bluuebunny/crossref_metadata_2025 huggingface dataset:
Thermomechanical effects on adsorbed water in clays around a heat source
Authors: Ma Chenmin , Hueckel Tomasz
Published: August 2005

Numerical results of the simulations of the saturated clay response to a line heat source with a constant power output are presented and compared to the analytical solutions. Mixture theory of two interacting thermoelastic constituents is employed for the modelling. In this theory, mass transfer between the adsorbed water and bulk water is included to simulate the degeneration of adsorbed water into bulk water occurring at elevated temperatures. A finite difference method with non‐uniform mesh is adopted to determine both the near‐ and far‐field behaviour. The degeneration of adsorbed water into bulk water is more pronounced close to the heat source. This may produce a lower excess pore water pressure, a higher permeability increase, and accelerate the water flow in the vicinity of the heat source.
The analysis of pollutant migration through soil with linear hereditary time‐dependent sorption
Authors: Smith David W. , Rowe R. Kerry , Booker John R.
Published: August 2005

This paper presents a non‐equilibrium sorption dispersion–advection transport model for the analysis of pollutant migration through soil. The formulation involves a convolution integral of the product of the rate of change of concentration and a time‐dependent sorption coefficient, suggesting an integral transformation of the governing equations. This facilitates the primary purpose of this paper, to incorporate a time‐dependent solute sorption process into a computationally efficient and accurate semi‐analytic Laplace transform method. An application of the non‐equilibrium sorption model for backfiguring dispersion–advection equation parameters from experimental data is presented, and the implications of non‐equilibrium sorption on the design of landfill liners is explored by means of an illustrative example.
A Godunov method for localization in elastoplastic granular flow
Authors: Pitman E. Bruce
Published: August 2005

The equations governing the elastic‐plastic deformation of granular materials are typically hyperbolic, or contain small‐magnitude damping or rate effects. A finite element algorithm is the standard method for the numerical integration of these systems. In particular, finite elements allow great flexibility in the design of grid geometry. However, modern finite difference methods for hyperbolic systems have been successful in aerodynamics computations, resolving wave structures more sharply than finite element schemes. In this paper we develop a finite difference scheme for granular flow problems. We report on a second‐order Godunov‐type scheme for the integration of hyperbolic equations for the elastoplastic deformation of a simple model of granular flow. The Godunov method includes a characteristic tracing step in the integration, providing minimal wave dispersion, and a slope limiting step, preventing unphysical oscillations.

The granular flow model we consider is hyperbolic, but hyperbolicity is lost at a large value of accumulated plastic strain. This loss of hyperbolicity is a tell‐tale signal for the formation of a shear band within the sample. Typically, when systems lose hyperbolicity a regularization mechanism is added to the model equations in order to maintain the well posedness of the system. These regularizations include viscosity, viscoplasticity, higher‐order gradient effects or stress coupling. Here we appeal to a very different kind of regularization. When the system loses hyperbolicity and a shear band forms, we treat the band as an internal boundary, and impose jump conditions at this boundary. Away from the band, the system remains hyperbolic and the integration step proceeds as usual.
Finite element modelling of rock‐socketed piles
Authors: Leong E. C. , Randolph M. F.
Published: August 2005

Rock socketed piles have a number of features which differentiate them from other types of piles. The generally stubby geometry leads to more even distribution of capacity between shaft and base. However, the low ratio of pile modulus to rock modulus leads to high compressibility and this, coupled with a tendency for the load transfer response along the shaft to exhibit strain‐softening, gives rise to an overall response where the shaft capacity may be fully mobilized, and potentially degraded, before significant mobilization of base load.

The paper presents results of finite element analyses of the response of rock‐socketed piles, with particular attention to the shaft response with and without intimate base contact. The shaft interface uses a model, developed from principles of tribology, that includes dilation (and strain‐hardening) prior to peak shaft friction, followed by strain‐softening at larger displacements. The results of the study are shown to be consistent with field measurements, and to capture effects of the absolute pile diameter on the peak shaft friction. It is also shown that intimate base contact mitigates significantly the degree of strain‐softening of the shaft response.
A 2D coupled finite element and boundary element scheme to simulate the elastic behaviour of jointed rocks
Authors: Carter J. P. , Xiao B.
Published: August 2005

In this paper a coupled finite and boundary element formulation is developed for the analysis of excavation in jointed rock. The presence of joints in the rock mass has been included implicitly by treating it as an appropriate anisotropic elastic continuum. The boundary element formulation for an anisotropic medium is briefly discussed. Good agreement has been found between numerical and analytical solutions for several example problems, demonstrating the accuracy of the present formulation. Numerical solutions are also presented for the problems of a deep circular tunnel and a basement excavated in a variety of jointed rock masses.
On the indentation of a poroelastic layer
Authors: Selvadurai A. P. S. , Yue Z. Q.
Published: August 2005

The paper examines the axisymmetric contact problem related to the indentation of a fluid saturated poroelastic layer by a smooth rigid punch. The layer rests in bonded contact with a rigid impermeable base and the surface of the layer is considered to be either permeable or impermeable. The paper develops the integral equations governing the problem for the generalized case where the pore fluid exhibits compressibility. The numerical results presented in the paper illustrate the influence of the relative layer thickness, drainage conditions and the compressibility of the pore fluid on the degree of consolidation settlement of the indenting punch.
A semi‐analytical method for the wave‐induced seabed response
Authors: Rahman M. S. , El‐Zahaby Khalid , Booker John
Published: August 2005

A general semi‐analytical method is presented for the analysis of seabed response under wave action during a storm. The seabed is idealized as a poro‐elastic medium filled with a single compressible fluid with anisotropic flow. The coupled process of fluid flow and deformation of soil skeleton is formulated in the framework of Biot's theory.

The analysis for the response of homogeneous seabed of finite thickness under a plane progressive wave is developed first, followed by an extension for the case of a layered seabed. A generalization for three‐dimensional response of seabed is also developed for a general wave field which provides the analyses for seabed response under short‐crested or standing waves in the vicinity of a structure. Some numerical examples illustrating the proposed analyses are also presented.
Finite layer analysis of the behaviour of a raft on a consolidating soil
Authors: Small J. C. , Zhang B. Q.
Published: August 2005

A numerical method is developed in this paper for the analysis of the behaviour of a raft resting on a consolidating soil. The response of the raft under an applied loading is determined using the finite layer method for the soil and the finite element method for the raft. By considering deflection compatibility on the contact surface, the distribution of contact pressure is computed at various time steps. The settlement and bending moment in the raft is then evaluated by applying the calculated contact pressure back to the raft. It is shown that, in some cases, the maximum moment in the raft occurs during consolidation and that checking the final moment in the raft by use of elastic theory may not be sufficient.
CLoE, a new rate‐type constitutive model for geomaterials theoretical basis and implementation
Authors: Chambon René , Desrues Jacques , Hammad Walid , Charlier Robert
Published: August 2005

The paper describes the basic ideas and the main features of a new class of constitutive laws, in the framework of incrementally non‐linear constitutive equations. CLoE is a generic name for that new class of laws, with reference to consistency at the limit surface, and explicit localization analysis. A top–down analysis of the model is presented, and illustrated by examples.
Dual‐porosity behaviour of naturally fractured reservoirs
Authors: Bai M. , Ma Q. , Roegiers J.‐C.
Published: August 2005

A dual‐porosity model based on the modified formulation by Barenblatt et al. has been presented for the simulation of naturally fractured reservoirs. It is shown that neglecting terms in the flow governing equations may not be justified for some particular physical circumstances. The analytical solution of the proposed dual‐porosity model for a finite naturally fractured reservoir subjected to a constant outer boundary pressure is obtained using the Hankel transform technique while taking into account the transient flow in the matrix blocks. Both solution accuracy and efficiency are achieved utilizing an optimized algorithm when solving the inherent Bessel functions. This research indicates that the transient fluid pressure profiles in naturally fractured reservoirs are critically controlled by the permeability ratio between matrix and fractures, and by the compressibilities of fluid, fractures and solid grains. The fluid pressure change is substantially delayed if the permeability ratio becomes increasingly smaller. The dual‐porosity behaviour is most obvious when the compressibility of the fractures decreases relative to the increases of compressibility of the solid grains.
Monica—A computer algorithm for solving boundary value problems using the double‐hardening constitutive law Monot: I. Algorithm development
Authors: Hicks M. A.
Published: August 2005

The principal features involved in the implementation of the double‐hardening constitutive law Monot1 into a general purpose computer algorithm called MONICA2,3 are described. These include details of general program structure and of steps taken to overcome problems such as computer storage, computer run‐time, algorithm stability and problems associated with the stress–strain singularity which exists at the intersection of the two yield surfaces.
Uncoupling of coupled flows in soil—a finite element method
Authors: Sheng Daichao , Axelsson Kennet
Published: August 2005

Coupled flow of water, chemicals, heat and electrical potential in soil are of significance in a variety of circumstances. The problem is characterized by the coupling between different flows, i.e. a flow of one type driven by gradients of other types, and by the dual nature of certain flows, i.e. combined convection and conduction. Effective numerical solutions to the problem are challenged due to the coupling and the dual nature.

In this paper, we first present a general expression that can be used to represent various types of coupled flows in soil. A finite element method is then proposed to solve the generalized coupled flows of convection‐conduction pattern. The unknown vector is first decomposed into two parts, a convective part forming a hyperbolic system and a conductive part forming a parabolic system. At each time step, the hyperbolic system is solved analytically to give an initial solution. To solve the multi‐dimensional hyperbolic system, we assume that a common eigenspace exists for the coefficient matrices, so that the system can be uncoupled by transforming the unknown vector to the common eigenspace. The uncoupled system is solved by the method of characteristics. Using the solution of the hyperbolic system as the initial condition, we then solve the parabolic system by a Galerkin finite element method for space discretization and a finite difference scheme for time stepping.

The proposed technique can be used for solving multi‐dimensional, transient, coupled or simultaneous flows of convection‐conduction type. Application to a flow example shows that the technique indeed exhibits optimality in convergence and in stability.
On the mechanical response of saturated cemented materials—part I: Theoretical considerations
Authors: Pietruszczak S. , Pande G. N.
Published: August 2005

Terzaghi's ‘effective stress’ principle, though originally developed for soils, has been extensively applied to water saturated cemented materials (such as concrete, rocks, masonry units, etc.). There are, however, serious reservations regarding its validity for this class of materials. In this paper an alternative stress decomposition is proposed. It is based on average stress measures in constitutents, i.e. the solid matrix and water. Constitutive relations governing the undrained response of a cemented aggregate mixture, treated as a brittle‐plastic material, are derived. The framework is illustrated by some numerical examples pertaining to the behaviour of saturated concrete.
On the mechanical response of saturated cemented materials—part II: Experimental investigation and numerical simulations
Authors: Pietruszczak S. , Turu G. , Pande G. N.
Published: August 2005

Results of experimental investigation and numerical simulations of the mechanical response of the saturated cemented materials are reported. Saturated as well as dry samples cored from commercially available fire bricks are used. The samples were tested in a triaxial rock cell at different initial confining pressures. The tests have been simulated using the constitutive framework proposed in Part I of this paper. The results both experimental and numerical, provide the evidence in support of the proposed stress decomposition, thereby questioning the validity of Terzaghi's principle for the considered class of materials.
Multicontrast MRI of remyelination in the central nervous system
Authors: Merkler Doron , Boretius Susann , Stadelmann Christine , Ernsting Tristan , Michaelis Thomas , Frahm Jens , Brück Wolfgang
Published: August 2005

Although magnetic resonance imaging (MRI) represents the most sensitive tool for the detection of white matter abnormalities in patients with multiple sclerosis (MS), the heterogeneity of MS placques severely hampers the elucidation of specific pathophysiological processes. In order to identify putative MRI markers for de‐ and remyelination, we employed the cuprizone mouse model which leads to a selective and reversible demyelination of the corpus callosum with little or no axonal damage. Apart from histopathology, animals were studied with high‐resolution three‐dimensional MRI in vivo using multiple contrasts. While individual MRI findings significantly correlated with electron microscopy, the differentiation of regions with normal, demyelinated or remyelinated white matter by one contrast alone was less specific than by histology or electron microscopy. However, an accurate MRI prediction of the in vivo myelin status was achieved by a discriminant function analysis using a combination of T1, T2 and magnetization transfer contrast. With a correct assignment of 95% of all animals examined, the procedure will allow for the survey of new therapeutic approaches aiming at improved remyelination. Copyright © 2005 John Wiley & Sons, Ltd.
Time integration for spherical acoustic finite–infinite element models
Authors: Coyette Jean‐Pierre , Meerbergen Karl , Robbé Mickaël
Published: August 2005

In this paper, we analyse the numerical time integration of models of exterior acoustics. The major challenge lies in the instabilities that may arise from the infinite elements. In this paper we consider the special case of spherical infinite elements formulations, which have shown their relevance for industrial applications. We propose a method that combines Crank–Nicholson's method with a filtering step by the backward Euler method. The paper is illustrated with an example relevant to industry. Copyright © 2005 John Wiley & Sons, Ltd.
Basis of finite element methods for solid continua
Authors: Pian Theodore H. H. , Tong Pin
Published: August 2005

Finite element methods can be formulated from the variational principles in solid mechanics by relaxing the continuity requirements along the interelement boundaries. The combination of different variational principles and different boundary continuity conditions yields numerous types of approximate methods. This paper reviews and reinterprets the existing finite element methods and indicates other alternative schemes. Plate bending problems are used to compare the relative merits of the various methods.
A conforming quartic triangular element for plate bending
Authors: Irons Bruce M.
Published: August 2005

The theory, function generator routine and testing procedures are given for a six‐node 18 degree of freedom triangular element. At corner nodes the variables are the displacement and the two slopes. At midside nodes the variables are the displacement, the slope normal to the side, and the rate of change of this along the side—i.e., the rate of torsion. Of two options, one divides the triangle into three and takes different quartic displacements in the three regions, and the other uses displacement functions with singularities at the vertices. According to a test which compares the energies of the two formulations by eigenvalues, the second is the better if the integration is accurate. The same test, together with others based on finite differences and on nodal values, etc. checks the correctness of the routine decisively.
Transmission of vibration in beam systems
Authors: Henshell R. D. , Warburton G. B.
Published: August 2005

Three methods for finding natural frequencies and modes of complex structures composed of beam elements are described and compared. The analysis is extended to include hysteretic damping for the determination of response and transmissibility without a modal analysis. Experimental comparison is given for the response of a simple engineering structure.
Elasto‐plastic solutions of engineering problems ‘initial stress’, finite element approach
Authors: Zienkiewicz O. C. , Valliappan S. , King I. P.
Published: August 2005

The paper presents first a general formulation of the elasto‐plastic matrix for evaluating stress increments from those of stresses for any yield surface with an associated flow rule. A new ‘initial stress’ computational process is proposed which is shown (1) to yield more rapid convergence than alternative approaches (2) to permit large load increments without violating the yield criteria and thus simply to establish lower bound solutions. Several solutions showing stress distribution, strain development and growth of plastic enclaves are given both for the von Mises and for Coulomb (Drucker) type yield surfaces. Load reversal and thermoplastic behaviour are dealt with.
A refined triangular plate bending finite element
Authors: Bell Kolbein
Published: August 2005

The derivation of the stiffness matrix for a refined, fully compatible triangular plate bending finite element is presented. The Kirchhoff plate bending theory is assumed. Six parameters or degrees of freedom are introduced at each of the three corner nodes resulting in an 18 degree of freedom element. This refined element is found to give better results for displacements and particularly for internal moments than any plate bending element, regardless of shape, previously reported in the literature.
Analysis of large deflection of plates by the finite element method
Authors: Kawai Tadahiko , Yoshimura Nobutoshi
Published: August 2005

The large deflection problem of a rectangular plate is analysed by using the finite element method and employing the iteration technique. In the present study, the stiffness matrix of a rectangular plate element for bending proposed by Greene is employed, and results of numerical examples duly justifies applicability of the present method.
Numerical solution and utilization of Green's functions
Authors: Gallof S. , Kaplan B.
Published: August 2005

A numerical method for obtaining the Green's functions for Laplace's, Poisson's, and the transient heat diffusion equations is presented. The Green's functions thus obtained are then employed to rapidly obtain numerical solutions of the above equations by matrix multiplication, with subsequent considerable savings in machine time.
A general theory of finite elements. I. Topological considerations
Authors: Oden J. Tinsley
Published: August 2005

This paper presents a general theory of finite elements. The concept of finite elements is cast in a general topological framework valid for spaces of finite dimension. It is shown that the idea of finite element models can be developed in higher‐dimensional spaces, independent of specific co‐ordinate systems, for any type of continuous abstract function defined on the space. Generalizations of the familiar Lagrange and Hermite interpolation functions are presented as well as a general statement of the notion of generalized variables and conjugate fields. It is also shown that admissible finite elements can be developed for non‐Euclidean spaces of finite dimension. Topological properties of finite element models are examined in Part I of the paper. Part II is devoted to certain applications.
A finite element method of viscoelastic stress analysis with application to rolling contact problems
Authors: De S. Lynch Francis
Published: August 2005

A completely numerical method for steady state linear viscoelastic stress analysis is presented by means of the finite element approach. Numerical representations of the measured viscoelastic constitutive relations are used. This method is developed to obtain steady state solutions to mixed boundary value problems in which the character of the boundary conditions at a point changes with time. Such problems cannot be handled by direct application of the correspondence theorem. A numerical example of viscoelastic sheet rolling is presented along with an experimental verification of the solution by photo‐viscoelastic observations.
A frontal solution program for finite element analysis
Authors: Irons Bruce M.
Published: August 2005

The program given here assembles and solves symmetric positive–definite equations as met in finite element applications. The technique is more involved than the standard band–matrix algorithms, but it is more efficient in the important case when two‐dimensional or three‐dimensional elements have other than corner nodes. Artifices are included to improve efficiency when there are many right hand sides, as in automated design. The organization of the program is described with reference to diagrams, full notation, specimen input data and supplementary comments on the ASA FORTRAN print‐out.
Thermomechanical analysis of viscoelastic solids
Authors: Taylor Robert L. , Pister Karl S. , Goudreau Gerald L.
Published: August 2005

This paper is concerned with the development of a computational algorithm for the solution of the uncoupled, quasi‐static boundary value problem for a linear viscoelastic solid undergoing thermal and mechanical deformation. The method evolves from a finite element discretization of a stationary value problem, leading to the solution of a system of linear integral equations determining the motion of the solid. An illustrative example is included.
A finite element application of the modified Rayleigh–Ritz method
Authors: Morley L. S. D.
Published: August 2005

Considerable attention has been devoted in the literature on numerical methods towards securing energy convergence of solutions for, say, linearly elastic plate bending problems. Although energy convergence is necessary it by no means follows that the derived bending moments and shearing forces converge uniformly at a given point and it is this kind of feature which the engineer is really seeking.

This question is examined in the context of a problem which is of particular interest to the civil engineering field and concerns the bending of a square plate under uniformly distributed load; the plate has simply supported edges and contains a central square hole with free edges. The solution to this multiply connected and mixed boundary value problem is obtained through a recently developed modification to the Rayleigh–Ritz method which has very general application and renders the solution mathematically valid up to the internal corner points where the bending moments are singular. Use is made of triangular equilibrium finite elements in conjunction with continuous eigenfunctions. Although it is already known that the order (i.e. the eigenvalue) of the singularity at the internal corners is available by inspection, it is an interesting feature of the present solution that a good approximation to the amplitude is also obtained by an inspection of the finite element results.
Two‐dimensional automatic mesh generation for structural analysis
Authors: Frederick C. O. , Wong Y. C. , Edge F. W.
Published: August 2005

This paper presents a labour‐saving method of discretizing irregular and inhomogeneous two‐dimensional continua into triangular elements. The method uses a magnetic pen to record node point data and a computer program to generate element data. This technique eliminates the tedium in the manual generation of data and the delay due to mistakes which would otherwise arise frequently for a complex mesh.
Convergence of a finite element procedure for solving boundary value problems of the fourth order
Authors: Ženíšek Alexander , Zlámal Miloš
Published: August 2005

Convergence of a finite element procedure for the solution of the fourth‐order equations is proved. A generalization of this result is mentioned and some remarks concerning the numerical results obtained at the Computing Centre of the Technical University in Brno are given.
Finite element analysis of torsional and torsional–flexural stability problems
Authors: Barsoum Roshdy S. , Gallagher Richard H.
Published: August 2005

Stiffness matrices are formulated for the torsional and lateral stability analysis of structures composed of flexural members by the matrix displacement method. The formulations are based upon approximate displacement fields which represent the action of the element in simple flexure. Example problems, for which exact solutions are known, illustrate the accuracy and convergence characteristics of the derived formulations.
Buckling analysis by means of non‐linear programming
Authors: Gisvold Kaare M. , Moe Johannes
Published: August 2005

This paper demonstrates the applicability of general non‐linear programming methods to the solution of buckling problems. The minimum energy formulation of the buckling condition is shown to yield an unconstrained non‐linear programming problem, for which several numerical methods of solution are readily available. Some of these methods are discussed and numerical results are presented for stiffened plates with in‐plane as well as lateral loads.
Analysis of thick and thin shell structures by curved finite elements
Authors: Ahmad Sohrabuddin , Irons Bruce M. , Zienkiewicz O. C.
Published: August 2005

A general formulation for the curved, arbitrary shape of thick shell finite elements is presented in this paper along with a simplified form for axisymmetric situations. A number of examples ranging from thin to thick shell applications are given, which include a cooling tower, water tanks, an idealized arch dam and an actual arch dam with deformable foundation.

A new process using curved, thick shell finite elements is developed overcoming the previous approximations to the geometry of the structure and the neglect of shear deformation.

A general formulation for a curved, arbitrary shape of shell is developed as well as a simplified form suitable for axisymmetric situations.

Several illustrated examples ranging from thin to thick shell applications are given to assess the accuracy of solution attainable. These examples include a cooling tower, tanks, and an idealized dam for which many alternative solutions were used.

The usefulness of the development in the context of arch dams, where a ‘thick shell’ situation exists, leads in practice to a fuller discussion of problems of foundation deformation, etc., so that practical application becomes possible and economical.
A gradient computational procedure for the solution of large problems arising from the finite element discretization method
Authors: Fried Isaac
Published: August 2005

A computational procedure based on gradient iterative techniques is proposed for the solution of large problems to which the finite element method is applicable. In linear problems the procedure can be used either for solving the set of algebraic equations or for the complete inversion of the matrix of coefficients. Special attention is focused on the practical aspects of the procedure concerning its realization on the digital computer.
A simple matrix–vector handling scheme for three‐dimensional and shell analysis
Authors: Ahmad Sohrabuddin , Zienkiewicz O. C. , Irons Bruce M.
Published: August 2005

A simple program carrying out various vector operations in two‐ or three‐dimensional spaces is presented. The listings are given in A.S.A. FORTRAN IV. The program is of particular application in various forms of three‐dimensional and shell analysis as it can create and transform locally orthogonal co‐ordinates, etc. While these applications motivated its design, it is of very general use one such application is illustrated by applying the program to general perspective projection.
An automatic reordering scheme for simultaneous equations derived from network systems
Authors: King Ian P.
Published: August 2005

A procedure is presented for the automatic renumbering of network type equations prior to solution by sparse matrix techniques. The method takes an arbitrary input sequence and creates an order which makes possible solution of complex network systems by reducing demand for computer storage and time.

Examples are presented to demonstrate the procedure in action and show that, even in cases where the system has been carefully numbered, considerable improvement can be achieved. The procedure is also applicable to band matrix solution techniques.
The application of diakoptics and the escalator method to the solution of very large eigenvalue problems
Authors: Brameller A. , Lo K. L.
Published: August 2005

The eigenvalue method is well‐known as an aid to the solution of a wide range of engineering problems. In power system analysis it has relevance to travelling wave phenomena,1 sensitivity and dynamic stability in synchronous multimachine2 systems, critical speed calculation, vibration of structures and other related topics. The method of numerical solution of eigenvalues depends on the size and nature of the problem and often where large matrices are involved presents great difficulties.

This paper describes in detail the application of the escalator method and diakoptics to large eigenvalue problems. The escalator method is a well‐established one which consists of a systematic way of escalating from a 2 × 2 matrix up to any desired order in steps of one row and column at a time. The diakoptical method reduces computer storage, calculation time and improves accuracy. This results in the more economical solution of large and complicated problems which cannot be conveniently solved by any orthodox method. The paper deals with problems of degeneracy and means of overcoming these by simple routine processes. It concludes by indicating the particular advantages of the method and its usefulness for a wide variety of general engineering problems.
The finite difference and localized Ritz methods
Authors: Croll J. G. A. , Walker A. C.
Published: August 2005

The conventional central finite difference equations for the plane stress extension of flat plates are derived as a localized Ritz process. A dual differential‐variational discretization of this type enables common classification of the finite difference and finite element methods. Also, it provides alternative methods of establishing sufficiency conditions and relative rates of convergence for discrete systems derived from a localized Ritz process, and the existence of solution bounds for discrete systems derived using difference procedures.
Axial wave propagation in membrane shells of revolution
Authors: Counts J. , Bennett J. G.
Published: August 2005

The dynamic finite element technique, which is referred to in the literature as ‘computer‐analysis’, is applied to wave propagation problems occurring in finite and semi‐infinite linearly elastic membranes of revolution. Both semi‐infinite and finite versions of cylindrical and conical membranes are considered, and a finite membrane having a meridional curve which is parabolic is solved. The source of excitation is generally a constant velocity motion of one end of the membranes, but the results for a stress‐pulse input at one end of a semi‐infinite cylindrical membrane are also given. The results for the finite membranes are new, and the results for the semi‐infinite problems are discussed with respect to previously published results. The two‐dimensional state of stress in the membrane requires careful ordering of the calculations, and the boundary conditions for finite membranes are shown to follow logically from this ordering of the calculations. The difference in the solutions resulting from prescribing an axial or a tangential velocity excitation at the end of a conical membrane is presented, and the mesh size necessary for convergence to the solution is indicated. The graphs of the results clearly indicate regions in space and time where the membrane model should be replaced by the shell formulation to represent a realistic structure. The technique is shown to be self‐contained and independent of any formal method such as the method of characteristics.
Dynamic programming and the solution of the biharmonic equation
Authors: Distéfano Néstor
Published: August 2005

The numerical solution of the biharmonic equation in a rectangular domain is presented in the context of continuous dynamic programming techniques. The equations are specialized to the solution of elastic rectangular plates. A suitable approximate expression of a certain functional equation containing derivatives only in one direction is used to derive equations for the stiffness and flexibility matrices of the plate. It is shown that those matrices satisfy matrix Riccati equations subject to suitable initial conditions. It is also shown that the condition of optimality in the Hamilton‐Jacobi‐Bellman equation directly expresses a classical variational principle, i.e. the principle of complementary energy. Some numerical examples are finally presented.
Non‐linear programming for the plastic analysis of local deformations in shell structures
Authors: Morris A. J.
Published: August 2005

The paper presents an analysis of the response of plastic spherical and cylindrical shells subjected to loads applied through a rigid boss. Special emphasis is placed on following the load‐deflection behaviour of these structures after the application of the yield‐point load in order to predict the appearance of any snapping action.

The method of analysis assumes that upper bound calculations are applicable and that the associated velocity fields can be represented by a series of piecewise continuous polynomials. The internal dissipation of energy for the structures are then written in terms of the coefficients of these polynomials and the values appropriate to the solution are found by using a non‐linear programming routine.

The results of this analysis are correlated with a non‐dimensional boss size parameterpand compared with the results of experimental investigations. Mention is also made of the possible effects of initial imperfections.
A steepest gradient method for optimum structural design
Authors: Templeman Andrew B.
Published: August 2005

This paper describes a search procedure for finding the unconstrained maximum or minimum of a function of many independent variables. If this function represents the volume, cost, stiffness, etc. of a structure and each of the independent variables is associated with a parameter governing the geometry of the structure then designs of optimum geometry may be made in certain cases with the assistance of this search procedure. The procedure consists of steepest gradient calculations used in conjunction with a reverse Fibonacci location process. A ridge‐following technique is included to speed convergence in addition to localized exploration in the region of an optimum.

The search procedure has been programmed for computer use and an outline of its structural design applications is presented together with an example of its efficiency in a specific case.
Trigonometric function representations for rectangular plate bending elements
Authors: Chakrabarti Subrata
Published: August 2005

A study of bending of plates for small deformations by applying the finite element method is presented in this paper.

A new class of displacement functions has been developed for rectangular bending elements. For the first time a method is proposed for the derivation of displacement functions in which trigonometric expressions that had apparently failed to yield satisfactory results in earlier attempts can be used along with polynomial terms.

The derivation leads to conforming type of displacement functions which satisfy the convergence criterion. The approach also demonstrates how many more new displacement functions can be found.
Dynamic response analysis of geometrically non‐liner structures subjected to high impact
Authors: Gupta K. K.
Published: August 2005

An efficient digital computer method is presented for the determination of propagation of elastic stresses and deformations in certain geometrically non‐linear structures subjected to high impact loading. The finite element matrix displacement approach utilizing curved quadrilateral shell elements in conjunction with a nodewise predictor–corrector method employing Runge–Kutta extrapolation techniques has been adopted for the present solution.

The related computer program written in FORTRAN V for the UNIVAC 1108 computer has proved to be effective for the solution of a range of practical problems including rectangular and cylindrical panels. Numerical results are presented for a relevant structure, the cell container and the negative electrode of an impact‐resistant battery subjected to high impact, simulating its free landing on a planetary surface.
Mixed finite element method for axisymmetric shells
Authors: Elias Z. M.
Published: August 2005

A mixed variational formulation is used as basis for developing a mixed finite element method for axisymmetric shell. The independent unknowns of the method are the axial and radial displacement components, the rotation of the normal to the middle surface and the meridional bending stress couple. The basic element is a frustrum of curved meridian. General advantages of the mixed method are presented, one of which is the possibility of using piece‐wise linear functions of the meridional arclength to represent the basic unknowns. Test results are presented for plate bending, transverse shear deformation, membrane behaviour, edge‐zone bending, bending near the junction of two shells, convergence of the method and accuracy of middle surface curvature interpolation. Shell geometries considered are cylindrical, conical, spherical and ellipsoidal. Good results are obtained which should increase interest in the relatively less known and less tested mixed method as compared to the stiffness method.
A finite element approach to optimal design of plastic structures in plane stress
Authors: Maier G. , Zavelani‐Rossi A. , Benedetti D.
Published: August 2005

Plane stress structures of any shape and boundary conditions are simulated by finite element models with homogeneous stress and strain fields in each element. Besides the given live loads, dead loads (such as self‐weight) depending on the unknown thickness distribution are allowed for. Possible practical requirements on geometry (minimum thickness, areas of equal thickness, areas of thickness variation in a prescribed way) are taken into account. Yield surfaces of the materials are piecewise linearized. On this basis the minimum weight design problem is formulated in terms of a linear program. This program is dualized and the pair of dual programming problems is discussed. The mechanical interpretation leads to the generalization of some known limit design theory results.

Some numerical examples are given at the end.
A survey of optimal structural design under dynamic constraints
Authors: Pierson Bion L.
Published: August 2005

Recent published research on structural optimization subject to dynamic constraints is reviewed, and suggestions for further work are offered. Both methods for handling constraints on natural frequencies and methods for treating the more difficult constraints on quantities directly related to the dynamic response are discussed. Computational aspects are emphasized throughout.
Integral equation method for soulution of boundary value problems of structural mechanics, Part I. Ordinary differential equations
Authors: Hajdin Nikola , Krajcinovic Dusan
Published: August 2005

This paper presents a method of numerical solution of boundary value problems governed by a set of ordinary differential equations. The highest derivative is chosen as the unknown function. Governing equations are transformed into a set of integral equations. The kernels of integral equations turn out to be influence functions for deflection and/or bending moments of a corresponding beam, and can, therefore, be computed using well‐known methods of structural analysis. Finally, the unknown function (highest derivative) is approximated in a defined manner and the solution is obtained through numerical integration.
Convergence and accuracy of three finite difference schemes for a two‐dimensional conduction and convection problem
Authors: Runchal A. K.
Published: August 2005

The convergence and accuracy characteristics of two commonly used finite difference schemes, namely the central and the upwind difference, are compared with a scheme recently proposed by Spalding. For a simple two‐dimensional problem with conduction and convection, it is shown that the scheme proposed by Spalding is preferable choice both from the point of view of accuracy and that of the convergence. The extension of the conclusion to a general case must await further substantiation.
Use of the least squares criterion in the finite element formulation
Authors: Lynn Paul P. , Arya Santosh K.
Published: August 2005

This paper presents a new method of formulating the finite element relationships based on the least squares criterion. To overcome the high degree of inter‐element continuity, a method of reducing the original governing differential equation to a set of equivalent system of first‐order differential equations is proposed. The validity of the method is demonstrated by means of several numerical examples. In particular, application of the method to problems with unknown variational functionals is considered.
Finite element solution algorithm for viscous incompressible fluid dynamics
Authors: Baker A. J.
Published: August 2005

A numerical solution algorithm employing the finite element concept of solid mechanics is derived for the transient laminar two‐dimensional flow of an incompressible viscous fluid. Through dependent variable transformation, the problem is uniformly recast into the solution of a quasi‐linear elliptic boundary value‐problem, for which the finite element solution theory is established. The algorithm is uniquely user‐oriented in accepting the generalized elliptic boundary condition specification of any non‐coordinate‐surface solution do main closure segment and on employing an arbitrarily irregular computational latticc. Numerical results are presented for several problems in internal flow illustrating solution accuracy, convergence, versatility and the ability to predict imbedded regions of recirculating flow.
The analysis of dislocation systems by the finite element method
Authors: Owen D. R. J. , Prakash A.
Published: August 2005

It is shown how the stress field due to any prescribed continuous distribution of dislocations can be determined. The finite element method is employed giving wide freedom with regard to boundary geometry and material properties. The presentation is limited to situations which conform to either the standard plane or anti‐plane conditions. Some results are obtained for simple dislocation configurations and compared with theoretical expressions available. Solutions are then obtained to problems in which the material behaves elasto‐plastically, a limiting shear stress criterion being employed. Finally the analysis of discrete edge dislocations by use of the slab analogy is presented.
On the automatic selection of independent displacement variables in general purpose finite element codes
Authors: Barlow John
Published: August 2005

The problem of generation of surplus displacement variables in general purpose finite element codes, using the displacement method, is discussed. A method of automatic selection of independent variables is proposed which eliminates abortive computer runs from this source and saves engineer data preparation. Extensions of the algorithm are outlined and the uniqueness of solution demonstrated by an example.
Singularity programming: A numerical technique for determining the effect of singularities in finite difference solutions illustrated by application to plane elastic problems
Authors: Emery A. F. , Segedin C. M.
Published: August 2005

This paper contains a description of a numerical technique designed to overcome the difficulties encountered in the approximate solution of two‐dimensional discretized field problems when there are singularities arising from sharp corners, discontinuities, point sources, etc. The essence of the method is to modify the discretization by incorporating in the numerical computations the known analytical form of the singularities. The method is applicable to a wide variety of linear two‐dimensional field problems, and is illustrated herein with plane elastic problems.
Determination of stress intensity factors in cracked plates by the finite element method
Authors: Yamamoto Yoshiyuki , Tokuda Naoaki
Published: August 2005

Stress fields near crack tips in an elastic body can be specified by the stress intensity factors which are closely related to the stress singularities arising from the crack tips. These singularities, however, cannot be represented exactly by conventional finite element models. A new method for the analysis of stresses around cracks is proposed in this paper on the basis of the superposition of analytical and finite element solutions. This method is applied to several two‐dimensional problems whose solutions are obtained analytically, and it is shown that their numerical results are in excellent agreement with analytical ones. Sufficiently accurate results can be obtained by the conventional finite element analysis with rather coarse mesh subdivision. Computational efforts are then considerably reduced compared with other methods.
Accuracy of the finite element analysis for the elastic plate with a circular hole
Authors: Radaj D.
Published: August 2005

This paper compares the results obtained by the finite element method with ‘exact’ solutions to a given set of problems. These are the stresses on the boundary of a hole in an infinite plate, the plate being subjected to three different types of loading. Two types of element are used for these plane stress problems, triangular elements with constant strains and tri‐ angular elements with linearly varying strains. The problems are solved for two different meshes and the results shown are stresses along a radial section and the values derived for stress concentrations against the number of unknowns in each mesh.