bluuebunny/crossref_metadata_2025_split huggingface dataset:
Exponential splines difference scheme for singular perturbation problem with mixed boundary conditions
Authors: Stojanović M. 
Published: August 2005

AbstractWe generate an exponential splines difference scheme for a one‐dimensional singularly perturbed selfadjoint problem along with general boundary conditions of the third kind. We obtain \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm O(h min(}h,\sqrt \varepsilon)) $\end{document} accuracy if one has Dirichlet's boundary conditions on the right end point, and order one in the remaining cases. These results are supported by numerical experiments.
A finite‐element implementation of a mixed extremum principle for linear elasticity
Authors: Chandler H. W. 
Published: August 2005

AbstractA method is given which can be used for finding approximate solutions to problems in linear elasticity. It is an extension of the use of an extremum principle mentioned by Prager and Synge1 involving both the stresses and the strains. By using this principle Hooke's Law can be approximately imposed on statically admissible stress fields and kinematically admissible strain fields which contain adjustable parameters. The extension uses the same extremum principle to impose approximately the symmetry of the stress tensor as well. This allows the use of a vector stress function, applicable to 2D and 3D problems, which, while ensuring that the equations of force equilibrium are satisfied, does not impose the symmetry of the stress tensor.A mixed finite‐element formulation is developed with the displacement vector and a vector stress function as nodal variables. A simple 2D finite‐element program is described which implements this method and an example of its use is discussed. Advantages over some existing mixed formulations are: it allows permissible stress jumps across a surface; the global matrix is symmetric and positive‐definite; only C0 continuity is needed between the elements for both types of variable.
The h–p‐version of the finite‐element method in the plate modelling problem
Authors: Babusǩa I. , Li L. 
Published: August 2005

AbstractThe paper addresses the problem of plate modelling within the framework of the h–p‐version of the finite‐element method. A natural hierarchy of models is constructed. The lowest member of the hierarchy is the well‐known Reissner–Mindlin model. It is shown that higher degree elements do not show any locking effects for the models under consideration.
Performance of mapped infinite elements for exterior wave scattering applications
Authors: Moyer E. Thomas 
Published: August 2005

AbstractThe mapped infinite element of Zienkiewicz et al. is investigated for three‐dimensional wave scattering applications. The optimal location of the infinite elements as a function of frequency is considered. Near‐field and far‐field convergence are each examined. The results demonstrate that the mapped infinite element is an extremely effective absorbing boundary condition for many applications. In addition, if far‐field accuracy is the desired computational quantity, the infinite elements can be located extremely close to the scatterer surface, significantly reducing the problem dimensionality.
A new space‐marching technique: Internal/external incompressible flows
Authors: Zhu Zili , Fletcher Clive A. J. 
Published: August 2005

AbstractA new space‐marching technique is developed and shown to be robust and efficient for both internal and external flows. The new marching technique solves the coupled governing equations at two adjacent streamwise locations simultaneously, and the streamwise pressure gradient is discretized with central‐differencing instead of the more usual forward‐differencing in the marching direction. The governing equations are solved by marching either in the main flow direction or in the reverse direction, with ‘departure‐free’ solutions.
A cyclic symmetry approach to the structural dynamic analysis of bladed discs
Authors: Omprakash V. , Ramamurti V. 
Published: August 2005

AbstractThis paper presents the development of a cyclic symmetric approach to the complete stress, free vibration, transient and stationary response analysis of rotating tuned bladed disc systems taking into account all the complications involved. Starting from Biezeno's approach to the analysis of individual blades and discs, the continuing development of different methodologies and their limitations as applied to practical systems are discussed. The advantages, versatility and usefulness of the present approach are demonstrated by means of the results obtained for a number of cases both by theoretical and experimental means.
Fractional step solution to slack tide oxygen balance equation
Authors: Li C. W. 
Published: August 2005

AbstractA time‐stepping split‐operator method is developed to obtain the steady‐state solution of the slack tide oxygen balance equation, which takes different formulations at the aerobic and the anaerobic regions, while the direct iterative solution of the steady‐state equation can lead to an oscillatory behaviour. The method treats the advection step by the minimax characteristics method, the dispersion step by the central difference method, and the decay step by an analytical solution. Using a large time step (1 tidal cycle) to be compatible with the model formulation, the solution obtained is in good agreement with the exact solution and the computational effort is low.
Application of the method of moments to acoustic scattering from fluid‐filled bodies of arbitrary shape
Authors: Rao Sadasiva M. , Raju P. K. , Sun S. P. 
Published: August 2005

AbstractThe method proposed in this paper provides a computational technique for solving acoustic scattering problems associated with arbitrarily shaped two‐ or three‐dimensional fluid‐filled bodies. In particular, using free‐space Green's functions along with the associated boundary conditions on the surface of the body, a pair of coupled integral equations are derived. The equations are then solved by approximating scatterer geometry by either linear segments or triangular patches, for the two‐ or three‐dimensional cases, respectively, and employing the method of moments. The method presented in this work is simple, efficient and applicable to truly arbitrary geometries. Numerical results are presented for certain canonical shapes and compared with other available data.
An explicit formulation of a triangular plate‐bending element with shear
Authors: Sengupta Dipak 
Published: August 2005

AbstractPlate‐bending elements with the inclusion of transverse shear effects are important in analysing problems of transverse bending of relatively thick plates. Several such elements are available. Recently another element with a triangular geometry has been suggested. The construction of the element stiffness matrix follows conventional procedure which involves rigorous matrix computations. An alternative method of obtaining the stiffness matrix explicitly for such an element is suggested in the present work. Thus the process of matrix inversion and a considerable degree of matrix multiplications can be avoided in constructing the element stiffness matrix. Explicit expressions worked out may be conveniently used in microcomputers.
Symmetry of the stiffness matrices for geometrically non‐linear analysis
Authors: Badawi M. , Cusens A. R. 
Published: August 2005

AbstractThe efficiency is compared of three procedures developed for geometrically non‐linear analysis with a Lagrangian co‐ordinate system and leading to the formulation of a symmetric secant stiffness matrix. The first, based upon the principle of total potential energy with a special form of the strain energy expression, is due to Mallett and Marcal.1 The second, due to Wood and Schrefler,2 achieved symmetry of the secant matrix by correlation of a procedure based on the virtual work principle with the Mallett–Marcal procedure. The authors3 have recently developed a new symmetric secant matrix procedure also based on the virtual work principle.The aim of this paper is to draw attention to the time‐consuming operations involved in the Mallett–Marcal procedure and to highlight the new secant and tangential stiffness matrix formulations, which are different from those of Wood and Schrefler and easier to compose. This paper also demonstrates how the Wood–Schrefler procedure can be modified to accommodate the new formulation.
Accuracy of some plate models for clamped‐in boundary conditions
Authors: Li L. , Babuška I. 
Published: August 2005

AbstractThe paper shows that the well‐known Reissner–Mindlin plate model for the clamped‐in boundary condition does not capture the boundary layer behaviour for the bending moments. This boundary layer is present in 3‐D formulation. In contrast the proposed (1,1,2) model shows this boundary layer. The strength of the boundary layer for the (1,1,2) model is analysed.
Parallel grid generation/optimization using block‐domain decomposition
Authors: Bova S. W. , Carey G. F. 
Published: August 2005

AbstractThe use of a parallel Schwarz‐type domain decomposition procedure for 2‐D block‐structured grid generation, together with grid optimization for smoothness, orthogonality and solution accuracy, is investigated. The grid optimization algorithm considered is based on the Brackbill–Saltzman construction, a variational method which seeks to generate optimum grids by minimizing a weighted integral of three grid properties. The resulting grid generation equations are quasilinear, elliptic, partial differential equations, and therefore relatively expensive to solve. Good speed‐up factors are obtained, with efficiencies above 90 per cent on the shared‐memory Alliant FX‐8 multi‐processor, and on the Symult Systems Series 2010, a message‐passing, distributed memory system. In order to obtain such speed‐ups for typical problems, approximately 99 per cent of the code must be capable of concurrent execution. Grid refinement studies with adaptation to the compressible flow solution using the Euler equations suggest that a significant improvement in the resolution of shock waves can be achieved efficiently by this scheme.
A 3‐D refinement algorithm suitable for adaptive and multi‐grid techniques
Authors: Rivara Maria‐Cecilia , Levin Cristian 
Published: August 2005

AbstractA 3‐D refinement algorithm for tetrahedral meshes is presented and discussed. An empirical study of the reduction of solid angle size due to repeated subdivisions has shown the algorithm to be in practice a powerful and reliable tool for mesh refinement suitable to be combined with adaptive finite‐element methods and multi‐grid algorithms.
A new way to measure the accuracy of the BEM solution
Authors: Zhong Xiaoguang 
Published: August 2005

AbstractIn this paper a new algorithm for the computation of singular integrals (1/r or 1/r2) is presented. The limit of inner domain variables, as an inner point approaches the boundary, can be computed by this algorithm. Based on the difference between this limit and the corresponding given values in boundary conditions, an objective measurement of the accuracy of a BEM solution is suggested. This objective measurement is used to estimate the error of a BEM solution. Several numerical examples are given.
Iterative techniques for non‐linear eigenvalue buckling problems
Authors: Mirasso Anibal E. , Godoy Luis A. 
Published: August 2005

AbstractStructural stability problems under displacement‐dependent loads often take the form of non‐linear eigenvalue problems in which the eigenvalue is raised to an exponent. Iterative techniques are considered in this work for the solution of non‐linear eigenproblems of the form (K ‐ λK1 ‐ K2(λp))x = 0. The problem is linearized at each iteration using two alternative procedures: through updating the stiffness matrix K or else by updating the initial stress matrix. Numerical examples are used to illustrate the difficulties associated with the first technique, whereas it is shown that the second one yields better convergence rates than other existing techniques.
Semi‐numerical iterative series solution of linear algebraic equations with ‘MATHEMATICA’
Authors: Ioakimidis N. I. 
Published: August 2005

AbstractThe computer algebra system MATHEMATICA is applied to the iterative solution of systems of linear algebraic equations where the matrix of the coefficients depends on a parameter. The solution is found in a Taylor‐Maclaurin series form with respect to this parameter at an appropriate point and, therefore, the system can be solved only once and for all even if the parameter varies. All three popular iterative methods, that is, the Gauss–Jacobi, the Gauss–Seidel and the successive overrelaxation method are used in particular applications. The complete MATHEMATICA procedure for the last of these methods is also presented. Two elementary applications to structural mechanics are also made and further possibilities are discussed.
Large eddy simulation of backward‐facing step flow
Authors: Kobayashi Toshio , Morinishi Youhei , Oh Keon‐Je 
Published: August 2005

AbstractRecirculating flow around a backward‐facing step is calculated by large eddy simulation (LES). The reattachment length is found to be xR/H = 8 for a Smagorinsky constant of C =0.15, and xR/H = 9 for C =0.10. In the recirculating region, three eddy structures can be observed in the instantaneous streamline distributions, and the location of the reattachment point varies according to the size of these eddies. The stream‐wise turbulence intensities at the start of the recirculating region around the step are considerably reduced by LES in comparison with the values predicted by the k – ϵ model, but they have somewhat higher values than those of the k – ϵ model as it approaches the reattachment point.
Fully stressed configuration of statically indeterminate trusses
Authors: Wang Bo Ping 
Published: August 2005

AbstractProcedures are derived in this paper for defining fully stressed statically indeterminate trusses under a single loading condition for the particular case where redundant supporting members are added to a determinate truss. If the orientations of the redundant members are prescribed, their length can be computed easily from the fully stressed conditions. The cross‐sectional areas of truss in fully stressed configuration (FSC) are not unique. The minimum weight FSC can be determined with use of linear programming. Several examples are included to illustrate the general formulation.
Equivalent versions of the quick scheme for finite‐difference and finite‐volume numerical methods
Authors: Johnson Richard W. , MacKinnon Robert J. 
Published: August 2005

AbstractA recent article by Leonard and Mokhtari (1990) discusses the order of accuracy of discrete equations used for numerical simulation. They maintain that discrete operators derived for the finite‐volume method should be Taylor‐series‐analysed using the various points that appear in a finite‐volume discrete equation. The current paper argues that any discrete scheme must be analysed from a single point. It is shown that while Leonard's finite‐difference QUICK scheme is O(h3)‐accurate, his implementation of QUICK for the finite‐volume method is only O(h2). An alternative finite‐volume formulation is shown to yield a locally third‐order‐accurate operator in the final discrete equation. Also, third‐order‐accurate formulae are discussed for various numerical implementations. Numerical examples are included to demonstrate actual rates of convergence for various operators.
Multi‐rate numerical methods for diffusion problems
Authors: Choudhury S. Roy 
Published: August 2005

AbstractThe one‐dimensional diffusion equation is solved using a recent class of multi‐rate numerical algorithms collectively referred to as waveform relaxation methods. The methods enable different parts or blocks in the system to take widely different time steps by decoupling the blocks in the time domain. Significant speed‐up is obtained over the results using a composite trapezoidal rule/second‐order backward Euler time‐stepping scheme without blocking. Possible implementation strategies for two‐dimensional diffusion are briefly discussed.
A note on multiple reciprocity integral formulation for the Helmholtz equation
Authors: Kamiya N. , Andoh E. 
Published: August 2005

AbstractThe multiple reciprocity method (MRM) is known as a method for elimination of domain integrals appearing in the integral equation in the framework of the direct‐type boundary‐element formulation. The method employs the fundamental solution of a part of the adjoint operator corresponding to the original differential equation. In this paper we discuss the relation between the conventional integral equation formulation of the Helmholtz equation and that derived by means of the MRM formulation. The latter, formulated in terms of real‐valued variables, is proved to be a special case of the general complex‐valued formulation.
Consistent diagonal mass matrices for the isoparametric 4‐node quadrilateral and 8‐node hexahedron elements
Authors: Sauer Gerhard 
Published: August 2005

AbstractDiagonal mass matrices offer computational advantages in many applications. Their general use is confronted, however, with the fact that usual finite‐element formulations generate consistent mass matrices. Some methods have been suggested to diagonalize these consistent matrices. These methods are largely founded on an intuitive basis. They abandon the classical way of calculating finite‐element matrices. In an attempt to overcome this deficiency, a procedure is presented which enables direct calculation of consistent diagonal mass matrices for the isoparametric 4‐node quadrilateral and 8‐node hexahedron. This procedure is based on an expansion of the interpolation functions and the selection of an appropriate integration order. It is shown that the consistent diagonal mass and the associated stiffness matrices represent the dynamic structural properties with good accuracy.
Adaptive mesh generation and transformation of triangular to quadrilateral meshes
Authors: Rank Ernst , Schweingruber Manfred , Sommer Markus 
Published: August 2005

AbstractIn this paper an algorithm for generating pure triangular or pure quadrilateral meshes for arbitrary polygonal domains is presented. The first part shows a triangulation procedure being as suitable for local mesh refinement as for local mesh coarsening. In the second part an algorithm for transformation of triangular grids to quadrilateral meshes of the same relative mesh density is introduced. Two simple strategies are shown which can easily be implemented into any existing triangulation algorithm.
On the accuracy of time‐stepping schemes for dynamic problems with negative stiffness
Authors: Xie Y. M. , Wood W. L. 
Published: August 2005

AbstractThis paper examines the behaviour of various time‐stepping schemes used in structural dynamic analysis when applied to models with negative stiffness. It is found that under such circumstances the accuracy of the numerical solution is greatly affected by the choice of integration parameters of the scheme. Optimal parameters for the Newmark family and the SS32 family have been investigated.
Use of a p‐version finite‐element formulation for compressible lubrication calculations
Authors: Nguyen Steve H. 
Published: August 2005

AbstractTo obtain accurate gas‐bearing lifts and moments, finite‐difference and conventional finite‐element techniques often require excessively large degrees of freedom. In this paper we avoid this problem by solving the compressible gas‐bearing solution by the p‐version finite‐element method. The lubrication finite‐element equation is formulated based on the weighted residual approach, and the resulting nonlinear equations are solved iteratively by the Newton–Raphson procedure. To achieve higher‐order solutions the formulation utilizes the C0 hierarchical shape functions to describe the element pressure field. A numerical example is included to demonstrate the simplicity of modelling and the rapid convergence characteristics of the present p‐formulation. An efficient numerical strategy, which utilizes the most recent polynomial pressure solution available as an estimate for the next higher polynomial level calculations, shows a 50 per cent reduction in the required computational effort for the low‐flying Winchester air‐bearing slider presented here. When compared against results obtained from conventional h‐version finite‐element models, the p‐formulation yields better accuracy with fewer degrees of freedom required.
On perturbation behaviour in non‐linear dynamics
Authors: Carstensen C. , Wriggers P. 
Published: August 2005

AbstractThe static bifurcation criterion, i.e. singularity of the tangential stiffness matrix, is discussed in the sense of non‐linear dynamics since it is sometimes used in the engineering literature. In this paper the connection between static stability, i.e. that the tangential stiffness matrix is positive‐definite, and insensitivity, i.e. local damping of small perturbations, is proved. Since, in general, there is no connection between insensitivity and asymptotic stability, the concept of sensitivity cannot replace the classical stability theory of motion.
Balancing domain decomposition
Authors: Mandel Jan 
Published: August 2005

AbstractThe Neumann–Neumann algorithm is known to be an efficient domain decomposition preconditioner with unstructured subdomains for iterative solution of finite‐element discretizations of difficult problems with strongly discontinuous coefficients (De Roeck and Le Tallec, 1991). However, this algorithm suffers from the need to solve in each iteration an inconsistent singular problem for every subdomain, and its convergence deteriorates with increasing number of subdomains due to the lack of a coarse problem to propagate the error globally. We show that the equilibrium conditions for the singular problems on subdomains lead to a simple and natural construction of a coarse problem. The construction is purely algebraic and applies also to systems such as those that arise in elasticity. A convergence bound independent of the number of subdomains is proved and results of computational tests are reported.
Superconvergent patch recovery techniques – some further tests
Authors: Zienkiewicz O. C. , Zhu J. Z. , Wu J. 
Published: August 2005

AbstractA modification has been introduced to the new superconvergent patch derivative recovery technique recently developed (Zienkiewicz and Zhu, 1991). By use of a locally normalized co‐ordinate system, the application of this technique can now be applied to higher‐order finite‐element shape functions. Numerical studies are carried out for up to 6th‐order elements in one dimension and for up to quartic elements in two dimensions, and superconvergent results are obtained for all examples tested.
Completed Richardson extrapolation
Authors: Roache Patrick J. , Knupp Patrick M. 
Published: August 2005

AbstractThe Richardson extrapolation method, which produces a 4th‐order‐accurate solution on a subgrid by combining 2nd‐order solutions on the fine grid and the subgrid, is ‘completed’ – in the sense that a higher‐order‐accurate solution is produced on all the fine grid points.