bluuebunny/crossref_metadata_2025 huggingface dataset:
A second order finite element method for the one‐dimensional Stefan problem
Authors: Bonnerot R. , Jamet P.
Published: August 2005

We describe a finite element method for the one‐dimensional Stefan problem. The elements are quadrilaterals of the space‐time plane which are determined at each time‐step in relation with the position of the free boundary. The method appears as a generalization of the classical Crank‐Nicolson scheme, since it is identical to this scheme in the case of rectangular elements; it has the advantage of providing a simple and accurate determination of the free boundary. Numerical experiments show that the order of accuracy is equal to 2.
A few remarks on the paper: ‘Parameters of Gamma and Beta distribution’
Authors: Phillips D. T. , Beightler C. S. , Éliás E. J.
Published: August 2005

The paper shows a procedure for estimating the shape parameter of a Gamma distribution from a sample. This procedure uses a rapidly converging iteration to solve the maximum‐likelihood equation and suggests a simple formula for determing the starting value.
A general quadrilateral plate element
Authors: Torbe I. , Church K.
Published: August 2005

The stiffness matrix and consistent nodal load vector for a general quadrilateral plate element are developed for both in‐plane and bending analysis. The basis chosen for the development is the hybrid stress method because

it has been shown to produce results of relatively high accuracy.

it employs only primary nodes and

all integration required in the derivations can be achieved in closed form.

Various numerical examples, relating to both plane stress and bending conditions, are considered in order to establish the validity and generality of the derivations.
Spectral analysis using Fourier Transform techniques
Authors: Resch Francois J. , Abel Rudolf
Published: August 2005

The present study is intended as a guide for those who wish to undertake spectral analyses using Discrete Fast Fourier Transforms. Points of particular difficulty in using Fourier Transforms are derived in some detail. Experimental results are offered to illustrate the mathematical derivations. Finally the case of a signal with discontinuities along the time‐axis is discussed.
Higher order finite element methods for the solution of compressible porous bearing problems
Authors: Rohde S. M. , Oh K. P.
Published: August 2005

Finite element methods are used to solve hydrodynamic lubrication problems involving compressible lubricants and porous bearing solids. The particular calculation scheme permits solution at high compressibility numbers (Λ > 100) to be obtained without any numerical difficulty. Finite element and finite difference results for the porous, gas lubricated journal bearing are presented and compared.
A note on numerical computation of elastic contact problems
Authors: Francavilla A. , Zienkiewicz O. C.
Published: August 2005

A simple procedure of obtaining flexibility matrices in terms of contact pressures at possible contact points of two bodies allows the frictionless contact pressures to be solved as a quasi‐linear problem. Iteration is limited in general to very few cycles and, as small matrices are handled, can be very economical.

Excellent accuracy of this procedure is demonstrated.
Average and complete incompressibility in the finite element method
Authors: Thompson Erik G.
Published: August 2005

The constraint of incompressibility is incorporated into the finite element method for plane strain through the use of a Lagrange multiplier. Depending on the approximating function chosen for this multiplier, the constraint condition can be satisfied everywhere within the element or only in an average sense for the entire element. A study of these two approaches from the point of view of rate of convergence and computer time is presented.
A finite element solution program for large structures
Authors: Cheung Y. K. , Khatua T. P.
Published: August 2005

A straightforward and general computer program for assembling and solving (using Gauss elimination technique) widely sparsed finite element matrix equations with very large bandwidth and capable of handling different degrees‐of‐freedom and variable bandwidth at different nodes, is described herein. The program assembles any type of finite elements having arbitrary number of nodes and each node may have differnt degrees‐of‐freedom. It requires only a small core memory in the computer, although a fast random access device is also needed. The two very important features of this program are (i) it does not store any zero submatrices within the band and (ii) during the solution of equations all operations dealing with zero submatrices within the band are automatically skipped and thus the savings of a considerable amount of disc storage space and computer time can be effected in many cases. Another feature is that many right hand sides can be handled simultaneously. Hence the program is very economical for structures having widely sparsed matrix equations. A listing of the computer program written in FORTRAN IV for CDC 6400 computer is readily available from the authors, but unfortunately could not be given here because of lack of space. The program is so general that it can be used to solve a wide class of finite element problems without actually having to understand fully the techniques behind it.
Calculation of stress intensity factors in three dimensions by finite element methods
Authors: Blackburn W. S. , Hellen T. K.
Published: August 2005

Finite element methods are used to calculate the stress intensity factors for three‐dimensional geometries containing a number of depths of crack subjected to various loads. Special elements are used at the tip to represent the variation of the displacement with respect to the square root of the distance from the tip. The stress intensity factors are determined by comparison of the displacements in the special elements, by a method of virtual crack extensions, and, in one case, by an integral around the tip. With meshes containing between 50 and 100 quadratic isoparametric elements, results accurate to within 1 per cent or 4 per cent (depending on case) of known solutions are demonstrated.
Calculation of vibration frequencies by a hybrid element method based on a generalized complementary energy principle
Authors: Brandt Klaus
Published: August 2005

Based on a generalized complementary energy principle the derivation of the element matrices is presented for calculation of natural frequencies. The degrees‐of‐freedom are not defined on nodal points but in an abstract way. No restrictions about the number of interpolation functions in the interior and at the boundaries of the element have been introduced. The exact solution of the discretized element equations leads to the dynamic stiffness matrix while the approximate solution results in a linear eigenvalue problem. Plate bending problems are used to study the convergence of frequencies depending on the degrees of interpolation functions within the element and on its boundaries and on the number of elements.
Finite element solutions of the non‐self‐adjoint convective‐dispersion equation
Authors: Prakash Anand
Published: August 2005

Finite element formulations based on the Galerkin and variational principles have been developed for the self‐adjoint and non‐self‐adjoint problems represented respectively by the flow and convective‐dispersion equations in the cylindrical polar system of co‐ordinates. The formulation based on the variational principle is shown to be restricted to dispersion‐dominant transports only. The Galerkin method is demonstrated to be more versatile and free from convergence and stability problems. The computational scheme based on the Galerkin principle is shown to be equally valid for both convection and dispersion dominant transports. The numerical results obtained are verified with known analytical solutions. It is concluded that the suggested scheme can be used in solving a variety of field problems involving groundwater dispersion.
Cold sheet rolling, the thermoviscoelastic problem, a numerical solution
Authors: Batra R. C.
Published: August 2005

The coupled system of equations governing the thermomechanical deformations of a viscoelastic sheet while it is being cold rolled is solved numerically. The pertinent energy equation is solved by the finite difference method and the mechanical problem is solved by the finite element method using uniform first order rectangular elements. The developed computer program enables one to compute the complete deformation and temperature fields in the sheet. Results presented graphically include the temperature distribution, the stress distribution at the middle surface, the contact pressure distribution and the asymmetric surface deformation of the sheet.
A strategy for the solution of problems involving large deflections, plasticity and creep
Authors: Bushnell David
Published: August 2005

A strategy for solving problems involving simultaneously occurring large deflections, elastic‐plastic material behaviour, and primary creep is described. The incremental procedure involves a double iteration loop at each load level or time. In the inner loop the material properties are held constant and the non‐linear equilibrium equations are solved by the Newton–Raphson method. These equations are formulated in terms of the tangent stiffness. In the outer loop the plastic and creep strains are determined and the tangent stiffness properties are updated with use of a subincremental algorithm. The magnitude of each time subincrement is determined such that the change in effective stress is less than a preset percentage of the effective stress. The strategy is implemented in a computer program, BOSOR 5, for the analysis of shells of revolution. Examples are given of elastic‐plastic deformations of a centrally loaded flat plate and elastic‐plastic‐creep deformations of a beam in bending. The major benefits of the subincremental technique are the increased reliability with which problems involving non‐linear plastic and time‐dependent material behaviour can be solved and the greatly relaxed requirement on the number of load or time increments needed for satisfactory results.
First Cesaro sums for high order finite elements near singularities
Authors: Rossow M. P. , Mehta A. K. , Petruska G.
Published: August 2005

High order finite elements often exhibit an oscillatory behaviour near stress singularities which appears similar to the Gibbs phenomenon in the theory of Fourier series. It is known that under certain conditions the average of successive partial sums (the first Cesaro sum) of a Fourier series exhibiting the Gibbs phenomenon will converge monotonically to the function being approximated. An analogous device introduced for high order finite element approximations near a stress singularity successfully smooths the oscillations of the computed stress.
On an eigensystem routine due to K. K. Gupta
Authors: Whiston G. S.
Published: August 2005

An eigensystem subroutine ‘EASI’ due to K. K. Gupta is critically discussed. Some faults are pointed out and remedial measures which have been adopted in practice are presented. The result is a consistently reliable convergent algorithm which has solved narrow bandwidth problems of order up to 1000 × 1000.
A classification and survey of numerical methods for boundary value problems in ordinary differential equations
Authors: Aktas Z. , Stetter H. J.
Published: August 2005

The objective of the paper is a survey and classification of available numerical methods for boundary value problems with an emphasis on two point boundary value problems. In the paper a general two point boundary value problem is stated first and later available numerical methods are classified into five main groups according to their approach in numerical solution. In the next sections of the paper, each of these main groups are described and appropriate subgroups are defined and discussed.
Numerical integration on a triangle
Authors: Hillion Pierre
Published: August 2005

Approximations, with any arbitrary degree, of integrals on a triangle are obtained as a product (different from Stroud's conical product formulas) of one‐dimensional Gauss–Jacobi formulas.
On the elastic plastic initial‐boundary value problem and its numerical integration
Authors: Son Nguyen Quoc
Published: August 2005

An interative approach is proposed for the numerical analysis of elastic–plastic continua. This approach gives after convergence an implicit scheme of integration of the evolution problem, and is concerned with elastic‐perfectly plastic materials and with hardening standard materials. Under a generalized assumption of positive hardening, the proof of convergence of the iterative solutions is given. Some numerical examples by the finite element method are also discussed.
Finite element post‐buckling analysis for frames
Authors: Care R. F. , Lawther R. E. , Kabaila A. P.
Published: August 2005

Presented in this paper is a direct method of analysis of the elastic non‐linear behaviour of frames. Emphasis is given to the method's capability of tracing the post‐buckling path from a bifurcation point although the method can also trace the non‐linear behaviour of frames with eccentricities. The method is proposed as an alternative to the main methods currently in use, the perturbation method and the incremental method. Conditions for equilibrium and stability are developed from a variational approach to the total potential. A finite element approximation is made and an efficient solution technique for the resulting non‐linear equations is developed.

Results for three frames are given demonstrating good agreement with solutions generated from other approaches.
Creep analysis of reinforced and prestressed concrete structures under non‐uniform temperature distributions, using elastic solutions
Authors: Jordaan I. J. , Khalifa M. M. A.
Published: August 2005

The analysis of stresses and deformations in concrete structures subjected to temperature gradients is described. As a result of the spatial variation of temperature, the creep compliance is a function of position. Previous work has shown that the constitutive equations for concrete creep can be expressed in a form which is invariable although ageing is included in the analysis. Thus viscoelastic methods can be used and correspondence principles can be developed; emphasis is placed in the present work on those which are based on the Laplace transform. A particular form is described, in which replacement of the elastic modulus by a function of the transformed creep compliance gives transformed values of stress; these values are easily obtained numerically by the finite element method using elastic analyses. The transformed values of stress are then expressed as approximate functions of the transformed creep compliance; inversion of the ensuing functions gives the stress as an approximate function of time. Two applications are given; the first considers a simple axially loaded column with reinforcement and the second deals with a thick cylinder subjected to a temperature gradient.
Analysis of active ladder network by using coates flow graphs and continuants
Authors: Cichocki Andrzej , Osowski Stanislaw
Published: August 2005

A simple method for solving the matrix equation describing the general active ladder network, is presented. Using Coates flow graphs and continuants the expressions for current, voltage, and also example of application are given.
Security assessment of gas networks
Authors: Li P. M. , Hindi K. S. , Brameller A.
Published: August 2005

A measure of the severity of a pipeline failure is the minimum reduction in load in the network necessary to ensure that no node falls below its minimum pressure. The expected loss of sales is calculated as the product of the minimum reduction in load and the expected duration of the period during which the pipeline will be in the inoperable state, and thus reflects both the severity and the frequency of the failure. Consequently, this index, whose evaluation involves network theory, optimization and probability theory, serves as a measure of the insecurity of the gas network.

The security index can be evaluated for all points within a system, providing a basis of comparison between the relative vulnerability of different parts. The relative level of security of different design proposals can also be assessed using this index.
Compact computation of natural frequencies and buckling loads for plane frames
Authors: Williams F. W. , Howson W. P.
Published: August 2005

Existing theory is assembled to give a method which needs only the core of a mini‐computer to calculate the eigenvalues of large rigidly jointed plane frames with certainty, the eigenvalues being natural frequencies and critical load factors in free vibration and buckling problems, respectively. The method is illustrated by annotated listings of vibration and buckling programs, each involving under two hundred Fortran statements and with low number storage requirements (see Table I). The use of the programs as ‘black boxes’ is fully explained, with illustrative examples.

The member theory used is the ‘exact’ classical Bernoulli‐Euler uniform member theory. Possible applications include: evaluation of answers from approximate methods; calculation of critical loads for substitution in the modified Merchant‐Rankine formula to estimate collapse loads of frames; and calculation of shifts in natural frequencies caused by structural damage, in connection with structural integrity monitoring of inaccessible structures.
Superposition method of finite element and analytical solutions for transient creep analysis
Authors: Yagawa G. , Miyazaki N. , Ando Y.
Published: August 2005

Based on the Lagrange multiplier's concept, a superposition method of analytical and finite element solutions has been developed to solve efficiently various non‐linear and/or time‐dependent problems in structural mechanics. According to the theory, the transient creep behaviour of a cantilever beam is analysed as an expository example.
A finite element convergence study for accelerating flow problems
Authors: Gartling D. K. , Nickell R. E. , Tanner R. I.
Published: August 2005

The convergence properties of several non‐linear solution procedures were examined with respect to the accelerated flow of a fluid in a converging channel (the Hamel problem), using two different finite element computer programs with different elemental construction. The Reynolds number varied from that for creeping flow to 1088 without exceeding the radius of convergence. Special attention was given to the successive substitution and Newton–Raphson solution algorithms, with a significant advantage in rate of convergence noted for the latter.
Nodal grafting for crack propagation studies
Authors: Ingraffea A. R.
Published: August 2005

A simple, efficient method for propagating cracks through a finite element mesh is presented: nodes, borrowed from other points in the mesh, are ‘grafted’ along the advancing crack front. The method requires neither an increase in bandwidth nor a mesh regeneration. It can be easily implemented in any existing program using iso(sub)parametric elements of at least quadratic order.
Computational efficiency of non‐linear programming methods on a class of structural problems
Authors: Carpenter W. C. , Smith E. A.
Published: August 2005

Results are presented of an investigation as to the computational efficiency of several non‐linear programming algorithms on the constrained structural weight optimization of plane trusses and plane stress plates. The optimization algorithms considered are the methods of sequential linear programming, of feasible directions based on Zoutendijk's procedure P1, and of sequential unconstrained minimizations using the methods of Powell, Stewart, Fletcher–Powell, and Newton. Results are presented on computational efficiency as a function of number of design parameters and as a function of the function evaluation effort to derivative evaluation effort ratio.
Temperature load on thick curved shell elements
Authors: Wergeland J. H.
Published: August 2005

Temperature load on a shell is usually represented as initial strains in the tangent plane directions of the shell, since strains in shell surface normal directions are neglected. It is shown, however, that this simplification may give rise to significant errors for thick curved shell elements. A procedure to overcome this problem is presented. In particular the eight‐node subparametric thick shell element is considered.
An implicit‐iterative solution of the heat conduction equation with a radiation boundary condition
Authors: Williams S. D. , Curry Donald M.
Published: August 2005

In predicting temperatures with an implicit finite difference method there is a tendency for the surface temperature to oscillate if a non‐linear radiation boundary condition is imposed. An iterative method is described which eliminates these oscillations in temperature prediction.

Several examples are given that allow a comparison with other implicit methods. These examples are for cases which are typical of those that arise in practical applications. The results demonstrate that the method is remarkable in its ability to predict surface conditions without the debilitation of other methods in regard to step size control, along with the ease of incorporating it into the solution routine.
A cost comparison of two static condensation‐stress recovery algorithms
Authors: Cook Robert D. , Shah Vikram N.
Published: August 2005

We consider finite elements that have internal degrees‐of‐freedom. These d.o.f. are condensed before elements are assembled into the structure, and must be recovered later for use in element stress computation. References 1 and 2 describe two different ways to do the calculations. This paper compares the computational costs of the two methods. Test runs were made to assess costs. Relative costs depend on several factors. The factors are discussed, and suggestions are made as to the better method in various circumstances.
Solution of non‐linear differential equations by discrete least squares
Authors: Eason E. D. , Mote C. D.
Published: August 2005

A general‐purpose technique has been developed for solving non‐linear partial differential equations. A set of approximating functions with undetermined parameters is used to evaluate the differential equation and boundary conditions at discrete points, forming a set of residuals to be minimized. The parameters which minimize the sum of squared residuals are determined by a non‐linear least‐squares minimization technique. Initial value problems are solved by integrating the equations with respect to time at the fitting points by a predictor‐corrector algorithm. The resulting formulation is independent of the form of the problem and the approximating functions, so that a broad class of problems may be solved with a single computer program. The technique is applied to several boundary and initial value problems in one and two spatial dimensions. The tecnique is applied to several boundary and initial value problems in one and two spatial dimensions.
An integral method for computing the inductance and the a.c. resistance of parallel conductors
Authors: Deeley E. M. , Okon E. E.
Published: August 2005

In a previous paper1 a method was described for computing the current distribution and inductance of systems of infinitely‐long, perfectly‐conducting, straight conductors. The method relied on the solution of a Fredholm Integal equation of the first kind, and in the present paper the method is extended to equations of the second kind in order to study the inductance and a.c. resistance factor of resistive for which approximate formulas and experimental results exist, with which the method is in good agreement over a range of grequencies of particular practical practical interest. Results have also been obtained for rectangular conductors connected in parallel.
Adaptive step size selection for use with the continuation method
Authors: Schmidt William F.
Published: August 2005

An adaptive procedure for selecting the step size when incremental or continuation methods are used to solve sets of non‐linear equations is presented. The increment size is limited by requiring the corrective iteration procedure employed to reduce the drifting error to be within a contractive boundary at each level. The usefulness of the procedure is extended by the development of a set of conditions for detecting impending divergence of the corrective iteration process. These conditions, used in conjunction with the step size selection procedure permit the continuation of the solution through highly non‐linear regions and also provide a simple means of isolating a limit point, if one exists. Two additional benefits of the procedure are an effective convergence criterion for terminating the iteration process and a simple means for switching between the Newton‐Rephson and modified Newton‐Raphson iteration procedures. The paper concludes with a number of example problems, three are hyperelastic bodies at finite strain and the final example is the large displacement analysis of an elastic beam. The results illustrate that the procedure is computationally inexpensive, using only information normally obtained in a non‐linear analysis, flexible in the sense that a dense or sparse distribution of points along the total solution curve may be obtained, and effective, normally requiring less total computational effort than a constant step size procedure.
Analysis of explicit difference methods for a diffusion‐convection equation
Authors: Siemieniuch J. L. , Gladwell I.
Published: August 2005

We consider the numerical solution of a model one‐dimensional diffusion‐convection equation by a variety of explicit finite difference methods including conventional central and upwind replacements of the convection terms. We discuss commonly observed phenomena such as instability, unwanted oscillations in the numerical solution, and numerical diffusion and we present an analysis of these effects by simple mathematical techniques.
Convective difference schemes and Hermite interpolation
Authors: Fischer Karsten
Published: August 2005

A new method for numerically solving the convection equation is presented. The reduction of numerical errors is achieved by introducing an auxiliary variable and solving an auxiliary equation for the latter. The method is based on a Hermite interpolation of the convected quantity. Three explicit numerical versions of the method are investigated and compared with some of the most widely used schemes, and it is shown that the new method gives better physical results. Arguments are given that the usual mathematical series expansions do not work sufficiently well in that context. Instead of using linear stability analyses the quality of the method is investigated by numerical experiments.
Specification of skew conditions in finite element formulation
Authors: Mangalgiri P. D. , Dattaguru B. , Ramamurthy T. S.
Published: August 2005

Fields exhibiting skew symmetry occur frequently in structural problems. There are many situations where non‐skew‐symmetric functions are conveniently used to analyse these skew fields. Specification of force and displacement conditions on the skew axis reduces the analysis to a half of the domain. The difficulty in using such conditions in an FEM analysis is their non‐explicit nature. A method of overcoming this difficulty is developed using concept of generalized forces and displacements.
A comparison of Galerkin, collocation and the method of lines for partial differential equations
Authors: Hopkins T. R. , Wait R.
Published: August 2005

A number of numerical methods for parabolic paritial differential equations are discussed, they all reduce a single partial differential equation to a system of ordinary differential equations by discretization in the space variable(s). The discretizations can be finite element approximations (Galerkin and collocation) or finite difference approximations (methods of lines). The performances of the different methods are compared when used in conjunction with a variable time‐step ordinary differential equation integrator. Tables of results are given and the suitability of the discretizations is discussecd.
A quintic conforming plate bending triangle
Authors: Caramanlian C. , Selby K. A. , Will G. T.
Published: August 2005

A new family of conforming triangular plate bending elements, based on the Displacement Method of formulation, is developed in detail in Reference 9. The elements can be of any order n−4, and do not present excess nodal continuties at the corner nodes. For a given element, the assumed vertical displacement w consists of a polynomial expansion supplemented by three rational function. Polynomial completeness is of order n for even n, and of order n‐1 for odd values of n. This family is proposed as a desirable alternative to refined triangular elements which incorporate all three curvatures as corner node variables,8 or require constraint equations to enforce inter‐element compatibility,10 The purpose of this paper is to describe the quintic member of the family. The traditional difficulties associated with the discontinuous curvatures of the rational functions are solved in a straightforward fashion. The element has the same good accuracy as the other, well‐known, quintic triangle, 3,4,8 and some additional advantages accruning from the simplicity of its nodal variables. A similar performance can be anticipated with the other members of the family.
Improved finite difference formulas for boundary value problems
Authors: Gawain T. H. , Ball R. E.
Published: August 2005

This paper deals with the numerical solution of linear differential equations of fourth order by finite differences. It points out significant (but usually overlooked) errors which result from the conventional method of imposing the boundary conditions in such problems. Revised finite difference formulas are derived which apply near the boundaries and which eliminate the above errors. Three commonly encountered boundary conditions ar econsidered. These correspond, in the terminology of beam analysis, to a clamped end, to a simply supported end and to a free end. The improvement in accuracy that can be achieved with the revised formulas is illustrated by two representative examples. The revised formulas are shown to reduce the overall error of the numerical solution by a factor of about five in a typical case.
An improved algrorithm for heat conduction problems with phase change
Authors: Morgan K. , Lewis R. W. , Zienkiewicz O. C.
Published: August 2005

The algorithm in a earlier paper by Comini et al1 for handling the phase change in transient non‐linear heat conduction problems is simplified and improved. Two examples involving phase change are solved using quadratic isoparametric elements and it is demonstrated that very good accuracy may be achieved.
Sensitivity Of matrix eigenvalues
Authors: Davis George J. , Moler Cleve B.
Published: August 2005

A recent paper by Donald Gignac describes some difficulties with a certain matrix eigenvalue problem. This paper shows that the difficulties result from the naturue of the matrix itself. Quantities called condition numbers, which measure the sensitivity of the eigenvalues, are computed, and numerical results given.
Finite element methods for an optimal steady‐state control problem
Authors: Meric R. A.
Published: August 2005

An optimal steady‐state control problem governed by an elliptic state equation is solved by several finite element methods. Finite element discretizations are applied to different variational formulations of the problem yielding accurate numerical results as compared with the given analytical solution. It is sated that, for minimum computational effort and high accuracy, ‘mixed’ finite elements requiring only C° continuity, and approximating the control and state functions simultaneously are better suited to similar ‘fourth order’ problems.
Finite‐difference solution of an elliptic partial differential equation with discontinuous coefficients
Authors: Chmielewski G. E. , Hoffman G. H.
Published: August 2005

An algoritm is presented for point relaxation of an elliptic partial diferential equation at a grid station where its coefficient are discontinuous. Such equations can arise from the use of skewed co‐ordinate system based on discotinuous reference functions (lengths) to map a complicated physical geometry onto a simple computational domain. Efficary of the scheme is illustrated by examples involving potential flow in a sharply bent channel and in a conical diffuser.
Block iterative finite element preprocessed scheme for simulation of large non‐linear problems
Authors: Voss Clifford I. , Pinder George F.
Published: August 2005

The ‘Block Iterative Finite Element Preprocessed Scheme’ (BIFEPS) for finite element simulation combines two independent steps. In the ‘finite element preporcessing step’, spatial information about the finite element mesh is analysed and all integrals arising from the application of the Galerkin method are evaluated and stored on a permanent sequential storage unit (such as tape or disk). In the ‘block iterative step’, the preprocessed information is retrieved from permanent storage and the matrix equation is assembled and solved in an efficient manner according to a generalization of the block successive over‐relaxation iterative method. Significant advantages over common finite element simulation techniques are achieved in terms of both computer core requirements and execution time. Numerical experiments show that the advantages of BIFEPS are greatest for large, non‐linear simulation problems.
An analysis of a cubic isoparametric transformation
Authors: Woodford G. , Mitchell A. R. , McLeod R.
Published: August 2005

The general nine point isoparametric transformation is analysed with respect to a triangle with two straight sides and one curved side. Point placements are determined on the curved side which ensure that the Jacobian of the transformation remains positive inside and on the boundary of the triangle. Special cases of the transformation are considered which lead to implied curves of the form of symmetric cubics, parabolas, and explicit cubics respectively, thus enabling isoparametric transformations to match a variety of boundary shapes.
A stable finite element simulation of convective transport
Authors: Ben‐Sabar Ehud , Caswell Bruce
Published: August 2005

A finite element simulation of the equations of momentum and energy transport in fluids has been implemented with triangular elements. An attempt is made to single out the reasons for numerical instabilities reported by other investigators for convection–diffusion transport operations in fluid mechanics when the ratio of the convective to the diffusive terms, measured by the Reynolds and Peclét numbers, is of the order of a hundred. To this end, the equations are solved for several problems to permit a direct comparison with results of other formulations. It is shown that the appearance of instability can be delayed by a proper choice of boundary conditions, and its intensity can be reduced through the use of triangular finite elements. Results agree very well with theoretical solutions for particular test problems including flows with large convection effects, large dissipation effects and fluids with temperature dependent properties.
A variable thickness, curved beam and shell stiffening element with shear deformations
Authors: Ferguson G. H. , Clark R. D.
Published: August 2005

A family of 2‐D and 3‐D superparametric curved beam elements are introduced as a special form of general 2‐D and 3‐D isoparametric continuum elements. Each beam ‘subelement’ is rectangular incross section, however several elements may be offset and overlayed for the analysis of structural members of quite general section properties. A number of examples are presented in order to illustrate the validity and range of application of the element.
Stability analysis of explicit finite difference schemes for the Navier–Stokes equations
Authors: Rigal Alain
Published: August 2005

The stability analysis of the hyperbolic and parabolic explicit difference schemes presented in our previous paper 1 is improved on. Analysis of the Fourier components gives rise to stability limits that are very near the actual numerical stability limits.
Displacement oscillation in plane quadratic isoparametric elements in orthotropic situations
Authors: Holt J. S. , Hope P. S.
Published: August 2005

Long thin test specimens of orthotropic material are modelledby quadratic isoparametric finite elements in plane strain. Displacement oscillations occur down the long free edge of themodel with both reduced (2 × 2) and full (3 × 3) integration, themagnitude of the oscillations being affected by element aspectratio and the elastic constants of the material. The rate ofdiffusion of stress as predicted by the classical shear‐lag theory, being dependent on the material constants, is reflectedin the displacement oscillations near the load in 3 × 3integration. In 2 × 2 integration, however, this effect is swampedby the build‐up of oscillations away from the restraints in alowenergy deformation mode which becomes dominant as the elementaspect ration is increased. These latter voscillations arepredicted by the illconditioning of the structural stiffnessmatrix measured by a solution diagonal decay factor.
An explicit numerical method for solving transient combined heat conduction and convection problems
Authors: Gane C. R. , Stephenson P. L.
Published: August 2005

This paper describes an explicit numerical method for solving transient combined heat conduction and convection problems. Applications include the cooling of many types of engineering plant; for example, stator and rotor windings of turbogenerators and high voltage underground cables. The Du Fort–Frankel and the fully implicit finite difference schemes have been used to solve the conduction and convection equations, respectively. It is shown that, with a suitable order of calculation, the overall method becomes explicit. Computational procedures are outlined and stability, accuracy and convergence are considered. Numerical examples are given to illustrate the use of the method and to validate some of the theoretical points. Results have also been obtained using existing numerical methods and have been compared with those from the proposed method. For certain problems, it is shown that the proposed method uses less overall computing time than other methods such as that devised by Crank and Nicolson.
Stability of parallel flows by the finite element method
Authors: Saraph V. R. , Rao B. Vasudeva , Panikar J. T.
Published: August 2005

This paper presents and results obtained from the stabilitystudies of plane Poiseuille flow and magnetohydrodynamic flow by the finite element method. Applying Galerkin's weighted residual method and introducing the interpolation function in the exponetial form with respect to time, the governing flow equations are reduced to an eigenvalue problem. This formulation is much simpler than that of the asymptotic expansion method. Solutions are obtained directly in terms of velocity and pressure. Results of the critical Reynolds number obtained by this method compare well with those of other methods for plane Poiseuille flow and magnetohydrodynamic flow.
A note on plate bending analysis using triangular finite element TUBA 3
Authors: Pavlova Yuliana V. , Karamanski Todor D.
Published: August 2005

In Reference 1 a mistake has been made by the derivation of equation (40). The correct expression is shown in the present note.
Finite dynamic element formulation for a plane triangular element
Authors: Gupta K. K.
Published: August 2005

The higher order dynamic correction terms for the stiffness and inertia matrices associated with a triangular plane stress‐strain finite dynamic element are developed in detail. Numerical results presented indicate that the adoption of these matrices along with a suitable quadratic matrix eigenproblem solver effects a significant economy in the free vibration solution of structures when compared with the analysis based on the usual finite element procedure.

A FORTRAN IV computer program listing of the various relevant element matrices is also presented in the Appendix.
On the implementation of an application oriented software system
Authors: Peters F. J.
Published: August 2005

Some tools are presented that may be used when implementing an application oriented software system. FEMSYS, a system for calculations based on the finite element method, will serve as example. Features of a simple problem oriented language and its parsing are treated and also a generally applicable data structure for both internal and external data storage. It is indicated how a system can be implemented which is suited to the solution of both standard and non‐standard problems.
Finite element solutions of convective diffusion problems
Authors: Barrett K. E. , Demunshi G.
Published: August 2005

Three weighted residual methods are used to analyse several linear and nonlinear model problems related to the stream function–vorticity formulation of the Navier–Stokes equations. These methods are then used to solve the driven cavity problem. The results obtained at Reynolds numbers of 100 and 400 compare very favourably with those obtained by finite difference and spline methods on meshes using at least four times as many mesh points.
Calculation and inversion of K/K′ on a programmable calculation
Authors: Squire William
Published: August 2005

Approximate and exact methods are presented for computing a function, related to complete elliptic integrals of the first kind, which arise in the theory of microwave transmission lines. The method can be implemented on programmable hand calculators.
On inversion of complex matrices
Authors: Zielinski Adam
Published: August 2005

A method is presented for inverting an n × n complex matrix M = A + jB by using a real matrix inversion. The approach avoids the requirements of inverting a 2n × 2n real matrix as well as non‐singularity assumptions placed on A or B, or A + B, or A − B, as required by earlier methods.
Numerical solution of equations on the basis of approximation by the curve (x − p1)[y(x) − p2]2 − p3 = 0
Authors: Popovski D. B.
Published: August 2005

In this paper a new, one‐point iterative formula for solution of equations is presented.
Dynamic response of strip footings on elastic halfspace
Authors: Dasgupta S. P. , Rao N. S. V. Kameswara
Published: August 2005

Dynamic response of strip footings resting on a soil medium, idealized as an elastic halfspace, is obtained using the finite element discretization technique with constant strain rectangular elements consisting of 4CST elements. Boundary stresses have been computed using a combination of Rayleigh wave absorbing boundaries (RAB) and standard vicous boundaries (SVB). The influences of contact pressure distributions at the footing—soil interface, mass and frequency ratios on the dynamic response of a strip footing are studied. Effects of embedment, static surcharge, nonhomogeneity and nonlinear constitutive relations are shown. Results are compared with the existing solution and are presented graphically.
Some properties of a hybrid element method for water waves
Authors: Aranha J. A. , Mei C. C. , Yue D. K. P.
Published: August 2005

Two properties of hybrid element method for diffraction and radiation of water waves are examined. For long waves in shallow water the method is shown to give a unique solution for all frequencies. Thus, unlike several other known methods, there are no irregular frequencies for which the approximating matrix equation is singluar. For a sea of arbitrary depth, it is shown that all known global identities such as reciprocity and energy theorems are preserved by the discrete solution. Thus, satisfaction of these identities by the numerical solution is only a necessary but by no means sufficient condition for accuracy.
Difference schemes or element schemes?
Authors: Cushman John H.
Published: August 2005

Several examples are presented to illustrate how standard finite differnce schemes for the wave eqation (e.g. Lax–Wendroff, Leafrog, etc.) can be developed from finite element analysis. The development of the diffrence schemes from the element schemes is made possible by using Galerkin's method on both the spacial and temporal dimensions.
An alternative interpretation of superconvergence
Authors: Marshall Robert S.
Published: August 2005

The superconvergent property of the discrete solution to certain one‐dimensional problems is examined in the context of the weighted residual difference equations and their conservation properties. The difference equations are shown to satisfy the differential equation exactly at nodes and reproduce the derivatives at boundary nodes. The exact values for the first derivative at interior nodes follow from the conservation property when applied locally.
Transient heat conduction in a composite slab with variable thermal conductivity
Authors: Lin S. H.
Published: August 2005

Transient heat conduction in a composite slab is investigated in the present work by using the orthogonal collocation method. The present numerical method is found to be quite efficient and highly stable even for the power‐type temperature dependence of thermal conductivity which often cuases severe computational instability to many numerical methods.
New developments in the inelastic analysis of quasistatic and dynamic problems
Authors: Argyris J. H. , St. Doltsinis J. , Willam K. J.
Published: August 2005

The computational aspects are examined for the numerical analysis of inelastic structures and continua. In this context, the tracing of quasistatic and dynamic motions is considered with particular emphasis on the interaction of nonlinear and transient problems.

In the first part, explicit and implicit solution schemes are developed for the numerical integration of inelastic first‐order rte processes governing creep, viscoelasticity and viscoplasticity. In the second part, the exposition is extended to second‐order inertial problems and in particular to the field of dynamic plasticity, devoting special attention to the kinematics of finite deformation problems.
Derivation of first‐passage time distribution of a single lift for arbitrary traffic
Authors: Levy D. , Alexandrovitz A.
Published: August 2005

The distribution of the first‐passage time is of decisive importance in lift (elevator) design. It yields the easure of performance of the system, the expected number of stops, the interval (i. e. time elapsed between two successive departures from a given floor) and many other parameters and factors determining the required number of lifts in a building. The derivation is based on the transition probability matrix of the operation policy, and consists in solving a system of linear equations.
Buckling of skew plate structures using B‐spline functions
Authors: Mizusawa T. , Kajita T. , Naruoka M.
Published: August 2005

This paper presents a general procedure for calculating the buckling of stiffened skew plates by the Rayleigh‐Ritz method with B‐spline functions as co‐ordinate functions.

Convergence of the solutions is investigated in a few typical cases and is found satisfactory. The results are compared with existing values based on other numerical methods and found to be in good agreement. Buckling characteristics of stiffened skew plates are also studies with varying stiffness parameters of stiffeners, skew angles and aspect ratios.