bluuebunny/crossref_metadata_2025_split huggingface dataset:
Unconditionally stable staggered solution procedure for soil‐pore fluid interaction problems
Authors: Zienkiewicz O. C. , Paul D. K. , Chan A. H. C. 
Published: August 2005

AbstractThis paper presents a simple procedure for modifying the dynamic coupled soil‐pore fluid equations in a manner which allows a stable and efficient staggered solution procedure to be used. The solution method is simpler than an alternative suggested by Park15 and has a direct physical interpretation. This stabilized procedure is efficient in numerical time domain analysis of soil‐pore fluid occurring in earthquake and consolidation problems. Numerical examples of one and two dimensional saturated poroelastic media demonstrate the procedure.
Resolving membrane and shear locking phenomena in curved shear‐deformable axisymmetric shell elements
Authors: Tessler Alexander , Spiridigliozzi Luciano 
Published: August 2005

AbstractA simple two‐node axisymmetric shell element with shallowly curved meridian assumptions and the inclusion of shear deformation and rotary inertia is presented. The principal developments include: (a) consistent resolution of the membrane and shear related excessive stiffening (locking) via anisoparametric interpolations of the displacement variables; (b) further upgrading of strain energy by means of a shear relaxation (correction) parameter. The resulting element possesses an improved condition of the stiffness matrix, increased efficiency in explicit time integration and enhanced accuracy in coarse discretizations. Comprehensive vibration examples are carried out to assess the element performance. The numerical results demonstrate a wide applicability range with respect to element slenderness and curvature properties.
Stress and vibration analyses of anisotropic shells of revolution
Authors: Noor Ahmed K. , Peters Jeanne M. 
Published: August 2005

AbstractAn efficient computational strategy is presented for reducing the cost of the stress and free vibration analyses of laminated anisotropic shells of revolution. The analytical formulation is based on a form of the Sanders‐Budiansky shell theory including the effects of both the transverse shear deformation and the laminated anisotropic material response. The fundamental unknowns consist of the eight strain components, the eight stress resultants and the five generalized displacements of the shell. Each of the shell variables is expressed in terms of trigonometric functions (Fourier series) in the circumferential co‐ordinate, and a three‐field mixed finite element model is used for the discretization in the meridional direction.The shell response associated with a range of Fourier harmonics is approximated by a linear combination of a few global approximation vectors, which are generated at a particular value of the Fourier harmonic, within that range. The full equations of the finite element model are solved for only a single Fourier harmonic, and the response corresponding to the other Fourier harmonics is generated using a reduced system of equations with considerably fewer degrees of freedom.
Exact numerical solutions for radiative heat transfer in cylindrical furnaces
Authors: Selçuk Nevin , Tahiroglu Zeynep 
Published: August 2005

AbstractExact expressions for the distributions of the components of radiative flux density and the radiative energy source term in terms of wall and medium temperature distributions have been formulated for an emitting absorbing medium of constant properties bounded by black walls of a cylindrical enclosure. The accuracy of numerical solutions has been tested on an idealized enclosure for which exact analytical solution of the expressions is possible and shown to have six‐figure accuracy. The exact expressions have then been solved numerically for an enclosure problem based on data reported previously on a large scale experimental furnace. The principal feature of the data is highly non‐uniform temperature distributions which are typical of the conditions encountered in industrial furnaces. These data have been chosen because of their practical importance and the non‐availability of exact solutions for such data. The resulting exact solutions have been tabulated and are intended to serve in the future as standards for testing the accuracy of the approximate predictions produced using various three‐dimensional flux models in cylindrical configurations.
Curved composite boundary elements for second‐order two‐dimensional problems
Authors: Silva Paul J. , Mote C. D. 
Published: August 2005

AbstractFinite elements with a curved edge often require relatively large numerical effort to form.1–4 Relatively simple triangular elements with a single curved edge are developed in this paper for second‐order, two‐dimensional problems. A convex boundary element is formed as a composite of two straight‐edged triangles and a circular sector.Application of the convex composite boundary element results in less numerical effort for a comparable error in circular and elliptical domain test problems than the application of straight‐edged elements in all cases shown, and in most cases when compared to the curved isoparametric elements. For domains with concave boundaries, the application of straight‐edged, concave composite boundary and curved isoparametric elements give comparable accuracies and numerical efforts because of a fortuitous cancellation of error that occurs with straight‐edged elements in this case.
Non‐local and semi‐local optimal weighting functions for symmetric problems involving a small parameter
Authors: Givoli Dan 
Published: August 2005

AbstractThe method of optimal weighting functions for symmetric problems is described in a general form. It is based on a Petrov‐Galerkin formulation in which the best approximation property and other mathematical features are achieved for a chosen norm, different from the original ‘energy norm’ of the problem. The nonlocality of the weighting functions is shown to have only a minor effect on the efficiency of the method, although a localization scheme is also suggested. The method is applied to a one‐ and two‐dimensional singular perturbation problems, as well as to a cylindrical shell problem.
An eighteen‐node solid element for thin shell analysis
Authors: Ausserer M. F. , Lee S. W. 
Published: August 2005

AbstractAn eighteen‐node, three‐dimensional, solid element with 54 degrees of freedom is presented for the finite element analysis of thin plates and shells. The element is based on the Hellinger‐Reissner principle with independent strain. The assumed independent strain is divided into higher and lower terms. The stiffness matrix associated with the higher order independent strain plays the role of stabilization matrix. A modified stress‐strain relation decoupling inplane and normal strain is used to incorporate thin shell behaviour. Numerical results demonstrate that, with a properly chosen set of assumed strain, this element is effectively free of locking even for very thin plates and shells.
Damped dynamic substructures
Authors: Leung A. Y. T. 
Published: August 2005

AbstractThe dynamic substructure method is extended to lightly or heavily damped systems. Both internal and external dampings are considered. The damped dynamic flexibility associated with the slave co‐ordinates is first expanded in terms of the damped fixed interface natural modes and the condensed dynamic stiffness associated with the master co‐ordinates is formed subsequently. The convergence of the condensed dynamic stiffness with respect to the damped natural modes can be improved by means of the static matrices. Since the dynamic stiffness method is equivalent to the modal synthesis method, the component mode method and Kron's method, the theory presented here is readily applicable to these methods are restricted to symmetric damping matrices.
Boundary element analysis of an integral equation for three‐dmensional crack problems
Authors: Le Van A. , Peseux B. 
Published: August 2005

AbstractIn another paper, the authors proposed an integral equation for arbitrary shaped three‐dimensional cracks. In the present paper, a discretization of this equation using a tensor formalism is formulated. This approach has the advantage of providing the displacement discontinuity vector in the local basis which varies as a function of the point of the crack surface. This also facilitates the computation of the stress intensity factors along the crack edge. Numerical examples reported for a circular crack and a semi‐elliptical surface crack in a cylindrical bar show that one can obtain good results, using few Gaussian points and no singular elements.
Application of the boundary element method to dense dispersions
Authors: Durand Paul P. , Ungar Lyle H. 
Published: August 2005

AbstractThe boundary element method (BEM) is used to find the effective conductivity of a random dispersion of disks in a second material. Small separations between inclusions give rise to difficulties not usually associated with the use of the BEM. We find that the integration point spacing on a given surface element has to be of the order of the shortest distance between disks. The spacing requirement becomes a limitation at high densities, even when the ratio of the conductivity of the disks to that of the host material is close to one. This limitation is overcome by increasing the order of the integration scheme used rather than by increasing the number of surface elements. A more conventional concern is that the surface mesh itself must be sufficiently fine to represent the temperature and flux profiles. As with all simulations of dense dispersions, periodic boundary conditions have to be used and further, because random dispersions are of interest, averages of calculations over many configurations are needed. Taking account of the above considerations we calculate the first exact results for the effective conductivity of a dispersion of cylinders at a high (0.6) density. The influence of vectorization on the performance of the code is briefly mentioned, as are other possible improvements.
A local boundary integral equation method for potential problems
Authors: Fenner R. T. , Watson J. O. 
Published: August 2005

AbstractBoundary integral equation (boundary element) methods have the advantage over other commonly used numerical methods that they do not require values of the unknowns at points within the solution domain to be computed. Further benefits would be obtained if attention could be confined to information at one small part of the boundary, the particular region of interest in a given problem. A local boundary integral equation method based on a Taylor series expansion of the unknown function is developed to do this for two‐dimensional potential problems governed by Laplace's equation. Very accurate local values of the function and its derivatives can be obtained. The method should find particular application in the efficient refinement of approximate solutions obtained by other numerical techniques.
Finite‐element models of viscoelasticity and diffusion in adhesively bonded joints
Authors: Roy S. , Reddy J. N. 
Published: August 2005

AbstractThe paper contains a description of the finite‐element model based on Schapery's non‐linear viscoelastic constitutive equation for the adhesive, a non‐linear generalized Fickean diffusion model and an updated Lagrangian formulation of a two‐dimensional stress state, to analyse adhesively bonded joints. The finite‐element analysis program, called NOVA, is used to analyse a number of adhesive joints, and the results are compared with existing experimental results and analytical solutions.
Numerical modelling of wave‐induced currents in a breakwater situation
Authors: Yoo D. 
Published: August 2005

AbstractA numerical model system is developed to describe waves and wave‐induced currents in a breakwater situation, where refraction, diffraction, reflection and wave–current interaction may all play important roles in the transformation of waves. A turbulence transport model is employed to estimate the eddy viscosity, and the friction factors associated with the major variables are clearly defined using a high level closure of combined flow bed friction. The model system is tested against a laboratory situation, and the effects of reflection are demonstrated on the wave‐induced currents as well as on the wave distribution.
Numerical modelling for tide flow and pollutant transport in Taipong Bay, China
Authors: Xiaoyong Zhan 
Published: August 2005

AbstractA two‐dimensional finite difference alternating direction implicit (ADI) scheme numerical model to solve the vertically integrated form of the non‐linear hydrodynamics equations and convection–diffusion equation has been developed for the description of tide flow and pollutant transport in Taipong Bay, China. Computer software for the modelling is well designed to reduce storage and costs of computation. The computed results agree quite well with the observations available. The tidal level, tidal current, residual current and organic pollution in the bay are discussed based on the computed results and observed data. Applications for the environmental problems along the coast of the bay are also mentioned briefly.
The influence of the form of the log‐conductivity covariance on non‐Fickian dispersion in random permeability fields
Authors: Salandin Paolo , Rinaldo Andrea 
Published: August 2005

AbstractThe paper deals with non‐Fickian dispersion of inert solutes in random permeability fields. Attention is focused critically on the statistical characterization of the porous medium which affects pollutant dispersion in groundwater. After a brief account of recent results of stochastic theories of transport in porous media and of the fundamental indications of large‐scale field experiments, it is inferred from numerical studies that the particular choice of an analytical form of covariance of log‐conductivity has a poor influence on the overall dispersion process. In fact, different covariance structures with the same macroscale (a measure of the distance between two points beyond which the permeability ceases to be correlated) yield very similar dispersion processes. The result has a noteworthy bearing on field studies of pollutant dispersion in groundwater because it underlines the reliability of exponential correlation structures yielding analytical expression for time‐varying macrodispersion coefficients.
An introduction to the NSPCG software package
Authors: Kincaid David R. , Oppe Thomas C. , Joubert Wayne D. 
Published: August 2005

AbstractNSPCG is the most recent research‐oriented software package developed as part of the ITPACK Project at the Center for Numerical Analysis of The University of Texas at Austin. It is designed to solve large sparse systems of linear equations by a variety of different non‐symmetric preconditioned conjugate gradient methods. Several different sparse data storage schemes are available for storing the coefficient matrix of the linear system. Matrices with a wide range of structures from highly structured to completely unstructured can be accommodated. To limit memory requirements, the accelerators in the package can be called directly with the matrix stored in a user‐defined sparse data storage format (for example, from a particular application) by supplying some user‐written routines for certain matrix–vector operations.The main entry point into the package is through a single subroutine call. The various methods are accessed by using a particular naming convention for the first two parameters that in turn selects a preconditioner, an accelerator and a data storage scheme. Some of the basic preconditioners that are available are Jacobi, Incomplete LU Decomposition and Symmetric Successive Overrelaxation as well as block preconditioners. The user can select from a large collection of accelerators such as Conjugate Gradient (CG), Chebyshev (SI, for semi‐iterative), Generalized Minimal Residual (GMRES), Biconjugate Gradient Squared (BCGS) and many others. The package is modular so that almost any accelerator can be used with almost any preconditioner. One of the main purposes for the development of the package was to provide a common modular structure for research on iterative methods. The entire package is written in Fortran 77 with vectorization in mind for applications on supercomputers.
On a class of preconditioned iterative methods on parallel computers
Authors: Axelsson O. , Carey G. , Lindskog G. 
Published: August 2005

AbstractThe standard implementations of iterative solvers for finite element and finite difference methods frequently use a diagonal (Jacobi) preconditioner, particularly for element‐by‐element schemes. However, for such methods the actual order of the condition number with respect to mesh size is not reduced by the preconditioner. In the present paper we describe an iterative method where, in addition, the condition number is reduced by an order of magnitude. Moreover, the scheme may also be implemented as an element‐by‐element method. The method uses a generalized SSOR preconditioner and a wave front or multi‐frontal ordering of the mesh nodes. For a general irregular finite element mesh a striped irregular wave front ordering may be used. The performance of the method as well as various iterative acceleration techniques for a parallel computer are examined in the numerical studies.
Numerical analysis of two‐level finite difference schemes for unsteady diffusion–convection problems
Authors: Rigal Alain 
Published: August 2005

AbstractThis paper develops, for linear diffusion–convection model problems, the numerical analysis of some two‐time‐level second order finite difference schemes: modified centred, upstream weighted, Samarskii explicit and implicit schemes. The stability and related properties—dissipation, amplitude and phase errors, numerical diffusion and dispersion—are studied through Fourier analysis. The behaviour of the numerical solution is analysed from the matrix properties of the schemes with special emphasis on parabolicity and positivity. These analyses allow a comparison of the properties of every scheme, the main criterion being the efficiency of the scheme for strongly convective problems.
An operator‐splitting algorithm for two‐dimensional convection–dispersion–reaction problems
Authors: Ding Daoyang , Liu Philip L.‐F. 
Published: August 2005

AbstractAn operator‐splitting algorithm for the two‐dimensional convection–dispersion–reaction equation is developed. The flow domain is discretized into triangular elements which are fixed in time. The governing equation is split into three successive initial value problems: a pure convection problem, a pure dispersion problem and a pure reaction problem. For the pure convection problem, solutions are found by the method of characteristics. The solution algorithm involves tracing the characteristic lines backwards in time from a vertex of an element to an interior point. A cubic polynomial is used to interpolate the concentration and its derivatives on an element. For the pure dispersion problem, an explicit finite element algorithm is employed. Analytical solutions are obtained for the pure reaction problem. The treatment of the boundary conditions is also discussed. Several numerical examples are presented. Numerical results agree well with analytical solutions. Because cubic polynomials are used in the interpolation, very little numerical damping and oscillation are introduced, even for the pure convection problem.
A general finite element for beams or beam‐columns with or without an elastic foundation
Authors: Sirosh S. N. , Ghali A. , Razaqpur A. G. 
Published: August 2005

AbstractA general finite element is derived for beams or beam‐columns with or without a continuous Winkler type elastic foundation. The need to discretize members into shorter elements for convergence towards an ‘exact’ solution is eliminated by employing in the derivation of the element exact shape functions obtained from the equation of the elastic line. Inter‐nodal values of deflections, bending moments and shear forces are obtained using the exact shape functions and trigonometric series. The effect of heavy compressive or tensile axial forces on bending stiffness is treated as a linear problem by considering the axial force as a constant parameter affecting the stiffness. FORTRAN subroutines to compute the stiffness matrix, equivalent nodal forces, deflected shape, bending moments and shear forces are provided and verified by an example.
Numerical differentiation for use in integrating unified constitutive equations
Authors: Henshall G. A. , Tanaka T. G. , Miller A. K. , Lowe T. C. 
Published: August 2005

AbstractThe NONSS method for numerically integrating time‐dependent constitutive equations requires evaluation of the partial derivatives of the constitutive equations. A numerical method for evaluating these partial derivatives has been developed, thus avoiding the cumbersome task of analytically re‐deriving the partial derivatives when improvements to the constitutive model are evaluated. This method is based upon the adaptive finite‐difference algorithm published by Stepleman and Winarsky. Modifications of their algorithm are described that allow its efficient use within an extended version of NONSS, called NONSS‐ND.Using the MATMOD constitutive equations, the capabilities of NONSS‐ND are demonstrated by comparing the results of a wide variety of deformation simulations with those of NONSS, for which the derivatives are computed from analytical solutions. The numerical differentiation within NONSS‐ND is shown to be sufficiently accurate for use in integrating time‐dependent constitutive equations, but results in a 30–100 per cent increase in computation time. Multi‐element structural calculations are therefore found to be uneconomical, but NONSS‐ND is well suited for testing alternative constitutive models owing to its accuracy and its general applicability to highly non‐linear systems of differential equations.
Computation of thermal stresses in quasistatic non‐stationary thermoelasticity using boundary elements
Authors: Sládek V. , Sládek J. 
Published: August 2005

AbstractIn this paper we present the boundary integral formulation for the solution of quasi‐static problems of two‐dimensional uncoupled thermoelasticity. A detailed scheme for the numerical solution of the boundary integral equations and computation of internal stresses by regularized integral representation is developed in time formulation. The method is tested in a numerical example.
Duality and symmetry in mixed integral methods of elastostatics
Authors: De Freitas J. A. Teixeira 
Published: August 2005

AbstractMixed formulations for integral methods of elastostatic analysis of structures are presented. Both finite and boundary element approaches are considered. A governing system exhibiting symmetry is obtained in both cases by preserving duality in the descriptions of equilibrium and compatibility and reciprocity in the elastic constitutive relations. The theorems of virtual forces and displacements are interpreted as the energetic representation of static–kinematic duality. The quadratic programs associated with the governing system are identified as the theorems of minimum potential energy and co‐energy. Mathematical programming theory is used to establish conditions for the existence and uniqueness of solutions.