bluuebunny/crossref_metadata_2025_split huggingface dataset:
Solution of electrostatic problems by the p‐version of the finite element method
Authors: Szabó Barna A. 
Published: August 2005

AbstractThe main points of the finite element formulation of electrostatic problems are summarized and illustrated with a two‐dimensional example which is representative of wiring capacitance computations in VLSI circuit design. Quality control procedures in finite element analysis, based proper mesh design, p‐extension and extraction procedures are demonstrated.
A boundary value method for a class of nonlinear singular perturbation problems
Authors: Kadalbajoo Mohan K. , Reddy Y. N. 
Published: August 2005

AbstractA boundary value method is presented for solving a class of nonlinear, singularly perturbed, two‐point boundary value problems with a boundary layer on the left end of the underlying interval. By constructing a modified problem with a boundary layer correction, the boundary layer is dealt with separately. The method is iterative on the terminal point of the boundary layer. A lower bound for the terminal point of the perturbation parameter and some theoretical results of the method are discussed for linear problems. Finally, some numerical examples are presented to demonstrate the efficiency of the method.
Laplacian smoothing and Delaunay triangulations
Authors: Field David A. 
Published: August 2005

AbstractIn contrast to most triangulation algorithms which implicitly assume that triangulation point locations are fixed, ‘Laplacian’ smoothing focuses on moving point locations to improve triangulation. Laplacian smoothing is attractive for its simplicity but it does require an existing triangulation. In this paper the effect of Laplacian smoothing on Delaunay triangulations is explored. It will become clear that constraining Laplacian smoothing to maintain a Delaunay triangulation measurably improves Laplacian smoothing.
A comparison of solutions for adiabatic shear banding by forward‐difference and Crank‐Nicolson methods
Authors: Batra R. C. , Wright T. W. 
Published: August 2005

AbstractA set of non‐linear and coupled equations governing the thermomechanical deformations of a viscoplastic body undergoing simple shearing deformations is integrated in time by using the forward‐difference Galerkin finite‐element (FDGFE) method and the Crank‐Nicolson‐Galerkin finite‐element (CNGFE) method. In the latter scheme the number of unknown functions is increased so that the governing equations contain only first‐order spatial derivatives. It is shown that the solutions obtained by the two methods agree qualitatively; however, the CNGFE method seems to introduce some damping into the system for non‐polar materials, but none for dipolar materials.
Steady three‐dimensional thermal convection in a vertical rectangular enclosure
Authors: Chikhaoui A. , Maslanik M. K. , Sani R. L. 
Published: August 2005

AbstractThe numerical study of the steady 3D thermal flow regimes in a vertical enclosure with side‐wall heating and cooling is considered; a primitive variable Galerkin finite element method is used for the simulation in the Boussinesq approximation. The model consists of a rectangular box with vertical and horizontal aspect ratios, respectively, of lz = 12 (vertical length to box width) and ly = 8 (horizontal length to box width). The two large vertical plates are maintained at different and constant temperatures, and the remaining walls are assumed to be perfectly conducting. The enclosure is filled with a fluid of Prandtl number Pr=0.71, and the Grashof number Gr, based on the spacing between the large vertical walls, is up to 1.2 × 104. The 3D results presented herein were obtained with a 11 × 9 × 53 node mesh in half of the enclosure by imposing symmetry at the mid‐plane. The solution in the mid‐plane is compared with a 41 × 121 2D solution and laboratory observations at various Gr values. The transition between the monocellular and multicellular natural convective regimes is determined. The 3D aspect of the flow is illustrated and compared with the 2D solution. Near the onset of multicellular flow predicted by linear stability theory, the 2D and 3D simulations exhibit a steady multicellular structure. The calculated flow patterns are compared to visualizations obtained by smoke traces in physical experiments.
On the solution of heat conduction problems involving heat sources via boundary‐fitted grids
Authors: Grandi G. M. , Ferreri J. C. 
Published: August 2005

AbstractIt is shown that codes employing boundary‐fitted grids (BFG) in heat conduction problems involving heat sources must be implemented in strictly numerically conservative form if accurate results are to be obtained. It is demonstrated that, for one‐dimensional problems, non‐conservative form imply errors originated in grid non‐uniformity that cause a spurious increase in the heat source. This in turn leads to significant errors in the computed soution. Therefore the implementation of BFG codes using non‐conservative forms should be avoided. An application to an unsteady, axisymmetric benchmark problem involving a spherical, time‐decaying heat source is presented.
Calculation of interior values by the boundary element method
Authors: Paulsen Keith D. , Lynch Daniel R. 
Published: August 2005

AbstractThe boundary element method (BEM) provides a straightfoward mechanism for calculating interior values once the appropriate boundary values have been determined. However, the interior solution near the boundary can exhibit unusual behaviour resulting in large numerical inaccuracies. This ‘boundary layer’ effect has been noted but is largely unexplored in the BEM literature. In this paper the numerical inaccuracies are shown to stem from the inability of the quadrature to account for the Green's function near‐singularity. A simple scheme, which adds little extra computational effort, is used to remove the numerical inaccuracies at interior points close to the boundary by increasing the quadrature in the nearby boundary elements.
Parallel processing of central difference transient analysis for three‐dimensional nonlinear framed structures
Authors: Hajjar Jerome F. , Abel John F. 
Published: August 2005

AbstractThe central difference algorithm is a simple but effective time integration algorithm suitable for parallel processing. This paper discusses the development and implementation of the method for the fully nonlinear, transient dynamic analysis of three‐dimensional framed structures. A data structure is presented in which only one nearest‐neighbour communication is required per timestep, and potentially little overhead is incurred for the parallel implementation. Because this explicit method is only conditionally stable, the large disparity of natural vibrational frequencies of frame structures indicates that central difference analysis is most useful for applications having short‐duration loading. An example is presented indicating the speed‐up and efficiency of the algorithm when implemented in a distributed‐memory, coarse‐grained parallel processing environment.
A family of predictor‐corrector methods for second‐order hyperbolic equations
Authors: Twizell E. H. , Khaliq A. Q. M. 
Published: August 2005

AbstractA family of predictor‐corrector methods is used in PECE mode to obtain a numerical solution of a nonlinear second‐order hyperbolic partial differential equation. One particular predictor‐corrector combination is used to solve a problem from the literature.
Advantages of consistent over lumped methods for analysis of beams on elastic foundations
Authors: Griffiths D. V. 
Published: August 2005

AbstractA simple method for analysing laterally loaded piles is to consider the problem as a beam on an elastic foundation. In this representation, the finite element method is used to solve the governing differential equation, in preference to the more popular finite difference approaches. The pile is modelled using beam elements, and two different methods are compared for introducing the soil stiffness. The ‘consistent’ approach, where the governing differential equation is discretized using a Galerkin formulation, is shown to be considerably more accurate than a ‘lumped’ approach. The improvement is particularly noticeable when the finite element discretization becomes coarser. Some examples are presented to illustrate the differences, and comparisons are made with closed‐form solution.
An accurate five‐point implicit finite difference method for solving the one‐dimensional wave equation
Authors: Noye B. J. , Rankovic M. J. 
Published: August 2005

AbstractThe ‘modified equaivalent equation’ approach has been used to derive a highly accurate implicit finite difference method (FDM) for solving the classical wave equation in one space dimension, using a computational stencil extending over five spatial grid points. This approach involves minimising the error terms of the modified equivalent partial differential equation which corresponds to the finite difference equation (FDE).
3‐D infinite boundary elements and simulation of monolithic dam foundations
Authors: Chuhan Zhang , Chongmin Song , Guanglun Wang , Feng Jin 
Published: August 2005

AbstractBased on the asymptotic behaviour of the fundamental solution for 3‐D elasticity problems, this paper presents an infinite boundary element model (IBEM) and its interpolation form. By using the analytical solution for half‐space under a vertical loading, excellent accuracy of this model has been verified. As an engineering application, the infinite foundation of a monolithic gravity dam was modelled by IBEM and the dam itself by normal BEM, and the displacement and stress distributions of the dam were analysed. It was concluded that large structure and foundation problems can be solved by this coupling system with the advantage of having fewer degrees of freedom and less data preparations. The results also clearly show the great improvement of the 3‐D model for critical stresses of the dam over the 2‐D plane model for narrow canyons having a width‐height ratio less than 2·4. Thus, a more economical cross‐section for dams can be achieved by 3‐D analysis.
Non‐linear dynamic substructure analysis using direct integration of steady‐state solution
Authors: Lima E. C. P. , Coutinho A. L. G. A. , Alves J. L. D. 
Published: August 2005

AbstractA reliable and efficient dynamic substructure technique for the determination of the steady‐state response of structures with physical non‐linearities is presented. Although the algorithm is similar to component mode synthesis, enhanced substructure of Lanczos‐‐Ritz vectors are used, to account for the spatial distribution of the external and inertial loads. The steady‐state solution is computed from the transient response over a single excitation cycle. The non‐linear behaviour is accomplished by a purely iterative pseudo‐force method. The numerical results show the potential of such an approach for the analysis of large structures.
Performance of some globally mapped Lagrangian elements
Authors: Nath B. 
Published: August 2005

AbstractA study of the performance of some globally mapped Lagrangian elements is presented. The objective was to determine whether there were significant advantages to be gained from mapping. Results show that for biquadratic and bicubic elements, the only ones considered, mapping leads to considerably improved performance, in terms of both accuracy and convergence, over their conventional (unmapped) counterparts. On the debit side, however, the presence of ‘parasitic’ terms in the shape function(s) of mapped Lagrangian elements makes them less efficient than their counterparts of the serendipity family. Nevertheless, results offer sufficient incentive for further work on ways in which Lagrangian elements could be made more efficient for practical application.
Solidification of castings in metallic moulds
Authors: Naik H. B. , Dave A. K. 
Published: August 2005

AbstractA square‐shaped central section of a relatively long aluminium casting in a metallic mould is analysed as a two‐dimensional heat‐transfer problem. The latent‐heat liberation effect and property variation with temperature are accounted for using an integral averaging technique. The experimental air‐gap data available in the literature are made use of. The modified Newton‐Raphson method, along with the Crank‐Nicholson time‐marching scheme, is used for the solution.
On a BEM formulation for an axisymmetric heat‐conduction problem in a transversely isotropic medium
Authors: Ishida R. , Ochiai Y. 
Published: August 2005

AbstractIn this paper we deal with the boundary‐element formulation for the axisymmetric transient heat‐conduction problem of a transversely isotropic medium. The time‐dependent fundamental solution for the axisymmetric problem is used and the time integral is performed analytically. It is shown that the function obtained is separated into steady and transient parts and the singularity at the boundary integral is only in the steady part.
Reducing modal truncation error in the wave response analysis of offshore structures
Authors: Léger P. , Ricles J. M. , Robayo L. J. 
Published: August 2005

AbstractThe response of offshore structures subjected to wave loading is generally dominated by pseudo‐static behaviour which is not efficiently expressed in truncated modal co‐ordinates. In this paper, a new and efficient method has been developed to reduce modal truncation error in the numerical evaluation of transfer functions for the wave response of offshore structures. The solution is based on a transformation to a reduced system of generalized Ritz co‐ordinates using load‐dependent transformation vectors generated by a subspace iteration type of scheme from specified distributions of the dynamic loads. Numerical applications on a simple gravity platform model were used to establish systematic comparisons between the performance of the mode‐displacement, the mode‐acceleration and load‐dependent solutions using various numbers of transformation vectors.
Implicit methods for diffusion–convection equations
Authors: Patrício F. 
Published: August 2005

AbstractIn this work three implicit methods are considered for the solution of the constant‐coefficient diffusion‐convection equation. Two of these methods are seen to be first and second‐order accurate in time and to be L‐stable or L0‐stable, depending on the relation between the convection and diffusion parameters and the step size. The third one is seen to be third‐order accurate in time and is also L‐stable (L0‐stable). However, some oscillations may appear in the solution. To avoid these oscillations some restrictions are presented.
An integration procedure for curved boundary elements
Authors: Abdel‐Akher A. , Hartley G. A. 
Published: August 2005

AbstractIn the direct boundary element method (DBEM) of analysis, much of the numerical computation involves the integrations along a boundary. The integration is usually performed by quadrature, and in recent pevious papers by the authors1,2 it has been shown that integration can in general be carried out analytically, with the results of the integration presented as algebraic functions, and programmed accordingly. These results have, to this time, been presented for straight boundaries, with application to thinplate bending analysis only.For an arbitrary shaped curved element, the derivation of closed‐form expressions for boundary integrations is not possible. A semi‐analytical‐numerical procedure, based on representing the boundary as piecewise straight is developed in this paper. In this procedure, the boundary shape is considered dependent of the approximation of the boundary variables, and in the sense that each‘quadratic’ boundary element is considered geometrically to be made up of several piecewise cubic functions, the mulation might be termed‘super‐parametric’. Generally, a curved boundary does not necessarily imply need for higher‐order approximation of boundary variables, but does necessitate that the more applicated shape be accurately modelled.The integration procedure presented in this paper can be applied in other two‐dimensional problems.
The evaluation of domain integrals in the boundary element method
Authors: Pina H. L. 
Published: August 2005

AbstractIn the application of the boundary element method (BEM) source terms give rise to domain integrals. To keep in the spirit of this method these integrals should be transformed into boundary integrals. Infortunately this is possible only in some circumstances. In this paper we develop further an idea of Vijayakumar and Cormack (1987) to obtain other cases where such transformation is possible
Constructing second‐order structural models with specified mass submatrix condition numbers
Authors: Williams T. 
Published: August 2005

AbstractThis paper presents a simple new algorithm for constructing second‐order models for any given flexible structure, with these models satifsfying the constraint that each leading principal submatrix of the mass matrix must have a specified condition number. Now, the effects of rounding errors in practical computation generally increase with increasing condition number, i.e. as the matrix considered approaches singularity. Thus, the new models should prove useful for the systematic testing of the numerical properties of many algorithms in the dynamics and control of flexible structures.
Removal of integral singularities
Authors: Laures J. P. 
Published: August 2005

AbstractA procedure based on changing of independent variables is proposed. It allows one to reduce one‐dimensional (1D) and two‐dimensional (2D) singular integrals arising in fracture mechanics (in 2D and 3D problems, respectively). The final non‐singular expressions are exact and usually simpler than the original functions. They may therefore simplify analytical developments, and allow significant reduction of the computational time and an increase in the accuracy of numerical applications.
Finite‐element analysis for immiscible two‐phase fluid flow in deforming porous media and an unconditionally stable staggered solution
Authors: Xikui Li 
Published: August 2005

AbstractA finite‐element numerical model for immiscible two‐phase fluid flow in a deforming porous media is presented. The displacements, the pressures and the saturations of wetting phase are taken as primary unknowns of the model as the constraint about the capillary pressure between two fluid phases is applied. The governing equations and their finite‐element formulations are given in the paper. An unconditionally stable staggered solution procedure is devised for the integration of the formulations in the time domain. The stability analysis of the solution scheme is also carried out.
Substructure method for stress analysis of mass concrete structures
Authors: Bofang Zhu 
Published: August 2005

AbstractIn the finite‐element stress analysis of a mass concrete structure, owing to the effect of age of the concrete, it is necessary to compute a stiffness matrix and its inverse for every time increment. The computation is quite lengthy. In this paper a generalized substructure method is offered. It is assumed that the structure, consisting of m zones of different materials, is divided into m substructures, one for each zone. As every substructure is a homogeneous solid, the computation relevant to the substructure is required at the beginning only, and can be utilized repeatedly thereafter. Thus the computation is simplified remarkably.
On the numerical solution of a model air pollution problem with non‐smooth intial data
Authors: Seward W. L. , Kasibhatla P. S. , Fairweather G. 
Published: August 2005

AbstractWhile one of the distinguishing features of air pollution problems is the presence of a large number of randomly scattered discrete soucrces, little attention has been devoted to the proper treatment of such souces in standard numerical techniques. In this paper we consider a model air pollution problem in two space variables which can be transformed to the one‐dimensional diffusion equation with a Dirac delta function as the initial conditon. the primary purpose of this study is to investigate the effect of two ways of representing thishighly singular initial condition, namely by L2 projection and by mollification, in commonly used numerical methods basedc on a Galerkin semi‐discretization together with the θ method in the marching direction. We report the results of extensive numerical experiments which demonstrate, for example, that in general the numerical solution obtained with mollified initial data is more accurate near the intial point than that obtained using projected initial data. Moreover, it is verified that the‘smoothed’ Crank‐Nicolson method, in which the first two Crank‐Nicolson steps are replaced by four steps of the backward Euler method, is the most effective marching technique.
An easily implemented static condensation method for structural sensitivity analysis
Authors: Gangadharan S. N. , Haftka R. T. , Nikolaidis E. 
Published: August 2005

AbstractIn many situations, the sensitivity of the response of a structure to parameters affecting only a small part of the structure is desired. In such cases, it is efficient to use substructuring or static condensation approaches. However, static condensation is not available in all finite‐element codes, and its implementation requires access to and familiarity with the source code of the program. The present paper suggests an alternative version of static condensation for sensitivity calculations which is easy to implement without access to the source code of the finite‐element program. The proposed approach (black‐box method) is demonstrated by applying it in system identification of joint parameters of 3D frame structures using a direct method for evaluating the sensitivity derivatives of the structural response with respect to the joint parameters.
A curved triangular plate bending element for Kirchhoff plates using a C0 coharmonic mixed two‐field formulation
Authors: Campbell John S. , Horgan Bernice 
Published: August 2005

AbstractA curved triangular element is presented for thin Kirchhoff plates. A mixed, two‐field formulation is used, based upon the Marcus decomposition, in which the familiar biharmonic equation is supplanted by a pair of coupled Poisson‐type equations. Several examples of simply supported plates are given to illustrate the behaviour of this new formulation.
Finite‐element method for elastic wave propagation
Authors: Serón F. J. , Sanz F. J. , Kindelán M. , Badal J. I. 
Published: August 2005

AbstractThe object of this work is to analyse the computational aspects of the finite‐element method for the elastic wave equations. The necessary numerical techniques are analysed from the point of view of accuracy, performance and storage requirements when implemented in scalar and vector processors with large storage capacity. The method is implemented on an IBM 3090 with vector facility.For this implementation we consider five different time integration schemes (explicit and implicit central difference, Houbolt, constant average acceleration and Wilson), and in the implicit case, both direct (Gaussian decomposition) and iterative (successive over‐relaxation, Jacobi semi‐iterative, Jacobi conjugate gradient) sparse linear systems solvers. These solvers are taken from the ITPACK2C and ESSL libraries using in each case the adequate representation scheme; skyline, row‐wise and compressed diagonal.From our results it is concluded that constant average acceleration and explicit central difference are the most adequate integration methods and Jacobi conjugate gradient is the most efficient solver.