bluuebunny/crossref_metadata_2025 huggingface dataset:
Implicit integration in soil plasticity under mixed control for drained and undrained response
Authors: Alawaji H. , Runesson K. , Sture S. , Axelsson K.
Published: August 2005

An algorithm is outlined for the implicit integration of isotropic plasticity models for an arbitrary choice of mixed stress and strain control variables. Drained as well as undrained behaviour is considered. The closest‐point‐projection method in conjunction with a completely strain‐driven format is used in a core algorithm. In the drained case strain response variables are determined via iterations to satisfy equilibrium of prescribed and calculated stresses that correspond to the strain response variables. In the undrained case, on the other hand, strains and pore pressure are determined via simultaneous iterations to satisfy equilibrium and the incompressibility condition. The algorithm is applied to a new generalized cam‐clay model, and various iteration techniques are assessed. In particular, Newton iterations which employ the matrix of algorithmic tangent stiffness moduli are shown to compete favourably with more conventional methods.
Influence of construction technique on the performance of a braced excavation in marine clay
Authors: Smith I. M. , Ho D. K. H.
Published: August 2005

Finite element analyses are used to quantify the effects of construction technique on the performance of braced excavations. It is first shown that the computations can be continued to ‘collapse’ and that the results agree with limit plasticity solutions. A case study involving stratified deposits of marine clay and sand is used to carry out a Class C1 ‘prediction’ of field performance. The influence of construction technique on deformations and strut loads is shown. The results of the computations are in agreement with field observations, assuming a relatively ‘flexible’ construction technique. However, even if much ‘stiffer’ techniques had been used, large field deformations would have been unavoidable under certain circumstances.
Effect of sand lenses on groundwater flow and contaminant migration
Authors: San K. W. Edward , Rowe R. Kerry
Published: August 2005

The effect of homogeneous sand lenses on the groundwater flow in an otherwise homogeneous clayey deposit is examined by performing Monte Carlo simulations using a finite element flow model. In the simulations, the locations of the sand lenses are assumed to be mutually independent. The paper examines the effect on the flow field in a clayey deposit of (a) different percentages of sand lenses, (b) different hydraulic conductivities of the sand lenses, (c) different average sand lens sizes, (d) non‐uniformity of the sizes of the sand lenses, and (e) localization of the sand lenses. The effect of these non‐uniform flow fields on contaminant migration is then examined using a finite element contaminant transport model. For the range of cases considered it is shown that: the volume of sand lenses present has a greater influence than the shape, size, location and hydraulic conductivity of the sand lenses; simplified calculations performed using the geometric and harmonic means of hydraulic conductivity bracket the behaviour evident from more complex analyses; and the maximum impact on an aquifer separated from a waste disposal facility by a deposit containing sand lenses can be modelled to sufficient accuracy, using quite simple flow and contaminant transport models.
Transient response of a circular cavity in a poroelastic medium
Authors: Senjuntichai T. , Rajapakse R. K. N. D.
Published: August 2005

This paper considers the transient response of a pressurized long cylindrical cavity in an infinite poroelastic medium. To obtain transient solutions, Biot's equations for poroelastodynamics are specialized for this problem. A set of exact general solutions for radial displacement, stresses, pore pressure and discharge are derived in the Laplace transform space by using analytical techniques. Solutions are presented for three different types of prescribed transient radial pressures acting on the surface of a permeable as well as an impermeable cavity surface. Time domain solutions are obtained by inverting Laplace domain solutions using a reliable numerical scheme. A detailed parametric study is presented to illustrate the influence of poroelastic material parameters and hydraulic boundary conditions on the response of the medium. Comparisons are also presented with the corresponding ideal elastic solutions to portray the poroelastic effects. It is noted that the maximum radial displacement and hoop stress at the cavity surface are substantially higher than the classical static solutions and differ considerably from the transient elastic solutions. Time histories and radial variations of displacement, hoop stress, pore pressure and fluid discharge corresponding to a cavity in two representative poroelastic materials are also presented.
A finite element formulation in Lagrangian co‐ordinates for heat and fluid flow in compacting sedimentary basins
Authors: Wangen Magnus
Published: August 2005

This article presents a numerical model of heat and fluid flow in compacting sedimentary basins formulated in Lagrangian co‐ordinates. The Lagrangian co‐ordinates are the sediment particle positions of the completely compacted basin. A finite element formulation of excess water pressure and temperature in these Lagrangian co‐ordinates is presented, in addition to an equivalent formulation in the real co‐ordinates. The later formulation is also Lagrangian of nature, since the elements of the grid in the real co‐ordinates always frame the same sediment particles. In other words, it is the Lagrangian grid mapped to the real space. This is done in an iterative loop which solves for excess water pressure, and then updates the real co‐ordinates of the sediment particles. By comparing the two finite element formulations it is concluded that the one in real space is the simplest, most efficient and most precise.

The model is validated by comparison with two dimensionless one‐dimensional solutions, one analytical for the linear case, and one numerical for the non‐linear case. Both these one‐dimensional solutions are obtained on the unit interval, where the moving top boundary caused by continuous sedimentation is incorporated.
Finite element analysis of axisymmetric flow into partially penetrating wells
Authors: Singh Kamala K. , Dasgupta Shambhu P. , Ojha Triveni P.
Published: August 2005

The finite element method was used to solve the problem of flow to a partially penetrating strainer well in a leaky confined aquifer under steady and unsteady conditions. Predictions of the model were compared with reported pumping test data. A good agreement was obtained between them. The effects of penetration and screen position on discharge through imperfect well were studied. Results were compared with analytical solutions and presented graphically.
A finite element solution of a fully coupled implicit formulation for reservoir simulation
Authors: Sukirman Y. , Lewis R. W.
Published: August 2005

An iterative method is presented for solving a fully coupled and implicit formulation of fluid flow in a porous medium. The mathematical model describes a set of fully coupled three‐phase flow of compressible and immiscible fluids in a saturated oil reservoir. The finite element method is applied to obtain the simultaneous solution (SS) for the resulting highly non‐linear partial differential equations where fluid pressures are the primary unknowns. The final discretized equations are solved iteratively by using a fully implicit numerical scheme. Several examples, illustrating the use of the present model, are described. The increased stability achieved with this scheme has permitted the use of larger time steps with smaller material balance errors.
A note on the effect of mesh pattern on the lower‐bound bearing capacity of embedded strip footings
Authors: Sing D. N. , Basudhar P. K.
Published: August 2005

This study deals with the prediction of the lower‐bound bearing capacity of embedded smooth strip footings. The effect of mesh pattern on the result has been studied and a generalized mesh pattern has been proposed. The results obtained are compared with the computed solution using Meyerhof's bearing capacity equation.
Considering the effect of body force for regional land displacements
Authors: Lu Ruey‐Hsing , Yeh Hund‐Der
Published: August 2005

In this study, a general mathematical model was developed for land displacements that occur as a result of the pressure decline in confined and/or phreatic aquifers. Two equations were developed by employing the equilibrium (force balance) equation and the flow equation in a deforming aquifer system. Both of these equations were integrated over the thickness of the aquifer system once a regional model had been formulated. The change of the body force in saturated and unsaturated zones of aquifers was considered in the derivation of the equilibrium equation. It was assumed that no external loading or force acting on the aquifer system was present. Two coupled equations expressed in terms of the averaged dilation and pressure were then obtained. The pumping data sets given in the papers of Bear and Corapcioglu1,2 in 1981 and 1983 were analysed. Drawdown and displacements in a confined aquifer were demonstrated to be identical to those estimated by Bear and Corapcioglu.1 In the case of a phreatic aquifer, however, the results estimated by the present approach were slightly different from those obtained by Corapcioglu and Bear.2 The discrepancies in the results are possibly due to errors in the equations presented by Corapcioglu and Bear.2 The present approach was able to avoid several assumptions and complex procedures used by Bear and Corapcioglu,1,2 especially in the case of a phreatic aquifer, by taking into account the change in the body force.
Amplification of vertically propagating SH waves by multiple layers of Gibson soils
Authors: Davis Rob , Hunt Bruce
Published: August 2005

Using the Haskell–Thomson transfer matrix approach, an analytical solution is obtained for SH wave amplification by multiple layers of Gibson soils (i.e. viscoelastic layers with linearly varying shear moduli). Amplification spectra for typical soil and basement rock properties are calculated. A comparison of the Gibson soil response with that obtained for homogeneous soil models shows generally stronger amplifications associated with the Gibson soil.
Analysis of ‘infinitely long’ excavations using finite and boundary elements
Authors: Beer G. , Poulsen B. A.
Published: August 2005

The paper deals with the analysis of excavations which are very long and can, for all practical purposes, be considered to be infinitely long. Special infinite finite and boundary elements are developed for the modelling of the infinitely long part of such excavations. Test examples are presented which show the accuracy which can be obtained by using these elements. Finally, examples of application in mining and petroleum engineering are shown.
Analysis of compressible axially loaded piles in rock
Authors: Kodikara J. K. , Johnston I. W.
Published: August 2005

Analytical solutions are developed for the prediction of the load–settlement response of a compressible axially loaded cast in situ pile in rock. The principal input parameters are derived from the τ–z curve which applies to the contact zone between the pile shaft and the embedment material. For larger diameter piles in rock, these τ–z curves can differ markedly from curves that apply to piles in clay and may include a significant strain hardening region prior to reaching peak strength. In addition to the complete analyses which would normally require the use of a computer, simplified solutions suitable for hand calculations have been derived for the peak load and the pile head displacement to peak. An example of the application of these simplified design calculations is presented.
Calculation of the critical height of a homogenized reinforced soil wall: A numerical approach
Authors: Abdi R. , De Buhan P. , Pastor J.
Published: August 2005

This paper is devoted to the stability analysis of a vertical embankment in reinforced soil, assuming that a very large number of reinforcements are periodically distributed throughout the soil mass. The reinforced soil is modelled as a homogeneous medium that obeys a macroscopic yield condition.

Two numerical formulations of the homogenized problem, derived from the lower and upper bound theorems of limit analysis, respectively, with a finite element discretization technique, are described. They both lead to a linear programming problem, which is carried out by means of XPRESS industrial LP code.

The practical implementation of both the static and kinematic finite element programs on the case of a vertical reinforced earth wall results in close estimates of its failure height, which are in good agreement with available experimental data. This points to the ability of such programs to provide a rigorous evaluation of the limit loads of structures through the determination of lower bound and upper bound estimates sufficiently close to each other.
Strain localization analysis by elasto‐viscoplastic softening model for frozen sand
Authors: Oka Fusao , Adachi Toshihisa , Yashima Atsushi , Chu Lim Liong
Published: August 2005

The aim of the present paper is to numerically analyse the behaviour of frozen sand by using a viscoplastic constitutive model with strain softening. A constitutive model has been developed introducing the stress history tensor which is a functional of the stress history, with respect to a generalized time measure. It is shown that Adachi and Oka's model is applicable to the results of triaxial tests on a frozen Toyoura sand at different strain rates. First, the instability of the model is discussed within the framework of bifurcation theory. The model is then implemented into a FEM code to numerically simulate the behaviour under plane strain conditions. From the numerical results, it is revealed that the formation of shear bands is possible and the characteristics of strain localization, such as shear banding, depend on the strain rates.
Large strain static and dynamic semisaturated soil behaviour
Authors: Meroi E. A. , Schrefler B. A. , Zienkiewicz O. C.
Published: August 2005

The theoretical and computational aspects of large strain static and dynamic partially saturated soil analysis are presented. The soil is assumed to be a three‐phase material with a solid phase which may yield according to a generalized plasticity theory, whose liquid phase flows according to Darcy's law and where gaseous phase remains equal to the external ambient pressure. Permeability varies not only as a function of the degree of water saturation, but also as a function of the void ratio. These aspects are shown on several examples.
A simple model for inelastic footing response to transient loading
Authors: Deeks A. J. , Randolph M. F.
Published: August 2005

This paper presents a mechanical analogue which models the response of a rigid circular footing on an ideal elastoplastic half‐space to transient loads. In the rational analysis of pile‐driving dynamics, the response of soil at the base of a pile is often approximated by a footing on a semi‐infinite half‐space. Most existing base models employ the well‐known Lysmer analogue to model the elastic response of the soil at the pile base, and account for the inelastic soil behaviour through the inclusion of a plastic slider with a slip load equal to the ultimate failure load of the footing. The improved model provides a force response which is significantly closer to the ideal response than existing models. The paper commences with a review of analytical solutions for the dynamic response of a rigid circular footing on an elastic half‐space. Existing mechanical analogs for the system are reviewed, and an automatic matching process proposed which improves the accuracy of the analogs under transient loading. The inelastic response is then studied using the finite element method, and the mechanical analogs are modified to allow representation of the observed inelastic behaviour. Examples are presented illustrating close agreement between the proposed models and finite element analyses for a range of Poisson's ratio. The improved models have direct application for one‐dimensional models of pile driving, particularly in the back‐analysis of data from dynamic testing of piles. They are also applicable to studies of dynamic compaction.
Micromechanics modelling for stress–strain behaviour of brittle rocks
Authors: Li Chunlin
Published: August 2005

A micromechanics model for stress–strain behaviour of brittle rocks has been developed. Microcracking is the mechanism of the non‐linear deformation behaviour for brittle rocks in the pre‐peak stage. The non‐linear behaviour in this stage is simulated by considering the local axial splitting of microcracks. The relationships between the compressive stresses, the growth of microcracks, and the fracture‐induced deformation are analytically established. In the post‐peak stage the shear faulting predominates the process of deformation, which is simulated by a damage model. This micromechanics model is helpful in understanding the failure process in brittle rocks. The model can be used to simulate the complete stress–strain behaviour of rock. The model simulations are consistent with experimental results.
A model for the constant‐head pumping test conducted in vertically fractured media
Authors: Markle J. M. , Rowe R. K. , Novakowski K. S.
Published: August 2005

An analytical model for the constant‐head pumping test is developed for a partially penetrating well that has a finite thickness skin, and intersects a single vertical fracture. In the model, the fracture is fully confined and flow occurs only in the fracture. The model is developed using Laplace transform and finite Fourier transform methods. The model is to be used for analysing well test data from vertically fractured media and for verifying numerical models. Dimensionless curves are used to study the effects of a finite thickness skin and a partially penetrating wellbore. In the presence of a finite thickness skin, or a partially penetrating wellbore, a typical flow response for the constant‐head pumping test has three distinct periods of flow corresponding to small‐, intermediate‐ and large‐time. Small‐ and large‐time approximations are presented for the model. For tests where the wellbore is fully penetrating, or the partial penetration ratio is known, these approximations can be used to analyse field data.
Experimental and numerical study of sand–steel interfaces
Authors: Tejchman Jacek , Wu Wei
Published: August 2005

Experimental and numerical studies on and sand–steel interfaces are presented. Emphasis is laid on the effect of boundary conditions of the whole system and of localized deformation. The experiments with different roughness of steel surface, sand density, normal stress and grain size are carried out in a plane strain apparatus, a parallely guided direct shear apparatus and in a planar silo model with a movable bottom and parallel steel walls. During the test in the plane strain apparatus the localized zone is observed with the help of X‐rays. The results indicate a significant effect of wall roughness and boundary conditions of the whole system on the wall friction angle and the thickness of the localized zone along the steel surface.

An elastoplastic constitutive model established within the framework of a Cosserat continuum, capable of describing isotropic hardening, softening and dilatancy, is implemented in a finite element code. The model differs from the conventional theory of plasticity due to the presence of Cosserat rotation and couple stress using the mean grain diameter as the characteristic length. Finite element simulations of simple shear tests are presented. The additional boundary condition along the steel plate, characteristic of the Cosserat continuum, allows for modelling the different roughness of the steel plate with consideration of grain rotations. A comparison between the numerical calculations and the experimental results shows acceptable agreement.
Application of non‐associative hierarchical model for geologic materials for active earth pressure experiment
Authors: Ugai K. , Desai C. S.
Published: August 2005

A non‐associative constitutive model in the hierarchical single surface (HISS) approach was used to characterize the simulated (geologic) materials in a retaining wall model test. The constitutive model was implemented in a finite element procedure to predict the experimental behaviour of the retaining wall under active earth pressure conditions. In the model test, the backfill was made of aluminium rods of 5 cm length with a mixture of 3 and 1·6 mm diameters. The wall was 48 cm high and loading was simulated by rotating the wall about its base.

Bi‐axial compression tests were performed to obtain the strength and deformation constants of the backfill. The backfill was assumed to be an isotropic strain‐hardening cohesionless material under plane strain conditions which obeys the non‐associative δ1‐model developed by Desai et al.1 The results of the model test were predicted based on elastoplastic finite element calculations. Good agreements between predictions and experiments were shown for deformations of the backfill, and relations between active earth pressures and wall displacements.
Contact detection algorithms for three‐dimensional ellipsoids in discrete element modelling
Authors: Lin Xiaoshan , Ng Tang‐Tat
Published: August 2005

Using arrays of ellipsoidal particles in the Discrete Element Method (DEM) is one of the means to enhance simulations of granular materials. A major challenge in implementing ellipsoidal element to DEM is the development of an efficient and stable contact detection algorithm in order to properly detect contact formation and compute contact forces on the elements. In view of the current available methods in two‐dimensional (2D) condition, two different contact detection algorithms for ellipsoidal particles in 3D modelling are identified. Their accuracy and efficiency are compared and the results favour the algorithm based on the geometric potential concept. This algorithm has been implemented in the recently developed DEM code ELLIPSE3D.
The damped transient behaviour of finite beams and plates
Authors: Koenig Herbert A. , Davids Norman
Published: August 2005

The direct Finite Element Analysis which was successfully employed in the solution of dynamic flexural traveling wave problems is extended herein to provide the transient behaviour of finite beams and plates in which shear deformation and rotatory inertia are considered. The particle and angular velocities are exponentially damped so that the static solutions for these problems are obtained with the same analysis which provided the dynamic and transient cases. Three special cases are chosen as examples. In the first, a sinusoidally varying shear force is applied at the tip of a cantilever beam. The resonant characteristics of this beam for both the undamped and damped cases are studied. In the second, a step shear loading is applied to a cantilever beam and its damped dynamic history is studied. Finally, a circular plate whose outer edge is simply supported is impacted at its inner edge by a step moment and its damped transient behaviour is determined. The idea of the methods is potentially applicable to dynamic problems in general.
Improved deformation functions for the finite element anlysis of beam systems
Authors: Cohen E. , McCallion H.
Published: August 2005

Deformation functions which, in addition to satisfying the continuity conditions at nodes. Also satisfy. Approximately, the governing differential equation within the element allow system eigenvalues to be found more accurately, with a given number of elements, than is possible with previously published deformation functions. This is illustrated for the case of beams.
A method of solution for non‐linear simultaneous algebraic equations
Authors: Walker A. C.
Published: August 2005

The solution of the large numbers of non‐linear algebraic equations occurring in analyses of non‐linear structural systems using finite differences or finite elements is time consuming even for the fastest computers. This paper presents a method of solution based on a Taylor's expansion technique which is an aid in the solution of such systems of equations.

Examples presented show that in the finite element analysis of moderately non‐linear structural systems the technique provides sufficiently accurate solutions. For more non‐linear systems the technique provides excellent starting values for the Newton‐Raphson method.
End displacements of semi‐infinite cylinders due to annular loadings
Authors: Wilson E. A.
Published: August 2005

Surface displacements at the end of a semi‐infinite, circular cylinder due to an axisymmetric ring of forces on the end are examined. The solution which has been found may then be used to find surface displacements for general axisymmetric loadings by convolution. The solution, in tabular form, is given as corrections to the counter‐part half‐space solution.

The method of solution involves a three step superposition process. First, the displacement due to a ring of forces on a half‐space is found by using the Boussinesq solution. Then, the excess tractions on the half‐space, over that of the cylinder, are removed. This is done in two parts. The problem of an infinite cylinder with linearly varying pressure and shear over a short length of the lateral surface is solved by using Fourier integrals. This is used for the removal of the pressure and shear on the lateral surface of the cylinder by convolution. Next, the stresses at the mid‐section of the infinite cylinder are removed. This is done by finding a set of boundary conditions for the end which yields zero tractions on the lateral surface. Then a series of these boundary conditions is used to approximate the tractions which must be removed.

With the solution thus obtained, two sample problems are shown: 1. an elastic cylinder in contact with a half‐space; 2. a rigid punch in contact with an elastic cylinder.
A rectangular plate bending element the use of which is equivalent to the use of the finite difference method
Authors: Salonen E‐M.
Published: August 2005

A presentation is made of a rectangular plate bending element, the use of which corresponds to the finite difference method. The element stiffness matrix is arrived at by approximation of the strain energy of the element by suitably selected finite difference expressions which contain not only values in respect of the deflection, but also values of its first derivatives. On the basis of the connection found between the two methods, some changes are suggested in the finite difference method, which involve a more realistic way of considering the detailed distribution of the loading. The effect of these modifications is illustrated in two applications.
Minimum weight design of structures with application to elastic grillages
Authors: Moses Fred , Onoda Susumu
Published: August 2005

A review is given of some mathematical programming methods suitable for optimization of structures needing matrix methods for analysis. An application is presented for elastic flat grillages made of straight orthogonal beams normally loaded. Empirical relationships are used to relate beam section properties so that each beam element has only one design variable. Optimization results are obtained by methods of stress‐ratio, linear programming‐cutting plane and usable‐feasible gradient directions. A comparison of the efficiency of these methods is given for the grillage designs which are shown to have non‐convex stress constraints and numerous relative optima. Instances are given of non‐fully stressed global optima and fully stressed designs which are not local optima for cases with only stress constraints. Discussions include locating the global optima for grillage designs and extensions of the methods presented to other structural design problems.
Application of non‐linear programming to optimum grillage design with non‐convex sets of variables
Authors: Kavlie Dag , Moe Johannes
Published: August 2005

The application of non‐linear programming methods for the optimum design of statically indeterminate structures is discussed, with special emphasis on the design of elastic grillages loaded laterally and in plane. Some features of SUMT (sequential unconstrained minimization technique) are demonstrated by means of numerous examples of varying complexity. The Variable Metric method of search is discussed and compared to Powell's Direct Method. It is shown that non‐convex sets of design variables are often encountered in structural problems of the grillage type. SUMT may still be used, but the choice of starting value and initial response factor decisively influences the chance of finding the global optimum.

It is demonstrated that a fully stressed design may not necessarily correspond to the minimum weight design. Optimum design of grillages which are simultaneously subjected to lateral and in‐plane loads may be performed efficiently by means of non‐linear programming.
Automatic design of guyed masts subject to deflection constraints
Authors: Livesley R. K.
Published: August 2005

In the design of a guyed mast the design specification often imposes limits on the allowable deflection of the mast under wind and other lateral loads. While the deflected form of a mast depends on many different design parameters, the guy erection tensions form one of the simplest means of controlling the lateral displacements. The paper describes a procedure for calculating these tensions in the case of a mast required to have a specified set of displacements under a given set of lateral loads. It also discusses the case where specified deflections are not to be exceeded under a number of different loading conditions.
Transient field problems: Two‐dimensional and three‐dimensional analysis by isoparametric finite elements
Authors: Zienkiewicz O. C. , Parekh C. J.
Published: August 2005

The transient field problem of the type encountered in heat conduction problems is formulated in terms of the finite element process using the Galerkin approach. Curved two‐dimensional and three‐dimensional, isoparametric elements are used in a time‐stepping solution and their advantages illustrated by means of several examples.
A direct numerical method for the solution of field problems
Authors: Tottenham H.
Published: August 2005

A numerical method for the analysis of field problems is described. The algorithm is based upon the generalized Betti‐Maxwell theorem. Using a set of known solutions to problems with similar boundary conditions produces a set of ‘integral’ equations for the required solution. Using any convenient numerical integration formula reduces the problem to the solution of a set of simultaneous algebraic equations. The accuracy of the solution depends upon the accuracy of the integration formula as applied to the problem under consideration and is independent of the known auxiliary solutions. The method is described in detail as applied to harmonic problems.
A numerical solution for the symmetric melting of spheres
Authors: Grimado Philip B. , Boley Bruno A.
Published: August 2005

A numerical method is presented for the solution of the radially symmetric heat conduction problem in a melting sphere. The method employs the embedding technique; this permits the solution to be written in the form of an ordinary integro‐differential equation which is readily solved numerically by means of a forward integration scheme. The accuracy of the method is briefly discussed and numerical results for both constant and variable heat inputs are presented.
Numerical evaluation of the transonic wave drag integral
Authors: Shanbhag V. V. , Narasimha R.
Published: August 2005

This article describes‐a new method, suitable for use on a digital computer, for evaluating the singular double integral of Hayes which determines the transonic wave drag of a slender body. Comparison with known exact results and with an earlier computer program described by Eminton shows the present method to be accurate as well as economic in computer time.
Energy transfer through chains of impacting rods
Authors: Fu C. C. , Paul B.
Published: August 2005

A solution has been formulated, which allows one to analyse all the major performance characteristics in a chain of impacting elastic ‘rods’. By allowing one end of the elastic chain to impact against a surface which resists penetration according to a specified penetration law it is possible to analyse the impact system of a variety of mechanical devices such as percussive tools and squeeze film dampers. Virtually, unlimited variety in the number and geometry of the impacting rods, and virtually unlimited complexity in the form of the reaction of the terminal face is permitted. A computer program for treating one or two elastic rods has been developed. The program prints out all important stresses as well as the stress history at several selected points. It also prints out the depth of penetration, the energy transferred from rod to rod, the overall energy transfer into the receiver, rebound velocities and times of separation between rods and between rod and 4receiver. Agreement with exact solutions and experiments is demonstrated.
A curved element approximation in the analysis of axi‐symmetric thin shells
Authors: Giannini M. , Miles G. A.
Published: August 2005

The stiffness equation is derived for curved elements of orthotropic axi‐symmetric thin shells, and equivalent applied loads are found for shells subjected to initial strains, applied surface loads and body forces. The Lure approximation of thin shells and displacement field approximation by polynomials of arbitrary degree are included in the formulae derived.
Finite element with high degree of regularity
Authors: Dupuis G. , Goël J.‐J.
Published: August 2005

This paper deals with solving two‐dimensional variational problems of second‐ and third‐order by the finite element method. To each meshpoint are associated three or six basic functions of class C1 or C2. The expression of the admissible functions on a triangular and rectangular element are given here in a general form which is specially suitable for computation.
Behaviour and design of pin connected structures
Authors: Patnaik Suryanarayan , Dayaratnam Pasala
Published: August 2005

The feasibility of achieving a preassigned stress state by changing the stiffness of determinate and indeterminate pin connected structures is presented. A new force method with all element forces (or stresses or areas) as independent variables is developed. The possibility but futility of getting the element areas by inverting and pre‐multiplying the coefficient matrix with the external load vector when areas are chosen as variables is shown. The relationship existing between the compatibility equations and the plastic strength of pin connected structures is illustrated. Possible design methods for trusses under single or multiplicity of load conditions, the design of truss geometry and the relations between fully stressed and minimum weight structures are examined and illustrated through several examples.
Vibration analysis of rotating cantilever plates
Authors: Dokainish M. A. , Rawtani S.
Published: August 2005

A finite element technique is used to determine the natural frequencies and the mode shapes of a cantilever plate mounted on the periphery of a rotating disc. The plane of the plate is assumed to make any arbitrary angle with the plane of rotation of the disc. The distributed centrifugal force is resolved into two components—one acting in the plane of the plate and the other normal to the plate. The stresses produced in the middle surface of the plate due to the in‐plane forces are first determined. The increase in the bending stiffness of the plate elements due to these in‐plane stresses is obtained in a manner similar to that used in the stability analysis of plates. The component of the distributed centrifugal force normal to the plate surface is added to the inertia force.

From the results of computations carried out for various values of the aspect ratio, the speed of rotation, the disc radius and the setting angle, empirical formulae are derived giving the effect of these parameters on the natural frequencies. These empirical formulae are observed to be in agreement with the corresponding known formulae for rotating cantilever beams, when the aspect ratio is high.
Reduced integration technique in general analysis of plates and shells
Authors: Zienkiewicz O. C. , Taylor R. L. , Too J. M.
Published: August 2005

The solution of plate and shell problems by an independent specification of slopes and middle surface displacements is attractive due to its simplicity and ability of reproducing shear deformation. Unfortunately elements of this type are much too stiff when thickness is reduced.

In an earlier paper a derivation of such an element was presented1 which proved very successful in ‘thick’ situations. Here a very simple extension is made which allows the element to be economically used in all situations.

The improved flexibility is achieved simply by reducing the order of numerical integration applied to certain terms without sacrificing convergence properties. The process is of very wide applicability in improvement of element properties.
A numerical solution of axisymmetric problems in elastodynamics
Authors: Recker W. W.
Published: August 2005

The equations governing the axisymmetric dynamic deformation of an elastic solid are considered as a symmetric hyperbolic system of linear first‐order partial differential equations. The characteristic properties of the system are determined and a numerical method for obtaining the solution of mixed initial and boundary value problems in elastodynamics is presented. Two examples are considered.
A refined curved element for thin shells of revolution
Authors: Popov E. P. , Sharifi P.
Published: August 2005

A refined axisymmetric curved finite element for the analysis of thin elastic‐plastic shells of revolution is described in the paper. The improved element is obtained by employing cubic polynomials in terms of local Cartesian co‐ordinates for the assumed in‐plane and out‐of‐plane displacements. This introduces into the solution two internal degrees of freedom in the cord direction of each element. These internal degrees of freedom are removed by static condensation before assembling the individual element stiffness matrices, and are subsequently recovered after the nodal displacements are obtained. On comparison with the previous formulation, this procedure greatly improves the accuracy of the solution especially with regards to in‐plane stress‐resultants at discontinuities in the meridional curvature and interelement equilibrium of forces. The latter fact makes it possible to analyse shells with a discontinuous meridional slope. In using this element, improvement in the convergence of the elastic‐plastic solutions has also been observed.

Several examples illustrate the quality of solutions. The reported study is limited to axisymmetric loadings cum boundary conditions.
A sector element for thin plate flexure
Authors: Singh Saroj , Ramaswamy G. S.
Published: August 2005

This paper presents a sector shape of an element ideally suited for the analysis of sectorial and annular plates. A conforming function with twenty degrees of freedom is developed in polar co‐ordinates to represent the deformation of the element in bending. The finite element method is applied to some plate bending problems to illustrate the power and efficiency of sector elements.
Numerical solution of dynamical systems by direct application of Hamilton's principle
Authors: Vance John M. , Sitchin Amnon
Published: August 2005

In this paper, a method is described which allows a direct derivation of a set of first‐order finite difference equations to numerically compute the motion of any conservative or non‐conservative dynamic system with a finite number of degrees of freedom. The derivation of the method is based on an application of Lagrangian multipliers to a functional form of Hamilton's equations, and reduces the work required to obtain the most desirable form for numerical integration from the standpoint of computational efficiency and accuracy. For systems with many degrees of freedom, the required matrix inversions produce first derivatives of the co‐ordinates, instead of second derivatives, thus eliminating a potential source of error in numerical integration. Two examples are given to illustrate the method.
Convergence of eigenvalue solution in conforming plate bending finite elements
Authors: Lynn Paul P. , Dhillon Balaur S.
Published: August 2005

The convergence proof of plate eigenvalue solution from conforming displacement finite elements is presented. The analysis is based on converting a thick plate free vibration problem in to a corresponding isoperimetric variational problem. A conforming thick, plate element is used to illustrate the mathematical development. On the basis of the derived asymptotic rate of convergence of the approximate eigenvalues, the authors propose a practical method of improving the numerical solutions. Extension of the mathematical proof to cover classical thin plate finite elements is briefly discussed.
Numerical solution of a separtated viscous flow problem by a non‐uniform finite‐difference net
Authors: Gupta Murli M. , Manohar Ram P.
Published: August 2005

Two‐dimensional stagnation point flow of a viscous fluid is modified by the introduction of a thin plate placed symmetrically at the stagnation point. Separation of the boundary layer results in back flow near the plate even at small Reynolds numbers. The Navier–Stokes equations governing the flow are replaced by finite differences using unequal net spacing which is finer in the boundary layer. The choice of finite differences guarantees convergence of the iterative procedures used. Only those relaxation parameters, which are necessary to obtain convergence and also to make the method computationally efficient, have been used. Numerical results for Reynolds numbers 9, 100 and 400 are obtained.
Numerical approximation of one‐dimensional consolidation
Authors: Davis R. O.
Published: August 2005

A generalized finite difference scheme is developed to represent the one‐dimensional consolidation process. The difference equations are derived from integral balance equations which represent the soil as a mixture of two constituents. No restrictions are placed on the soil constitutive properties or stratigraphy. An approach to stability analysis for the scheme is outlined, and an example problem is presented.
A note on the estimation of critical damping in dynamic relaxation
Authors: Bunce J. W.
Published: August 2005

A new way of estimating critical damping in dynamic relaxation is proposed using the concept of a mass‐dependant load vector, a postulate concerning vibrations and Rayleigh's principle. The method should be particularly appealing in those not uncommon circumstances where the actual loads are approximately proportional to the masses for then the computer time required in evaluating the various constants would actually be a part of the problem‐solving time.
Optimum design of hypertatic structures
Authors: Majid K. I. , Anderson D.
Published: August 2005

The task of optimum design of structures is one that involves non‐linear Programming. This is particularly the case when deflection as well as stress limitation are imposed as design criteria. In this paper a Fundamental approach is presented for the minimum weight design of statically indeterminate elastic structure subject to non‐linear deflection and stress constrains.

The matrix force method is adopted to formulate the problem. The constraints thus derived prove to have separable variables and therefore can be linearized in a piecewise manner. The computation aspects concerning the restricted entry in to the simplex tableau are briefly discussed and illustrative examples are given to verify the validity of the proposed method.
Note on the ‘Alpha’‐constant stiffness method for the analysis of non‐linear problems
Authors: Nayak G. C. , Zienkiewicz O. C.
Published: August 2005

A procedure for the acceleration of convergence in non‐linear analysis using the modified Newton–Raphson problem is described. The process has been found useful in plasticity and large deformation studies and its application elsewhere can be envisaged.
On the rigid displacement condition
Authors: Clément P. , Descloux J.
Published: August 2005

This paper shows the importance of the rigid displacement condition when the finite element method is used for structures having little rigidity. The theoretical analysis is confirmed by numerical results obtained with a curved beam.
A finite element method for block adjustment problems of photogrammetry
Authors: Utku Senol
Published: August 2005

It is shown that the finite element method can be used advantageously in generating the normal equations of a given photogrammetric network for block adjustments. In this method aerial (or spatial) photographs of a block are processed one at a time, in any random order, to generate the portion of the coefficient matrix between the main diagonal and the variable band and the right hand vector of the normal equations, related with the adjustments to the control points. Any known information related with the adjustments may be imposed, and an internal control point relabelling scheme may be used during the assembly process, in order to minimize the actual computer storage area and the solution time requirements. The paper shows the analogies between the linear equilibrium problems of structural mechanics, and the block adjustment problems of photogrammetry, in order to enable the students of both fields to use the same computer software. In this context, plate‐point adjustment matrices and plate‐point load vectors for the adjustment problem (corresponding to the element stiffness matrices and the element load vectors of equilibrium problems) are defined and explicit expressions are given.
Note on an approximate method for computing consistent conjugate stresses in elastic finite elements
Authors: Oden J. T. , Reddy J. N.
Published: August 2005

A technique is described wherein improved stresses can be computed in finite element models based on displacement approximations. The method is based on the idea of consistent stress approximations and it approximates such stresses using the notion of a domain of influence of the stress intensity at a nodal point. Considerable improvement in accuracy of the stresses is obtained with little difficulty.
Stresses in a partly yielded notched bar—An assessment of three alternative programs
Authors: Owen D. R. J. , Nayak G. C. , Kfouri A. P. , Griffiths J. R.
Published: August 2005

The results of three finite element stress analysis programs are compared for the problem of the elasto–plastic bending of a notched beam under plane strain conditions. Both Tresca and von Mises yield criteria are considered and the numerical results are compared with an available analytical solution based on slip‐line field theory. The general conclusion is drawn that finite element methods can be used with confidence in elasto–plastic stress analysis.
A numerical method for the analysis of longitudinal elastic–plastic stress wave propagation
Authors: Ondracek E. , Haddow J. B.
Published: August 2005

A numerical method for the analysis of one‐dimensional propagation of elastic–plastic stress waves in cylindrical bars is proposed. The method is based on the division of the bar into elements of finite length and the solution of the equations of motion for these elements.

Numerical results are presented for semi‐infinite bars and a finite bar fixed at one end.