bluuebunny/crossref_metadata_2025 huggingface dataset:
Some remarks on Saint‐Venant's principle
Authors: Levine H. A. , Quintanilla R. , Payne L. E.
Published: August 2005

We consider a three‐dimensional hyperelastic cylinder in Ω = D × [0, ∞]. We study the asymptotic behaviour of the deformations of the cross‐sections in an equilibrium state. In this case we show that the solutions either have exponential decay or exponential growth. We give some initial conditions such that the latter case occurs.
Existence result and discontinuous finite element discretization for a plane stresses Hencky problem
Authors: Dhia H. Ben , Hadhri T. , Nedelec J. C.
Published: August 2005

We hereafter propose and analyse a discontinuous finite element method for a plane stress Hencky problem. For that purpose we begin by proving an existence result for the continuous problem. A kind of Green's formula between

and other intermediate results that may be of independent interest are presented and established separately. Then we formulate the discretized problem, give an existence result for it and prove a result of weak convergence of a subsequence of discrete solutions to a solution of the continuous problem.
Boundary integral equations for mixed Dirichlet, Neumann and transmission problems
Authors: Von Petersdorff T. , Leis R.
Published: August 2005

We consider a Helmholtz equation in a number of Lipschitz domains inn≥ 2 dimensions, on the boundaries of which Dirichlet, Neumann and transmission conditions are imposed. For this problem an equivalent system of boundary integral equations is derived which directly yields the Cauchy data of the solutions. The operator of this system is proved to be injective and strongly elliptic, hence it is also bijective and the original problem has a unique solution. For two examples (a mixed Dirichlet and transmission problem and the transmission problem for four quadrants in the plane) the boundary integral operators and the treatment of the compatibility conditions are described.
Quasilinear hyperbolic‐hyperbolic singular perturbation problem: Study of shock layer
Authors: Garbey M. , Eckhaus W.
Published: August 2005

We present the asymptotic analysis of a quasilinear hyperbolic–hyperbolic singular perturbation problem in one dimension. The leading part of the analysis concerns the construction of some shock layers associated with discontinuities of a hyperbolic problem. This study is a generalization of the case of viscous perturbation for a hyperbolic problem.
Admissibility and uniqueness of weak solutions to hyperbolic systems of balance laws
Authors: Kosiński Witold , Brosowski B.
Published: August 2005

A system of quasi‐linear first‐order equations written in the divergence form and constrained by the unilateral differential inequality (the second law of thermodynamics) with a strictly concave entropy function is analysed. In the class BV, i.e. a subset of regular distributions represented by functions of bounded variation in the sense of Tonelli‐Cesari, a weak solution to the system is defined. The parabolized version of the system is also discussed in order to define an admissible weak solution as a limit of a sequence of Lipschitz continuous solutions to the parabolic problem. It is proved that an admissible weak solution of the Cauchy problem is unique in the class BV.
Stability of a smooth flow in a Laval nozzle
Authors: Lar'kin Nikolaj , Wendland W.
Published: August 2005

A boundary‐value problem for a non‐linear second‐order equation of mixed type in a cylindrical domain is considered. This problem simulates the development of small disturbances in a transonic flow of a chemical mixture in a Laval nozzle.

The existence of a regular solution is proved with the help of a priori estimates for a corresponding linear problem and the contractive mapping theorem. The solution of the linear problem is constructed by the Galerkin method.
On a Galerkin‐averaging method for weakly non‐linear wave equations
Authors: Krol M. S. , Eckhaus W.
Published: August 2005

Solutions of weakly non‐linear wave equations can be approximated using Galerkin's procedure combined with the averaging method. In this paper existence and uniqueness of solutions are proved in suitably chosen function spaces. Error‐estimates lead us to results on asymptotic validity of the approximations. Some applications are indicated.
Regular solutions of transmission and interaction problems for wave equations
Authors: Mehmeti Felix Ali , Meister E.
Published: August 2005

Consider n bounded domains Ω ⊆ ℝ and elliptic formally symmetric differential operators A1 of second order on Ωi Choose any closed subspace V in \documentclass{article}\pagestyle{empty}\begin{document}$ \prod\limits_{i = 1}^n {L^2 \left({\Omega _i } \right)} $\end{document}, and extend (Ai)i=1,…,n by Friedrich's theorem to a self‐adjoint operator A with D(A1/2) = V (interaction operator). We give asymptotic estimates for the eigenvalues of A and consider wave equations with interaction.

With this concept, we solve a large class of problems including interface problems and transmission problems on ramified spaces.25,32 We also treat non‐linear interaction, using a theorem of Minty29.
Stability and optimal control of thermomechanical processes with non‐convex free energies of Ginzburg–Landau type
Authors: Sprekels Jürgen , Brosowski B.
Published: August 2005

In this paper we study a coupled non‐linear system of partial differential equations that models the dynamics of structural phase transitions in a one‐dimensional non‐viscous and heat‐conducting solid. The corresponding Helmholtz free energy density is assumed in Ginzburg–Landau form; to allow for phase transitions and hysteresis phenomena, it is not assumed convex in the order parameter. It is shown that the solution of the system depends continuously upon the data, and we prove an existence result for an associated optimal control problem.
Remarks on exponential splines, in particular a contour integral representation of exponential B‐splines
Authors: Walz Guido , Brosowski B.
Published: August 2005

In the present paper we consider spline functions which are piecewise exponential sums of the form Σ αμeμx. Using the notation of Schumaker [10], we construct recursively computable B‐splines of this space, where we make use of a complex contour integral.

Furthermore, it is shown that this definition of a B‐spline coincides in a certain sense with the ‘usual’ ones. which are based on the concept of generalized divided differences (e.g. [3, 12]).

Finally, some additional properties of exponential B‐splines are presented, including a differential relation.
Partition of energy in strongly damped generalized wave equations
Authors: Biler Piotr
Published: August 2005

Dissipative perturbations of hyperbolic equations such as utt + But + A2u = 0 with positive operators A, B are considered. The rates of decay and partition of energy theorems are established for solutions of these equations.
Global solutions of Yang–Mills–Higgs systems on four‐dimensional Minkowski space: II. Some properties of solutions
Authors: Łada A.
Published: August 2005

The paper concerns the properties of global solutions to the Cauchy problem of Yang–Mills–Higgs systems in the temporal gauge. The following properties are considered: global analyticity of solutions, an approximation property, conservation of the topological class of solutions, scattering of a part of the energy of solutions through a light cone.
Examples of embedded eigenvalues for the Dirichlet‐Laplacian in domains with infinite boundaries
Authors: Witsch Karl J.
Published: August 2005

For certain unbounded domains the Laplace operator with Dirichlet condition is shown to have an unbounded sequence of eigenvalues which are embedded into the essential spectrum. A typical example of such a domain is a locally perturbed cylinder with circular cross‐section whose diameter in some bounded subset is greater than at infinity.
The propagation problem and far‐field patterns in a stratified finite‐depth ocean
Authors: Gilbert R. P. , Xu Yongzhi
Published: August 2005

In this paper we investigate the direct problem associated with the scattering of ‘plane waves’ from an object submerged in an ocean of finite depth. An integral representation for the Dirichlet problem is found, from which a formula for the far‐field pattern evolves.

A density theorem is established concerning the set of all far‐field patterns. This theorem is essential for the reconstruction of the submerged object, the ‘inverse’ problem [2], [4], [5].
On some quasilinear hyperbolic–parabolic initial boundary value problems
Authors: Jiang Song , Racke Reinhard
Published: August 2005

We prove a local existence result for a coupled hyperbolic–parabolic initial boundary value problem.
A solution to the equations of shell theory
Authors: Buchanan J. L. , Gilbert R. P.
Published: August 2005

In this paper the Vekua‐Dikmen formulation of the equations of shell theory as a heirarchy are presented as a hypercomplex system. Using the function theory associated with this algebra the torsion problem is solved as an integral representation.
Boundary value problems to a certain class of non‐linear diffusion equations
Authors: Nagasawa Takeyuki
Published: August 2005

The first initial‐boundary value problem and the free boundary of Stefan's type for a certain class of non‐linear diffusion equations which arises in plasma physics are considered. For the first initial‐boundary value problem, the global existence of a classical and its large‐time behaviour are discussed. The free‐boundary problem is studied by the reduction to the first initial‐boundary value problem.
The global existence of solutions to the equations of motion of a viscous gas with an artificial viscosity
Authors: Neustupa JiřÍ
Published: August 2005

We deal with the system of equations of motion of a viscous barotropic fluid. The system contains an artificial viscosity, which depends on the density ρ of the fluid and is identically equal to zero for ρ ϵ 〈0, ρ2〉 (where, ρ2 is a given positive number). If ρ2 is chosen sufficiently large, the system coincides with the Navier–Stokes equations and the equations of continuity if the density has values that actually appear in real flows. The velocity is assumed to be equal to zero on the boundary of the flow field and the body force is not taken into account. Initial conditions need not be ‘small enough’. Applying the method of discretization in time, the existence of a weak solution on an interval of an arbitarary (but finite) length is proved and an estimate of the energy character is derived.
Global existence of weak solutions for a system of non‐linear Boltzmann equations in semiconductor physics
Authors: Mustieles Francisco José
Published: August 2005

In this paper we give a proof of the global existence of weak solutions for the semiconductor Boltzmann equation. This equation rules the evolution of the distribution function of carriers in the kinetic model of semiconductors. The main tool for the proof consists of a recent compactness result on velocity averages of solutions of transport equations. This result needs a L2‐estimate of the electric field, which is obtained from the energy estimate, using the original regularization procedure of the problem, proposed in this paper.
An approximation of the thermal field in a continuous casting process of a thin metal layer
Authors: Comparini Elena , Manni Carla
Published: August 2005

We consider the problem of a phase change in a continuous casting process: molten bronze is poured on to a moving steel strip cooled from below, in order to solidify the bronze. An estimate of the width of the solidification zone, depending on the thickness of the strip and on the casting velocity, is obtained, neglecting conduction in the direction of the strip motion.
The problem of equivalence in statistical mechanics of equilibrium
Authors: Schröter J. , Wegener R.
Published: August 2005

The physical problem of the equivalence of certain partition function in statistical mechanics leads to the following mathematical problem: Under what conditions is the logarithm of a Laplace–Stieltjes transform of the so‐called microcanonical partition function equal to a Legendre transform of the logarithm of the latter? The conditions we shall formulate turn out to be physically reasonable.
Asymptotic completeness in optical scattering
Authors: Jochmann F.
Published: August 2005

In this paper time‐dependent methods are developed in order to prove the existence of the wave operators and asymptotic completeness in the scattering theory of electromagnetic waves in inhomogeneous media.

The medium has a localized perturbation of the dielectric susceptibility. There are no regularity assumptions about the dielectric susceptibility.

It is shown directly that the range of the wave operator is the complete continuous subspace, and not just the absolutely continuous subspace of the generator of the time evolution describing the perturbed wave propagation.
On the theory of cylindrical resonators
Authors: Shestopalov Youri V.
Published: August 2005

This paper contains an introduction to the methods of operator‐valued functions for solving some non‐linear eigenvalue problems of the electrodynamics of guided waves. One simple example of the problem of fundamental frequencies for the rectangular‐slot resonator is considered that gives an opportunity to follow all the steps and features of this technique.
Local existence for solutions of fully non‐linear wave equations
Authors: Lesky Peter
Published: August 2005

Let Ω be a domain in ℝn and let mϵ ℕ; be given. We study the initial‐boundary value problem for the equation

with a homogeneous Dirichlet boundary condition; here u is a scalar function, \documentclass{article}\pagestyle{empty}\begin{document}$ \bar D_x^m u: = (\partial _x^\alpha u)_{|\alpha | \le m} $\end{document} and certain restrictions are made on F guaranteeing that energy estimates are possible. We prove the existence of a value of T>0 such that a unique classical solution u exists on [0, T]×Ω. Furthermore, we show that T → ∞ if the data tend to zero.
Exact solutions to the combined KdV and mKdV equation
Authors: Mohamad M. N. B.
Published: August 2005

This paper presents two different methods for the construction of exact solutions to the combined KdV and mKdV equation. The first method is a direct one based on a general form of solution to both the KdV and the modified KdV (mKdV) equations. The second method is a leading order analysis method. The method was devised by Jeffrey and Xu. Each of these methods is capable of solving the combined KdV and mKdV equation exactly.
Estimating ∇u by div u and curl u
Authors: Von Wahl Wolf
Published: August 2005

In this paper we obtain necessary and sufficient conditions for the validity of the estimate
magnified image
The constant c does not depend on u. u is a vector field with values in ℝ3. It is defined on a bounded set G of ℝ3 or an unbounded one, denoted by Ĝ. The boundary conditions are as follows: either the normal component of u vanishes or the tangential one does. Our conditions are expressed in terms of the Betti numbers of G or Ĝ.
An identification problem for a linear integrodifferential equation occurring in heat flow
Authors: Grasselli Maurizio
Published: August 2005

A linear integrodifferential equation describing the heat flow in a material with memory is considered. This equation contains a pair of time‐dependent convolution kernels that are unknown. Such kernels are recovered by using an overdetermined set of data. A local existence theorem for small times and the continuous dependence of the solutions on the data are shown.
Stationary Boltzmann's equation with Maxwell's boundary conditions in a bounded domain
Authors: Palczewski Andrzej
Published: August 2005

The paper deals with the stationary Boltzmann equation in a bounded convex domain Ω. The boundary ∂Ω is assumed to be a piecewise algebraic variety of the C2‐class that fulfils Liapunov's conditions. On the boundary we impose the so‐called Maxwell boundary conditions, that is a convex combination of specular and diffusive reflections. The non‐linear Boltzmann equation is considered with additional volume and boundary source terms and it has been proved that for sufficiently small sources the problem possesses a unique solution in a properly chosen subspace of C(Ω × ℝ3). The proof is a refined version of the proof delivered by Guiraud for purely diffusive reflection.
New results for guided waves in heterogeneous elastic media
Authors: Joly Patrick , Weder Ricardo
Published: August 2005

We prove the existence of guided waves propagating with a velocity strictly larger than theS(shear) wave velocity at infinity in the case of unbounded elastic media invariant under translation in one space direction and asymptotically homogeneous at infinity.

These waves correspond to the existence of eigenvalues embedded in the essential spectrum of the self‐adjoint elastic propagator.
On missing boundary conditions with unsteady incompressible Navier–Stokes flows
Authors: Hebeker F. K. , Wilde P.
Published: August 2005

We investigate an unsteady viscous flow problem where ‘good’ boundary conditions are available on part of the boundary only. This problem appears when the flow phenomena one is interested in are concentrated on part of the flow region and, for reasons of computational economy, are numerically computed in this subregion only. Assuming that outside of the subregion the flow is not subjected to any acceleration forces, we develop an (abstract) combined finite‐element/boundary element scheme to compute the flow approximately. This scheme leads to a proof of the existence of a weak solution of the corresponding Navier–Stokes problem as well.
Regularization of a non‐characteristic Cauchy problem for the heat equation
Authors: Hào Dinh Nho
Published: August 2005

The non‐characteristic Cauchy problem for the heat equation uxx(x,t) = u1(x,t), 0 ⩽ x ⩽ 1, − ∞ < t < ∞, u(0,t) = φ(t), ux(0, t) = ψ(t), − ∞ < t < ∞ is regularizèd when approximate expressions for φ and ψ are given. Properties of the exact solution are used to obtain an explicit stability estimate.
Interaction between two parallel tunnels
Authors: Ghaboussi Jamshid , Ranken Randall E.
Published: August 2005

A series of finite element analyses were performed to study the behaviour of a system of two parallel and adjacent tunnels. Various sequences of excavation of the two tunnels and installation of tunnel liners have been simulated in the analyses. Influence of various parameters on the behaviour of the two parallel tunnels has been investigated. The important parameters considered in this study are: the width of the pillar separating the two tunnels; the tunnel depth; support condition; sequence of excavation; and, to some extent, the influence of plastic yielding in the medium surrounding the two tunnels.
Treatment of hourglass patterns in low order finite element codes
Authors: Kosloff Dan , Frazier Gerald A.
Published: August 2005

Numerical codes which use a one‐point quadrature integration rule to calculate stiffness matrices for the 2‐D quadrilateral element and the 3‐D hexahedral element, produce matrices which are singular with respect to a number of displacement patterns, other than the rigid body patterns. In this paper an economical method is derived to remove this singularity and which also produces accurate flexural response. For rectilinear element geometry the method is equivalent to the incompatible model element of Wilson et al.7 For non‐rectilinear element geometry a slight modification of the scheme is required in order to assure that it passes the patch test. The method of this paper can also be used in finite difference codes which experience similar difficulties.
Geothermal heat extraction by water circulation through a large crack in dry hot rock mass
Authors: Bažant Zdeněk P. , Ohtsubo Hideomi
Published: August 2005

One proposed geothermal heat extraction scheme relies on water circulation in a large vertical crack created by hydraulic fracturing in a hot dry impermeable rock mass. Water flow, heat convection and crack opening widths are analysed by finite elements. Governing field equations of the problem are first set up rigorously and then various small terms are identified and neglected, retaining the effects of pressure gradient, buoyancy, velocity head (kinetic energy) and head loss due to viscous friction in the water flow equation, and the effects of heat convection in water and heat conduction in rock in the heat transfer equation. The finite element scheme for water flow is based on a variational principle that is typical for diffusion problems, and for heat transfer it is based on the method of least‐square residuals. The system of differential equations is highly non‐linear. The non‐linear terms and coefficients are treated in the fiaite element analysis as constant; the finite element analysisof, the steady‐state pressures, fluxes and temperatures is then iterated, evaluating all non‐linear terms and coefficients on the basis of the solution obtained in the previous iteration. Numerically calculated fields at various times after the start ofcooling are presented. They indicate some features favourable for the geothermal scheme, such as formation of eddy currents, and downward flux of water toward hotter rock. However, other important questions would have to be solved to gain full understanding, of this proposed geothermal scheme.
Consolidation due to shear loads distributed over a rectangular area
Authors: Shanker N. Babu , Sarma K. S. , Ratnam M. V.
Published: August 2005

The paper presents an analytical study of the consolidation of a semi‐infinite clay layer subjected to a shear load distributed over a rectangular area. Biot's theory is made use of, along with the three displacement functions suggested by Verruijt. A complex Fourier and Laplace transformation technique enables the solution to be obtained in terms of non‐dimensional parameters. Settlements and pore pressures under the loaded area are evaluated for two types of surface drainage conditions. Extension of the solutions to point loads is also suggested. The Mandel–Cryer effect is seen in the behaviour of the pore pressure.
A method to estimate the degree of consolidation of a non‐homogeneous clay layer
Authors: Ly Binh‐Le
Published: August 2005

A method is derived to estimate the degree of consolidation of a saturated, non‐homogeneous clay layer. In this method, the diffusion equation govering the dissipation of pore water pressure is transformed so that the pore water pressure can be expressed by a Fourier series. The Fourier coefficients are then evaluated along the trajectory of the diffusion process. The Fourier series does not converge point‐wise to the pore water pressure; instead, it converges to the pore water pressure in the mean., The Fourier series can be used to estimate the degree of consolidation, because, by Schwartz's inequality, convergence in the mean implies convergence in the degree of consolidation.
Effects of restricted flow at the surface of saturated clay
Authors: Deresiewicz H.
Published: August 2005

The deflection of, and the pore pressure at, the surface of a saturated clay mass are computed by modelling the mass mathematically as a consolidationg half‐space. Specifically, attention is focused on the effect of a surface cover which impedes, though does not entirely prevent, the flow of the pore water. A number of results of interest are reported, generalizing work reported earlier by McNamee and Gibson8.
Dynamic stiffness for rectangular rigid foundations on a semi‐infinite elastic medium
Authors: Kitamura Yasutoshi , Sakurai Shunsuke
Published: August 2005

The present paper deals with the dynamic steady‐state force‐displacement relationships (complex stiffness) for rectangular rigid foundations resting on a semi‐infinite medium, consisting of homogenous, isotropic, linear elastic materials. The foundations are considered to be excited under harmonic vertical and rocking vibration. This gives mixed boundary value problems which cannot be easily solved by analytical approaches. Therefore, a numerical method is proposed here. The method is based on quite, simple equations, and is straightforward in computation, compared with other methods. Although the proposed method gives just approximate solutions, it is satisfactory for engineering practices, and the soluations become highly accurate for a small value of ωB/Vs. The results obtained by the proposed method are compared with those of other methods to evaluate the accuracy of the results. The effects of length/width ratio and the area of the contact plane of the foundations are also discussed.
Discrete element analysis of pile instability
Authors: Smith Ian M.
Published: August 2005

Recently, instability of slender piles during installation has been analysed as a non‐conservative buckling process. For these results to be of potential use in practice, simple procedures are necessary whereby piles of arbitrary cross‐section installed in ground with arbitrarily varying properties can be treated. This paper lists discrete element matrices which enable the prediction of the onset of instability in piles assuming conservative or non‐conservative ground resistance. The same matrices can then be used to incorporate effects of incipient instability in driveability analyses.
Isotropic yield surfaces in three dimensions for use in soil mechanics
Authors: Van Eekelen H. A. M.
Published: August 2005

When using numerical methods in soil mechanics, one often needs to define a yield surface in three‐dimensional principal‐stress space. A special class of yield surfaces, given by J = (p+a)α(1−β sin 3ν)n, where ν is the Lode angle, is considered from the point of view of convexity and agreement with experimental data. Some recently proposed yield functions which belong to this class are compared. It is shown that the model with n = −0.229 is optimal as regards convexity, and can give reasonable agreement with the data.
Analysis of leaky sheetpile by Summary Representation
Authors: Karadi Gabor M. , De Miguel Enrique , Krizek Raymond J.
Published: August 2005

A numerical technique called Summary Representation was used to solve the problem of seepage through a leaky sheetpile; this particular method was selected owing to its accuracy and computational speed. Seepage parameters were evaluated quantitatively and the influence of the leakiness of sheetpiles in a porous medium underlain by an impervious horizontal stratum was determined. The case of a single sheetpile was first considered, and the effect of the depth of penetration and coefficient of leakiness on the total rate of flow and on the values of the exit gradient was analysed. Next, the flow under an impervious dam was considered to assess the accuracy of the method. Finally, the case of seepage under a dam with leaky sheetpiles at both ends was studied, including the effect of the leaky sheetpiles on the uplift pressure acting along the foundation of the dam. Patterns of seepage through the flow line deformation that is caused by the leakiness of the sheetpiles.
Determination of the critical slip surface in slope stability computations
Authors: Baker R.
Published: August 2005

The analysis of the stability of slopes using limiting equilibrium considerations necessitates the determination of the critical slip surface which yields the minimal factor of safety. The numerous methods currently available for slope stability analysis provide a procedure for assigning a factor of safety to a given slip surface, but do not consider the problem of identifying the critical conditions.

This paper presents an effective minimization procedure based on dynamic programming by which the minimal factor of safety, and the corresponding surface, are determined simultaneously. This procedure SSDP (Slope Stability by Dynamic Programming), couples the minimization scheme with Spencer's method of slope stability analysis. It may be applied to slopes of any geometry, layering, pore pressure and external load distributions. No arbitrary restrictions are placed on the shape of the slip surfaces, and the analysis satisfies all equilibrium equations.

Application of the procedure to slope stability problems reported in the literature shows that for a given slip surface the procedure yields factors of safety which are almost identical to those reported, but in every case a more critical slip surface, with a lower factor of safety, may be found.
An accuracy condition for consolidation by finite elements
Authors: Vermeer P. A. , Verruijt A.
Published: August 2005

Finite element solutions of consolidation problems often exhibit oscillating pore pressures, which tend to increase when the time steps are reduced. This phenomenon is investigated and a lower limit for the time steps is derived, in terms of the mesh size and the coefficient of consolidation near the draining boundary.
A statistical study of fabric in a random assembly of spherical granules
Authors: Oda M. , Nemat‐Nasser S. , Mehrabadi M. M.
Published: August 2005

It is commonly accepted that the mechanical behaviour of granular masses is strongly affected by their microstructure, namely the relative arrangement of voids and particles, i.e. the granular fabric. Therefore, parameters which characterize the granular fabric are of paramount importance in a fundamental description of the overall macroscopic stresses and deformation measures. In this paper several measures of granular fabric are introduced for a random assembly of spherical granules, using a statistical approach. In particular, a second‐order symmetric tensor, Fij, emerges from this consideration, which seems to be of fundamental importance for the description of fabric, and which is closely related to the distribution of the contact normals in the assembly. The relation between fabric measures presented here and those discussed by other investigators is also discussed.
Vibration of a rigid disc on a transversely isotropic elastic half space
Authors: Kirkner David J.
Published: August 2005

The problem of a massless, rigid disc vibrating harmonically on a ‘constrained’ transversely isotropic elastic half space is considered. The material is called constrained because it is assumed that the elastic constants satisfy a certain equation. The problem for each mode of vibration is reduced to the solution of a Fredholm integral equation of the second kind. Results are presented to show the general effect of the material anisotropy.
Incrementalization procedure for elasto‐plastic constitutive model with multiple, intersecting yield surfaces
Authors: Lade Poul V. , Nelson Richard B.
Published: August 2005

Constitutive models for description of the non‐linear stress‐strain behaviour of engineering materials are often developed and presented in forms which cannot be employed directly in non‐linear matrix computer analysis codes. Presented herein is a procedure for developing the incremental stiffness matrix for an elasto‐plastic material model with multiple, intersecting yield surfaces. Associated or non‐associated flow may occur on the individual yield surfaces. The material stiffness matrix is non‐symmetric if non‐associated flow occurs on any one of the yield surfaces. In order to illustrate the matrix forms which are generated, the case of a recently developed model with two yield surfaces is presented in detail. This model involves associated flow on one and non‐associated flow on the other yield surface.
On the dynamic stiffness of circular ring footings on an elastic stratum
Authors: Tassoulas John L. , Kausel Eduardo
Published: August 2005

Circular ring footings on an elastic stratum are considered. The static and dynamic stiffnesses are calculated using an efficient numerical technique. The results indicate that the static torsional and rocking stiffnesses of a ring footing do not deviate significantly from the corresponding stiffness of the circular footing for values of the inner‐radius‐to‐outer‐radius ratio up to about 0.75. The static horizontal and vertical stiffnesses change considerably only for values of this ratio greater than about 0.60. The change in the stiffness and damping coefficients is small for values of the ratio between 0 and 0.5.
Numerical simulation of unsteady fluid flow and propagation of a circular hydraulic fracture
Authors: Cleary M. P. , Wong S. K.
Published: August 2005

A computational procedure is developed for solving the problem of a circular hydraulic fracture propagating under the action of frac‐0fluid being pumped in at a central wellbore. The crack is modelled as continuous distributions of ring dislocations and the resulting elasticity singular integral equation is solved numerically. The fluid flow equations are approximated by local and global interpolation finite difference schemes. The coupling between elasticity and fluid flow is handled numerically, by, two different algorithms: one iterates on crack tip velocity whereas the other varies the time step size until it agrees with the chosen increment in crack length. Sample results are given; it is found that the velocity algorithm is computationally more, efficient and more stable. The model allows detailed tracing of pressure distribution and fluid flow in the fracture, even under complex conditions of cyclic injection and fluid rheology. It may serve as a stand‐alone model of (horizontal) hydrafracs–especially at shallow depths–or it may be used as a reference frame to test the various numerical formulation/algorithms required for the ongoing development of a fully 3‐D hydrafrac simulator.
Theoretical study on the stability of a reservoir created by the intersection of a fluid‐filled crack with an oblique joint for the extraction of geothermal heat
Authors: Abé H. , Hayashi K. , Arima S.
Published: August 2005

On the basis of the two‐dimensional theory of elasticity, the theoretical analysis of a vertical, fluid‐filled crack intersecting and oblique joint has been made for the extraction of geothermal heat from hot, dry rock masses, where the opening of the joint near a point of intersection and the frictional resistance against slips along the joint are taken into account. The stress intensity factors are evaluated for discussing crack kinking at the upper joint tip, and the sufficient conditions on theinclination of the joint and on the length between the upper joint tip and the point of intersection are obtained for keeping a fluid‐filled crack stable just beneath a joint. It is also shown that the volume of the stable reservoir created by using a joint is much larger than that of a fluidfilled crack in a jointless rock mass, even if the joint is oblique and is opened up by the fluid pressure.
Variational principles and finite element simulations for thermo‐elastic consolidation
Authors: Aboustit B. L. , Advani S. H. , Lee J. K.
Published: August 2005

In this paper, a general variational principle for the initial boundary value problem of quasi‐static thermoelastic consolidation is developed by assuming infinitesimal deformation and an incompressible fluid flowing through a linearly elastic solid. By manipulating the coupling operators, an extended form of the variational pronciple is derved. The associated finite element formulation based on this principle is presented and numerical applications for plane strain thermo‐elastic consolidation are revealed.
A large strain theory for the two dimensional problems in geomechanics
Authors: Kiousis Panagiotis D. , Voyiadjis George Z. , Tumay Mehmet T.
Published: August 2005

An incremental finite element formulation for elasto‐plastic bodies subjected to large strains and large displacements is presented in this paper. The formulation is in Lagrangian co‐ordinates (material description) and the plasticity model employed is the extended von Mises. The bearing capacity of a strip footing and the stability of an earth slope illustrate the applicability of this theory.
Vibration of a rigid footing—a finite model for the elastic half space
Authors: Damisa O.
Published: August 2005

A problem common to most numerical methods of analysing the vibration of a rigid body on an elastic half space is indentified especially as regards the arbitrary truncation of the semi‐infinite half space or the numerically expensive computations involved in some of the methods. This paper presents a boundary integral equation (BIE) method of defining a finite domain to replace the half space and consists of evaluating the BIE over the domain. A mathematical justification is provided for defining the domain, and the error involved in such truncation of the half space in shown to be small. Yet the computations are very cheap owing to the simple trigonometric/algebraic functions involved in the BIE. The accuracy of the method is quite commendable especially as seen from the results presented for the circular foundation for which analytical and experimental solutions are available for comparison.
Analysis of a point sink embedded in a porous elastic half space
Authors: Booker J. R. , Carter J. P.
Published: August 2005

Closed‐form solutions are presented for the steady‐state distributions of displacement, pore pressure and stress around a point sink embedded in a homogeneous, isotropic elastic half space. These solutions have been evaluated for a typical case of a sink (pump) buried in sand and the magnitude of the settlement of the ground surface has been estimated.
Finite element analysis of mechanisms of pile group behaviour
Authors: Pressley J. S. , Poulos H. G.
Published: August 2005

Solutions are presented for the non‐linear load‐settlement behaviour of square‐configuration pile groups. The groups are represented by an equivalent axially symmetric model, and a non‐linear finite element is used to examine the mechanisms of group behaviour and their variation with pile spacing. It is shown that, at close spacings, the block failure mechanism occurs, with significant plastic zones being developed below the group and full pile‐soil slip only being developed along the outer piles. As the pile spacing increases, the failure mechanism gradually changes to the ‘single‐pile’ mode, whereby full pile‐soil slip occurs along all piles. Within the limitations of accuracy of the finite element solution, the values of group settlement ratio and efficiency are in reasonable agreement with values derived from existing theories.
A hierarchical approach for constitutive modelling of geologic materials
Authors: Desai C. S. , Somasundaram S. , Frantziskonis G.
Published: August 2005

A hierarchical concept is proposed for the development of constitutive models to account for various factors that influence behaviour of (geologic) materials. It permits evolution of models of progressively higher grades from the basic model representing isotropic hardening with associative behaviour. Factors such as non‐associativeness and induced anisotropy due to friction and cyclic loading, and softening are introduced as corrections or perturbations to the basic model. The influence of these factors is captured through non‐associativeness manifested by deviation from normality of the plastic strain increments to the yield surface, F. Details of four models: isotropic hardening with associative behaviour, isotropic hardening with non‐associative behavioural anisotropic hardening and strain‐softening with a damage variable are presented. They are verified with respect to laboratory multiaxial test data under various paths of loading, unloading and reloading for typical soils, rock and concrete. The proposed concept is general, yet sufficiently simplified in terms of physical understanding, number of constants and their physical meanings, determination of the constants and implementation.
Influence of a wall system on the interaction between soil and foundation plates
Authors: Kujawski J. , Wiberg N.‐E.
Published: August 2005

The paper considers the influence of a building wall system on the interaction between the soil and the foundation plate. A simplified semi‐analytical finite element method gives an economical solution for large three‐dimensional soil‐structure interaction problems. The simplified method appears to be sufficiently accurate for engineering purposes.

Numerical results presented show significant influence of building walls on the foundation‐plate‐soil interaction.
Comparison of transmitting boundaries in dynamic finite element analyses using explicit time integration
Authors: Simons H. A. , Randolph M. F.
Published: August 2005

Explicit time integration schemes provide an efficient solution to non‐linear dynamic finite element analyses of geotechnical problems especially when high frequency response is important. Such explicit time integration schemes require one of two distinct transmitting boundary formulations to overcome the problem of radiation damping. These are the superposition boundary approach, which involves the cancellation of the reflected waves by combining the solutions of two different boundary conditions and the viscous boundary approach, which involves the absorption of incident wave energy by frequency independent viscous dashpots. The theoretical justification of these two approaches and their means of implementation are reviewed. The solutions obtained using the two different boundary approaches to the problem of a rigid massless circular footing vibrating on an elastic half‐space are compared with an independent theoretical solution. The performance of the boundaries for problems involving step loading is also examined and the implications for any loading pattern with a non‐zero time average are discussed.
Response of poroelastic halfspace to steady‐state harmonic surface tractions
Authors: Halpern Marc R. , Christiano Paul
Published: August 2005

Traditionally, most formulations of dynamic halfspace problems have represented the material as either an elastic or a viscoelastic solid. Herein the counterpart of Lamb's elastodynamic problem is reformulated and solved for a liquid‐saturated poroelastic halfspace using Biot's theory of poroelasticity. The responses of the solid and fluid phases are evaluated due to steady‐state harmonic concentrated loads applied to each phase at the surface. The solutions are presented over a broad range of permeabilities and are compared to solutions to Lamb's problem for equivalent drained and undrained solids. Methodology is then introduced by which these results are treated as Green functions for the solution of a mixed boundary‐value problem. namely, the response of the poroelastic halfspace to steady‐state harmonic vertical motion of a rigid. massless plate. It is observed that small differences exist among overall compliance functions for a drained solid, an undrained solid, and a liquid‐saturated porous, halfspace. However, use of the poroelastic model permits the distribution between effective skeletal normal stresses and fluid stresses to be determined.
Generalized displacements of a rigid elliptical anchor embedded at a bi‐material geological interface
Authors: Selvadurai A. P. S. , Au M. C.
Published: August 2005

The present paper examines the class of problems related to a flat rigid anchoring region which is embedded at a geological interface. The analysis focuses on the evaluation of the elastic stiffness of the embedded anchor. A boundary element technique is used estimate the axial, rotational and translational stiffnesses of the anchor. These estimates are compared with a set of bounds which are evaluated in exact closed form. These bounds are obtained by invoking kinematic and/or traction constraintsat the geological interface. The numerical results presented in the paper illstrate the manner in which the various stiffnesses of the anchoring region are influenced by the elastic properties of the surrounding geological media.
Effective stress analysis of seismic site response
Authors: Prevost Jean H.
Published: August 2005

A procedure is presented which allows site response analyses to be performed with any general multidimensional finite element analysis package. Numerical results which corrorate the theory are presented. Also, as an illustration of the procedure, results of an effective stress analysis for the scismic response and liquefaction of a horizontally layered saturated sand deposit are presented.
Vertical deformation of rigid foundations of arbitrary shape on layered soil media
Authors: Chow Y. K.
Published: August 2005

A numerical procedure is described for the analysis of vertical deformation of smooth, rigid foundations of arbitrary shape on homogeneous and layered soil media. The contact area at the interface of the foundation and soil medium is approximated by square subdivisions. The response of the system is then obtained from the superposition of the influence of the individual subdivisions. The flexibility influence coefficients are based on equivalent smooth, rigid circular areas with the same contact area as the square subdivisions. For foundations on a homogeneous, isotropic elastic half‐space, the flexibility coefficients are given analytically by the integrated forms of the Boussinesq's solution. For a layered soil medium, the flexibility coefficients are determined from an axisymmetric finite element analysis which is essentially two dimensional. Thus, there is no necessity for a full three‐dimensional finite element analysis. Comparison with solutions obtained using the integral transform technique for smooth, rigid rectangular foundations on a homogeneous, isotropic elastic half‐space shows good agreement. Parametric solutions are presented for the response of rectangular foundations on some ‘typical’ soil profiles. The use of a simplified method to estimate the settlement of rectangular foundations on a layered soil medium by superposing solutions for homogeneous, elastic strata is discussed.
Stability analysis of slopes with general nonlinear failure criterion
Authors: Zhang X. J. , Chen W. F.
Published: August 2005

The upper bound method of limit analysis of perfect plasticity is applied to stability problems of slopes with a general nonlinear failure criterion. Based on the upper bound method, a numerical procedure is suggested, which converts the complex system of differential equations to an initial value problem. Using this numerical procedure, an effective numerical method, called the inverse method, suitable for the solution of slope stability problems in soil mechanics with a general nonlinear failure criterion, is presented. A general nonlinear failure criterion for soils is also suggested, from which the effects of nonlinear failure parameters on the stability of slopes are discussed.
Circular plates on Pasternak elastic foundations
Authors: Dumir P. C.
Published: August 2005

This study deals with the geometrically nonlinear axisymmetric static and transient response of cylindrically orthotropic thin circular plates resting on Pasternak elastic foundations subjected to uniformly distributed loads. Clamped and simply‐supported plates with radially movable and immovable edges have been considered. The von‐Kármán type nonlinear governing equations have been solved using orthogonal point collocation method in the space domain and Newmark‐β scheme in the time domain. The maximum transient response to step loads has also been predicted from static response. The influence of the foundation parameters on the response has been investigated.
A stochastic approach in modelling and estimating geotechnical data
Authors: Christakos George
Published: August 2005

A rational approach for dealing with uncertainties in geotechnical performance predictions is presented. First, sources of uncertainty are identified and treated stochastically. Then, the relative importance of each source is analysed and its influence in the decision‐making process is evaluated. Strong inferences concerning the spatial structure of soils are drawn from field or laboratory measurements, while maintaining consistency with engineering knowledge and experimenal findings. Optimal estimates of soil properties are derived by a stochastic method which is mathematically meaningful and portrays adequately the real behaviour of the data. The method is powerful when the data exhibit homogeneous or non‐homogeneous characteristics, and works well with any kind of data support. Its applicability is illustrated in a case study involving field vane data. Furthermore, contributions and benefits of the results obtained to the geotechnical decisions and design are discussed.