bluuebunny/crossref_metadata_2025 huggingface dataset:
Evaluation of ‘specia’ finite elements with non‐conventional Gaussian quadratures
Authors: Bernhard Robert J. , Holger David K.
Published: August 2005

Finite elements with ‘Special’ basis functions have been proposed to develop better approximations for problems where the behaviour is known to be non‐polynomial. This paper discusses extension of Gaussian quadrature integration procedures of non‐conventional form to the evaluation of the finite element matrices for ‘Special’ elements. Algorithms for general ‘Special’ elements are discussed. The techniques are applied to ‘Special’ one‐ and two‐dimensional elements for spherically symmetric potential flow. The accuracy of the new ‘Special’ element is shown to be superior to linear and quadratic elements for spherically symmetric potential flow problems.
A numerical study of various algorithms related to the preconditioned conjugate gradient method
Authors: Jackson C. P. , Robinson P. C.
Published: August 2005

We present the results of a numerical study of the preconditioned conjugate gradient algorithm, the minimal residual algorithm, the biconjugate gradient algorithm and the bi‐minimal residual algorithm using both simple test matrices and more realistic test matrices derived from physical problems. The application of the methods to unsymmetric matrices is considered. We emphasize the importance of a good preconditioning, look at various methods including ICGG(n) and incomplete block factorization, and make some practical recommendations. Some of the folk‐lore surrounding the semi‐iterative methods is dispelled.
A unified set of single step algorithms part 3: The beta‐m method, a generalization of the Newmark scheme
Authors: Katona Michael C. , Zienkiewicz O. C.
Published: August 2005

Introduced herein is a generalization of Newmark's time marching integration scheme, called the β‐m method. Like the SSpj method (introduced in Parts 1 and 2 of this series), the β‐m method provides a gcneral single‐step scheme applicable to any set of initial value problems. The method is specialized by specifying the method order m along with rn integration parameters, β0, β1, …, βm−1. For a particular choice of m, the integration parameters provide a subfamily of methods which control accuracy and stability, as well as offering options for explicit or implicit algorithms. For the most part, attention is focused on the application to structural dynamic equations. Most well‐known methods (e.g. Newmark, Wilson, Houbolt, etc.) are shown to be special cases within the β‐m family. Hence, one computationally efficient and surprisingly simple algorithm unifies old and new methods. Stability and accuracy analyses are presented for method orders m = 2, 3 and 4 to determine optimal parameters for implicit and explicit schemes, along with numerical verification.
Necessary convergence conditions for upwind schemes in the two‐dimensional case
Authors: Roos H. ‐G.
Published: August 2005

This paper considers nine‐point difference schemes for a two‐dimensional boundary value singular perturbation problem without turning points and parabolic boundary layers. Necessary conditions are given for the uniform convergence (in the sense of the maximum norm) of a scheme. Using these conditions, several widely used schemes are analysed. It is shown that some common schemes are not uniformly convergent in ϵ. and that in some cases we are able to compute uniquely free parameters in the scheme. Some remarks on the treatment of a problem with a parabolic boundary layer are given.
Finite element method for in‐plane vibrations of rotating Timoshenko rings and sectors
Authors: Singh Kultar , Singh Bhupinder Pal
Published: August 2005

A simple and logical finite element formulation is presented for the analysis of rings and sectors, with Timoshenko effects. The elemental properties are derived from the governing differential equation of motion using the Galerkin method. A quintic polynomial, satisfying the compatibility of derivatives up to second order, has been used for the ring finite element. The interpolating function is the same as for a thin ring. The efficiency of the formulation has been illustrated by the numerical results presented.
An application of global approximations in the finite element method
Authors: Allen E. J.
Published: August 2005

A technique is described in which global approximations are used to improve the accuracy of the finite element method. The technique is theoretically based on two corollaries to the Lax–Milgram lemma which are presented in this paper. Basically, the technique consists of factoring the unknown function for which an approximation is desired into the product of a global approximation and a second unknown function. Finite element methods are appropriately applied to obtain an approximation to the second unknown function. The approximation to the original function then consists of the product of the specified global approximation and the approximation to the second unknown function. The advantage that finite element methods possess with respect to obtaining banded matrices is preserved in this technique. In addition, numerical examples indicate that the technique's accuracy is as much as a factor of fifty better than the accuracy obtained by directly applying a finite element method to approximate the original function.
Economical symmetrical quadrature rules for complete polynomials over a square domain
Authors: Dunavant D. A.
Published: August 2005

It is of interest in numerical analysis to develop symmetrical quadrature rules for integration of complete polynomial functions over a square domain with minimum computational effort. Gaussian product quadrature rules integrate such functions with maximum effort. Symmetrical quadrature rules are developed and presented for integration of complete polynomial functions up to 21st order with minimum computational effort.
Vibration analysis of rotating turbomachinery blades by an improved finite difference method
Authors: Subrahmanyam K. B. , Kaza K. R. V.
Published: August 2005

The problem of calculating the natural frequencies and mode shapes of rotating blades is solved by an improved finite difference procedure based on second‐order central differences. Lead‐lag, flapping and coupled bending–torsional vibration cases of untwisted blades are considered. Results obtained by using the present improved theory have been observed to be close lower bound solutions. The convergence has been found to be rapid in comparison with the classical first‐order finite difference method. While the computational space and time required by the present approach is observed to be almost the same as that required by the first‐order theory for a given mesh size, accuracies of practical interest can be obtained by using the improved finite difference procedure with a relatively smaller matrix size, in contrast to the classical finite difference procedure which requires either a larger matrix or an extrapolation procedure for improvement in accuracy.
On the effect of quarter‐point element size on fracture criteria
Authors: Yehia Nabil A. B. , Shephard Mark S.
Published: August 2005

The effect of the quarter‐point element size on the solution parameters of fracture criteria is investigated in view of its effect on the computed stress intensity factors. An analytical relationship between the error in calculating crack propagation increment and stress intensity for single mode problems is obtained while, for mixed mode problems, the investigation is based on numerical experimentation. The singular element size is found to have a substantial effect on both crack propagation angle and increment for the geometries considered.
Material modelling for accurate stresses in involute composites
Authors: Stanton Edward L.
Published: August 2005

Material modelling requirements for accurate stress fields in a nonuniform anisotropic composite are established for all six components of stress at a material point. The gauge section from a conical involute structure tested in an earlier investigation provides the case data for this modelling study. Stress results from a tricubic Hermite finite element model are shown to be in agreement with another computational analysis by Pagano using a Reissner energy formulation. Comparisons are made in the interior and at a corner with high interlaminar stress gradients. The small, but critical, matrix dominated stress components are shown to be very sensitive to modelling material orientation changes within each finite element. Uniform stress accuracy was obtained using distribution functions for material orientation of the same degree as the displacement functions, an isoparametric material geometry model.
Collocation time finite element procedures for integration of strongly nonlinear initial value problems
Authors: Kujawski Jerzy
Published: August 2005

By use of a collocation time finite element formulation a modification of the well‐known generalized midpoint method is derived. The new family possesses an additional free parameter. This allows for significant improvement of the numerical solution in strongly nonlinear situations. Numerical results show the accuracy of the proposed algorithm in comparison to the midpoint method.
The hybrid‐Trefftz finite element model and its application to plate bending
Authors: Jirouseka J. , Guex Lan
Published: August 2005

This paper presents a new hybrid element approach and applies it to plate bending. In contrast to more conventional models, the formulation is based on displacement fields which fulfil a priori the non‐homogeneous Lagrange equation (Trefftz method). The interelement continuity is enforced by using a stationary principle together with an independent interelement displacement. The final unknowns are the nodal displacements and the elements may be implemented without any difficulty in finite element libraries of standard finite element programs. The formulation only calls for integration along the element boundaries which enables arbitrary polygonal or even curve‐sided elements to be generated. Where relevant, known local solutions in the vicinity of a singularity or stress concentration may be used as an optional expansion basis to obtain, for example, particular singular corner elements, elements presenting circular holes, etc. Thus a high degree of accuracy may be achieved without a troublesome mesh refinement. Another important advantage of the formulation is the possibility of generating by a single element subroutine a large number of various elements (triangles, quadrilaterals, etc.), presenting an increasing degree of accuracy. The paper summarizes the results of numerical studies and shows the excellent accuracy and efficiency of the new elements. The conclusions present some ideas concerning the adaptive version of the new elements, extension to nonlinear problems and some other developments.
Effectiveness of linear bifurcation analysis for predicting the nonlinear stability limits of structures
Authors: Chang S.‐C. , Chen J.‐J.
Published: August 2005

As an effort to predict effectively the actual collapse load of a structure, a series of numerical studies on the stability of shell structures are made. The difference in formulation between the two types of linear buckling loads, the classical and the fully linearized, is first demonstrated. Their correlations with respect to the actual stability limit of the structure are compared, and finally the two types of critical load approximations are obtained at various stages of a nonlinear analysis to study the pattern of convergence to the actual collapse load. It is found that the fully linearized buckling analysis, when combined with nonlinear analysis, can serve as a useful tool for prediction of the stability limit of a structure. While for most types of structures the approximation is within engineering accuracy, the rate of convergence of the extrapolated critical load also gives some insight to the accuracy of the approximation.
DEM: A new computational approach to sheet metal forming problems
Authors: Cavendish James C. , Wenner Michael L. , Burkhardt John , Hall Charles A. , Rheinboldt Werner C.
Published: August 2005

Many current approaches to finite element modelling of large deformation elastic—plastic forming problems use a rate form of the virtual work (equilibrium) equations, and a finite element representation of the displacement components. Called the incremental method, this approach produces a three‐field formulation in which displacements, stresses and effective strain are dependent variables. Next, the formulation is converted to a one‐field displacement formulation by an algebraic time discretization which uses a low order explicit time‐stepping procedure to integrate the equations. This approach does not produce approximations which satisfy the discrete equilibrium equations at all times and, moreover, the advantage of the single‐field algebraic formulation is realized at the expense of very small time steps needed to produce stability and accuracy in the numerical calculations.

This paper describes a variant of the mixed method in which all three field variables (displacements, stresses and effective strain) are given finite element representations. The discrete equilibrium equations then generate a nonlinear system of algebraic equations whose solutions represent a manifold, while the constitutive equations form a system of ordinary differential equations. A commercially available, variable time step/variable order code is then used to integrate this differential/algebraic system. When applied to the problem of hydrostatic bulging of a membrane, the new approach requires far less computer time than the incremental method.
Control of zero‐energy modes in 9‐node plane element
Authors: Verhegghe Benedict , Powell Graham H.
Published: August 2005

For plane stress/plane strain analysis, the 9‐node quadrilateral element performs better than the corresponding 8‐node element, especially for non‐rectangular shapes. For improved element flexibility and lower computer cost, 2 × 2 quadrature is generally preferable to 3 × 3 quadrature. Unfortunately the 9‐node element contains spurious zero‐energy modes when under‐integrated. A method is proposed to restrain these modes without significant loss of accuracy or added cost.
Predicted axial temperature gradient in a viscoplastic uniaxial bar due to thermomechanical coupling
Authors: Allen D. H.
Published: August 2005

The thermomechanical response of a uniaxial bar with thermoviscoplastic constitution is predicted herein using the finite element method. After a brief review of the governing field equations, variational principles are constructed for the one‐dimensional conservation of momentum and energy equations. These equations are coupled in that the temperature field affects the displacements and vice versa. Due to the differing physical nature of the temperature and displacements, first‐order and second‐order elements are utilized for these variables, respectively. The resulting semi‐discretized equations are then discretized in time using finite differencing. This is accomplished by Euler's method, which is utilized due to the stiff nature of the constitutive equations. The model is utilized in conjunction with stress‐strain relations developed by Bodner and Partom to predict the axial temperature field in a bar subjected to cyclic mechanical end displacements and temperature boundary conditions. It is found that spacial and time variation of the temperature field is significantly affected by the boundary conditions. The nomenclature used is given in an Appendix.
Computer evaluation of singular integrals and their applications
Authors: Fabrikant V. I.
Published: August 2005

An algorithm and a standard subroutine are developed for the evaluation of singular integrals over arbitrary two‐dimensional domains. The integrand is a product of a Green's function with another function having a weak singularity at the boundary of the domain. Formulae are derived for an accurate estimation of the integral in the neighbourhood of the singularities. The integral over the rest of the domain is evaluated by a library subroutine. The software developed is applied to a study of some contact problems of the theory of elasticity for non‐classical domains.
Numerical solution of constrained non‐linear algebraic equations
Authors: Shacham Mordechai
Published: August 2005

The numerical solution of n non‐linear algebraic equations with n unknowns, when any or all of the variables are subjected to constraints, is discussed. Distinction is made between physical and absolute constraints. It is shown, using a set of test problems, that solution of constrained equations does require a special approach. It is found that the step length restricted Newton's method performs best for problems with absolute constraints. Physical constraints can be best handled using a continuation method or penalty functions.
Improved co‐ordinate transformations for finite elements: The Lagrange cubic case
Authors: Celia Michael A. , Gray William G.
Published: August 2005

A modified isoparametric co‐ordinate transformation is developed for the case of Lagrange cubic finite elements. This modified transformation produces significant improvements in solution accuracy while eliminating troublesome aspects of the standard isoparametric mapping. In particular, zero Jacobians in the standard transformation, which can occur in elements having non‐uniform node spacing, are completely eliminated with the new transformation. Within the analysis, the range of node locations for which the standard transformation is valid (the Jacobian does not vanish) is determined. The treatment of curved sides is discussed and illustrated. Example calculations using two‐dimensional serendipity elements show that the new transformation provides solutions that are as much as several orders of magnitude more accurate than those computed using the standard formulation.
A weak variational formulation for the propagation of Love waves
Authors: Serón F. J. , Badal J.
Published: August 2005

This paper describes the fundamental principles of the mathematical method used by the authors in discussing the direct geophysical problem of analysing the behaviour of the Atlantic continental margin of the Iberian Peninsula as a transmission medium of seismic energy.

In order to resolve this problem, a weak variational formulation is proposed, building up an approximate solution by means of a semidiscrete treatment with the finite element method.

The excitation of that non‐subductive ocean‐continent transition zone is supposed to be caused by Love waves normally incident at the continental boundary. The physical and geometrical parameters describing the model are obtained using as a starting point the experimental data known for this zone.

The work shows the main results that we have obtained, the geophysical interpretation of which can be seen in Reference 1. Finally we proposed a large variety of open problems to which analogous techniques can be applied, owing to the extended validity of the proposed method.
Surfaces of minimum area by FEM
Authors: Pramila A. , Virtanen S.
Published: August 2005

In many practical applications it is desired to describe a surface enclosing a given volume which has to possess a minimum area. Moreover, there are engineering criteria, e.g. the requirement of minimum resistance, which cannot be involved in the present interpolation algorithms of the existing CAD systems. The present paper describes an approach where the surface creation task is formulated as a constrained minimization problem. The pointwise specified co‐ordinates are used as boundary conditions. The volume enclosed is a constraint, and the functional under minimization is the surface area. Thus, as the viscous resistance is roughly proportional to the area of the wetted surface, the result approximates the form having minimum viscous resistance. The finite element method is employed and the elements used are C1 continuous isoparametric elements to be able to represent infinite slopes. In the light of applications studied thus far it can be said that the method converges and is thus capable of creating surfaces of minimum area enclosing a given volume.
Minimum weight design of cylindrical water tanks
Authors: Thevendran V. , Thambiratnam David P.
Published: August 2005

The paper deals with the minimum weight design of cylindrical water tanks. The design is to conform to BS5337. The design procedure used is a combination of the finite element analysis of structures and a numerical method of optimization. In the design, the internal radius and the height of the tank are fixed and the variation of wall thickness is treated as the unknown of the design. Only piecewise linear variations of thickness are considered. Results of some examples are presented and discussed.
A new mode renumbering algorithm for bandwidth reduction
Authors: Burgess I. W. , Lai P. K. F.
Published: August 2005

A new algorithm is presented for automatic renumbering of systems of interconnected nodes so as to minimize the bandwidth of the connectivity matrix. This is necessary to reduce storage requirements for banded matrix solution techniques. The method is based on those due to Cuthill and McKee1 and Gibbs, Poole and Stockmeyer.2 Under test against several other algorithms on a range of 20 examples of various types it always performed at least as well as, and in most cases better than, the best of the other methods. Seven examples are given in the paper, comparing final bandwidths with those produced by seven other algorithms.
Vibration and buckling of beam‐columns subjected to non‐uniform axial loads
Authors: Coulter Brett A. , Miller Robert E.
Published: August 2005

The small‐displacement free vibration of elastic Euler‐Bernoulli beams subjected to non‐uniform axial forces and the buckling of elastic columns are both analysed by means of various types of beam finite elements. The procedure incorporates beams and columns of varying cross‐sections, such as linear tapers, inhomogeneous beams and columns, distributed axial forces, elastic end and interior restraints and point masses with linear and rotary inertias. All of these topics individually or in some combinations have been analysed by others. The purpose of this paper is to bring together under a single umbrella the various problems studied by others, and to provide the solution to one problem apparently not yet solved—the buckling and vibration of tapered columns under non‐uniform axial thrust. The mass, stiffness and geometric stiffness matrices for the standard beam element are fully written out for direct incorporation into existing finite element programs. A FORTRAN subroutine for generating these matrices, and those for various higher‐order beam elements, is also provided.
An efficient finite‐difference scheme for multidimensional Stefan problems
Authors: Wood A. S.
Published: August 2005

In this paper the enthalpy approach for solving Stefan problems is applied to a three‐dimensional situation. A novel and particularly efficient finite‐difference scheme is then used to solve the resulting equations. As a starting solution for the numerical algorithm, a three‐dimensional result using the heat‐balance integral method is obtained for the case of heat flow in two phases with, possibly, different thermal properties.
Using elastic—plastic plane stress FEM programs to compute anti‐plane strain
Authors: Ståhle P.
Published: August 2005

Elastic—plastic anti‐plane strain problems can be solved by using FEM programs developed for plane stress. The technique does not involve any manipulations with the FEM code, but is merely a matter of specialization and of translation of notation. Two analytically solvable cases are chosen for demonstration.
The patch test for mixed formulations
Authors: Zienkiewicz O. C. , Qu S. , Taylor R. L. , Nakazawa S.
Published: August 2005

This paper presents a simple extension of the patch test to mixed formulations to provide the necessary and sufficient conditions for convergence. The general algebraic conditions of Babuska and Brezzi are given a simple form and a conceptual application of the patch tests serves to point out the instability of several well known formulations for incompressible problems. The test is also applied to mixed displacement—strain formulations of elasticity, and limiting formulations are noted.
Hybrid element method for unbounded electromagnetic problems in hyperthermia
Authors: Lynch Daniel R. , Paulsen Keith D. , Strohbehn John W.
Published: August 2005

Finite element and boundary element methods are described for predicting high‐frequency electromagnetic heating of tissue as a cancer therapy. For the class of clinical problems of interest, the patient is electrically inhomogeneous and best discretized by finite elements, but the unbounded nature of practical source configurations calls for a boundary element approach. A hybrid is introduced which couples the two methods and is superior in algebraic requirements to either method alone. The formulation is three‐dimensional and allows exact satisfaction of the electromagnetic jump conditions at interfaces separating distinct tissue types. Test cases show its validity for transverse magnetic and electric situations with known solutions. Examples of clinical applications are shown.
Derivation of Lagrangian and Hermitian shape functions for quadrilateral elements
Authors: El‐Zafrany A. , Cookson R. A.
Published: August 2005

This paper introduces a general theory for the derivation of the shape functions for the quadrilateral family of finite elements. The first section deals with the Lagrangian shape functions for the cases of uniform and boundary‐described elements. Two basic procedures are introduced; the first by linear combinations of side‐interpolations and the second by superposition. The remainder of the paper introduces a theory for the general uniform Hermitian element of any order. Details for quadrilateral elements, with first order derivatives are explained. All of the shape functions presented here were derived in the interval [0,1].

The shape functions, developed by such an engineering approach, have been used successfully in the ABSEA Finite Element System of Cranfield Institute of Technology.
A mechanical dynamic programming algorithm for structure optimization
Authors: Schnack Eckart , Spörl Uwe
Published: August 2005

Structure optimization for problems of solid mechanics is gaining in importance. Of special interest to the ship and aeroplane designer is optimizing changes in sections and hols in such a way that the largest value of the von Mises stress becomes as small as possible, to optimize the use of material. Also, the temporal beginning of crack propagation should be delayed as long as possible. A dynamic programming formulation for structure optimization is presented and mechanical theorems fix an iterative solution process.
Triangular and tetrahedral space‐time finite elements in vibration analysis
Authors: Bajer Czesław I.
Published: August 2005

Recently, several methods of time integration of the equations of motion have been proposed. Many of them result in square mass, damping and stiffness matrices. The space–time finite element method is an extension of the FEM, familiar to most engineers, over the time domain. A special approach enables the use of triangular, tetrahedral and hyper‐tetrahedral elements in time and space. By special division of the space–time layer the triangular matrix of coefficients in the system of equations can be obtained. A simple algorithm enables the storage of non‐zero coefficients only. Dynamic solution requires a small amount of the memory compared to other methods, and ensures considerable reduction of arithmetic operations. The method presented is also efficient in solving both linear and non‐linear problems. Matrices for a beam and plane stress/strain element are derived. Exemplary problems solved by the method described have proved the effectiveness of the application of triangular and tetrahedral space–time elements in vibration analysis.
Numerical shakedown analysis of axisymmetric sandwich shells: An upper bound formulation
Authors: Morelle Patrick
Published: August 2005

Shakedown analysis of axisymmetric elastic–perfectly plastic sandwich shells is performed here using a new upper bound formulation based on a special form of Koiter's theorem concerning piecewise linearized yield surfaces. Starting from finite element techniques and the Tresca sandwich yield condition, shakedown analysis is reduced to a linear programming problem which is solved by a powerful simplex algorithm. Numerical results are given for a number of examples and a comparison is made with a previously computed lower bound formulation.
Elastic‐plastic state of torispherical heads
Authors: Varga L. , Gara P. , Kollar Gy.
Published: August 2005

The value of the permissible pressure in torispherical heads is usually judged from the size of the permanent deformations after the first load cycle. The difficulty always lies in the determination of the maximum permanent strain caused by the pressure, as the strain depends on the changes of the elastic‐plastic state. The elastic‐plastic state of the heads can be, for example, found and well followed by the finite element method. Values obtained in this way are naturally valid only for the case examined. However, by extending the numerical investigations and by appropriately processing and evaluating the results certain regularities and generalizations can be recognized. On this basis certain approximations can be made, leading to a very simple and reliable calculation process.
Application of transmission‐line modelling (TLM) to thermal diffusion in bodies of complex geometry
Authors: Pulko S. , Mallik A. , Johns P. B.
Published: August 2005

The use of the TLM method for modelling thermal diffusion in bodies of complex geometries is described. Both regular and irregular orthogonal meshes are used. Results are compared with those obtained using finite element analysis.
Optimum load time history for non‐linear analysis using dynamic relaxation
Authors: Řeřicha Petr
Published: August 2005

A modification of the dynamic relaxation method is proposed which facilitates static analysis of non‐linear problems. Continuous loading in time is adopted instead of the ordinary step function of time. Inertia and damping forces arising during the loading process are kept at a minimum using an optimum load time history. This results from the stationary condition of an appropriate functional. The equation of motion is included as a subsidiary condition. Continuous load—deflection curves can be obtained. An incremental solution is avoided. Application of the method is extremely simple. Existing programs based on explicit time integration schemes can be easily adapted for it. Sample solutions are presented.
A turbulence model for buoyant and combusting flows
Authors: Spalding D. Brian
Published: August 2005

It is argued that ‘sifting’ phenomena, in which fragments of fluid subjected to larger body forces move through those subjected to smaller body forces, are prevalent in turbulent flows, and that they can be simulated by means of mathematical methods which have been developed for two‐phase flows.

A connection with Prandtl's mixing‐length theory is established; and it is deduced from the success of that theory for shear flows that there must exist a source term in the normal‐to‐wall‐velocity equations which is proportional to the gradient of along‐the‐wall velocity. This term is then included in the two‐fluid‐model equations.

Solutions of the equations are presented for a turbulent Couette flow in which the heating of one of the walls and the presence of a gravitational field can cause ‘sifting’ phenomena to become dominant. The friction and heat‐transfer coefficients, and the profiles of velocity and temperature, are computed and discussed, for flows both with and without buoyancy influences.
Three‐dimensional transient thermo‐elastic analyses by the BIE method
Authors: Chaudouet A.
Published: August 2005

The proposed method is the direct boundary integral equation (BIE) method applied to three‐dimensional transient heat transfer analyses and to corresponding elastostatic analyses under thermal loading. The mechanical and thermal problems are decoupled. For those not familiar with the BIE method, a short survey of the basic principles is given to help them understand the mathematical treatment, which is performed in the frame of distribution theory. The tempered elementary solution of the transient heat transfer problem contains time and space variables. The numerical treatment of the thermal equation is performed analytically with respect to time and numerically with respect to space in the same way as for steady state equations. Great care is paid to space integration in order to compute the values of the kernels precisely enough on the surface and inside the volume. The computational treatments of both problems are realized in such a way as to minimize computing time. Differences between transient and steady state analyses, on the one hand, and between elastostatic analyses with and without thermal loading, on the other, are emphasized. Finally, an analytical example shows the good behaviour of the proposed method to solve singular thermal problems and an industrial example shows the accuracy of the results obtained by using the BIE method to solve three‐dimensional thermo‐elastic problems.
An unstructured multigrid method for elliptic problems
Authors: Löhner R. , Morgan K.
Published: August 2005

A multigrid algorithm for implementation on unstructured meshes is proposed. The algorithm uses a sequence of unnested grids and requires the development of efficient inter‐grid interpolation procedures. It is demonstrated how elliptic problems can be solved in this fashion by using Jacobi smoothers.
A finite element method for free and forced convection heat transfer
Authors: Schnipke Rita J. , Rice James G.
Published: August 2005

A new finite element method is presented. This new method contains several novel features including a streamline upwind formulation for the advection terms and equal order interpolations for all variables: velocities, pressure, temperature and other fluid properties. This new formulation uses an iterative solution method greatly reducing the computer storage requirements. The validity of the new finite element method was tested on both a natural convection problem, a thermally driven cavity, and a forced convection problem, a heated cylinder in cross‐flow. The predicted results compared favourably with a benchmark solution for the cavity and an empirical correlation for the cylinder in cross‐flow.
Numerical models for the thermo‐mechanical evolution of Atlantic‐type continental margins
Authors: Cloetingh S. A. P. L. , Wisse G.
Published: August 2005

We have developed a versatile finite element approach to analyse stresses and displacements induced in thermally thinned and thickened geological structures. Material and geometric non‐linearities form an important aspect of the finite element simulation. The changes in geometry are incorporated by a multipoint constraint procedure. The method takes into account temperature‐dependent variations in rheological properties of the medium, including the presence of a brittle–ductile transition. We illustrate the application of the method for specific geophysical problems associated with the temperature history of the earth's crust at continental margins of the Atlantic type.
Pulverized coal conversion in downflow gasifier
Authors: Phuoc T. X. , Durbetaki P.
Published: August 2005

The behaviour of coal particles undergoing pyrolysis in a downflow reactor is modelled in two dimensions using integral approximation. The governing equations are solved numerically by marching procedures using Adams–Moulton and Romberg integration methods. The conversion of coal particles is studied in terms of chemical kinetics, hydrodynamic flow of volatiles and the heat transfer mechanism at the interface. The conversion increases with decreasing velocity, solid loading, particle diameter and total pressure. Owing to large amounts of gas production, the influence of pyrolysis on the gas‐particle heat transfer and drag coefficients becomes important at large particle diameters. For particle diameters less than 100 μm, such influence is minimal.
Numerical simulation in precision castings
Authors: Hamar R.
Published: August 2005

Microporosities often appear during the solidification of foundry pieces. They result from the volume contraction of the alloy during its solidification. Thermal transfers between alloy and mould check the solidification. They are estimated by a finite volume method, including specific calculation of the mould filling‐up, the alloy solidification and the resulting feeding of the mould.

The calculation uses a geometrical enmeshment of the whole mould, generating numerous elements of different sizes. From the experimental fluid flow measurement, the mould filling‐up may be described step by step by the computer, as can the initial thermal transfer. Thermal transfers are related to the solidification enthalpic release obtained from quantitative differential thermal analysis. They are also related to the fluid flow induced by solidification shrinkage.

Such a calculation leads to the location of the microporosities, from which pressure drops can be estimated during solidification.
Mixing and solidification of a turbulent liquid jet in a co‐flowing stream
Authors: Enright P. G. , Katgerman L. , Ludwig J. C. , Rogers S.
Published: August 2005

A mathematical model has been developed to quantify the effects of process conditions during turbulent solidification and mixing of a liquid metal jet in a confined co‐flowing molten metal stream.

The modelling has been split into three parts. First, a single phase model with no latent heat effects to consider the solidification potential. Secondly, a two phase model where the second phase is comprised of solid particles which solidify during mixing of the two streams. Thirdly, a two phase model where the second phase consists of the inner jet, which is assumed to break up into droplets of given size, and solid particles are allowed to form by solidification within the droplets.

The results show that the thermal history (solidification path) of the solid phase formed is affected by latent heat and particle size, which implies that solidification, nucleation and jet fragmentation events should be included dynamically to ensure realistic predictions.
On the extrusion of visco‐elastic fluids subject to viscous heating
Authors: Milthorpe J. F. , Tanner R. I.
Published: August 2005

The die‐swell occurring during the extrusion of a visco‐elastic fluid has been extensively examined in recent years, both experimentally and numerically. These investigations have been mainly confined to isothermal flows. If the material is initially relatively cool, however, viscous heating may lead to proportionally large changes in temperature and material properties, with significant effects on die‐swell. An iterative computational model is presented which describes the flow of Maxwell and Oldroyed fluids subject to the effect of temperature gradients induced by viscous heating and thermal boundary conditions. Predictions are presented for extrusion from both slit and axisymmetric dies.
The method of moving asymptotes—a new method for structural optimization
Authors: Svanberg Krister
Published: August 2005

A new method for non‐linear programming in general and structural optimization in particular is presented. In each step of the iterative process, a strictly convex approximating subproblem is generated and solved. The generation of these subproblems is controlled by so called ‘moving asymptotes’, which may both stabilize and speed up the convergence of the general process.
Treatment of material discontinuities in finite element computations
Authors: Mackinnon R. J. , Carey G. F.
Published: August 2005

We consider finite element analysis of problems with discontinuous material coefficients. For applications in which the material interface crosses an element, we develop special elements with an embedded flux constraint at the interface. This new procedure is compared with the standard finite element method with interface coincident with the element boundary and with an existing method proposed by Steven.1 Supporting numerical studies are conducted and rates of convergence for the solution and interface flux are examined. Some local superconvergence behaviour is observed.
Finite element solution of three‐dimensional incompressible fluid flow problems by a preconditioned conjugate residual method
Authors: Robichaud Michel P. , Tanguy Philippe A.
Published: August 2005

A new algorithm for the solution of the three‐dimensional Navier–Stokes equation using the mixed formulation and an incomplete factorization technique is presented. The linear system obtained at each modified Newton–Raphson iteration is solved by the preconditioned conjugate residual method (PCR) using an out‐of‐core incomplete LU factorization as preconditioning. This factorization is performed on a matrix stored by a new static storage method called the packed skyline method. The performance of the proposed algorithm is assessed for the wall‐driven cubic cavity problem using the Q −P1 enriched element.
Numerical tests for assessing finite element model convergence
Authors: Verma A. , Melosh R. J.
Published: August 2005

New requirements for finite element model convergence are defined. It is shown that the presence of constant strain states in an element is not sufficient to guarantee convergence.

Numerical tests are proposed to assess convergence, direction of convergence, monotonicity of convergence, convergence rate and monotonicity of convergence rate. The proposed tests are mathematically stronger and more general than existing tests.
Trefftz method: Fitting boundary conditions
Authors: Zieliński A. P. , Herrera I.
Published: August 2005

The paper presents various ways of fitting the boundary conditions in the T‐complete functions method. The authors point out the distinct advantages of the orthogonal collocation in comparison to the equidistant collocation and the integral fit. The convergence of the Collatz error measures and the conditioning of the solution matrices are investigated in detail.
The uniqueness characteristics of mixed finite element methods in linear elasticity
Authors: Boot J. C.
Published: August 2005

Having established the non‐uniqueness, in general, of quadratic–linear functionals in elasticity, the investigative work on this topic is reviewed, whence it is noted that there is no existing formal approach for the identification of either the causes of singular solutions or suitable remedial measures that might ensure their elimination. A comparison of the weighted averages obtained from the single field and Reissner's principles is then used to identify a higher order uniqueness criterion for the latter. A detailed consideration of the application of the new condition to the arch equations demonstrates how and why singular solutions can be obtained, and thence how suitable forms of remedial action can often be identified. Finally, several other classes of problem are briefly investigated in order to show how the criterion can be used to explain the full range of known behaviour of the mixed methods.
A self‐adaptive co‐ordinate transformation for efficient numerical evaluation of general boundary element integrals
Authors: Telles J. C. F.
Published: August 2005

Almost all general purpose boundary element computer packages include a curved geometry modelling capability. Thus, numerical quadrature schemes play an important role in the efficiency of programming the technique. The present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two‐dimensional, axisymmetric and three‐dimensional applications. Emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of Gaussian quadrature scheme's within the near‐singularity range. The procedure can easily be implemented into existing BE codes and presents the important feature of being self‐adaptive, i.e. it produces a variable lumping of the Gauss stations toward the singularity, depending on the minimum distance from the source point to the element. The self‐adaptiveness of the scheme also makes it inactive when not useful (large source distances) which makes it very safe for general usage.
A hybrid BEM model
Authors: Schnack E.
Published: August 2005

The hybrid stress method is very successful for stress concentration problems.1–7 Especially for problems of fracture mechanics, procedures can be found that work efficiently for two‐ and three‐dimensional problems. The rate of convergence with this method, evidently, is higher than that with conventional FE models. The BEM procedure, too, works more efficiently, but shows some essential disadvantages against the FEM, such as that for the direct method no symmetric positive definite matrix can be found and that there occur numerical problems at corners.8,9 This happens also when BEM and FEM are even coupled commonly.10–12. In the following, a hybrid BEM model will be described which combines the advantages of both the FEM and the BEM. It will be shown in this paper that BEM is very successful in formulating finite element functions for the hybrid assumed stress method.
A numerical method for dynamic analysis of a general cross‐section rod under combined loads
Authors: Nagaya Kosuke , Goto Tetsuro , Sasaki Toyonori , Ikai Shigeo
Published: August 2005

This paper is concerned with a method for obtaining stresses in a rod of arbitrary cross‐section subjected to combined loads of bending, shearing and torsion which are the complicated functions of time. In the first step, the analysis derives the bending moment, shearing force and torsional moment by use of a combination method of the Laplace transformation and Fourier series expansion. The transient stresses are obtained based on the two‐dimensional theory of elasticity, but in which the Fourier expansion collocation procedure is applied to deal with the complex boundary shape of the cross‐section. To affirm the validity of this analysis, experimental tests are also carried out for an oval rod subjected to the three combined transient loads.
Norm methods and partial weighting in multicriterion optimization of structures
Authors: Koski Juhani , Silvennoinen Risto
Published: August 2005

Methods for generating Pareto optimal solutions to a multicriterion optimization problem are considered. The norm methods based on the scalarization of the original multicriterion problem by using the l‐norm are discussed in a unified form and a parametrization suitable for different interactive design systems is suggested. In addition, an alternative approach which, instead of scalarization, reduces the dimension of the multicriterion problem is proposed. This is called the partial weighting method and it can beinterpreted as a generalization of the traditional scalarization technique where the weighted sum of the criteria is used as the objective function. The first of these two approaches (norm method) is very flexible from a designer's point of view and it can be applied also in non‐convex cases to the determination of the Pareto optimal set whereas the latter (partial weighting method) is especially suitable for problems where the number of criteria is large. Throughout the article several illustrative truss examples are presented to augment the scanty collection of multicriterion problems treated in the literature of optimum structural design.