bluuebunny/crossref_metadata_2025 huggingface dataset:
Parametric infinite element for seepage analysis
Authors: Honjo Yusuke , Pokharel Gyaneswor
Published: August 2005

A set of mapping functions in the form of convergent series for an infinite element, which is capable to include the infinitely distanced constant head boundary condition from the area of disturbance (e.g. pumping), is proposed based on the asymptotic far‐field behaviour of typical seepage flow problems. The derived mapping functions have been successfully used in three‐dimensional point symmetric, two‐dimensional axi‐symmetric and one‐dimensional unidirectional flow for the fixed head boundary at infinite distance. The result shows excellent agreement with analytical solution. For the first time, the mapping function of an infinite element is presented in the form of a convergent series. The infinite elements are really capable of reducing the cost and efficiency of conventional finite element analysis. Finally, a figure is also proposed to indicate the required size of the near field to obtain accurate drawdown at specified locations based on some calculations for two‐dimensional radial flow case.
Green's functions for a fully coupled thermoporoelastic material
Authors: Smith David W. , Booker John R.
Published: August 2005

The Green's functions for a set of fully coupled linear equations governing thermal consolidation of a homogeneous isotropic material are presented. The Green's functions are evaluated for one, two and three spatial dimensions, and in the Laplace and real‐time domains. The Green's functions are employed in a boundary integral analysis of a simple problem to demonstrate the influence of full coupling on the field quantities.
Shakedown in layered pavements under moving surface loads
Authors: Collins I. F. , Wang A. P. , Saunders L. R.
Published: August 2005

Elastic–plastic deformations in pavements consisting of layers of different frictional materials are investigated. The upper bound, kinematic shakedown theorem is used to obtain estimates of the critical shakedown loads. Fully general three‐dimensional deformations are considered. The influence of the loading distribution, interactions between loads, and the effect of varying the thickness, stiffness and strength of the layers are explored. Consequences of this investigation for particular existing designs of flexible pavements are investigated. In particular, it is found that the strength of the subgrade has no effect on the magnitude of the critical shakedown load.
Calculation of kinetic rate constants from steady‐state soil profile concentration measurements
Authors: Barry D. A. , Parlange J.‐Y. , Hensley P. J.
Published: August 2005

We derive a simple approximation for the steady‐state distribution of solute subject to an arbitrary, irreversible transformation in a soil profile under the condition of steady fluid flow. The approximation accounts for the effect of dispersion in both the surface boundary condition and the transport equation. The accuracy of the approximation is determined explicitly for the cases of zero‐ and first‐order kinetics, where exact solutions are available. Data from a numerical scheme are used to check the approximation's accuracy for the widely used Michaelis–Menten kinetic rate. It is shown that existing approximations in which the effect of dispersion in the transport equation is ignored can affect significantly the value determined for the Michaelis–Menten saturation constant. Parameters found when the new method is applied to experimental data are found to agree closely with those estimated directly from a least‐squares fitting.
On overestimation of displacements in numerical calculation of zoned dams
Authors: Doležalová Marta
Published: August 2005

Overestimation of displacements in numerical calculations can occur if some requirements are not met by the constitutive relations. Along with consideration for small strain behaviour of soils1 the stiffening effects of unloading in shear should be taken into account. The latter problem is analysed in the paper using embankment dams as a typical example. Strain and stress paths in their cores and shells were derived from field measurement results and frequent path direction changes during seemingly monotonic loading process were discovered. Proportional loading test results of isotropically and anisotropically consolidated sand allowed interpretation of the in situ paths by the incremental theory of plasticity and distinction between the sections where unloading and reloading in shear develop. Furthermore, the analysis of these tests showed a marked stiffening of the soil due to unloading as well as neutral loading in shear. The strain redistribution due to material inhomogeneity, either inherent or introduced by the loading process, was identified as a common reason for the frequent occurrence of this phenomenon. Consequently, overestimations in displacement calculations can be brought about by neglecting this important effect by the constitutive model used. Accordingly, the unit response envelopes of some typical constitutive laws have been checked from this special point of view, and the models properly describing this phenomenon selected.
Analysis of fully coupled thermomechanical behaviour around a rigid cylindrical heat source buried in clay
Authors: Seneviratne H. N. , Carter J. P. , Booker J. R.
Published: August 2005

The problem of fully coupled consolidation and heat flow around a rigid cylindrical heat source buried in clay has been studied. The governing equations of the problem are summarized in the paper and a finite element time‐marching scheme to obtain an approximate solution to the governing equations is described. The stress–strain behaviour of the skeleton of the saturated soil has been represented by both a linear elastic model and the modified Cam clay soil model. The results of a limited parametric study are presented with the aim of understanding the major mechanisms of soil behaviour close to buried canisters of hot radioactive waste. A range of soil properties has been included in the study, and the effects of soil disturbance during canister emplacement have also been considered.
Boundary element analysis of Biot consolidation in layered elastic soils
Authors: Chiou Yaw‐Jeng , Chi Shue‐Yeong
Published: August 2005

Biot's linear consolidation analysis of three‐dimensional fluid saturated layered soils is investigated. The time marching method, uncoupled boundary element method, and successive stiffness method are applied for the numerical modelling of this study. Settlement induced by surface loading and land subsidence due to pumping is studied. The results show that settlement induced by surface loading is mainly influenced by the properties of the soil layer, and that the settlement is larger for soil layers with smaller stiffness and greater thicknesses. The land subsidence induced by pumping is influenced by the properties of the soil layer as well as by the permeability of the pumped layer and the conditions at the top and bottom boundaries. The land subsidence is larger for soil layers with a smaller stiffness, lower permeability of the pumped layer, deeper pumping depth, larger pumping rate and an impervious top surface.
Cyclic mobility behaviour of sand by the three‐dimensional strain space multimechanism model
Authors: Akiyoshi T. , Matsumoto H. , Fuchida K. , Fang H. L.
Published: August 2005

The cyclic mobility behaviour of sand by the three‐dimensional (3‐D) strain space multimechanism model based on the micromechanics of granular material is investigated. The constitutive properties are characterized by the volumetric and shear mechanisms for the initial isotropic soil. The 3‐D shear mechanism is decomposed into a number of microscopic plane‐strain shear mechanisms in various orientations, each of which in turn consists of a number of microscopic simple shear mechanisms. Using an appropriate summation of mechanisms, the total deformation behaviour can be obtained by evaluating contributions from each mechanism. Based on the some assumptions, the dilatancy model proposed by Iai et al.1 is extended from the two‐dimensional (2‐D) space to the 3‐D space. Comparisons of theoretically predicted results are made with experimental measurements.
Monica—A computer algorithm for solving boundary value problems using the double‐hardening constitutive law Monot: II. Algorithm validation
Authors: Hicks M. A.
Published: August 2005

The computer algorithm MONICA1, which incorporates the double‐hardening constitutive law Monot2, has been tested on a large number of numerical examples. This paper summarizes the validation process, which has included consideration of both single element stress paths and multi‐element boundary value problems. These results show MONICA to be effective for analysing practical problems using a soil model of the double‐hardening type. They also demonstrate the ability of Monot to model a wide range of material responses. Problems involving pore pressure changes are identified as an area in which this form of analysis is of particular use3,4.
One‐dimensional, semi‐analytical solution for time‐dependent behaviour of a seam
Authors: Nawrocki Pawel A.
Published: August 2005

The paper provides a one‐dimensional, semi‐analytical study of face advance in a coal seam assuming a Bingham type of material model. The changes in vertical stress and deformation in the seam due to change in the geometric configuration of the excavation are analysed. The general analytical formulae defining stresses and strains for an arbitrary time instant i Δt(i = 1,2,…) are derived, and the size of the viscoplastic zone near the opening and its evolution with time are determined. The influence of the seam extraction rate on the stability of the seam and rock burst occurrence is discussed in the light of the developments presented in this paper.
Modelling convection in solidification processes using stabilized finite element techniques
Authors: Samanta Deep , Zabaras Nicholas
Published: August 2005

Solidification of dendritic alloys is modelled using stabilized finite element techniques to study convection and macrosegregation driven by buoyancy and shrinkage. The adopted governing macroscopic conservation equations of momentum, energy and species transport are derived from their microscopic counterparts using the volume‐averaging method. A single domain model is considered with a fixed numerical grid and without boundary conditions applied explicitly on the freezing front. The mushy zone is modelled here as a porous medium with either an isotropic or an anisotropic permeability. The stabilized finite‐element scheme, previously developed by authors for modelling flows with phase change, is extended here to include effects of shrinkage, density changes and anisotropic permeability during solidification. The fluid flow scheme developed includes streamline‐upwind/Petrov–Galerkin (SUPG), pressure stabilizing/Petrov–Galerkin, Darcy stabilizing/Petrov–Galerkin and other stabilizing terms arising from changes in density in the mushy zone. For the energy and species equations a classical SUPG‐based finite element method is employed with minor modifications. The developed algorithms are first tested for a reference problem involving solidification of lead–tin alloy where the mushy zone is characterized by an isotropic permeability. Convergence studies are performed to validate the simulation results. Solidification of the same alloy in the absence of shrinkage is studied to observe differences in macrosegregation. Vertical solidification of a lead–tin alloy, where the mushy zone is characterized by an anisotropic permeability, is then simulated. The main aim here is to study convection and demonstrate formation of freckles and channels due to macrosegregation. The ability of stabilized finite element methods to model a wide variety of solidification problems with varying underlying phenomena in two and three dimensions is demonstrated through these examples. Copyright © 2005 John Wiley & Sons, Ltd.
Numerical treatment of mixed boundary value problems in two‐dimensional elastostatics
Authors: Feldmann Jay W. , Prager W.
Published: August 2005

Finite difference treatment of two‐dimensional problems in elastostatics is usually based on the differential equations for the displacement vector or the Airy stress function, depending on whether boundary conditions are on displacement or stress. In either case, determination of stresses requires numerical differentiation and therefore use of a rather fine grid. Moreover, neither method is suited to the treatment of mixed boundary conditions. The alternative method developed in this paper uses the first derivatives of the displacement components at the grid points as basic variables and hence does not require numerical differentiation in the evaluation of stresses. Appropriate finite difference equations are established, and their use is discussed in connection with a specific example with known explicit solution.
A polygonal finite element for plate bending problems using the assumed stress approach
Authors: Alwood R. J. , Cornes G. M. M.
Published: August 2005

The assumed stress distribution approach is used to derive the stiffness matrix of a plate‐bending element of general polygonal shape having any number of nodes. The effect of assuming various numbers of unknown coefficients in the stress distributions is examined and the convergence properties of the resulting elements compared with others derived form assumed displacements.
Mass condensation : A semi‐automatic method for reducing the size of vibration problems
Authors: Ramsden J. N. , Stoker J. R.
Published: August 2005

The paper presents a method for reducing the size of a vibration analysis by generating an inertia matrix referred to a limited set of ‘master’ vibrational freedoms. In designing a computer program to perform this mass condensation process, the emphasis has been on providing a two way interface between structural analysis and vibration analysis programs. The transformation from the full set of degrees of freedom to the master set makes extensive vibration calculations economically feasible giving solutions in terms of the amplitudes of the master freedoms. However, by reversing the transformation after completion of a vibration analysis, it is possible to restore the full set of freedoms, allowing automatic plotting of mode shapes in full detail, and re‐entry to the structural analysis program for the purpose of computing dynamic stresses.

A worked example is given. This is a realistic machine tool structure rather than the simple plates or beams which are usually used for illustration purposes. Natural frequencies and mode shapes, calculated with various degrees of condensation, are compared with those obtained by using all possible freedoms. A comparison is also made with an intuitive selection of ‘lumped masses’.
New displacement hybrid finite element models for solid continua
Authors: Tong Pin
Published: August 2005

The proposed finite element model is based on separate assumptions of interior and interelement displacements and on the assumed boundary tractions of each individual element. The associated variational functional for this model is presented. This method has the same merits of the assumed stress method (References 3 and 4) in that a compatible displacement function at the interelement boundary can be easily constructed, while it can easily be used for shells with distributed loads.
Convergence studies of eigenvalue solutions using two finite plate bending elements
Authors: Lindberg Garry M. , Olson Mervyn D.
Published: August 2005

The convergence rates of eigenvalue solutions using two finite plate bending elements are studied. The elements considered are the well‐known 12 degree of freedom, non‐conforming rectangular element and the 16 degree of freedom, conforming rectangular element. Three problems are analysed, a square plate simply supported on two opposite sides with the other two sides clamped, simply supported, or free. Closed form, finite element solutions for these problems are obtained by using shifting E‐operators.

With few exceptions, eigenvalue solutions found with the non‐conforming element converge from below the exact answers at an asymptotic rate of n−2, where n is the number of elements on a side. However, since the array size needed for such convergence is very large, little can be said about the convergence rates for practical arrays. The conforming element solutions converge from above at an asymptotic rate of n−4. A comparison of the errors involved in using these two elements shows that the conforming element is far superior to the non‐conforming element.
Design of digital filters by computer
Authors: Edwards R. , Bradley A.
Published: August 2005

Digital filters are finding wide applications in signal processing aspects of such fields as engineering, geophysics and biosignal analysis. The design of a digital filter and its realization with near minima computer word length are two problems which can be solved by computer‐aided design techniques In this paper, the automated design of the initial filter (recursive type) only is considered. Both of the basic design methods—the direct and indirect approaches—have been analysed, and compute programs have been written to implement the various design techniques. The present program are limited to the design of flat loss type filters specified by their gain rather than their phase character istics. although provision has been made to allow for other types of design in the indirect approach Design examples are given, and the results analysed with a view to the suitability and limitations of the different design techniques.
Finite element analysis of elastic contact problems using differential displacements
Authors: Wilson E. A. , Parsons B.
Published: August 2005

A technique of differential displacements is presented whereby problems involving elastic contact are solved by the finite element method. The technique is applied to axisymmetric situations in which statically indeterminate conditions occur and is shown to provide a means for resolving these conditions in terms of contact stresses. Three typical engineering problems are analysed to demonstrate the technique in cases where body forces, thermal gradients and external applied forces are acting.
Numerical prediction of the temperature distribution in the initial region of a two‐dimensional turbulent film cooling configuration
Authors: Sucec James
Published: August 2005

The velocity field of a semi‐contained turbulent jet, as constructed by Abramovich, is used to arrive at the temperature distributions in the initial region of a turbulent flow film cooling situation taking into account both the development of the jet boundary layer and the wall boundary layer. After suitable profiles of eddy thermal conductivity are established, a finite difference form of the thermal energy equation is derived, shown to be unconditionally stable, and solved numerically with the aid of an IBM System 360 computer to yield the temperature distributions. Wieghardt's parameter for collapsing the temperature profiles onto a single curve in film cooling situations, when suitably modified, also collapse the analytical results to essentially a single curve even as near as 2·7 slot heights from the injection point, thus verifying the temperature similarity in film cooling which has been experimentally observed even very near the injection point. Results in graphical form are presented which allows one to construct the actual temperature profile for a fairly wide range of the relevant parameters.
The application of three‐dimensional finite elements to a cylinder‐cylinder intersection
Authors: Hellen T. K. , Money H. A.
Published: August 2005

Recent advances in finite element techniques have enabled full three‐dimensional stress analyses to be undertaken. Economy and accuracy can only be achieved simultaneously if the characteristics of the element are understood. Preparatory work is described in which suitable pitching and disposition of brick‐type elements are established for the analysis of cylinders.

The information derived is put to use in the analysis of a cylinder–cylinder intersection. A favourable comparison is made with an independently computed solution.
Kinematically consistent unsteady aerodynamic coefficients in supersonic flow
Authors: Appa Kari
Published: August 2005

A finite element method to determine unsteady aerodynamic influence coefficients, consistent with the stiffness and inertia properties of a lifting surface in supersonic flow, is described. This is basically a kinematic method, which reduces the dynamical equations of a non‐conservative system to a simple and elegant form. It is illustrated by application to a delta wing using triangular elements to calculate steady and unsteady lift and moment coefficients. Throughout the calculations only a coarse grid system has been employed and the answers have been compared with available results.
Numerical solution of the dynamic stability problems
Authors: Krajcinovic Dusan , Herrmann George
Published: August 2005

A novel integral equation technique is employed for the analysis of dynamic stability problems. The governing equation of the linearized parametric resonance problem is transformed into an integral equation. The kernel of the integral equation is computed as the influence function for the deflection and/or bending moment of a corresponding beam.

The highest derivative of the governing function (in our case fourth derivative of the displacement function) is chosen as the basic unknown. Using the formal analogy with the differential equation of the beam flexure this highest derivative is comprehended as some unknown transverse ‘load’. The distribution of this ‘load’ is a priori assumed to be polygonal. Using elementary methods of structural analysis, the displacements due to the assumed ‘load’ are determined. These displacements, arrayed into a square matrix, approximate the kernel of the governing integral equation.

The subsequent procedure via Hill's determinant is a conventional one. The results prove to be accurate enough even for a very modest number of points of integration. This reflects the fact that the method is based on numerical integration rather than on numerical differentiation.
Rules governing the numbers of nodes and elements in a finite element mesh
Authors: Ewing D. J. F. , Fawkes A. J. , Griffiths J. R.
Published: August 2005

In any mesh, rules exist that interrelate the number of internal and external sides, vertices, etc. and the total number of elements. These are given explicitly for plane meshes of triangles and quadrilaterals, and for solid meshes of tetrahedra and cuboidal elements. The method is quite general and discovers all such independent rules that exist. Thus, for a plane mesh of T elements having Vi internal and Vb boundary vertices and Si internal and Sb boundary sides, then

where H is the number of internal boundaries (holes) there might be. For solid meshes, these two‐dimensional equations relating elements to sides generalize to

where there are Fb boundary and Fi internal faces. Unfortunately, there is no direct generalization of the two‐dimensional equations relating vertices and elements: it is only possible to do this by including the Ei internal and Eb boundary edges:

where there are H through holes and h cavities.
Finite element formulation of general electrothermoelasticity problems
Authors: Oden J. T. , Kelley B. E.
Published: August 2005

This paper is concerned with the development of consistent discrete models, via the concept of finite elements, of linear and non‐linear electrothermomechanical behaviour of continuous bodies. In the development, general energy balances are utilized to derive equations governing electromagnetic fields over an element and coupled equations of motion and heat conduction of a typical element of the continuum. These equations make it possible to study a general class of field problems involving arbitrary geometries and boundary conditions. Sample problems are included.
On a direct‐iterative eigensolution technique
Authors: Dong Stanley B. , Wolf Joseph A. , Peterson Frederick E.
Published: August 2005

Two variations of an iterative scheme are presented for the solution to algebraic eigensystems. These algorithms are used in conjunction with the method of reduced generalized co‐ordinates so that n number of frequencies and mode shapes are obtained simultaneously. The bases of the scheme are the well‐known results of Stodola–Vianello and Gram–Schmidt. Advantages of the present schemes are realized both in computational effort and in computer storage. Examples are presented to illustrate the convergence characteristics.
A note on data checking for large framework analysis
Authors: Flower W. R. , Schmidt L. C.
Published: August 2005

Sources of data errors in the analysis of large frameworks are listed. Outputs of various forms for error detection are discussed; emphasis is given to the advantages of graphical output. For further error detection, a few procedures that can be included in computer programs are listed.
Vibration of circular and annular plates using finite elements
Authors: Kirkhope J. , Wilson G. J.
Published: August 2005

The finite element method is applied to the free transverse vibration of circular and annular plates of varying thickness. An annular element is derived which incorporates the number of diametral modes in the deflection function. This results in an element having only four degrees of freedom, these being the deflection and slopes at the inner and outer radii of the element at an anti‐node of the particular vibration mode. Thickness variation in the radial direction is readily introduced, and stiffness and inertia matrices are presented for elements with linear and parabolic variations in thickness.

The method is checked with several numerical examples. Calculations of free vibration of circular and annular plates of constant, linear and parabolic thickness variation are compared with available exact solutions.
Numerical methods for Orr–Sommerfeld problems
Authors: Gersting John M. , Jankowski Daniel F.
Published: August 2005

Five previously employed numerical methods for the solution of Orr–Sommerfeld problems have been compared to each other and to a new method, the differential method of near‐orthonormalized integration. Brief summaries of each method are included. The comparison, based on seven factors, reflects the results of an implementation of a computer program for each method for the classic Orr–Sommerfeld problem of plane Poiseuille flow. This comparison shows that the new method and the algebraic finite difference method are currently the best available numerical solution methods for the problems in this class, with the new method being less problem dependent.
A lumped parameter element for the analysis of hyperbolic paraboloid shells
Authors: Mohraz Bijan
Published: August 2005

This paper presents the derivation of the stiffness matrix for a lumped parameter hyperbolic paraboloid shell element. This element is used to obtain solutions to hyperbolic paraboloid shells with various edge conditions. Numerical example for three types of support conditions (a simple support, a clamped edge and a shell supported by concentric edge beams) are presented. To illustrate the applicability of the method, the results obtained by the lumped parameter element are compared with those obtained by well‐known methods of analysis such as the variational procedure, the finite difference and the finite element method.
Propagation of transient pules from a spherical cavity in a viscoelastic medium
Authors: Amoudi Jacob
Published: August 2005

The problem of an impulsively applied pressure acting on the surface of a spherical cavity in a linear viscoelastic medium is solved by an approximate inversion of the Fourier transform. The method can be applied to general models of viscoelasticity described by the Boltzmann superposition principle, with relaxation or creep functions given analytically or numerically in the time or the frequency domain.
Anisotropic tapered elements using displacment models
Authors: Tinawi René A.
Published: August 2005

Two FORTRAN IV subroutines that generate the stiffness, mass and geometric matrices for plate bending and plane stress elements using displacement models are described. The elements can be of either rectangular or triangular shape with anisotropic properties together with a linear variation in thickness. Although such a formulation is straightforward theoretically, emphasis has been placed on the programming technique where the amount of algebra involved in the matrix manipulations is avoided. Exact integration is automatically performed since a closed‐form solution con be obtained.
Finite element analysis of the linearized BGK Boltzmann equation
Authors: Bramlette T. Taz , Leonard J. W.
Published: August 2005

The weighted residual and finite element methods are combined to yield a numerical solution scheme for the linerized BGK Boltzmann equation which describes the dynamic behaviour of gases in all flow régimes ranging from the free molecular to the continuum régime.

The potential of the proposed method is illustrated by application to the problem of cylindrical Couette flow. Numerical results are compared with alternate numerical solutions and experimental data.
Integral equation method for solution of boundary value problems of structural mechanics, Part II. Elliptic partial diffeerential equations
Authors: Hajdin Nikola , Krajcinovic Dusan
Published: August 2005

The method presented in Part I of this paper1 is extended to problems governed by a system of partial differential equations. The basic clarity and simplicity of the method is preserved.

The domain of integration is covered by a net of orthogonal (not necessarily equidistant) straight lines. Choosing again highest derivatives with respect to each of the co‐ordinates as unknowns, it is possible to reduce the problem to a system of integral equations along the lines of the adopted net.

The subsequent procedure is basically the same as in Part I. The results prove to be of remarkable accuracy even for very coarse nets.
A novel finite difference formulation for differential expressions involving both first and second derivatives
Authors: Spalding D. B.
Published: August 2005

It is shown that the upwind difference scheme of formulating differential expressions, in problems involving transport by simultaneous convection and diffusion, is superior to the central differences scheme, when the local Peclet number of the grid is large. Even better schemes are derived and discussed. It is pointed out that the best finite differences analogues are found by approximating differential expressions as a whole, and that simple (e.g. one‐dimensional) exact solutions form a useful, legitimate and independent source of these optimum algebraic formulae.
A numerical method for coupled differential equations
Authors: Denman Eugene D.
Published: August 2005

This paper describes a numerical method for solving first‐order coupled matrix differential equations. Recursive equations are used to find ‘reflection’, ‘transmission’ and ‘source’ coefficients; these coefficients are then used to construct the vector solution to the differential equations. The method can be used to solve linear and non‐linear differential equations with specified initial or two‐point boundary values. Numerical results for several initial value problems are given in the paper.
Unsteady MHD duct flow by the finite element method
Authors: Wu S. T.
Published: August 2005

In this paper, we are concerned with applying the finite element method to seek an approximate numerical solution to a class of unsteady magnetohydrodynamic flow in ducts with arbitrary cross‐section. A consistent discrete model for the MHD flow equation with a small magnetic Reynolds number has been developed via the concept of finite elements. A numerical example of MHD flow in a rectangular duct is given, and its results of velocity profiles are compared with the results obtained by other methods.
Bending and vibration of multilayer sandwich beams and plates
Authors: Khatua T. P. , Cheung Y. K.
Published: August 2005

A finite element displacement analysis of multilayer sandwich beams and plates, each with n stiff layers and n−1 weak cores, is presented. Each layer of the sandwich structure may have individual orthotropic properties of its own and the bending rigidities of the stiff layers are taken into account while direct stresses in cores are neglected in the analysis. The condition of common shear angle for all cores, which has been used by several authors is not implied in the formulation.

Several examples on bending problems have been solved using lower‐order elements and the accuracy of the results has been shown to be excellent. Two higher‐order elements have also been developed but have not been found to yield much better results.

The free vibration problems of multilayer sandwich structures have also been solved, and good accuracy is demonstrated.
Study in particle percolation: Computer program
Authors: Moore Carolyn , Masliyah Jacob
Published: August 2005

A description of a computer program giving the path of a percolating smooth spherical particle through a three‐dimensional cluster of stationary spheres, under the influence of a gravitational field is presented.The history of the moving particle starting with an arbitrary velocity and position is followed. The coefficient of restitution for the spheres is an input variable. When the gravitational force approaches zero and the coefficient of restitution is unity, the computer program can also be utilized for the treatment of radiative heat transfer and for Knudsen diffusion in packed beds.
A finite element method for non‐self‐adjoint problems
Authors: Kikuchi Fumio
Published: August 2005

This paper presents a general theory and application of the finite element method for some special class of non‐self‐adjoint problems. The formulation employed here is based on the Galerkin method for linear boundary value and eigenvalue problems described by the partial differential equations of elliptic type, and it can be regarded as an extension of the usual displacement method formulated by the use of the principle of minimum potential energy. In order to illustrate its validity and feasibility, the method is applied to the problems of the two‐group neutron diffusion equations and of the stability of a non‐conservative system.
A high order finite element for completely incompressible creeping flow
Authors: Thompson Erik G. , Haque M. I.
Published: August 2005

A finite element method for simulating the creeping flow of an incompressible material is presented. The method allows for (1) a quadratic approximation of the velocity field, (2) material incompressibility everywhere within an element and (3) the ability to follow the flow through large changes of the material boundaries. A candle slowly bending under its own weight is simulated for illustrative purposes.
Computation of upper and lower bounds to the frequencies of elastic systems by the method of Lehmann and Maehly
Authors: Chang Tish‐Chun , Craig Roy R.
Published: August 2005

A method, called the Lehmann‐Maehly method, for determining upper and lower bounds for eigenvalues, which was introduced by Bazley and Fox4 in 1964, is applied to the determination of bounds to the frequencies of elastic systems. In reviewing the fundamental theory involved, the present paper emphasizes the physical significance of the adjoint operators T and T* employed. An error in the paper by Bazley and Fox is noted and it is pointed out that with the corrected theory it is possible to use the Lehmann‐Maehly method as a procedure for computing converging sequences of upper and lower bounds merely by varying a constant, the shifting constant. Thus, sequences of bounds are shown to be easily obtainable without prior knowledge of rough bounds, and the procedure for obtaining the bounds is not significantly more difficult to apply than the familiar Rayleigh‐Ritz method for upper bounds. Since displacements and stresses are independently varied, the displacement functions used in the approximation procedure are only required to satisfy prescribed displacement boundary conditions while the stress functions only need satisfy the natural (stress) boundary conditions. Operators are derived for a non‐ uniform beam based on Timoshenko beam theory. Tables of bounds computed by the Lehmann‐Maehly method and also the Rayleigh‐Ritz method are given as an illustrative example.
Convergence, accuracy and stability of finite element approximations of a class of non‐linear hyperbolic equations
Authors: Oden J. T. , Fost R. B.
Published: August 2005

Numerical stability criteria and rates of convergence are derived for finite element approximations of the non‐ linear wave equation utt−F(ux) = f(x, t), where F(ux) possesses properties generally encountered in non‐linear elasticity. Piecewise linear finite element approximations in x and central difference approximations in t are studied.
Spectral analysis on a small computer
Authors: Kinns R.
Published: August 2005

The design and implementation of software for real‐time spectral analysis on an IBM 1130 with 8k core is described. The procedures for estimation of coherence and cross‐spectra are discussed in detail.
Anisotropic parametric plate discrete elements
Authors: Palacol E. L. , Stanton E. L.
Published: August 2005

A limitation of most plate and shell discrete elements now in use is the shape of their undeformed geometry. Typically, the plan form of these elements is a straight‐sided triangle or quadrilateral that linearly approximates the undeformed geometry while often using higher‐order polynomials to approximate the deformed geometry. This modelling difference leads to inefficiencies that can be eliminated, as demonstrated by a new parametric discrete element based entirely on bicubic Hermite polynomials. This representation of element geometry corresponds to the bicubic Coon's surface patch widely used in design, which allows a common mathematical model for design and analysis. Consideration is given to automating the generation of these patches. Solutions are presented for several plate bending and plate stretching problems. The solutions are in good agreement with closed‐form solutions and photoelastic results in the case of a stress‐concentration problem. These data demonstrate that the new parametric discrete element maintains solution accuracy for plates with curved boundaries.
Numerical solution of the integral equations for optimal sequential filtering
Authors: Kalaba R. E. , Spingarn K.
Published: August 2005

Inhomogeneous Fredholm integral equations occur frequently in communication theory where it is desired to determine optimal receivers and filters for signal detection and estimation. In this paper an initial value method is utilized to determine the Fredholm resolvent and the solution of the integral equation. Numerical results are given for a simple example. The method is of particular interest where sequential solutions are desired.
Finite element bending analysis of multilayer plates
Authors: Mawenya A. S. , Davies J. D.
Published: August 2005

The development of a general quadratic multilayer plate element is presented for the analysis of arbitrarily layered curved plates. In the formulation, each layer of the multilayer plate can have different orthotropic properties and can deform locally. Examples of bending problems are presented which demonstrate the applicability of the formulation.
The finite element analysis of elasto‐plastic materials by use of dislocation dipole systems
Authors: Owen D. R. J. , Prakash A.
Published: August 2005

It is shown how the stress field due to any prescribed continuous distribution of dislocation dipoles can be determined. This technique then forms the basis of a general method of solution of elasto‐plastic material problems. The presentation is limited to situations which conform to either plane stress or strain conditions. Some results are obtained for relatively simple geometrical and loading configurations and compared with classical plasticity solutions. Finally, the method is applied to the problem of a circular hole in a finite strip under tension.
Mesh generation program for highway excavation cuts
Authors: Kalkani E. C.
Published: August 2005

The mesh generation program described here generates the nodes and the elements for excavated highway slopes, applies boundary conditions, searches for the nodes and the elements in each layer excavated and plots the mesh with the numbering of nodes, elements and material types.
Finite element analysis of elasto‐plastic shells
Authors: Bäcklund Jan , Wennerström Hans
Published: August 2005

A finite element analysis applicable to elasto‐plastic shells of arbitrary shape is presented. Small‐deflection behaviour of thin shells subjected to monotonically increasing static loads is considered. The material is assumed to be originally isotropic, following the von Mises yield criterion and the Prandtl‐Reuss flow rule. A flat triangular element with twelve degrees of freedom is used in the analysis. Within each element both membrane forces and bending moments are assumed to be constant. Some numerical results are included to illustrate the merits of the element.
The rectangular plane stress element by Turner, Pian and Wilson
Authors: Fröier M. , Nilsson L. , Samuelsson A.
Published: August 2005

One of the first finite elements presented was that by Turner et al.1 Pian2 presented a hybrid plane stress element and Wilson et al.3 presented a non‐conforming displacement element. It is shown that the three resulting stiffness matrices are identical.
Stresses in nearly incompressible materials by finite elements with application to the calculation of excess pore pressures
Authors: Naylor D. J.
Published: August 2005

A number of problems are analysed by the displacement method to assess the stress accuracy at very low compressibilities. ‘Parabolic’ isoparametric elements are used. It is found that the mean stress becomes grossly in error at the centre and edges of each element as the compressibility is reduced whereas the deviatoric stress components do not. All stress components retain good accuracy at the ‘reduced’ integration sampling points (2 × 2 Gauss). ‘Exact’ integration yields a similar stress distribution to ‘reduced’ but the mean stress is grossly in error at the integration points (3 × 3 Gauss). Exceptions, however, occur.

These findings are interpreted, and a rule for predetermining whether or not accurate stresses can be obtained at the integrating points is suggested. Thus it is shown that the displacement method is suitable for analysing materials which for practical purposes are incompressible.

A procedure is then presented for analysing porous media‐both linear and non‐linear‐by separating the stiffness into ‘effective’ and ‘pore fluid’ components. This allows excess pore pressure to be calculated explicitly. Applications to saturated soils are given which make use of the findings of the first part of the paper.
Finite element solutions for an equilateral triangle
Authors: Daly P.
Published: August 2005

In a two‐dimensional space of points on an equilateral triangle grid, a single difference equation holding at each node is found from the finite element formulation of the wave equation for all published polynomial orders of the functional expansion. Assuming homogeneous boundary conditions on any equilateral triangle whose edges and vertices pass through the grid points, the eigensolutions of the difference equation are found exactly and thus provide an excellent test problem for the programmer or engineer. The advantage of the present method over other formulations is that the number of linear operations required to produce the difference equation is minimal.
Bicubic fundamental splines in plate bending
Authors: Antes H.
Published: August 2005

This paper deals with solving the two‐dimensional variational problem for plate bending by the Ritz method using bicubic fundamental splines. It is a piecewise polynomial method, very adaptable to practical numerical computation, and can be an alternative for the well‐known Finite Element Method1.
Cycle bases for the flexibility analysis of structures
Authors: Cassell A. C. , de C. Henderson J. C. , Kaveh A.
Published: August 2005

Two methods are presented for the automatic selection of a cycle basis leading to a sparse flexibility matrix for the analysis of rigid‐jointed skeletal structures.

The first method having a local approach forms a maximal set of admissible minimal cycles, while the second having a global approach constructs admissible minimal cycles on the ordered chords of a shortest route tree. A cycle ordering algorithm is also given to reduce the band width of the corresponding flexibility matrix.
Spline‐blended approximation of Hartmann's flow
Authors: Gheri G. , Cella A.
Published: August 2005

The steady state flow problem known in magnetohydrodynamics as Hartmann's flow is converted into variational formulation and is given an approximate solution by means of the spline blended interpolation technique. The equations of motion consist of two coupled potential flow problems with homogeneous boundary conditions. The spline blended interpolation method is reduced here, because of the shape of the domain, to a cartesian product of cardinal splines with trigonometric or ordinary polynomials. ‘Exact’ boundary conditions are presented by the blending technique. The numerical results indicate that high accuracy is possible with relatively few unknowns.
The application of quasilinearization to non‐linear systems
Authors: Kelsey Stephen J.
Published: August 2005

This paper presents a method of solving systems of simultaneous non‐linear partial differential equations using the method of lines and the method of quasilinearization‐superposition in combination. The advantages of the method over those methods more generally used are discussed and an example of the application of the method to the two‐dimensional momentum and energy equations considering temperature‐dependent and/or shear‐rate dependent viscosity is given.
An application of least squares to one‐dimensional transient problems
Authors: Lewis Roland W. , Bruch John C.
Published: August 2005

The method of ‘least squares’, which falls under the category of weighted residual processes, is applied as a time‐stepping algorithm to one‐dimensional transient problems including the heat conduction equation, diffusion‐convection equation, and a non‐linear unsaturated flow equation. Comparison is made with other time‐stepping algorithms, and the least squares method is seen to offer definite advantages.
A finite element analysis of general deformation of sheet metals
Authors: Gotoh M.
Published: August 2005

A polynomial shape function of triangular elements for finite element analysis of general deformation of sheet metals with or without orthotropic anisotropy is proposed. And general formulation for large deformation and large strain analysis with non‐linearity of material property, say plasticity, is given. Some numerical examples are examined with respect to hydraulic bulging.
Steady magnetohydrodynamic flow past a circular cylinder
Authors: Ingham D. B.
Published: August 2005

The steady two‐dimensional, viscous, electrically conducting flow around a circular cylinder is investigated. The flow and magnetic field are uniform and parallel at large distances from the cylinder. The equations and boundary conditions are derived for arbitrary values of R, Rmand β, where R is the Reynolds number, Rm the magnetic Reynolds number and β, the ratio of the square of the Alfvén speed to the square of the main stream speed. Because of the large number of parameters involved, the numerical solution is restricted to R = 40, Rm = 1 and infinity and 0 ⩽ β ⩽ 4. Also the cylinder is taken to be a perfect conductor, this avoids having to compute the magnetic field within the cylinder.

The numerical computations for the non‐magnetic case, i.e. β = 0, are presented and are found to be in good agreement with existing results. The effect of increasing the strength of the magnetic field (i.e. increasing β) on the drag coefficient, the size and position of the standing vortex and the increasing effect of the upstream propagation of disturbances are examined.