bluuebunny/crossref_metadata_2025_split huggingface dataset:
Sloshing in two‐dimensional container with inclined side walls—boundary‐element approach
Authors: Kamiya N. , Miyazawa H. 
Published: August 2005

AbstractNon‐linear wave motion on the free water surface in a two‐dimensional container subjected to external periodical excitation is considered in this paper. In order to analyse the problem for arbitrary container geometries, a solution scheme using free surface Lagrangean particles is employed. Fluid motion is assumed to be governed by the Laplace equation in terms of the velocity potential with a non‐linear pressure equation on the surface. The boundary element method with explicit time marching is used by the fluid region boundary discretization alone at each time increment. Various containers with an inclined side wall are analysed for the horizontal sway motion and compared.
Free vibrations of spatial rods — A finite‐element analysis
Authors: Karami G. , Farshad M. , Yazdchi M. 
Published: August 2005

AbstractIn this paper, a general finite‐element (FE) formulation has been developed for natural frequency analysis of spatial rod systems. Accordingly, the frequency analysis of spatially curved and pretwisted rods, with either constant or varying cross‐section on distributed elastic or point supports has been carried out. First, an appropriate finite‐element equation is developed utilizing the governing equations (equations of motion, kinematical relations and constitutive relations) of a spatial rod. The time‐dependent governing equations are then solved to find the modal shapes as well as the natural frequencies of the discretized system. The master element, developed herein, comprises 12 degrees of freedom (six at each end) and contains the rigid body motion as well as the deformation modes. This element has the generality of embodying the special cases of prismatic, curved and pretwisted elements, both with either linear or constant curvature changes. To verify the formulations several numerical examples are presented.
Axisymmetric potential flow calculations. Part 1: Analysis mode
Authors: Barron R. M. , Zhang S. , Chandna A. , Rudraiah N. 
Published: August 2005

AbstractUsing a natural body‐fitted co‐ordinate system, based on the streamlines, incompressible potential flow over an axisymmetric body at zero incidence is formulated as a Dirichlet boundary‐value problem for the unknown co‐ordinate r(x, ψ). Flow over various body shapes is computed using a finite‐difference scheme and SLOR, on both uniform and clustered grids. The results show excellent agreement with previous researchers. The coding is very simple, the formulation can be extended to compressible flows and can also be used to solve the inverse problem.
Imposing linear constraints in finite‐element analysis
Authors: Webb J. P. 
Published: August 2005

AbstractIt is often necessary to impose linear constraints on solutions obtained with the finite‐element method. This can be done by the penalty method or by eliminating dependent variables. The penalty method requires the careful selection of a penalty parameter and may lead to an inexact imposition of the constraints. Elimination is preferable because it is exact. The zero rows that elimination generates in the coefficient matrix can be removed by reducing the order of the matrix, or by adding back the constraints. The latter approach has the advantage of keeping the imposition of constraints separate from matrix assembly. However, straightforward addition of multi‐point constraint equations destroys the symmetry of the matrix. A new method of adding the constraints preserves matrix symmetry.
Moving and deforming finite‐element simulation of two‐dimensional Stefan problems
Authors: Zabaras Nicholas , Ruan Yimin 
Published: August 2005

AbstractA new moving/deforming FEM analysis of two‐dimensional phase change problems is presented. The region occupied by the solid phase is divided into a non‐moving element region and a moving region consisting of the finite elements next to the freezing interface. A transfinite mapping method is used to generate new finite‐element meshes and motion in the liquid phase during simulations. Several two‐dimensional Stefan problems are analysed and discussed in relation to analytical solutions and other numerical techniques.
The zero‐normal‐stress condition in plane‐stress and shell elastoplasticity
Authors: De Borst Rene 
Published: August 2005

AbstractThe use of elastoplastic models in calculations of shell and plate structures, or more generally in stress situations in which one normal stress component is forced to be zero, usually leads to complicated algorithms. This leads to cumbersome programming, which in turn may easily entail errors in the code. Moreover, the fraction model for cyclic plasticity cannot be used within most algorithms since the normal stress perpendicular to the plane of the element is not necessarily zero for each of the fractions. In this contribution an algorithm will be presented that enforces a zero‐stress condition at integration point level, while obviating the need to develop special subroutines for plane‐stress or shell plasticity. The algorithm is based upon an implicit integration of the stress‐strain law and can be combined with the newly developed technique of consistent tangent operators.
A modified method of incompatible modes
Authors: Ibrahimbegovic Adnan , Wilson E. L. 
Published: August 2005

AbstractThe original method of incompatible modes proposed by Wilson et al. (1973) is modified such that a constant strain and hence convergence of the method is ensured. The proposed modification is valid for other forms of incompatible modes besides the original suggestion. The least‐squares stress recovery, introduced herein, provides high accuracy in stress computations.
An analysis of dead zones in the process of direct extrusion through single‐hole flat die
Authors: Slużalec Andrzej 
Published: August 2005

AbstractAn analysis of dead zones in the extrusion process is presented. Theoretical formulations of the metal forming process are recalled. Results of calculations show the distribution of metal velocity and relationships between angle of dead zone and friction coefficient, extrusior ratio and geometry of container. A comparison of finite‐element results with existing experiments is presented.
Internal force expansion method for stress reanalysis in structural optimization
Authors: Bofang Zhu 
Published: August 2005

AbstractIn the optimum design of large structures, the greater part of the computation time is consumed in stress reanalysis. The internal force expansion method is proposed to reduce the computation time; it is more efficient than the well‐known stress expansion method. Experience shows that only two iteration cycles are required when this method is applied in structural optimization.
On numerical solution of third‐order boundary‐value problems
Authors: Tirmizi Ikram A. 
Published: August 2005

AbstractA fourth‐order method is developed for the approximation of the solution of certain two‐point boundary‐value problems involving third‐order linear and non‐linear differential equations. The method arises from a four‐point recurrence relation involving exponential terms, these being replaced by Padé approximants. The convergence of the method is discussed. The method is tested on two problems to demonstrate the practical usefulness of the approach.
Computing principal‐value integrals in 3‐D BEM for time‐harmonic elastodynamics – A direct approach
Authors: Guiggiani M. 
Published: August 2005

AbstractCurrent methods to deal with Cauchy principal‐value (CPV) integrals in advanced boundary‐element implementations have been almost entirely based on indirect approaches (such as the rigid‐body motion in elastostatics). The present paper illustrates an alternative direct approach for the rigorous treatment and numerical evaluation of general CPV integrals in three‐dimensional problems. The method has general validity. It can be applied in any field of applied mechanics and with curved boundary elements of any order and type. As expected, the mesh pattern around the pole does not affect the numerical results.
On hypersonic flow over two‐dimensional aerofoils
Authors: Hemdan Hamdi T. 
Published: August 2005

AbstractThis paper considers the problem of hypersonic flow past two‐dimensional thin aerofoils with sharp leading edges and attached shock waves. The analysis relies on another recent formulation of the hypersonic small disturbance theory, HSDT. The equations are reduced to a complicated functional‐differential equation for which an iterative numerical scheme is employed. In each iteration both the functional and differential parts of the functional‐differential equation are eliminated, thus reducing it to an algebraic equation. The iterative scheme is found to be stable and rapidly convergent, and the results obtained for the surface pressure and shock wave compare well with other exact and approximate methods.
Vibration analysis of coil springs by means of isoparametric curved beam finite elements
Authors: Stander Nielen , Du Preez R. J. 
Published: August 2005

AbstractAn investigation is conducted on the performance of the curved isoparametric cubic beam element for analysing vibrational behaviour of coil springs. Firstly, the results of full and uniformly reduced integration are compared for three static problems. Uniformly reduced integration is shown to yield surprising accuracy, even for curved and pretwisted beams. In the latter case of a shear loaded cantilever beam, exact internal force values are obtained. Since element geometry is described by nodal co‐ordinates and cross‐sectional orientation only, the element proves to be ideal for modelling both helical and non‐helical sections of coil springs. In addition, the formulation is easy to implement and simpler than those of previous ‘helical spring elements’. It is shown that accurate values for modal frequencies can be obtained with relatively coarse meshes.
A boundary integral formulation for natural convection flows
Authors: Ramesh P. S. , Lean M. H. 
Published: August 2005

AbstractA novel solver for natural convection flows based on the boundary integral equation method is presented here. The solver can be used to obtain flow solutions in arbitrary 2–D geometries with modest computational effort. Both the vorticity and thermal transport equations are treated as modified Helmholtz equations and solved using boundary integral methods. The non‐linear inertial terms partially manifest themselves as volume sources which are computed iteratively using a method of characteristics approach. The buoyancy term is treated as a volume vorticity source. Rapid computation of the volume fields at each iteration level is achieved by precomputing the influence coefficient matrices. Results are presented for flow in a cavity driven by both shear and buoyancy.
Average strain quadrilateral elements
Authors: Stolle D. F. E. 
Published: August 2005

AbstractThis paper describes an approach for implementing quadrilateral finite elements which uses B matrices of average strain when assembling element stiffness matrices. The approach avoids isoparametric transformations, thereby making stiffness matrix assembly and stress calculations more efficient. An example is presented which compares the proposed approach and those based on Gauss quadrature integration.
Second‐order, numerical methods for the solution of equations in population modelling
Authors: Wang Yigong , Twizell E. H. , Price W. G. 
Published: August 2005

AbstractA second‐order explicit method is developed for the numerical solution of the Ricatti (logistic) initial‐value problem u′ ≡ du/dt = αu(1 ‐ u), t > 0, u(0) = U0, in which α ≠ 0 is a real parameter. The method is based on two first‐order methods which appeared in an earlier paper by the authors (Twizell et al.1). In addition to being chaos‐free and of higher order, the novel method is seen to converge to the correct, stable, steady‐state solution for any value of the parameter α, provided the denominator of the method does not vanish. Convergence is monotonic or oscillatory depending on the magnitude of the product αl, where l is the parameter in the discretization of the independent variable t. This dependence of the type of convergence on αl is likened to the behaviour of the well known Crank–Nicolson method for solving the simple heat equation. Conversion of the numerical method to a reliable, empirical model for predicting the limited growth of successive generations of a population is given. When extended to the numerical solution of Fisher's equation, in which the quadratic polynomial αu(1 – u) appears as the reaction term, the numerical solution is found by solving a linear algebraic system at each time step, as opposed to solving a non‐linear system, which often happens when solving non‐linear partial differential equations.
Stochastic boundary‐element method for reliability of structural strength
Authors: Weidong Wen , Deping Gao 
Published: August 2005

AbstractThe stochastic boundary‐element method (SBEM) is developed in this paper for the reliability analysis of a structural component. The integral equations of BEM are derived partially by a random variable, and the integral equations of SBEM are established. Considering the applied loads and the limitation of material strength to be a Gauss distribution, the numerical results of two examples are given for the problems of stochastic stress‐strain and reliability. The results show good agreement with those obtained from Monte Carlo simulation and theoretical solutions.
Vibration of annular sector plates using spline strip method
Authors: Mizusawa Tomisaku , Kajita Tateo 
Published: August 2005

AbstractThis paper presents the vibrations of annular sectorial plates with two opposite radial edges simply supported using the spline strip method. To demonstrate the convergence and accuracy of the present method, several examples are solved, and results are compared with those obtained by the analytical method and by other numerical methods. Stable convergence and excellent accuracy are obtained using the high‐order spline strip models. Accurate frequencies of annular sector plates with different sector angles, radii ratios and tapered thickness in the angular direction are shown in tabular form.
A consistent finite‐element formulation of non‐linear elastic cables
Authors: Ibrahimbegović Adnan 
Published: August 2005

AbstractA finite‐element approach for computing cable structure fully non‐linear response is presented in this work. Both the problems of statics and of dynamics are considered. The formulation encompasses arbitrary large strains and displacements. A very general constitutive equation for non‐linear elastic cables can be posed by an adequate choice for the strain energy function. In this work we consider two model problems, posed by St. Venant's and Ogden's material models. The proposed formulation is set in a fixed reference frame which yields a very efficient finite‐element implementation. The additional advantage of setting the formulation in a fixed reference frame is a bilinear form of the kinetic energy and a simplified solution procedure for dynamic equilibrium equations. Consistent linearization is used at each step of the Newton algorithm to obtain the tangent operators, which provide the quadratic rate of the solution convergence. This is demonstrated in the numerical examples presented herein.
A comparison of FAC and PCG methods for solving composite grid problems
Authors: Heroux Michael A. , Thomas J. W. 
Published: August 2005

AbstractThe fast adaptive composite grid method (FAC) is a multi‐level adaptive method for the discretization and solution of partial differential equations. This paper compares the speed of solution of the resulting discrete equations by the FAC algorithm and a preconditioned conjugate gradient scheme. Comparisons and information concerning the solutions are given for several model problems.
Multigrid solution of the advection–diffusion equation with variable coefficients
Authors: Marx Yves P. 
Published: August 2005

AbstractA multigrid method for the solution of the linear multi‐dimensional advection–diffusion equation with variable coefficients is presented. The method efficiently combines odd–even relaxations with semi‐coarsening. Theoretical and computational convergence rates are given for a large range of advection–diffusion coefficients to demonstrate the efficiency of the method. The construction of the coarse‐grid operator is also discussed in detail since it may have a strong influence on the convergence of the multigrid process when the direction of convection changes.
A multigrid algorithm for mixed finite‐element problems
Authors: Rubart Lothar 
Published: August 2005

AbstractThe analysis of steady incompressible flow is based on the equation of motion and the continuity constraint together with appropriate boundary conditions. Besides the inertia term, also the extra stress term becomes non‐linear in the case of generalized Newtonian fluids. By application of mixed finite‐element methods the conservation equations are reduced to a system of non‐linear algebraic equations. At each step of a Newton‐Raphson scheme a linear subproblem with a non‐symmetric and indefinite coefficient matrix has to be solved. A multigrid method for these systems is presented, where the smoothing iteration is a modification of Uzawa's algorithm based on an augmented Lagrangian functional. The method is applied to the numerical simulation of vortex breakdown in a cylindrical vessel, where the computations are performed for real shear‐thinning fluids. Dimensionless groups, a Reynolds number and a non‐Newtonian parameter are introduced, and the dependence of the convergence rate on these parameters is discussed.
An effective multigrid method for high‐speed flows
Authors: Swanson R. C. , Turkel E. , White J. A. 
Published: August 2005

AbstractWe consider the use of a multigrid method with central differencing to solve the Navier–Stokes equations for high‐speed flows. The time‐dependent form of the equations is integrated with a Runge–Kutta scheme accelerated by local time‐stepping and variable‐coefficient implicit residual smoothing. Of particular importance are the details of the numerical dissipation formulation, especially the switch between the second and fourth difference terms. Solutions are given for two‐dimensional laminar flow over a circular cylinder and a 15‐degree compression ramp.
Recursive filters determined from implicit formulations
Authors: Raymond William H. 
Published: August 2005

AbstractA numerical procedure is used to identify the relationship between recursive and implicit filters. We find that the implicit filters can each be decomposed into two recursive filters at each grid point location by using Choleski matrix factorization. Specifically, the implicit second‐order sine filter yields the traditional first‐order recursive filter, while we recover the standard second‐order recursive sine filter from its fourth‐order implicit counterpart. This approach thus provides an alternative to traditional methods for calculating the coefficients associated with the recursive sine filters. We also find that we cannot recover the traditional form for the recursive tangent filter from the implicit tangent filter.
Hierarchical method for elliptic problems using wavelet
Authors: Cai Zhiqiang , Weinan E. 
Published: August 2005

AbstractIn this paper we explore the hierarchical structures of wavelets, and use them for solving the linear systems which arise in the discretization of the wavelet–Galerkin method for elliptic problems. It is proved that the condition number of the stiffness matrix with respect to the wavelet bases grows like O(log2 H/h) in two dimensions, and the condition number of the wavelet preconditioning system is bounded by O(log2 H/h) in d dimensions, instead of O(h−2) if the scaling function bases are used.
Variational validation of a membrane finite element with drilling rotations
Authors: Allman D. J. 
Published: August 2005

AbstractIt is shown that a triangular membrane finite element with vertex ‘drilling rotations’ which was developed in earlier publications is, in fact, a correct implementation of a variational principle. The existence of a variational principle is a crucial factor which places the earlier work on a secure theoretical foundation. It implies superior computational characteristics of the finite‐element equations and provides valuable guidance on practical issues such as the consistent treatment of boundary conditions.
Improved finite‐difference solutions of the diffusion equation for heat conduction
Authors: Bhattacharya M. C. 
Published: August 2005

AbstractA number of improved finite‐difference solutions of explicit form have been reported recently. The choice of a particular solution of these improved explicit forms is dependent on the value of the non‐dimensional time step as well as whether the process involves cooling or heating. The conditions for stable operation are clarified in the paper. Two new improved solutions of implicit forms are also reported in the paper. These new solutions give better accuracy compared to the conventional Crank–Nicolson and pure implicit methods, and have unrestricted stability.
Application of iterative global/local finite‐element analysis. Part 2: Geometrically non‐linear analysis
Authors: Whitcomb John D. , Woo Kyeongsik 
Published: August 2005

AbstractA geometrically non‐linear global/local technique was developed and tested. This technique uses separate global and local finite‐element models. Iteration is used to enforce equilibrium between the global and local models. The results of this initial study suggest that the technique can be used to reduce both computer memory and CPU requirements.
Matrix filter for correcting experimental data
Authors: Lukasiewicz S. 
Published: August 2005

AbstractThe paper presents a filtering algorithm which corrects the results of measurements of certain physical quantities if any additional information about the measured values is known. The algorithm is very effective in one‐dimensional as well as in two‐dimensional problems where additional constraints are presented in the form of differential equations. For example, this technique can be used to correct the measurements of certain dynamic quantities if some information about motion of examined bodies is known. It can also be used to correct the strain field measurements if the conditions of continuity of strain field are included.
Finite‐element computer simulation of atmospheric convection with anisotropic eddys
Authors: Mann Kenneth J. 
Published: August 2005

AbstractA computer simulation is made of cellular convection in an anisotropic atmosphere in an attempt to more closely approximate the observed values with those obtained from mathematical models. A finite‐element Galerkin technique, with Taylor approximation and Crank–Nicolson, is employed and comparisons are made with the author's earlier finite‐element models of isotropic convection and with finite‐difference models. It is found that postulates from physics on the effect of anisotropy on cellular atmospheric convection, with its increase in the aspect ratio, are well modelled with this finite‐element technique.
A simple time‐step control scheme
Authors: Givoli Dan , Henigsberg Ilan 
Published: August 2005

AbstractA simple automatic time‐step control procedure is devised for use in implicit one‐step time‐integration schemes. First‐ and second‐order semi‐discrete systems of equations emanating from finite‐element spatial discretization are considered. The varying time‐step interval is controlled by the relative distance between the solution in two consecutive time steps, using the solution update formula of the time integrator under consideration. A model problem involving the vibrations of a membrane is used to demonstrate the performance of the scheme.