bluuebunny/crossref_metadata_2025_split huggingface dataset:
A coupled analysis method for structures with independently modelled finite element subdomains
Authors: Aminpour Mohammad A. , Ransom Jonathan B. , McCleary Susan L. 
Published: August 2005

AbstractA new method for analysing plate and shell structures with two or more independently modelled finite element subdomains is presented, assessed, and demonstrated. This method provides a means of coupling local and global finite element models whose nodes do not coincide along their common interface. In general, the method provides a means of coupling structural components (e.g., wing and fuselage) which may have been modelled by different analysts. In both cases, the need for transition modelling, which is often tedious and complicated, is eliminated. The coupling is accomplished through an interface for which three formulations are considered and presented. These formulations are: collocation, discrete least‐squares, and hybrid variational. Several benchmark problems are analysed and it is shown that the hybrid variational formulation provides the most accurate solutions.
Numerical modelling for scattering of waves in three‐dimensional cracked material
Authors: Han Sixiong , Ichikawa Yasuaki 
Published: August 2005

AbstractIn this paper, a mathematical model is proposed for the problem of the scattering of plane waves in a three‐dimensional cracked materials. Instead of obtaining closed‐form solutions as in conventional theoretical analysis methods, this approach, called the Equivalent Nodal Force (ENF) method formulates the mechanical effects of cracks as an equivalent nodal force in a numerical procedure, and physically translates cracked material into an equivalent continuous one. Several mechanical relations between waves and cracks are evident from this method. Also the results of several numerical calculations are presented and these are compared with those obtained by the conventional methods.
An efficient assumed strain element model with six DOF per node for geometrically non‐linear shells
Authors: Park Hoon C. , Cho Chahngmin , Lee Sung W. 
Published: August 2005

AbstractThe present paper describes an assumed strain finite element model with six degrees of freedom per node designed for geometrically non‐linear shell analysis. An important feature of the present paper is the discussion on the spurious kinematic modes and the assumed strain field in the geometrically non‐linear setting. The kinematics of deformation is described by using vector components in contrast to the conventional formulation which requires the use of trigonometric functions of rotational angles. Accordingly, converged solutions can be obtained for load or displacement increments that are much larger than possible with the conventional formulation with rotational angles. In addition, a detailed study of the spurious kinematic modes and the choice of assumed strain field reveals that the same assumed strain field can be used for both geometrically linear and non‐linear cases to alleviate element locking while maintaining kinematic stability. It is strongly recommended that the element models, described in the present paper, be used instead of the conventional shell element models that employ rotational angles.
Finite strip analysis of imperfect laminated plates under end shortening and normal pressure
Authors: Dawe D. J. , Wang S. , Lam S. S. E. 
Published: August 2005

AbstractThe finite strip method is developed to predict the geometrically non‐linear response of rectangular laminated plates subjected to progressive end shortening whilst initial imperfection and/or applied pressure loading are also present. The development is an extension of earlier work concerned with perfect, unpressurized laminates which have simply supported loaded ends at which lateral in‐plane expansion is either allowed freely or is prevented completely. The analysis is conducted in the contexts of classical plate theory and first‐order shear deformation plate theory, in turn. A number of applications involving both isotropic plates and laminated plates is described.
A posteriori estimation and adaptive control of the pollution error in the h‐version of the finite element method
Authors: Babuška I. , Strouboulis T. , Upadhyay C. S. , Gangaraj S. K. 
Published: August 2005

AbstractIn References 1 and 2 we showed that the error in the finite‐element solution has two parts, the local error and the pollution error, and we studied the effect of the pollution error on the quality of the local error‐indicators and the quality of the derivatives recovered by local post‐processing. Here we show that it is possible to construct a posteriori estimates of the pollution error in any patch of elements by employing the local error‐indicators over the mesh outside the patch. We also give an algorithm for the adaptive control of the pollution error in any patch of elements of interest.
Interior and boundary difference equations for hyperbolic differential equations
Authors: Lick Wilbert , Ziegler Kirk , Lick James 
Published: August 2005

AbstractInterior and boundary difference equations are derived for several hyperbolic partial differential equations by means of an integral method. The method is applied to a simple transport equation, to waves in a compressible, isentropic fluid, and to surface waves in shallow water. Boundary conditions treated are (a) a perfectly reflecting boundary, (b) an open boundary with outgoing waves and a specified incoming wave, and (c) a partially reflecting boundary. For open boundaries, the major assumption for the algorithms to be valid is that outgoing waves can be defined, an assumption equivalent to the most general statement of Sommerfeld's radiation condition. The difference equations obtained are conservative, second‐order accurate, two time‐level, explicit, and stable (for one‐dimensional, time‐dependent problems) for cΔt/Δx ⩽ 1 where c is the wave speed, Δt is the temporal grid size, and Δx is the spatial grid size. Numerical calculations demonstrate the excellent accuracy of the procedure.
Solution of governing differential equations of vibrating cylindrical shells using B‐spline functions
Authors: Peng‐Cheng Shen , Jian‐Guo Wang 
Published: August 2005

AbstractThe cubic B3‐spline functions and eigenfunctions are used to obtain the approximate solution for the vibration of cylindrical shells in this paper. Unified computational schemes suited for various types of boundary conditions are formulated here. In comparison with the conventional finite elements method and finite strip method, the main features of the present method are higher accuracy, fewer unknowns, ease in programming, and economy in computer solution. The numerical results are given and compared with other numerical solutions.
Amplification of surface ground motion by an inclusion of arbitrary shape for harmonic surface line loading
Authors: Dravinski M. , Mossessian T. K. 
Published: August 2005

AbstractThe plane strain model for the Lamb's problem with an elastic inclusion of arbitrary shape embedded completely within an elastic half space is investigated by using an indirect boundary integral equation method for steady‐state elastodynamics. The surface of the half space is subjected to vertical or horizontal harmonic line loads. The displacement field is evaluated throughout the elastic medium so that the continuity of the displacement and traction fields along the interface between the half space and the inclusion is satisfied in a least‐square sense. The numerical results demonstrate that the presence of the inclusion may cause locally very large amplification of the surface ground motion and that the amplification pattern depends upon the frequency and the type of the input load, the impedance contrast between the half space and the inclusion, the type of the inclusion, and the location of the observation point at the surface of the half space.
A highly accurate and stable explicit finite difference solution to the convection‐dispersion equation with varying velocity and dispersion coefficients
Authors: El‐Ageli Muktar Ali , Menzie Don E. 
Published: August 2005

AbstractBased on the implicit form of the finite difference analogue to the convection‐dispersion equation of variable velocity and dispersion coefficients, a highly accurate and stable explicit finite difference scheme has been developed by extending the von Rosenberg linear scheme to the varying cases. This variable velocity and dispersion coefficient scheme has been tested for the entire range of (2D/vΔ x) between zero and unity, the region where no completely satisfactory numerical method has been previously available. No oscillations or numerical dispersion were observed in any of the solutions.
Solution of general ordinary differential equations using the algebraic theory approach
Authors: Celia Michael , Herrera Ismael 
Published: August 2005

AbstractThe algebraic theory for numerical methods, as developed by Herrera [3–7], provides a broad theoretical framework for the development and analysis of numerical approximations. To this point, the technique has only been applied to ordinary differential equations with constant coefficients. The present work extends the theory by developing a methodology for equations with variable coefficients. Approximation of the coefficients by piecewise polynomials forms the foundation of the approach. Analysis of the method provides firm error estimates. Furthermore, the analysis points to particular procedures that produce optimal accuracy. Example calculations illustrate the computational procedure and verify the theoretical convergence rates.
Convergence of an element‐partitioned subcycling algorithm for the semi‐discrete heat equation
Authors: Hughes Thomas J. R. , Belytschko Ted , Liu Wing Kam 
Published: August 2005

AbstractA convergence analysis is performed for an element‐partitioned subcycling algorithm for the semi‐discrete heat equation. It is shown that the algorithm generally attains first‐order rate‐of‐convergence.
An efficient boundary element method for a class of parabolic differential equations using discretization in time
Authors: Ingber M. S. 
Published: August 2005

AbstractA new boundary element method using discretization in time is proposed to solve a class of parabolic differential equations. The method treats the term containing the time derivative as a forcing term. This necessitates the introduction of additional unknowns in the interior of the domain. At the same time, however, values for the dependent variable are determined directly in the interior. The boundary element formulation is reduced to essentially solving a Poisson equation. The accuracy and efficiency of the method are demonstrated with several examples.
The algebraic theory approach for ordinary differential equations: Highly accurate finite differences
Authors: Herrera Ismael 
Published: August 2005

AbstractThis article reports further developments of Herrera's algebraic theory approach to the numerical treatment of differential equations. A new solution procedure for ordinary differential equations is presented. Finite difference algorithms of 0(hr), for arbitrary “r” are developed. The method consists in constructing local approximate solutions and using them to extract information about the sought solution. Only nodal information is derived. The local approximate solutions are constructed by collocation, using polynomials of degree G. When “n” collocation points are used at each subinterval, G = n + 1and the order of accuracy is 0(h2n−1). The procedure here presented is very easy to implement. A program in which n can be chosen arbitrarily, was constructed and applied to selected examples.
Optimization of computational grids
Authors: Pardhanani Anand , Carey Graham F. 
Published: August 2005

AbstractWe consider the problem of mesh grading or gridr‐point redistribution using optimization techniques. Some representate forms of the objective functions are considered and the assocated scaling parameterization and nonlinear programming algorithms examined. Numerical results for representative test problems involving two‐and three‐dimensional grids are presented.
Numerical methods for structured population models: The Escalator Boxcar Train
Authors: de Roos A. M. 
Published: August 2005

AbstractA numerical integration method is introduced for the class of hyperbolic partial differential equations that occur in physiologically structured population models. These equations describe the time evolution of the population density‐function over the individual state‐space Ω. Exploiting the biological interpretation of the equation, this density‐function is represented by a set of moments over a collection of subdomains in Ω, moving along the characteristics of the partial differential equation (PDE). These moments are readily interpreted as numbers of individuals in a cohort, mean individual state in a cohort, etc. The numerical method consists of approximating the differential equations.The method appears to be very efficient for this special type of PDE. It combines such desirable properties as as lack of dispersion and dissipation and a preservation of monotonicity of the density function along the characteristics with a strong relation to the biological background of the equations for these moments to arrive at a closed system of ordinary differential equations. The method also allows one to incorporate the usual type of nonlinearities that occur in physiologically structured population models. A numerical example is presented as an illustration of the application of the method.
Two different approaches for the treatment of boundary singularities
Authors: Michavila F. , Gavete L. , Díez F. 
Published: August 2005

AbstractThe finite element treatment of boundary singularities in elliptic problems has demanded that special techniques be developed. Many of these use some form of singular element in the neighborhood of a singular point.For a homogenous second‐order problem, defined in a domain with a polygonal boundary, we studied three cases with different singularity orders. Some results about the accuracy of the solution are presented. Numerical results have been obtained using Akin singular triangular elements with three and six nodes and quadrilateral elements having four and eight nodes. The behavior of the gradient in each of these elements is also analyzed. However, these elements are not completely satisfactory, so that an alternative technique using curved isoparametric elements is given here. The results obtained with the two methods are compared. Conclusions about numerical accuracy of each method, the order of integration and the simplicity of application are made.
A network model for incompressible two‐fluid flow and its numerical solution
Authors: Chou S. H. 
Published: August 2005

AbstractIn this paper we consider an incompressible version of the two‐fluid network model proposed by Porsching (Nu. Methods Part. Diff. Eq., 1, 295–313 [1985]). The system of equations governing the model is a mixed system of differential and algebraic equations (DAEs). These DAEs are then recast, through proper transformation, into a system of ordinary differential equations on a submanifold of ℝn, for which uniqueness, existence, and stability theorems are proved. Numerical simulations are presented.
An experimental performance analysis for the rate of convergence of collocation on general domains
Authors: Mu Mo , Rice John R. 
Published: August 2005

AbstractThis paper presents an experimental performance analysis for the rate of convergence of collocation on general domains using a bicubic Hermite basis. Twenty domains are selected for the experiment from the population of PDEs on nonrectangular domains found in Realistic PDE Solutions for Non‐rectangular Domains (C. J. Ribbens and J. R. Rice, CSD‐TR 639, Department of Computer Sciences, Purdue University, 1986), including one rectangle for comparison. The result shows that the convergence of the ELLPACK module COLLOCATION behaves as O(h4) on all 19 of the nonrectangular domains. This set includes a large variety of nonrectangular domains (only two have reentrant corners). We conclude that, with very high probability, this collocation module has O(h4) convergence on general domains.The experiment is made by using the Performance Evaluation System (PES) of ELLPACK, which includes the population of PDEs on nonrectangular domains. Several performance analysis tools are used to analyze the rate of convergence, the most informative is a visual examination of the convergence behavior.
A parallel domain reduction method
Authors: Brezzi Franco , Douglas Cralg C. , Marini L. Donatella 
Published: August 2005

AbstractWe relate a particular version of a parallel multigrid method to a domain decomposition method, showing that the parallel multigrid method reduces computation to a small portion of the domain and then extends the solution to the entire domain using the correct reflections to get the exact solution. We extend a particular example to double the parallelism in a nonobvious manner. While the techniques of this paper are applied to twodimensional problems, they can be applied to higher dimensional problems in an obvious manner.
Solution of the advective‐dispersive transport equation using a least squares collocation, Eulerian‐Lagrangian method
Authors: Bentley L. R. , Pinder G. F. , Herrera I. 
Published: August 2005

AbstractNumerical solution of the advective‐dispersive transport equation is difficult when advection dominates. Difficulties arise because of the first‐order spatial derivatives which can be elminated by a local coordinate transformation to the characteristic lines of the first order hyperbolic portion of the equation. The resulting differential equation is discretized using a finite difference in time and finite elements in space employing cubic Hermite basis functions. The residuals at individual collocation points are then computed. The sum of the squares of the residuals is minimized to form the necessary set of algebraic equations. The method has performed well in one‐dimensional test problems.
The thermistor: A problem in heat and current flow
Authors: Westbrook D. R. 
Published: August 2005

AbstractThe thermistor is an electrical device that can be used as a current surge protector. The basis of its operation is the temperature‐dependent electrical conductivity that drops by 4 to 5 orders of magnitude over a temperature range of 100–200°C. In the present work the coupled heat and electrical current problems are examined with the conductivity modeled by a step function. A numerical scheme is suggested for the nonlinear coupled problem. Convergence of this scheme for some boundary conditions is demonstrated and some numerical results are given.
Scattering of elastic waves by nonaxisymmetric three‐dimensional dipping layer
Authors: Eshraghi Hossein , Dravinski Marijan 
Published: August 2005

AbstractUsing a boundary method, we investigated the scattering of elastic plane harmonic SH, SV, P, and Rayleigh waves by three‐dimensional nonaxisymmetric dipping layers embedded in an elastic half‐space. The valley was subjected to incident Rayleigh wave and oblique incident SH, SV, and P waves. The method utilized spherical wave functions to express the unknown scattered field. These functions satisfy the equation of motion and radiation conditions at infinity but they do not satisfy the stress‐free boundary conditions at the surface of the half‐space. The boundary and continuity conditions are imposed locally in the least‐square‐sense at several points on the layer interface and on the surface of the half‐space. A comparative study was done to examine the validity and limitations of the two‐dimensional approximations (antiplane and plane strain models) of three‐dimensional models. It is demonstrated that the two‐dimensional approximations may be inadequate to represent actual displacement field for three‐dimensional irregularities.
Convergence properties of a class of boundary element approximations to linear diffusion problems with localized nonlinear reactions
Authors: Peirce Anthony P. , Askar Attila , Rabitz Herschel 
Published: August 2005

AbstractWe consider a boundary element (BE) Algorithm for solving linear diffusion desorption problems with localized nonlinear reactions. The proposed BE algorithm provides an elegant representation of the effect of localized nonlinear reactions, which enables the effects of arbitrarily oriented defect structures to be incorporated into BE models without having to perform severe mesh deformations.We propose a one‐step recursion procedure to advance the BE solution of linear diffusion localized nonlinear reaction problems and investigate its convergence properties. The separation of the linear and nonlinear effects by the boundary integral formulation enables us to consider the convergence properties of approximations to the linear terms and nonlinear terms of the boundary integral equation separately.For the linear terms we investigate how the degree of piecewise polynomial collocation in space and the size of the spatial mesh relative to the time step affects the accumulation of errors in the one‐step recursion scheme. We develop a novel convergence analysis that combines asymptotic methods with Lax's Equivalence Theorem. We identify a dimensionless meshing parameter θ whose magnitudé governs the performance of the one‐step BE schemes. In particular, we show that piecewise constant (PWC) and piecewise linear (PWL) BE schemes are conditionally convergent, have lower asymptotic bounds placed on the size of time steps, and which display excess numerical diffusion when small time steps are used. There is no asymptotic bound on how large the tie steps can be–this allows the solution to be advanced in fewer, larger time steps. The piecewise quadratic (PWQ) BE scheme is shown to be unconditionally convergent; there is no asymptotic restriction on the relative sizes of the time and spatial meshing and no numerical diffusion. We verify the theoretical convergence properties in numerical examples. This analysis provides useful information about the appropriate degree of spatial piecewise polynomial and the meshing strategy for a given problem.For the nonlinear terms we investigate the convergence of an explicit algorithm to advance the solution at an active site forward in time by means of Caratheodory iteration combined with piecewise linear interpolation. We consider a model problem comprising a singular nonlinear Volterra equation that represents the effect of the term in the BE formulation that is due to a single defect. We prove the convergence of the piecewise linear Caratheodory iteration algorithm to a solution of the model problem for as long as such a solution can be shown to exist. This analysis provides a theoretical justification for the use of piecewise linear Caratheodory iterates for advancing the effects of localized reactions.
A generalized finite difference method for solid mechanics
Authors: Dow John O. , Jones Michael S. , Harwood Shawn A. 
Published: August 2005

AbstractProcedures are developed that improve the applicability of the finite difference method to problems in solid mechanics. This is accomplished by formulating the coefficients of the Taylor series expansion used to approximate derivative quantities in terms of physically interpretable strain gradients. Improvements realized include modeling of boundary conditions that has intuitive appeal and the use of irregular grids in a natural manner. These developments are demonstrated for the analysis of plane stress problems with traction boundary conditions. The results compare well with finite element solutions. The approach suggests further generalization of the finite difference method.