bluuebunny/crossref_metadata_2025_split huggingface dataset:
Numerical solution of a time‐like Cauchy problem for the wave equation
Authors: Klibanov Michael , Rakesh  
Published: August 2005

AbstractLet D ⊂ ℝn be a bounded domain with piecewise‐smooth boundary, and q(x,t) a smooth function on D × [0, T]. Consider the time‐like Cauchy problem
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Given g, h for which the equation has a solution, we show how to approximate u(x,t) by solving a well posed fourth‐order elliptic partial differential equation (PDE). We use the method of quasi‐reversibility to construct the approximating PDE. We derive error estimates and present numerical results.
Abstract Besov space approach to the non‐stationary Navier–Stokes equations
Authors: Kobayashi Takayuki , Muramatu Tosinobu 
Published: August 2005

AbstractThe local existence, uniqueness and regularity of solutions of the initial‐value problem for non‐stationary Navier–Stokes equations are studied via abstract Besov spaces. The assumptions about Ω the initial data and the external force are improved on by rather simple proofs.
Inhomogeneous Timoshenko beam equations
Authors: Arosio Alberto , Panizzi Stefano , Paoli Maria Gabriella 
Published: August 2005

AbstractThe so‐called Timoshenko beam equation is a good linear model for the transverse vibrations of a homogeneous beam. Following the variational approach of Washizu, the governing equation is deduced in the case when the physical/geometrical parameters of the beam vary along its axis. The equation may not be studied by means of the iterated use of Fourier series. However, a convenient change of variables permits us to prove the well‐posedness of the associated Cauchy problem for a beam with sliding ends (the solution is intended in a mild sense). The proof is given in an abstract framework.
Analysis of the thermoelastic model of a plate with non‐linear shape memory alloy reinforcements
Authors: Hoffmann K.‐H. , Zochowski A. 
Published: August 2005

AbstractIn this paper we study the questions of the existence and uniqueness of the solutions for a thermoelastic system of equations magnified image magnified image in a two‐dimensional domain, where both the viscosity v and the rigidity D are positive. It seems that such a system has up to now been considered in a one‐dimensional setting only. The change of dimensions enforces the growth conditions with respect to θ and the additional regularity of the data. The existence of solutions in the case of the Neumann boundary conditions for θ and some weak regularity of data is proved. Under stronger regularity conditions the uniqueness is also established. The system has an interpretation as a plate reinforced by a shape memory alloy (SMA) wire mesh.
Local bifurcation from characteristic values with finite multiplicity and its application to axisymmetric buckled states of a thin spherical shell
Authors: Tan Nguyen Xuan 
Published: August 2005

AbstractThe purpose of this paper is to study bifurcation points of the equation T(v) = L(λ,v) + M(λ,v), (λ,v) ϵ Λ × D in Banach spaces, where for any fixed λ ϵ Λ, T, L(λ,·) are linear mappings and M(λ,·) is a nonlinear mapping of higher order, M(λ,0) = 0 for all λ ϵ Λ. We assume that λ is a characteristic value of the pair (T, L) such that the mapping T – L(λ,·) is Fredholm with nullity p and index s, p > s ⩾ 0. We shall find some sufficient conditions to show that (λ,0) is a bifurcation point of the above equation. The results obtained will be used to consider bifurcation points of the axisymmetric buckling of a thin spherical shell subjected to a uniform compressive force consisting of a pair of coupled non‐linear ordinary differential equations of second order.
Low Reynolds number deformation of compound drops in shear flow
Authors: Power Henry 
Published: August 2005

AbstractThe method developed by Rallison and Acrivos (1978) to solve the deformation of a single drop due to exterior shear flow for a small Reynolds number is extended to the problem of the deformation of a compound drop. The result is found in terms of a Fredholm integral equation of the second kind, which is shown to have a unique solution and the solution is given by means of a uniformly convergent Neumann series.
Finite deformation of an elasto‐plastic soil
Authors: Carter J. P. , Booker J. R. , Davis E. H. 
Published: August 2005

AbstractPresented in this paper is a formulation and a numerical solution method for problems which involve finite deformations of an elasto‐plastic material. The governing equations are cast in rate form and the constitutive laws are formulated in a frame indifferent manner. Particular reference is made to the finite deformation of soil. Plastic failure is described by a general yield condition and plastic deformation by an arbitrary flow rule. Several examples are treated numerically.
Visco‐plastic behaviour during the excavation phase of a salt cavity
Authors: Fossum Arlo F. 
Published: August 2005

AbstractThe stress field and flow characteristics are studied for a cavity with the shape of a prolate spheroid in dome salt with emphasis given to the excavation phase. A semi‐empirical creep law is derived from thermodynamic principles and experimental results. In this paper, an elementary non‐linear form is used in the kinetic relation. A finite element solution procedure is discussed which incorporates the creep law, excavation sequence, and arbitrary non‐homogeneous initial stress field.
Stability analysis of a jointed beam
Authors: Chugh Ashok K. 
Published: August 2005

AbstractA numerical step‐by‐step procedure, analogous to the ‘Initial Stress Method,’ is presented for the analysis of a single‐layer jointed rock beam subjected to gravity loads and in‐plane in situ formation pressure. The joints are permitted to open at locations where the flexural stresses exceed flexural strength. The material properties may be different for each rock block and joint. A detailed algorithm is given for the solution of the problem. The results of several analyses indicating the relative effects of initial formation pressure, transverse load, stiffness of the joint material, and joint spacing on the response of a jointed beam are presented. The convergence characteristics of the numerical procedure are included. The joint material is assumed to be ‘no‐tension’ type. Both the geometric and material non‐linear effects are considered.
A case study of the surface subsidence of the Polesine area
Authors: Schrefler B. A. , Lewis R. W. , Norris V. A. 
Published: August 2005

AbstractThe Polesine, a region in the northeast of Italy, has experienced considerable surface subsidence due to the withdrawal of water and gas from the underlying reservoir sediments. These settlements have been well documented and form the basis of a comparison study with a finite element consolidation model. It is shown that the model is capable of simulating the field behaviour during production and also after the closure of the wells.
The economic analysis of raft foundations
Authors: Wood L. A. 
Published: August 2005

AbstractAn approximate method, using a simplified soil model, for predicting the behaviour of raft foundations subjected to applied vertical forces and moments will be outlined. Results obtained for circular rafts of finite rigidity are compared with those obtained, from more rigorous solutions, by other authors. Satisfactory agreement is obtained for the surface settlements and raft bending moments over a wide range of soil inhomogeneity. Finally, the versatility of the method of analysis is illustrated for an unusual asymmetrical structure. Computed total and differential settlements are shown to be in reasonable agreement with measured values and those predicted by an independent plane strain finite element analysis.
Associated and non‐associated constitutive relations for undrained behaviour of isotropic soft clays
Authors: Banerjee P. K. , Stipho A. S. 
Published: August 2005

AbstractIncremental theory of plasticity has been used to derive associated and non‐associated stress–strain relations for analysing the undrained stress‐strain response of isotropic normally and lightly overconsolidated clays. A series of comparisons between the theoretical stress‐strain‐pore pressure response and laboratory test results for 3 in. × 6 in. samples of very high degree of repeatability and reproduceability have been described. From these comparisons it can be seen that both the associated and, non‐associated Cam clay models appear to give consistently the best correlations between the theoretical results and the experimental observations.
The response of a deep rigid anchor due to undrained elastic deformations of the surrounding soil medium
Authors: Selvadurai A. P. S. 
Published: August 2005

AbstractThe equations governing the undrained linear elastic behaviour of a saturated soil are formally similar to the equations governing slow of an incompressible Newtonian viscous fluid. This principle of equivalence can then be effectively employed to obtain the load‐deflection reiationship for a deep rigid anchor with the shape of a solid of revolution which is embedded in bonded contact with an unbounded incompressible elastic medium. It is found that the load‐deflection relationship for the deep rigid anchor can be directly recovered from the expression for the drag induced on an impermeable object with the same size and shape as the anchor, which is appropriately placed in a slow viscous flow region of uniform velocity.
Slipping strip analysis of reinforced earth
Authors: Naylor D. J. , Richards H. 
Published: August 2005

AbstractReinforced earth in plane strain is idealized as a homogeneous material with the strips attached to the elastic soil matirx by a conceptual shear zone. A ‘no‐slip’ finite element model is derived by assigning a large shear modulus to the shear zone. Relaxation of this modulus using a tangential stiffness algorithm in conjunction with a Mohr–Coulomb strip‐slip criterion allows slipping to be simulated.The finite element formulation is validated and the finite element discretization assessed by comparisons against exact solutions for a simple test problem.An idealized reinforced earth wall example is used to demonstrate the feasibility of the method and to answer the question: ‘is slipping significant?’ The method is shown to be potentially useful, and slipping is shown to be significant.
Non‐linear seismic response and liquefaction
Authors: Zienkiewicz O. C. , Chang C. T. , Hinton E. 
Published: August 2005

AbstractThe essential cause of the growth of pore pressure during cyclic loading is identified as an ‘autogenous’ shrinkage or densification of the solid phase of the soil and this is related to a strain path parameter. Introduction of this ‘shrinkage’ coupled with an elasto‐plastic behaviour of the soil skeleton allows a full non‐linear dynamic analysis to be conducted up to the point of structural failure for any earthquake input. Explicit time marching procedures are used. The procedure outlined is applicable to all problems of complex geometry and for conditions of undrained or partially drained behaviour at a moderate computational cost.
A numerical solution of an irrigation flowfield
Authors: Bruch John C. 
Published: August 2005

AbstractTwo‐dimensional seepage from an array of triangular channels into permeable soil underlain at a finite depth by a drain has been solved by using the Baiocchi method. The use of this approach allowed a simple formulation of the seepage problem through extension of the solution region to an a priori known region. The new problem was treated numerically by using the S.O.R. method combined with projection. This technique proved to be very accurate when compared with analytical results and efficient from a computer programming standpoint.
Analytical studies of pile wandering during installation
Authors: Burgess I. W. 
Published: August 2005

AbstractIn a previous paper it was established with very simple assumptions that piles might undergo a directional instability during placement, of a type more usually found in aerodynamic problems. The study is here extended to piles driven into soils whose shear strength and lateral reaction modulus can vary with depth. The analysis consists of a parametric study of the effect of linear variation of the soil parameters with depth on the critical lengths for instability, and a comparison of site evidence with the critical lengths obtained from a stepwise‐constant representation of the variation of soil parameters with depth. The theory is shown to give very reasonable estimates of the depths at which major deviation starts, although there is a pressingneed for more detailed site and laboratory data.
The analysis of finite elasto‐plastic consolidation
Authors: Carter J. P. , Booker J. R. , Small J. C. 
Published: August 2005

AbstractA theoretical formulation and a numerical solution method are proposed for the problem of the time dependent consolidation of an elasto‐plastic soil subject to finite deformations. The soil is assumed to be a two‐phase material with a skeleton which may yield according to a general yield criterion with plastic flow governed by a general flow law, and whose pore fluid flows according to Darcy's Law. Governing equations are cast in a rate form and constitutive laws are expressed in a frame indifferent manner. The method of analysis is illustrated by several examples of practical interest for both a soil with an elastic skeleton and a soil with an elasto‐plastic skeleton which obeys a Morh–Coulomb yield criterion and a non‐associated flow law.
Observed and predicted test pile behaviour
Authors: Ottaviani Mario , Marchetti Silvano 
Published: August 2005

AbstractThe results obtained from a loading test on a bored, cast‐in‐place pile instrumented with six pairs of load cells at different levels are compared with the results obtained from a non‐linear finite element analysis based on the geotechnical parameters of the cohesive soils in which the pile was bored.Settlements computed using deformability parameters obtained by a standard laboratory test were much larger than the measured settlements. Satisfactory results are instead obtained assuming Ei=1000cu and cα=cu.The distribution of the vertical stresses within the pile and of the shear stresses in the soil adjacent to the pile obtained by the numerical analysis are compared with the measured values.A fair agreement is found at loads below failure but differences between experimental and computed values are found at loads close to failure.
An algorithm and a modular subroutine for the CAP model
Authors: Sandler I. S. , Rubin D. 
Published: August 2005

AbstractA cap model algorithm and the associated FORTRAN subroutine, CAP, are presented. The algorithm lends itself to a wide range of soil and rock cap models, and can easily be incorporated into most dynamic codes. The routine permits the user to obtain flexibility with respect to changes in functional forms and parameters with minor coding changes.
On hypoelasticity and plasticity approaches to constitutive modelling of inelastic behaviour of soils
Authors: Mróz Z. 
Published: August 2005

AbstractA comparative discussion of constitutive rate equations generated by using the hypoelasticity and plasticity theories is presented. If is shown that these two approaches are equivalent for the loading process but differ essentially in defining the unloading (or reverse loading) paths. The multisurface plasticity formulation proves to be more convenient in incorporating memory rules of particular loading events, whereas loading‐unloading criteria used in hypoelasticity may result in an unrealistic prediction of material response for some loading paths, and in particular, for cyclic loading. The violation of the continuity condition between loading–unloading domains in proposed constitutive relations3,4 limits their applicability to some particular classes of loading paths.
Settlement of inhomogeneous consolidating soils—II: The symmetrically loaded mass
Authors: Mahmoud M. S. , Deresiewicz H. 
Published: August 2005

AbstractWe continue our study of the consolidation of inhomogeneous clay soils with an analysis of the response of a soil mass, whose shear modulus increases linearly with depth, to axially symmetric pressure on its surface. This extends the work reported in Part I on the corresponding one‐dimensional problem of a clay column, and generalizes researches of Gibson and coworkers on the elastic model of the soil (i.e., the initial response).Because of great mathematical complexity when Poisson's ratio is allowed to assume arbitrary values, we have confined ourselves (as did Gibson in several of his papers) to variations of the modulus from a zero surface value, this being in reasonable accord with published test results on London clay. The deflection of points within this region, the deflection relative to the central one (that is, the shape of the deformed loading area), as well as the absolute deflection of surface points exterior to the load.
A simplified analytical method for soil penetration analysis
Authors: Yankelevsky David Z. , Adin Moshe A. 
Published: August 2005

AbstractA new one‐dimensional model for penetration analysis of a rigid projectile into a soil target is presented. The soil medium is represented by a set of discs of constant thickness, responding in the radial direction under plain strain regime. When penetration through a typical disc occurs, the projectile displaces soil material and a radial plastic shock wave propagates in the disc. The interaction pressure between the projectile and soil material is compatible with the motion of the contact boundary, between them. The instantaneous resistive force is obtained by summation of the contributions of all the discs which are in contact with the nose surface of the projectile. Soil is considered as a ‘floating’ ideally locking material, in which the locking volumetric strain is adjusted to the physical stress–strain properties of the soil material. Friction between projectile and soil is assumed to be negligible. Comparison is made with both twodimensional computer program results and experimental data, and very good agreement is observed. Comparison with other analytical methods reveals that the present model most closely resembles existing experimental results and permits further analysis of the problem as predictions of target response and of stress distribution on the projectile nose. The calculations require very small amounts of computer time. Analysis with the present model yields an efficient and comprehensive means to analyse penetration and perform parameter analysis.
A concept of correction functions to account for non‐associative characteristics of geologic media
Authors: Desai C. S. , Siriwardane H. J. 
Published: August 2005

AbstractA new and simple concept based on the idea of correcting for non‐associative characteristics of (geologic) media is presented. A special form of the concept is adopted and introduced in a critical state plasticity model. An example problem of behaviour of a soil tested under triaxial conditions is included. The concept can permit a simplified treatment of non‐associativeness and under certain assumptions can allow use of existing formulations of plasticity by maintaining symmetry of the associated matrices.
Boundary element methods for two‐dimensional problems of transient ground water flow
Authors: Banerjee P. K. , Butterfield R. , Tomlin G. R. 
Published: August 2005

AbstractDirect and indirect formulations of the boundary element methods are described for two‐dimensional problems of transient ground water low. A numerical algorithm for obtaining solutions to complete any two‐dimensional problem is outlined. The algorithm has been applied successfully to several problems which demonstrate its usefulness in practice.
Earthquake waves in a random medium
Authors: Chu L. , Askar A. , Cakmak A. S. 
Published: August 2005

AbstractMeasurements are conducted with small samples in the laboratory and thus for all practical purposes the medium is macroscopically homogeneous. On the other hand, the uncertainties and the irregular changes in situ are macroscopic inhomogeneities. This work is an attempt to account for these stochastic changes in the elastic properties and density in a rational manner. The method used is that of Karal and Keller which is based on the use of the Green's function and neglect of third‐order correlations. The resulting integral equations are solved by Laplace transform. The analysis indicates that the energy decay in the mean motion through random mode coupling introduces damping into even a purley'elastic medium and enhances the damping in a significant manner in a hysteretic viscoelastic medium. This consideration is important in relating the damping and dispersion characteristics of wave in situ to those measured in the laboratory. The formulation is extended to multilayer systems through transfer matrices and to arbitrary inputs by Fourier transform. Sample calculations are presented for single and multilayer systems to obtain response spectra and for the response to Gaussian and actual earthquake input motions.
Mixed discretization procedure for accurate modelling of plastic collapse
Authors: Marti Joaquin , Cundall Peter 
Published: August 2005

AbstractCollapse loads are overestimated by finite‐element or finite‐difference procedures when the material discretization does not allow locally incompressible plastic flow: for example, constant‐strain triangles or tetrahedra give unacceptable results. The use of different discretizations for the isotropic and deviatoric parts of the strain tensor is advocated for preventing this problem. The technique can be easily implemented in existing two‐ and three‐dimensional computer programs. Its effectiveness is demonstrated by several examples.
A continuum finite element approach for rock failure and rubble formation
Authors: Benzley S. E. , Krieg R. D. 
Published: August 2005

AbstractA continuum finite element formulation that models the failure of a rock mass, the collapse of this rubble into a void space and the associated bulking of the rubble is presented. This formulation is incorporated into a finite element computer program that treats the large deformation non‐linear motion of axisymmetric and two‐dimensional continua. A dynamic relaxation procedure is used for the solution algorithm. Example calculations are given that demonstrate the formulation.
Simulation of air storage aquifer by finite element model
Authors: Meiri David , Karadi Gabor M. 
Published: August 2005

AbstractA finite element model is developed to simulate the behaviour of an aquifer used as storage space for a compressed air energy storage (CAES) system. The governing equations describing a two‐phase flow of air and water are coupled non‐linear partial differential equations and are solved by the Galerkin approach. The resulting computer model is applied to a gas percolation problem. Upon verification of the numerical results, the model is employed to simulate the air‐water displacement in a storage reservoir during daily air cycling. The corresponding saturation variations and the effects of reservoir permeability on the system are presented. The results obtained are essential in establishing storage design and stability criteria for long‐term operation of compressed air energy storage systems.