bluuebunny/crossref_metadata_2025_split huggingface dataset:
An indirect boundary integral equation method for poroelasticity
Authors: Rajapakse R. K. N. D. , Senjuntichai T. 
Published: August 2005

AbstractThis 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

AbstractSeveral 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

AbstractAn 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

AbstractThe 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

AbstractIn 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

AbstractMaterial 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

AbstractAn 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

AbstractThe 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

AbstractPreconditioning 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

AbstractRank 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

AbstractThe 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

AbstractMethods 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

AbstractA 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

AbstractSome 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

AbstractApproximate 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

AbstractThe 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

AbstractThe 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

AbstractThis 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.
The elasto‐plastic indentation of a half‐space by a rigid sphere
Authors: Hardy C. , Baronet C. N. , Tordion G. V. 
Published: August 2005

AbstractUsing 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

AbstractThe 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

AbstractA 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

AbstractThe 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

AbstractA 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

AbstractThe 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.