bluuebunny/crossref_metadata_2025 huggingface dataset:
Generation of flow nets using fem nodal potentials and bilinear shape functions
Authors: Fan Yuehui , Tompkins F. D. , Drumm E. C. , Von Bernuth R. D.
Published: August 2005

A method for generating both equipotential lines and streamlines directly based upon nodal potentials and bilinear shape functions is presented. The method involves post‐processing a finite element (FE) solution utilizing typical four‐node isoparametric quadrilateral elements. The application of the method can be important in the interpretation of FE analysis results, especially when inhomogeneous, anisotropic, unconfined or/and other complicated conditions exist. Compared with conventional techniques to generate flow nets which depend upon both the potential and stream functions, the method presented is simpler and more powerful.
Resilient characterization of pavement materials
Authors: Uzan Jacob
Published: August 2005

The paper presents an approach for characterizing pavement materials using the modified linear elastic behaviour. The secant modulus of elasticity is expressed in terms of the stress invariants and an expression for the secant Poisson's ratio is derived using path independence of the total work along a closed loading cycle. Triaxial test results of granular base–subbase materials which exhibit strong non‐linear behaviour and dilatancy are analysed and presented. The constitutive law is included in a finite element program and results of pavement analyses are discussed. It is found that the secant Poisson's ratio of granular base materials reaches values between 0·6 and 0·7, indicating a volume increase under high stress ratios. The pavement response predicted using the above material characterization is compatible with non‐destructive test results.
A finite element analysis of direct shear tests on stiff clays
Authors: Cividini Annamaria , Gioda Giancarlo
Published: August 2005

A finite element analysis is presented of some direct shear tests carried out on samples of a stiff, heavily overconsolidated clay. The effects of softening are accounted for through a simple material model which views this phenomenon as a consequence of an intrinsic loss of strength of the material taking place when plastic strains increase. After illustrating the main characteristics of the finite element approach, with particular reference to the correct determination of the non‐reversible strains, its use in the interpretation of the mentioned shear tests is discussed. Some comments are also presented on the mesh dependence of the numerical results, and on the use of a relation between material parameters and element size which reduces this negative effect. Finally, the solution procedure is applied to the simulation of a compression test in order to investigate the possibility of numerically detecting the ‘spontaneous’ (i.e. not directly induced by the boundary conditions) formation of shear zones within the specimen.
Analytical modelling of hammer impact for pile driving
Authors: Deeks A. J. , Randolph M. F.
Published: August 2005

Estimation of the drivability of piles requires modelling of the hammer impact in order to provide the input force wave at the pile head. Historically, this has been achieved through a numerical model of the hammer components (ram, cushion and anvil), which is then linked with that of the pile in order to effect the drivability analysis. This paper presents an analytical model of hammer impact, based on lumped ram and anvil masses separated by a cushion with internal damping, and connected to the pile which is modelled as a dashpot. Force–time responses derived from the analytical model are compared with actual field data, and also with results from commercially available numerical models of hammer impact. The analytical model is then used to explore the characteristics of hammer impact, with particular attention to combinations of parameters that lead to hammer bounce and, hence, significant loss of energy transferred to the pile.
Modelling coupled heat and contaminant transport in groundwater
Authors: Hensley P. J. , Savvidou C.
Published: August 2005

This paper presents the results of a research programme conducted on the geotechnical centrifuge at The University of Western Australia to investigate coupled heat and contaminant transport in the soil surrounding a buried waste source. The phenomena which govern heat and contaminant transport through porous media are discussed, the principles of geotechnical centrifuge modelling are outlined, and relevant scaling laws that govern the relationship between a centrifuge model and the prototype, with respect to the problem of coupled waste transport, are presented. A model test, simulating two‐dimensional migration from a buried heat and contaminant source, is described, and the results from four model tests are presented. The experimental data show that hydraulic instability is responsible for the transport of contaminant in the soil around the source and that the mode of instability is determined by the magnitude of the effective Rayleigh number.
Finite element modelling of three‐phase flow in deforming saturated oil reservoirs
Authors: Lewis R. W. , Sukirman Y.
Published: August 2005

A numerical simulation is presented for three‐dimensional three‐phase fluid flow in a deforming saturated oil reservoir. The mathematical formulation describes a fully coupled governing equation systen which consists of the equilibrium and continuity equations for three immiscible fluids flowing in a porous medium. An elastoplastic soil model, based on a Mohr–Coulomb yield surface, is used. The finite element method is applied to obtain simultaneous solutions to the governing equations where displacement and fluid pressures are the primary unknowns. The final discretized equations are solved by a direct solver using fully implicit procedures. The developed model is used to investigate the problems of three‐phase fluid flow in a deforming saturated oil reservoir.
An ellipse‐based discrete element model for granular materials
Authors: Ting John M. , Khwaja Mahmood , Meachum Larry R. , Rowell Jeffrey D.
Published: August 2005

The discrete element method (DEM) models granular materials numerically as a collection of particles rather than as a continuum. Difficulties can arise when using the more common circular and polygonal shapes for modelling real granular materials. In particular, use of discs and spheres leads to typically low aggregate internal friction angles compared with real materials. This paper presents the detailed formulations for using the ellipse shape in discrete element modelling. Robust algorithms for computing ellipse‐ellipse and ellipse‐wall intersections are presented. Also shown are equations to assist in parameter selection and evaluation of macroscopic stresses and strains from the contact data. An initial validation test suite on rods of varying particle aspect ratio are presented. These results indicate that the ellipse‐based DEM results in mechanical behaviour that is similar, both qualitatively and quantitavely, to the behaviour of real soils.
Numerical solution for the dilation of a fluid‐saturated porous elastic sphere due to a point source of fluid at the centre of the sphere
Authors: Solomon A. , Mason D. P. , Nicolaysen L. O.
Published: August 2005

Mathematical modelling of the ascent of free fluid through relatively strong rock, deep in the Earth's mantle, presents a challenge in geomechanics. Here the medium is considered as fluid‐saturated, porous, elastic and bounded, and the fluid enters at a point source. An explicit finite difference method is developed for the numerical solution to the problem of the dilatation of a fluid‐saturated porous elastic sphere due to a point fluid source of constant strength at the centre of the sphere. A cubic spline interpolant is used to evaluate a definite integral which occurs in the boundary condition for the pore fluid pressure at the surface of the sphere. The numerical solutions for the dilatation and pore fluid pressure are compared with analytical solutions and the absolute and relative errors of the numerical solutions are calculated. When the fluid source is switched on, the pore fluid pressure starts to decrease, reaches a minimum value and then steadily increases. The initial time rate of decrease of the pore fluid pressure is independent of the radial distance from the source. It decreases as the radius of the sphere increases and vanishes for a point fluid source in an infinite porous elastic medium.
A review of models for predicting the thermomechanical behaviour of soft clays
Authors: Seneviratne H. N. , Carter J. P. , Airey D. W. , Booker J. R.
Published: August 2005

This paper critically examines the use of the modified Cam clay stress–strain model in predicting the thermomechanical behaviour of soft clays. The equations governing the thermomechanical behaviour of a saturated soil are summarized and their methods of solution are briefly discussed. The observed thermomechanical soil behaviour reported in the literature has been compared with the predictions made using the modified Cam clay model. In making these comparisons, two extensions of the well‐known modified Cam clay model have been considered: one proposed by Britto et al.1 in which heating induces thermal stresses and strains in the soil but has no direct effect on the work hardening, and the other proposed by Hueckel and Borsetto2 in which a change in temperature also affects the yield surface. The comparisons are confined to the behaviour of normally and lightly overconsolidated clays, where the modified Cam clay is known to perform well. Apart from the effect of a single heating–cooling loop, cyclic behaviour is not considered. It is concluded that both models provide reasonable predictions under isotropic stress conditions. Although exhaustive comparisons have not been made for deviatoric stress excursions (because of the lack of experimental data), it appears from preliminary studies that neither model performs particularly well for this form of loading.
Continuum model and analysis of wick‐drained systems
Authors: Amirebrahimi Amir M. , Herrmann Leonard R.
Published: August 2005

An equivalent homogeneous continuum theory is developed for modelling discretely drained soil stratum. The model accounts for the local horizontal flow to discrete vertical drains such as wick or sand or stone columns as well as direct vertical drainage of the soil and global horizontal flow due to non‐uniform horizontal conditions. Calibration curves for the model are presented for the case of no soil smear due to the drain installation and for the case when smear exists. The model is implemented in both analytical and finite element analyses for those cases where no well resistance is present and when it is of importance. The accuracy and applicability of the model is demonstrated for simple one‐ and two‐ layered problems including smear and well resistance.
An approximate analysis procedure for piled raft foundations
Authors: Clancy P. , Randolph M. F.
Published: August 2005

A piled raft foundation comprises both piles and a pile cap that itself transmits load directly to the ground. The aim of such a foundation is to reduce the number of piles compared with a more conventional piled foundation where the bearing effect of the pile cap, or raft, is ignored. This paper describes a ‘hybrid’ approach for the analysis of piled raft foundations, based on a load transfer treatment of individual piles, together with elastic interaction between different piles and with the raft. The numerical analysis is used to evaluate a simple approximate method of estimating the overall response of the foundation from the response of the component parts. The method leads to estimates of the overall foundation stiffness, the proportion of load carried by the pile group and the raft, and an initial assessment of differential settlements. Parametric studies are presented showing the effect of factors such as raft stiffness and pile spacing, length and stiffness, and a worked example is included demonstrating the accuracy of the approximate design approach.
Numerical modelling of transient contaminant migration problems in infinite porous fractured media using finite/infinite element technique. Part II: Parametric study
Authors: Zhao Chongbin , Valliappan S.
Published: August 2005

Using the numerical model presented in the first paper of this research,1 a parametric study has been carried out in this paper to investigate the effect of several important parameters on the transient contaminant transport in infinite porous fractured media. From the related numerical results, it has been demonstrated that: (1) transmissive coefficient between the porous block and the fissured network has a significant influence on the value of the concentration but has little effect on the speed of contaminant transport; (2) porosities in the porous block and fissured network have a significant influence on the maximum value of the concentration; (3) average linear velocity of flow has a significant influence on both the concentration distribution and speed of contaminant transport; (4) dispersion coefficient of the medium affects not only the shape of the concentration versus time curve but also the peak value of the concentration.
Interpretation of cone penetration results in multilayered soils
Authors: Vreugdenhil Roger , Davis Rob , Berrill John
Published: August 2005

A simple approximate analysis is presented for interpretation of cone penetration results when the cone resistance is affected by layering of soils with different stiffnesses. It is argued that the cone resistance senses the presence of a nearby layer elastically, and an approximate elastic analysis is developed to quantify the effect. Good comparisons with calibration chamber experimental results are found.
A three‐invariant smooth cap model with mixed hardening
Authors: Schwer Leonard E. , Murray Yvonne D.
Published: August 2005

A cap model is presented that uses a multiplicative formulation to define a smooth (continuous derivative) failure surface that includes the third stress invariant. This formulation offers several advantages over previous cap model formulations: elimination of ‘corner’ coding, resulting in a numerical algorithm suitable for vectorization; a three stress invariant implementation that is easily specialized to classical failure surfaces or generalized to represent observed material response; and a framework for easily implementing additional model features such as kinematic hardening as demonstrated.
Unified 3D critical state bounding‐surface plasticity model for soils incorporating continuous plastic loading under cyclic paths. Part I: Constitutive relations
Authors: Crouch Roger S. , Wolf John P.
Published: August 2005

The unified three‐dimensional (3D) critical state bounding‐surface plasticity model gUTS enables clays, silts and sands to be treated within a single framework. Furthermore, loose and dense states of a particular soil subjected to a wide range of confinements are viewed as a single material defined by the same set of constants. The model is able to handle both monotonic and complex cyclic paths including those involving a rotation of the principal stress directions. The model incorporates the following features: combined use of radial and deviatoric mapping rules and the use of an apparent normal consolidation line for sands; use of a non‐associated flow rule where the ratio of the rates of volumetric plastic strain to deviatoric plastic strain is a function only of the ratio of deviatoric to mean effective stresses and the Lode angle; adoption of a bi‐linear critical state line projected onto the plane of the void ratio versus logarithm of mean effective stress; inclusion of a sub‐elliptic, or super‐elliptic, segment in the plastic dilatancy surface for stress ratios less than critical; use of elliptic segments in the deviatoric planes; movement of the projection centre in the deviatoric mapping region and incorporation of a plastic stiffening effect for cyclic paths which repeatedly load in the same deviatoric direction.
Wave‐induced soil response in an unsaturated anisotropic seabed of finite thickness
Authors: Hsu J. R. C. , Jeng D. S.
Published: August 2005

An analytical solution for the wave‐induced soil response is developed for a seabed of finite thickness subject to a three‐dimensional (3‐D) wave system produced by two intersecting waves of equal properties. These 3‐D exact solutions for the pore pressure and effective stresses, proposed for a non‐cohesive soil matrix of finite depth in a homogeneously unsaturated and anisotropic condition, are readily reducible to the limiting two‐dimensional cases of progressive and standing waves, for which no explicit solutions are available for finite thickness. The effects of soil isotropy, degree of saturation, seabed thickness and grain size on the wave‐induced pore pressure are discussed in detail. The explicit solutions presented in this study for the wave‐induced pore pressure and effective stresses should benefit the laboratory experiments and field monitoring programs carried out in soil of finite depth.
Localization problems in plasticity using finite elements with adaptive remeshing
Authors: Zienkiewicz O. C. , Huang Maosong , Pastor M.
Published: August 2005

Various computational procedures have from time to time been suggested to solve problems involving strain localization. One of these is adaptive remeshing — but here occasional failures were experienced if the original mesh was not suitably aligned. We show in this paper that such failures are mainly due to non‐robust formulation of the plasticity problem — and illustrate an automatic and generally applicable adaptive procedure on several examples.
Response of a circular opening in a friable low‐permeability medium to temperature and pore pressure changes
Authors: Wang Yarlong , Dusseault Maurice B.
Published: August 2005

A general analysis using an incremental elastic, perfectly plastic constitutive stress–strain relationship for poroelastoplastic materials is presented to simulate an opening in a low‐permeability friable porous medium under non‐isothermal conditions. Analytical solutions are obtained for the stresses and strains around a 2‐D plane strain circular borehole. An expansion potential is introduced by combining the strains induced by temperature and pore pressure changes. Steady‐state pressures and temperatures are considered, and a non‐associated plastic flow rule is applied to calculate plastic strains. Focusing on stress distribution near a circular opening, the classic solutions for those stresses under dry and isothermal conditions are used to compare with the newly derived solution. The general poroelastoplastic effect and the thermal effect on sand production and borehole stability are addressed. We suggest that the knowledge of stress history is critical to achieve adequate solutions for displacement and stress in friable media such as clays, shales and oil sands.
Crack stability analysis for rock fracture toughness tests
Authors: Wang Qi‐Zhi
Published: August 2005

A stable crack extension is a precondition for fracture toughness tests using chevron‐notched specimens. The paper analyses the stability problem for crack extension in two chevron‐notched specimens suggested by ISRM. Stability factors are calculated with various compliances of testing machine under different loading conditions. It is pointed out that the loading manner, compliance of the testing machine, as well as the specimen configurations have great influence on crack growth stability.
On the linear relations of V–ln p and ln v–ln p for isotropic consolidation of soils
Authors: Hashiguchi K.
Published: August 2005

The well‐known linear relation between the specific volume and the logarithm of the pressure for the isotropic consolidation has been widely incorporated into elastoplastic constitutive equations of soils. It is, however, indicated in this article that this relation has several physically unaccepted properties. Instead of this relation it is recommended to incorporate the linear relation between both logarithms of the volume and the pressure into constitutive equations, which does not have any of the unrealistic properties.
Bifurcations at a spherical cavity in a compressible solid with spherical isotropy
Authors: Chau K. T.
Published: August 2005

This paper investigates bifurcations, including surface mode and localized mode of deformations, at a spherical cavity in an infinite compressible solid with spherical isotropy. Two types of surface modes are found satisfying the zero traction rate conditions on the surface of the hole: (1) the torsional modes, corresponding to bifurcations with zero radial velocity and zero rate of dilatation; and (2) the spheroidal modes, corresponding to bifurcations with zero rate of spin on the tangential planes. Both of these bifurcations can be written in terms of surface harmonics of degree n. Three‐dimensional pictures of some of the bifurcation modes are devised for both torsional and spheroidal modes, showing both the displaced nodes and nodal lines. Torsional bifurcation occurs only if the ratio of the radial shear modulus to the tangential shear modulus (Gr/Gt) vanishes. Three types of spheroidal modes are possible depending on the combination of the five material parameters; their eigenvalue equations are obtained analytically. As expected, numerical results show that the conditions of bifurcations are independent of the size of the spherical hole. Radial bifurcation modes (n = 0) are always possible at the peak applied stress; and pre‐peak bifurcations are also possible for mode shapes composed of surface harmonics of higher degree (n > 0). Spherically isotropic solids (i.e. Gt/Gr < 1) are more conducive to bifurcations than isotropic solids if n > 2. Surface mode with large degree (n → ∞ ) is not necessarily the lowest possible bifurcation; this finding differs from the conclusion by Bassani et al.1 for incompressible isotropic solids.
A generalized procedure for the optimum design of nailed soil slopes
Authors: Sabhahit N. , Basudhar P. K. , Madhav Madhira R.
Published: August 2005

A new method is proposed for the optimum design of nailed soil slopes. A rigorous method of stability analysis, namely the Janbu's method, is modified in the limit equilibrium formulation, considering the effect of reinforcement. Only the tensile resistance of the reinforcement is included and the effects of shear and bending neglected. The total reinforcement force required to raise the factor of safety to a desired value has been minimized with the inclinations of the reinforcement and the distribution of the reinforcement forces as decision variables. In order to illustrate the efficacy of the proposed method, the results are compared with the available solutions. The effect of the number and relative locations of the reinforcements on the amount of reinforcement required, is studied. The lengths of reinforcement required to raise the factor of safety to various desired values and the corresponding optimum designs are presented. The acceptability of the critical surface is verified, by ensuring that the shear and normal stresses are positive along the critical surface.
Thermoelastic and thermoplastic response of a porous space submitted to a decaying heat source
Authors: Giraud A. , Rousset G.
Published: August 2005

A general solution scheme is developed for one‐dimensional and non‐isothermal consolidation problems for fluid‐saturated, porous, thermoelastic media. Two fundamental parameters which describe the coupling effects between thermal, hydraulic and mechanical behaviour are: ratio of thermal and hydraulic diffusivity and ratio of thermomechanical deformabilities in drained and undrained conditions. The solution scheme has been applied to the nuclear waste disposal problem. A solution for a thermoporoelastic rock mass containing a decaying heat source is presented. Numerical results show that coupling effects are most pronounced for low permeability and high porosity media such as deep compressible clays. This corresponds to a low value of the ratio of hydraulic and thermal diffusivities and a high value of the ratio of deformabilities in drained and undrained conditions.

Comparison with numerical simulations taking into account the non‐linear and non‐reversible behaviour of the rock mass is presented. It shows that the thermoelastic model is quite correct for temperature and displacement fields, and gives maxima of the pore pressure and stress elevations.
An indirect boundary integral equation method for poroelasticity
Authors: Rajapakse R. K. N. D. , Senjuntichai T.
Published: August 2005

This paper presents an indirect boundary integral equation method for analysis of quasi‐static, time‐harmonic and transient boundary value problems related to infinite and semi‐infinite poroelastic domains. The present analysis is based on Biot's theory for poroelastodynamics with fluid viscous dissipation. The solution to a given boundary value problem is reduced to the determination of intensities of forces and fluid sources applied on an auxiliary surface defined interior to the surface on which the boundary conditions are specified. A coupled set of integral equations is established to determine the intensities of forces and fluid sources applied on the auxiliary surface. The integral equations are solved numerically in the Laplace domain for quasi‐static and transient problems, and in the frequency domain for time‐harmonic excitations. The kernel functions of the integral equation correspond to appropriate Green's functions for a poroelastic full space or half‐space. The convergence and numerical stability of the present scheme are established by considering a number of bench mark problems. The versatility of the present method is demonstrated by studying the quasi‐static response of a rigid spheroidal anchor, and time‐harmonic and transient response of a rigid semi‐circular tunnel.
Seepage design charts for flat bottom dams resting on heterogeneous media
Authors: Naouss Wissam A. , Najjar Yacoub M.
Published: August 2005

Several researchers have developed numerical models that are capable of computing the flow in porous media by implementing the finite difference or the finite element method. In order to make an efficient use of such models, the results of flow estimates were compiled and plotted to form different sets of design charts. These design charts can be used to estimate the seepage quantity and exit gradient in heterogeneous media under flat bottom dams. A numerical model, employs the finite difference technique, was developed to solve for piezometric head and seepage velocity at all nodal locations within the permeable strata. The paper contains a description of the procedure adopted to calculate seepage quantity and exit gradient from the numerical results. The applicability and validity of the charts were examined and compared with flownets and relevant existing mathematical approximations. The present analysis yields accurate results in estimating seepage quantity and exit gradient compared with the mathematical approximation.
Analytical solution for two‐dimensional dynamic consolidation in frequency domain
Authors: Valliappan S. , Yazdi J. Tabatabaie , Zhao Chongbin
Published: August 2005

An analytical solution to the two‐dimensional wave propagation in fluid‐saturated half‐space subjected to a strip load with vertical harmonic oscillation at the surface is presented. The basic equations have been derived on the basis of Biot's linear theory of poro‐elasticity and then solved using Fourier complex transform for the horizontal direction. The importance of a number of soil characteristics including compressibility, degree of saturation and soil permeability has been examined. It is shown that the effect of pore fluid is dominant only for fully saturated soils with incompressible solid grains and low permeability. For partially saturated, compressible or very permeable soils, the stresses would be mainly transferred to solid part and there will be considerable reduction in pore pressure amplitude.
Seepage flow around tunnels in swelling rock
Authors: Anagnostou G.
Published: August 2005

The swelling phenomenon in tunneling is numerically modelled as a coupled hydraulic‐mechanical process. The present communication focuses on the significance of the constitutive seepage flow equations, as well as on the importance of the hydraulic boundary conditions. The observed absence of swelling deformations at the tunnel walls and the crown can be explained as a consequence of varying hydraulic boundary conditions along the excavation boundary. According to the presented numerical results, the non‐linearity of the unsaturated flow equations has a decisive qualitative influence on the predicted deformation field.
The influence of tunnel excavation on the hydraulic head
Authors: Anagnostou G.
Published: August 2005

In this paper an alternative method is proposed for computing the effect of tunnelling on the piezometric head field during construction. The seepage flow equations, usually formulated in a fixed co‐ordinate system are here reformulated within a frame of reference that advances together with the tunnel heading. The governing equations contain the advance rate as an additional parameter, and are solved by the finite‐element method. The quasi‐steady state (i.e. the steady state in the moving frame of reference) can then be computed in a single step. Selection of a marching scheme in the time domain is, therefore, rendered unnecessary. Thanks to the economy of the proposed method, it has been possible to carry out comprehensive parametric studies, the results of which are presented in a dimensionless form. The applicability of the computational method to poroelastic problems is also addressed.
Tracing the equilibrium path by dynamic relaxation in materially nonlinear problems
Authors: Siddiquee M. S. A. , Tanaka T. , Tatsuoka F.
Published: August 2005

Material non‐linearity in non‐associated high friction materials exhibiting post‐peak softening such as granular materials poses a great problem in solving the non‐linear differential equations. In this regard, a dynamic relaxation (DR) family of solutions provides a very strong tool to solve. In this paper, the DR method is evaluated from the viewpoint of its ability to trace the whole equilibrium curve in the load–displacement (stress–strain) space. In the case of material non‐linearity, usually there is a snap‐through. This problem has been handled in three ways: (1) load control with a real time dynamic solution at post‐peak, (2) direct displacement control and (3) arc‐length control. These three methods of non‐linear equilibrium path tracing are critically evaluated with respect to their speed of convergence, accuracy of the solution and states of unequilibrium. Finally, the results of multi‐element FEM simulations of a bearing capacity test of a strip footing on sand carried out to validate the DR methods are presented.
A large strain analytical solution for cavity contraction in dilatant soils
Authors: Yu H. S. , Houlsby G. T.
Published: August 2005

An infinite dilatant elastic–plastic soil mass contains a single cylindrical or spherical cavity within which a slowly increasing pressure is applied. The removal of the cavity pressure takes place after a partly plastic state of the soil has been reached. Closed form solutions for the stress and displacement fields in the soil during any stage of the unloading process are derived. The non‐associated Mohr–Coulomb yield criterion is used to account for dilation of the soil during shearing. Large strains are taken into account by adopting an appropriate strain definition within the plastically deforming region.
Oscillatory soil response and liquefaction in an unsaturated layered seabed
Authors: Hsu J. R. C. , Jeng D. S. , Lee C. P.
Published: August 2005

The subject of wave‐induced soil response in a real seabed has attracted the attention of geotechnical and coastal engineers over the last three decades, for which several basic theories have been developed. However, the evaluation of soil liquefaction has not been attempted theoretically in a seabed with multiple sub‐layers, in which homogeneity in soil properties can be assumed within each layer. In this study, a semi‐analytical approach is presented for obtaining solutions for the pore pressure and effective stresses in a non‐cohesive layered seabed of finite thickness subject to a system of three‐dimensional waves. Based on the numerical results for a layered seabed, influences of soil characteristics (relative layer thickness, permeability ratio and shear modulus) on seabed responses are described. Special attention is given to the effect of placing a coarser material as a top layer for protecting an underlayer of finer sediment. Although only a three‐layered seabed is explicitly solved in this study, the procedure outlined can readily be extended to a multi‐layered soil system. The three‐dimensional solutions can also be applied to the two‐dimensional progressive or standing wave systems.
S/P images of upper triangular M‐matrices
Authors: Beauwens R. , Notay Y. , Tombuyses B.
Published: August 2005

Preconditioning by approximate factorizations is widely used in iterative methods for solving linear systems such as those arising from the finite element formulation of many engineering problems. The influence of the ordering of the unknowns on their convergence behaviour has been the subject of recent investigations because of its particular relevance for the parallel implementation of these methods. Consistent orderings are attractive for parallel implementations and subclasses of these orderings have been shown to also enhance the convergence properties of the associated preconditioned iteration scheme. The present contribution is concerned with one such class of orderings, called S/P consistent orderings. More precisely, we review here their known properties and we propose a new definition which enlarges their scope of application. A device, called S/P image of an upper triangular M‐matrix, provides a criterion for checking S/P consistency and a means to compute a relevant parameter, called maximal reduction ratio. All known properties of S/P consistent orderings are generalized to the new definition.
Low‐rank revealing QR factorizations
Authors: Chan Tony F. , Hansen Per Christian
Published: August 2005

Rank revealing factorizations are used extensively in signal processing in connection with, for example, linear prediction and signal subspace algorithms. We present an algorithm for computing rank revealing QR factorizations of low‐rank matrices. The algorithm produces tight upper and lower bounds for all the largest singular values, thus making it particularly useful for treating rank deficient problems by means of subset selection, truncated QR, etc. The algorithm is similar in spirit to an algorithm suggested earlier by Chan for matrices with a small nullity, and it can also be considered as an extension of ordinary column pivoting.
Upper bound of the constant in the strengthened C.B.S. inequality for FEM 2D elasticity equations
Authors: Margenov S. D.
Published: August 2005

The basic theory of the strengthened Cauchy–Buniakowskii–Schwarz (C.B.S.) inequality is the main tool in the convergence analysis of the recently proposed algebraic multilevel iterative methods. An upper bound of the constant γ in the strengthened C.B.S. inequality for the case of the finite element solution of 2D elasticity problems is obtained. It is assumed that linear triangle finite elements are used, the initial mesh consisting of right isosceles triangles and the mesh refinement procedure being uniform. For the resulting linear algebraic systems we have proved that γ2<0.75 uniformly on the mesh parameter and on Poisson's ratio ν ϵ (0, 1/2). Furthermore, the presented numerical tests show that the same relation holds for arbitrary initial right triangulations, even in the case of degeneracy of triangles.

The theoretical results obtained are practically important for successful implementation of the finite element method to large‐scale modeling of complicated structures. They allow us to construct optimal order algebraic multilevel iterative solvers for a wide class of real–life elasticity problems.
Discrete element methods for the plastic analysis of structures subjected to cyclic loading
Authors: Armen H. , Isakson G. , Pifko A.
Published: August 2005

Methods for the analysis of complex, highly redundant structures subjected to intermittent loads causing biaxial membrane stress and stress reversal into the plastic range are presented. The Bauschinger effect in multi‐axial stress is taken into account by the use of Ziegler's modification of Pragers kinematic hardening theory. The implementation of this plasticity theory in the discrete element methods involves the application of the loading in small increments. A linear relationship between increments of plastic strain and of stress, arising out of the theory, is used in conjunction with a linear matrix equation that governs the elastic behaviour of the structure. In the latter equation, plastic strains are interpreted as initial strains. A solution to the linear matrix equation, expressed in terms either of stress or of total strain, may be obtained by utilizing one of two alternative procedures. The methods are capable of treating materials which exhibit elastic–plastic behaviour involving ideal plasticity, linear or non‐linear strain hardening, or limited strain hardening. Application is made to several representative structures. Comparison of some of the results with existing test data for both monotonic and reversed loading shows good correlation.
Vibration of frames and other structures with banded stiffness matrix
Authors: Gupta K. K.
Published: August 2005

A general digital computer method based on a Sturm sequence procedure is described for determining the natural frequencies and associated modes of undamped free vibration of frames and other structures whose stiffness and mass matrices are of band form. A program which uses the method for the analysis of plane multi‐storey building frames is outlined, and numerical results are presented for a simple test case and for a 19‐storey frame.
The effectiveness of excessive nodal continuities in the finite element analysis of thin rectangular and skew plates in bending
Authors: Smith Ian M. , Duncan William
Published: August 2005

Some typical results of an extensive series of evaluations of parallelogram‐shaped plate bending elements with increasing levels of sophistication are presented. It is shown that, contrary to experience in other fields of stress analysis, this sophistication does not lead to striking improvements in accuracy in the solution of simple rectangular and skew plate problems. A computational procedure is described whereby stiffness matrices may be automatically generated from the minimum of input data specifying the displacement modes prescribed for the element.
Matrix dynamic and instability analysis with non‐uniform elements
Authors: Gallagher Richard H. , Lee Chen‐Hsiung
Published: August 2005

Approximate formulations of non‐uniform beam element stiffness matrices for dynamic and elastic instability analysis are derived. Displacement functions for the uniform beam segment are employed in this development. Moment of inertia and area of the element are prescribed by arbitrary powers of the axial co‐ordinate. Numerical results are obtained and compared with both analytical solutions and numerical solutions based upon stepped representations using uniform section elements. The significance of the inclusion of taper considerations within individual elements upon solution accuracy and convergence characteristics is also examined. This subject problem and solution approach demonstrates that the upper bound character of minimum energy solutions may be difficult to exploit under practical circumstances.
Stress and deformation analysis of fibrous composite materials by point matching
Authors: Lessa Arthur W. , Clausen William E. , Agrawal G. K.
Published: August 2005

The point matching numerical method and its generalization, the method of boundary point least squares, have been successfully applied to numerous boundary value and eigenvalue problems. The present paper demonstrates the application of these techniques to problems in the micromechanics of fibrous composite materials, i.e. determination of elastic moduli and stress concentrations for parallel‐fibre materials which are loaded transversely with respect to the fibres. The solution technique utilizes exact solutions of the governing equations of plane elasticity for each component fibre and its surrounding matrix material in a typical repeating section of the composite material. The continuity conditions for stresses and displacements between fibre and matrix and the repeatability conditions at the boundary of the repeating section are satisfied approximately in a pointwise manner. Some special numerical techniques which were found to be particularly useful in applying the point matching method to these problems are delineated. The method is demonstrated for composite materials having circular, elliptical and square fibres in regular, staggered arrays. Numerical results are given which show the accuracy of the method as well as stress concentration and composite elastic moduli data.
Dynamic analysis of structures using the rank force method
Authors: Robinson John , Petyt Maurice
Published: August 2005

The application of the finite element rank force method for the dynamic analysis of redundant structures is presented. The applied loading consists of discrete and distributed loads. Both forced and free vibrations are considered, the latter yielding latent vectors corresponding to dynamic redundancies.

It is shown that the dynamic properties of an element are given by a static flexibility matrix, an inverse mass matrix, a damping parameter and a displacement vector representing the effect of the applied distributed loading.
Concave programming and piece‐wise linear programming
Authors: Rozvany G. I. N.
Published: August 2005

This paper discusses the mathematical foundations of a technique that has been used extensively in structural optimization.1–6 Two basic problems are considered. The first of these is the concave programming problem which consists of finding the global minimum of ‘piece‐wise concave functions’ on ‘piece‐wise concave sets’. Since any function can be approximated by a piece‐wise concave function, this method could in principle be used to find the global minimum in non‐convex optimization problems. The second one is the piece‐wise linear programming problem in which the objective function is convex and piece‐wise linear. The iterative method outlined for handling this problem is shown to be much more efficient than the standard simplex method of linear programming.
Generation of two‐ and three‐dimensional finite elements
Authors: Boisserie J. M.
Published: August 2005

Many of the known finite elements are based on a variational procedure in a functional basis of monomials. The present paper attempts to formulate completely a finite element procedure which is non‐variational on a functional basis which is left to the choice of the user.
The elasto‐plastic indentation of a half‐space by a rigid sphere
Authors: Hardy C. , Baronet C. N. , Tordion G. V.
Published: August 2005

Using the finite element method, a detailed study of the deformations and stresses produced in an elastic‐perfectly plastic half‐space indented by a rigid sphere was done. The analysis covers the transition region from the maximum elastic contact load to a state where this load has been increased one hundredfold. Experimental results available in the literature are in good agreement with the analysis. In solving repeatedly the large number of linear equations involved in the solution of the problem, it was found profitable, in order to save computer time, to modify the direct elimination method. This technique is described in some details in the paper.
A finite‐deflection analysis of shallow arches by the discrete element method
Authors: Dawe D. J.
Published: August 2005

The discrete element displacement method is used to analyse the finite‐deflection behaviour of shallow arches. The arches are idealized as assemblies of shallow curved elements and the necessary properties of the displacement patterns in these elements are discussed. Numerical solutions of the geometrically non‐linear problem are obtained by directly minimizing the total potential energy of the system.
Improved numerical integration of thick shell finite elements
Authors: Pawsey Stuart F. , Clough Ray W.
Published: August 2005

A quadratic thick shell element derived from a three‐dimensional isoparametric element was first introduced by Ahmad and co‐workers in 1968. This element was noted, however, to be relatively inefficient in representing bending deformations in thin shell or thin plate applications. The present paper outlines a selective integration scheme for evaluating the stiffness matrix of the element, in which each component of the strain energy is evaluated separately using a different Gaussian integration grid for each contribution. By this procedure, the excessive bending stiffness of the element, which results from the use of me quadratic interpolation functions, is avoided.

The improved performance of this element, as compared with the original thick shell element, is demonstrated by analyses of a variety of thin and thick shell problems.

Editors' note: A similar development was outlined by O. C. Zienkiewicz and co‐workers in lnt. J. num. Meth. Engng, 3, 275–290 (1971). Some important details differ between the two papers which are thus complementary.
Matrix differential equation and higher‐order numerical methods for problems of non‐linear creep, viscoelasticity and elasto‐plasticity
Authors: Bažant Z. P.
Published: August 2005

The constitutive equation is assumed in a very general form which includes as special cases non‐linear creep, incremental elasto‐plasticity as well as viscoelasticity represented by a chain of n standard solid models. Subdividing the structure into N finite elements, the problem of structural analysis is formulated with a system of 6N(n + 1) ordinary non‐linear first‐order differential equations in terms of the components of stresses and strains in the elements. This formulation enables one to apply Runge–Kutta methods or the predictor–corrector methods.
The numerical calculation of turbulent boundary layer development
Authors: Ferriss D. H.
Published: August 2005

A mathematical model of the two‐dimensional, incompressible turbulent boundary layer in arbitrary pressure gradient described and solved in earlier work1 is solved by an implicit finite difference method. Comparisons of skin friction coefficient and momentum thickness values for the two methods for four test cases of different character indicate that the present method is a useful alternative to the method of characteristics which was used in previous work.

One feature of the present method is that allowance is made for the logarithmic character of the velocity profile when constructing one of the finite difference expressions.
The finite element method applied to ideal gaseous mixtures
Authors: Secrest B. G. , Boyd W. W.
Published: August 2005

The finite element technique is extended to an ideal gaseous mixture to study diffusion of several gaseous species in a carrier gas under various geometries and flow conditions. This is accomplished by obtaining the finite element analog of the balance of mass for each species, along with the corresponding equations for the balance of mass, momentum and energy for the mixture. Numerical results are obtained for a steady‐state, incompressible, isothermal, viscous mixture of two gases for several boundary conditions. Favourable agreement is obtained between the finite element results and analytical solutions.