for the horizontal sway motion and compared.
Finite‐element design sensitivity analysis for non‐linear potential problems
Authors: Mäkinen Raino
Published: August 2005

Design sensitivity analysis is performed for the finite‐element system arising from the discretization of non‐linear potential problems using isoparametric Lagrangian elements. The calculated sensitivity formulae are given in a simple matrix form. Applications to the design of electromagnets and airfoils are given.
A practical method for computing the exponential of a matrix and its integral
Authors: Westreich David
Published: August 2005

A practical algorithm is described for the computation of the transition matrix and its integral of a time‐invariant state‐space system. It is based on the partial Taylor expansion of the matrices, and methods for reducing computations and increasing accuracy are given.
Free vibrations of spatial rods — A finite‐element analysis
Authors: Karami G. , Farshad M. , Yazdchi M.
Published: August 2005

In this paper, a general finite‐element (FE) formulation has been developed for natural frequency analysis of spatial rod systems. Accordingly, the frequency analysis of spatially curved and pretwisted rods, with either constant or varying cross‐section on distributed elastic or point supports has been carried out. First, an appropriate finite‐element equation is developed utilizing the governing equations (equations of motion, kinematical relations and constitutive relations) of a spatial rod. The time‐dependent governing equations are then solved to find the modal shapes as well as the natural frequencies of the discretized system. The master element, developed herein, comprises 12 degrees of freedom (six at each end) and contains the rigid body motion as well as the deformation modes. This element has the generality of embodying the special cases of prismatic, curved and pretwisted elements, both with either linear or constant curvature changes. To verify the formulations several numerical examples are presented.
Axisymmetric potential flow calculations. Part 1: Analysis mode
Authors: Barron R. M. , Zhang S. , Chandna A. , Rudraiah N.
Published: August 2005

Using a natural body‐fitted co‐ordinate system, based on the streamlines, incompressible potential flow over an axisymmetric body at zero incidence is formulated as a Dirichlet boundary‐value problem for the unknown co‐ordinate r(x, ψ). Flow over various body shapes is computed using a finite‐difference scheme and SLOR, on both uniform and clustered grids. The results show excellent agreement with previous researchers. The coding is very simple, the formulation can be extended to compressible flows and can also be used to solve the inverse problem.
Imposing linear constraints in finite‐element analysis
Authors: Webb J. P.
Published: August 2005

It is often necessary to impose linear constraints on solutions obtained with the finite‐element method. This can be done by the penalty method or by eliminating dependent variables. The penalty method requires the careful selection of a penalty parameter and may lead to an inexact imposition of the constraints. Elimination is preferable because it is exact. The zero rows that elimination generates in the coefficient matrix can be removed by reducing the order of the matrix, or by adding back the constraints. The latter approach has the advantage of keeping the imposition of constraints separate from matrix assembly. However, straightforward addition of multi‐point constraint equations destroys the symmetry of the matrix. A new method of adding the constraints preserves matrix symmetry.
Moving and deforming finite‐element simulation of two‐dimensional Stefan problems
Authors: Zabaras Nicholas , Ruan Yimin
Published: August 2005

A new moving/deforming FEM analysis of two‐dimensional phase change problems is presented. The region occupied by the solid phase is divided into a non‐moving element region and a moving region consisting of the finite elements next to the freezing interface. A transfinite mapping method is used to generate new finite‐element meshes and motion in the liquid phase during simulations. Several two‐dimensional Stefan problems are analysed and discussed in relation to analytical solutions and other numerical techniques.
The zero‐normal‐stress condition in plane‐stress and shell elastoplasticity
Authors: De Borst Rene
Published: August 2005

The use of elastoplastic models in calculations of shell and plate structures, or more generally in stress situations in which one normal stress component is forced to be zero, usually leads to complicated algorithms. This leads to cumbersome programming, which in turn may easily entail errors in the code. Moreover, the fraction model for cyclic plasticity cannot be used within most algorithms since the normal stress perpendicular to the plane of the element is not necessarily zero for each of the fractions. In this contribution an algorithm will be presented that enforces a zero‐stress condition at integration point level, while obviating the need to develop special subroutines for plane‐stress or shell plasticity. The algorithm is based upon an implicit integration of the stress‐strain law and can be combined with the newly developed technique of consistent tangent operators.
The eccentricity issue in the design of plate and shell elements
Authors: Crisfield M. A.
Published: August 2005

The paper proposes that the criterion of ‘eccentricity invariance’ should be considered when designing plate and shell elements. It shows that many such elements do not satisfy this criterion.
A modified method of incompatible modes
Authors: Ibrahimbegovic Adnan , Wilson E. L.
Published: August 2005

The original method of incompatible modes proposed by Wilson et al. (1973) is modified such that a constant strain and hence convergence of the method is ensured. The proposed modification is valid for other forms of incompatible modes besides the original suggestion. The least‐squares stress recovery, introduced herein, provides high accuracy in stress computations.
An analysis of dead zones in the process of direct extrusion through single‐hole flat die
Authors: Slużalec Andrzej
Published: August 2005

An analysis of dead zones in the extrusion process is presented. Theoretical formulations of the metal forming process are recalled. Results of calculations show the distribution of metal velocity and relationships between angle of dead zone and friction coefficient, extrusior ratio and geometry of container. A comparison of finite‐element results with existing experiments is presented.
Internal force expansion method for stress reanalysis in structural optimization
Authors: Bofang Zhu
Published: August 2005

In the optimum design of large structures, the greater part of the computation time is consumed in stress reanalysis. The internal force expansion method is proposed to reduce the computation time; it is more efficient than the well‐known stress expansion method. Experience shows that only two iteration cycles are required when this method is applied in structural optimization.
On numerical solution of third‐order boundary‐value problems
Authors: Tirmizi Ikram A.
Published: August 2005

A fourth‐order method is developed for the approximation of the solution of certain two‐point boundary‐value problems involving third‐order linear and non‐linear differential equations. The method arises from a four‐point recurrence relation involving exponential terms, these being replaced by Padé approximants. The convergence of the method is discussed. The method is tested on two problems to demonstrate the practical usefulness of the approach.
Computing principal‐value integrals in 3‐D BEM for time‐harmonic elastodynamics – A direct approach
Authors: Guiggiani M.
Published: August 2005

Current methods to deal with Cauchy principal‐value (CPV) integrals in advanced boundary‐element implementations have been almost entirely based on indirect approaches (such as the rigid‐body motion in elastostatics). The present paper illustrates an alternative direct approach for the rigorous treatment and numerical evaluation of general CPV integrals in three‐dimensional problems. The method has general validity. It can be applied in any field of applied mechanics and with curved boundary elements of any order and type. As expected, the mesh pattern around the pole does not affect the numerical results.
On hypersonic flow over two‐dimensional aerofoils
Authors: Hemdan Hamdi T.
Published: August 2005

This paper considers the problem of hypersonic flow past two‐dimensional thin aerofoils with sharp leading edges and attached shock waves. The analysis relies on another recent formulation of the hypersonic small disturbance theory, HSDT. The equations are reduced to a complicated functional‐differential equation for which an iterative numerical scheme is employed. In each iteration both the functional and differential parts of the functional‐differential equation are eliminated, thus reducing it to an algebraic equation. The iterative scheme is found to be stable and rapidly convergent, and the results obtained for the surface pressure and shock wave compare well with other exact and approximate methods.
Vibration analysis of coil springs by means of isoparametric curved beam finite elements
Authors: Stander Nielen , Du Preez R. J.
Published: August 2005

An investigation is conducted on the performance of the curved isoparametric cubic beam element for analysing vibrational behaviour of coil springs. Firstly, the results of full and uniformly reduced integration are compared for three static problems. Uniformly reduced integration is shown to yield surprising accuracy, even for curved and pretwisted beams. In the latter case of a shear loaded cantilever beam, exact internal force values are obtained. Since element geometry is described by nodal co‐ordinates and cross‐sectional orientation only, the element proves to be ideal for modelling both helical and non‐helical sections of coil springs. In addition, the formulation is easy to implement and simpler than those of previous ‘helical spring elements’. It is shown that accurate values for modal frequencies can be obtained with relatively coarse meshes.
A boundary integral formulation for natural convection flows
Authors: Ramesh P. S. , Lean M. H.
Published: August 2005

A novel solver for natural convection flows based on the boundary integral equation method is presented here. The solver can be used to obtain flow solutions in arbitrary 2–D geometries with modest computational effort. Both the vorticity and thermal transport equations are treated as modified Helmholtz equations and solved using boundary integral methods. The non‐linear inertial terms partially manifest themselves as volume sources which are computed iteratively using a method of characteristics approach. The buoyancy term is treated as a volume vorticity source. Rapid computation of the volume fields at each iteration level is achieved by precomputing the influence coefficient matrices. Results are presented for flow in a cavity driven by both shear and buoyancy.
Multi‐order initialization of CG solution of FE discretizations
Authors: Fried I. , Budinsky N.
Published: August 2005

The conjugate gradient method holds great appeal for the solution of the stiffness equation set up with finite elements. Inexpensive, low‐order finite‐element discretization solutions are suggested as initial guesses for higher‐order, more accurate, discretizations.
Average strain quadrilateral elements
Authors: Stolle D. F. E.
Published: August 2005

This paper describes an approach for implementing quadrilateral finite elements which uses B matrices of average strain when assembling element stiffness matrices. The approach avoids isoparametric transformations, thereby making stiffness matrix assembly and stress calculations more efficient. An example is presented which compares the proposed approach and those based on Gauss quadrature integration.
Second‐order, numerical methods for the solution of equations in population modelling
Authors: Wang Yigong , Twizell E. H. , Price W. G.
Published: August 2005

A second‐order explicit method is developed for the numerical solution of the Ricatti (logistic) initial‐value problem u′ ≡ du/dt = αu(1 ‐ u), t > 0, u(0) = U0, in which α ≠ 0 is a real parameter. The method is based on two first‐order methods which appeared in an earlier paper by the authors (Twizell et al.1). In addition to being chaos‐free and of higher order, the novel method is seen to converge to the correct, stable, steady‐state solution for any value of the parameter α, provided the denominator of the method does not vanish. Convergence is monotonic or oscillatory depending on the magnitude of the product αl, where l is the parameter in the discretization of the independent variable t. This dependence of the type of convergence on αl is likened to the behaviour of the well known Crank–Nicolson method for solving the simple heat equation. Conversion of the numerical method to a reliable, empirical model for predicting the limited growth of successive generations of a population is given. When extended to the numerical solution of Fisher's equation, in which the quadratic polynomial αu(1 – u) appears as the reaction term, the numerical solution is found by solving a linear algebraic system at each time step, as opposed to solving a non‐linear system, which often happens when solving non‐linear partial differential equations.
Stochastic boundary‐element method for reliability of structural strength
Authors: Weidong Wen , Deping Gao
Published: August 2005

The stochastic boundary‐element method (SBEM) is developed in this paper for the reliability analysis of a structural component. The integral equations of BEM are derived partially by a random variable, and the integral equations of SBEM are established. Considering the applied loads and the limitation of material strength to be a Gauss distribution, the numerical results of two examples are given for the problems of stochastic stress‐strain and reliability. The results show good agreement with those obtained from Monte Carlo simulation and theoretical solutions.
Vibration of annular sector plates using spline strip method
Authors: Mizusawa Tomisaku , Kajita Tateo
Published: August 2005

This paper presents the vibrations of annular sectorial plates with two opposite radial edges simply supported using the spline strip method. To demonstrate the convergence and accuracy of the present method, several examples are solved, and results are compared with those obtained by the analytical method and by other numerical methods. Stable convergence and excellent accuracy are obtained using the high‐order spline strip models. Accurate frequencies of annular sector plates with different sector angles, radii ratios and tapered thickness in the angular direction are shown in tabular form.
A consistent finite‐element formulation of non‐linear elastic cables
Authors: Ibrahimbegović Adnan
Published: August 2005

A finite‐element approach for computing cable structure fully non‐linear response is presented in this work. Both the problems of statics and of dynamics are considered. The formulation encompasses arbitrary large strains and displacements. A very general constitutive equation for non‐linear elastic cables can be posed by an adequate choice for the strain energy function. In this work we consider two model problems, posed by St. Venant's and Ogden's material models. The proposed formulation is set in a fixed reference frame which yields a very efficient finite‐element implementation. The additional advantage of setting the formulation in a fixed reference frame is a bilinear form of the kinetic energy and a simplified solution procedure for dynamic equilibrium equations. Consistent linearization is used at each step of the Newton algorithm to obtain the tangent operators, which provide the quadratic rate of the solution convergence. This is demonstrated in the numerical examples presented herein.
A comparison of FAC and PCG methods for solving composite grid problems
Authors: Heroux Michael A. , Thomas J. W.
Published: August 2005

The fast adaptive composite grid method (FAC) is a multi‐level adaptive method for the discretization and solution of partial differential equations. This paper compares the speed of solution of the resulting discrete equations by the FAC algorithm and a preconditioned conjugate gradient scheme. Comparisons and information concerning the solutions are given for several model problems.
Multigrid solution of the advection–diffusion equation with variable coefficients
Authors: Marx Yves P.
Published: August 2005

A multigrid method for the solution of the linear multi‐dimensional advection–diffusion equation with variable coefficients is presented. The method efficiently combines odd–even relaxations with semi‐coarsening. Theoretical and computational convergence rates are given for a large range of advection–diffusion coefficients to demonstrate the efficiency of the method. The construction of the coarse‐grid operator is also discussed in detail since it may have a strong influence on the convergence of the multigrid process when the direction of convection changes.
A multigrid algorithm for mixed finite‐element problems
Authors: Rubart Lothar
Published: August 2005

The analysis of steady incompressible flow is based on the equation of motion and the continuity constraint together with appropriate boundary conditions. Besides the inertia term, also the extra stress term becomes non‐linear in the case of generalized Newtonian fluids. By application of mixed finite‐element methods the conservation equations are reduced to a system of non‐linear algebraic equations. At each step of a Newton‐Raphson scheme a linear subproblem with a non‐symmetric and indefinite coefficient matrix has to be solved. A multigrid method for these systems is presented, where the smoothing iteration is a modification of Uzawa's algorithm based on an augmented Lagrangian functional. The method is applied to the numerical simulation of vortex breakdown in a cylindrical vessel, where the computations are performed for real shear‐thinning fluids. Dimensionless groups, a Reynolds number and a non‐Newtonian parameter are introduced, and the dependence of the convergence rate on these parameters is discussed.