bluuebunny/crossref_metadata_2025 huggingface dataset:
Control‐volume energy‐balance fe formulation of the 8‐node hexahedron element
Authors: Abboud J. B. , Hardisty H.
Published: August 2005

A general subdomain integral approach to finite‐element analysis is presented, based on the application of the principle of conservation of energy to steady‐state heat transfer in solids. The principal object of the paper is to use this method to formulate equations for a general three‐dimensional distorted brick element. First the three‐dimensional solution domain is divided into hexahedron elements. Each node is surrounded by a control volume so that the entire solution domain is filled with non‐overlapping, three‐dimensional control volumes. Each element in the global co‐ordinate system is mapped onto a master cubical element in a local isoparametric system. The temperature within each element is interpolated using trilinear shape functions. An energy balance is then performed on each control volume as element matrices are assembled into the global system matrix. Several test problems are presented both to demonstrate the method and to assess its accuracy.
Vector finite‐element analysis using IBM 3090–600e VF
Authors: Min Chang Shik , Gupta Ajaya Kumar
Published: August 2005

A finite‐element computer program consists of four basic modules, namely, computation of element stiffness matrices, assembly of the global stiffness matrix, solution of the system of linear simultaneous equations, and calculation of stresses. Vector algorithms consisting of direct vector Fortran code and the Engineering and Scientific Subroutine Library (ESSL) routines are presented for these modules. Numerical investigations were conducted using the IBM 3090–600E VF computer.

For element stiffness matrix calculation, using a vector length equal to the number of elements produced speed‐up in the range of 3·2 to 3·7 over the corresponding scalar code. The vectorized global element stiffness matrix assembly was accomplished with the help of an INDEX array and the ESSL routine DAXPYI that resulted in the speed‐up of 2·6 to 4·3. The ESSL routines DPBF and DPBS gave speed‐up of 7·7 to 53·6 over a scalar Gaussian solver. The scalar‐to‐vector speed‐up for the stress calculation ranges from 2·2 to 5·33. The speed‐up of the totally vectorized program over the scalar program is from 7·4 to 51·9.

As would be expected, the equation solution takes up the most computational effort in a finite‐element analysis. For the models we analysed the equation solution consumed 93 per cent to almost 100 per cent of the total CPU time in the scalar computations. Vectorizing the equation solver only reduces the percentage of its share to the range of 63 per cent to 88 per cent. In a totally vectorized program, the share of the equation solver effort is 85 per cent to 97 per cent. For the models analysed, the additional speed‐up accomplished by vectorizing the whole program over the one with a vectorized equation solver only was from 10 per cent to 40 per cent.
Surface pressure solution for boundary‐element analysis of stokes flow
Authors: Ingber Marc S. , Li Jing
Published: August 2005

Analysis of creeping flow problems using the boundary‐element method is now well established. The method is based on the transformation of the governing partial differential equations into a boundary integral equation for the velocity at arbitrary field points in terms of the surface velocities and tractions. Associated with the velocity boundary integral equation is a pressure boundary integral equation. The singularities contained in the kernel functions for the pressure boundary integral equation are an order higher than for the velocity boundary integral equation. Hence, for field points along the boundary of the domain, the pressure boundary integral equation is hypersingular, causing difficulties in evaluating the surface pressure. A method of regularization for the pressure boundary integral equation in which the hypersingular integral is converted into a Cauchy principal value integral is discussed. Some example applications are presented.
Application of finite‐element‐based solution technologies for viscoplastic structural analyses
Authors: Arya Vinod K.
Published: August 2005

Finite‐element solution technology developed for use in conjunction with advanced viscoplastic models is described. The development of such solution technology is necessary for performing stress/life analyses of engineering structural problems where the complex geometries and loadings make the conventional analytical solutions difficult. The versatility of the solution technology is demonstrated by applying it to viscoplastic models possessing different mathematical structures and encompassing isotropic and anisotropic materials. The computational results qualitatively replicate deformation behaviour observed in experiments on prototypical structural components.
A fourier expansion based particular integral approach for non‐boundary loadings in boundary‐element method
Authors: Zeng Xiaogang , Saigal Sunil
Published: August 2005

The analysis of loads applied within the domain of a body cannot presently be done with the boundary‐element method using a boundary‐only discretization. Such load cases include patch loads applied over a part of the domain of the object, point loads and line loads. A treatment for such load cases is presented in this paper. The object being considered is embedded in a finite domain and the applied loading is first expressed in terms of a Fourier series expansion. The particular integral solution for the governing differential equation is next obtained at the boundary nodal points for the series expansion loading. These particular integrals at the boundary nodes completely represent the effect of the applied loading and contribute an addition to the ‘force vector’ in the standard boundary‐element equations.
A C1 triangular interpolant suitable for scattered data interpolation
Authors: Goodman T. N. T. , Said H. B.
Published: August 2005

We present here a method of constructing a triangle interpolant which interpolates position and partial derivatives specified at the three vertices of the triangle. The method employs the cubic Bézier triangular patch technique. The data given enable us to determine the appropriate Bézier control points so that adjacent patches meet with C1 continuity. However, the interior control point for the patch is replaced by three separate points, due to the implementation of three local schemes, each of which satisfies the boundary conditions on only one side of the triangle. Convex combination is used to blend these three local schemes.
Moderate degree cubature formulas for 3‐D tetrahedral finite‐element approximations
Authors: Gellert M. , Harbord R.
Published: August 2005

Some new moderate degree cubature formulas for tetrahedra are derived. The suitability of various types of rules for the finite‐element technique is discussed exhaustively. Consequently, the newly developed formulas supplemented by lower degree known ones are tabulated for the purpose of direct application in finite‐element programming. All the formulas are presented in a virtually machine‐independent form.
A refined quadrilateral element for the finite‐element analysis of plates
Authors: Lachemi M. , Lahoud A. E.
Published: August 2005

The finite‐element formulation of a conforming plate‐bending element having the shape of a general quadrilateral is presented. The element has four nodes with six degrees of freedom per node. The accuracy and efficiency of the element is tested by considering several examples of plates in bending and comparing the results with those obtained using other elements or other methods of analysis.
Elimination of the boundary layer effect in BEM computation of stresses
Authors: Sladek V. , Sladek J.
Published: August 2005

The paper presents a new numerical method of the computation of stresses and displacements at internal points using boundary elements. The accuracy of the computation is reasonable even if the internal point is very close to the boundary. The numerical algorithm is developed for both the two‐ and three‐dimensional problems. The accuracy of the numerical computations based on the proposed method is illustrated in a test problem of 2‐D elastostatics.
A cross‐reduced integration technique for a bilinear shell element without zero‐energy modes
Authors: Zhong Zhi‐Hua
Published: August 2005

A reduced integration technique employed in a bilinear shell element is described. While the reduced integration technique solves the problem of ‘locking’ and improves the computational efficiency, it does not introduce any zero‐energy mode in the shell element. The shell element is based on the concept of laminas and fibres. The reduced integration is such that integration points are chosen both along the central fibre and on the reference lamina. Shear strains on the reference lamina are averaged to solve the locking problem and eliminate possible zero‐energy modes.
Implicit numerical integration algorithms with de Casteljau predictors
Authors: Yanilmaz Mehmet , Balkir Sina
Published: August 2005

A common approach for solving initial value problems representing algebraic differential equations is to formulate the solution as a polynomial function. This paper presents predictor based integration formulae by formulating the solution function as a vector valued Bernstein polynomial, namely a Bézier function. The Bézier function subdivision theorem leads to a predictor evaluation algorithm for the next solution point using de Casteljau's iterative control vertex generation technique. It is shown that the convergence of the algorithms is a consequence of the use of the Bernstein uniform approximation basis and that the de Casteljau predictor evaluation scheme leads to a computationally simple estimate of the local truncation error.
Exponential splines difference scheme for singular perturbation problem with mixed boundary conditions
Authors: Stojanović M.
Published: August 2005

We 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

A 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

The 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

The 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

A 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

This 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

A 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

The 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

Plate‐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

The 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

The 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

The 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.
The Zienkiewicz–Zhu error estimator for multiple material problems
Authors: Nambiar Rajiv V. , Lawrence Kent L.
Published: August 2005

The validity of the Ziekiewicz–Zhu a posteriori error estimator for elasticity problems involving more than one material is examined. A simple modification to the estimation process is suggested to obtain acceptable error indicators and error estimator values for problems involving multiple materials.
A 3‐D refinement algorithm suitable for adaptive and multi‐grid techniques
Authors: Rivara Maria‐Cecilia , Levin Cristian
Published: August 2005

A 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

In 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

Structural 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

The 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

Recirculating 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

Procedures 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

A 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

The 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

The 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

Diagonal 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

In 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

This 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

To 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

The 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.
Wave distribution in fibre members subjected to kinematic forcing
Authors: Tesar Alexander , Svolik Jan
Published: August 2005

The paper is concerned with the solution of non‐linear wave distribution in structural fibre members subjected to dynamic kinematic forcing. The development of reliable and efficient techniques for numerical handling of wave distribution based on the application of combined finite‐element and transfer matrix approaches is emphasized. Illustrative numerical solutions are presented.
Balancing domain decomposition
Authors: Mandel Jan
Published: August 2005

The 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

A 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

The 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.
A choice of interpolation schemes for the boundary‐element method in elastodynamics
Authors: Wu T. W. , Lee L.
Published: August 2005

It is known that the boundary‐element coefficient matrices in steady‐state elastodynamics are frequency‐dependent. For a multifrequency run, the coefficient matrices have to be reformed at each different frequency. This procedure usually involves heavy numerical integration, and hence is very time consuming. In this paper, two interpolation schemes are initially introduced to accelerate the process of matrix reformation without sacrificing the solution accuracy. In the first scheme, the coefficient matrices are first slightly transformed and then interpolated in the frequency domain. In the second scheme, the Green function is interpolated in the spatial domain. Comparison between these two schemes both in terms of accuracy and efficiency is presented. Finally, a hybrid scheme that takes advantage of the best of both interpolation schemes is proposed. Numerical examples are given to demonstrate the three different interpolation schemes.
Stream function vorticity solution using high‐p element‐by‐element techniques
Authors: Barragy E. , Carey G. F.
Published: August 2005

A p‐type finite‐element scheme is introduced for Navier‐Stokes problems in a fully coupled stream function/vorticity formulation. The resulting coupled non‐linear system is solved using a Newton iteration with incremental continuation in the Reynold's number. A biconjugate gradient (BCG) scheme in an element‐by‐element setting is applied to solve the linearized system at each Newton iteration. Pseudo‐element block preconditioners produce a practical PBCG method, even for ill‐conditioned systems arising from high‐p elements in the case of Stokes flow. The problem at higher Reynolds numbers further limits p.
Perturbation analysis of vibration modes with close frequencies
Authors: Chen Su‐Huan , Liu Zhong‐Sheng , Shao Chun‐Sheng , Zhao You‐Qun
Published: August 2005

This paper focuses on how parameter changes in a vibration system expressed by a discrete eigenvalue problem affect vibration modes in the special case of closely spaced eigenvalues, i.e. ‘eigenvalue clusters’. For this class of problems, a perturbation analysis is developed that can be used to compute changes in eigenvalues and eigenvectors in response to small parameter changes. The analysis is applied to a 6‐degree‐of‐freedom spring‐mass system containing a single pair of closely spaced eigenvalues.
The virtual contact loading method for elastic contact problems
Authors: Zhao Hua , Li Zhong‐Hua , Kuang Zhen‐Bang
Published: August 2005

The virtual contact loading method (VCLM), a highly efficient numerical method to solve elastic contact problems, is proposed in this paper. Having applied virtual loads on the possible contact region (PCR) of a structure system, we carried out the usual finite‐element calculations only once and made a local iteration analysis in PCR then the contact region (shape and size), contact state (stick, slide or mixed), contact normal and shear stress distributions, and the stress and displacement fields in contact bodies were all obtained simultaneously. This method is very simple and easy to use.

The elastic contact problems for cylinder–cylinder are solved in this paper and the results agree well with those in previous work.
Validation of finite‐element codes for prediction of machining distortions in forgings
Authors: Chandra U.
Published: August 2005

When a forging is machined to its net shape, unacceptably large distortions can occur if the final part shape is complex. Such distortions can be predicted with the application of the finite‐element method. However, numerical errors associated with the finite element technique can render such predictions unreliable. This paper presents benchmark problems for verifying the accuracy of machining distortions predicted by any prospective finite‐element code. Also, a comparison between two industry‐standard general‐purpose codes, ANSYS and ABAQUS, is presented.
Error study on numerical approximation of radiation boundary condition for one‐dimensional wave equation
Authors: Zhu L. , Li C. W.
Published: August 2005

The radiation boundary condition is frequently used at the artificial outflow boundary created in the numerical computation of fluid flow problems to allow outgoing waves to leave the domain undisturbed. However, the numerical approximation of the radiation boundary condition will produce errors which will affect the interior solution. In this work the errors due to two different numerical approximations of the radiation boundary condition are studied, with the one‐dimensional wave equation being used as the model equation. A theoretical analysis shows that: (a) if the numerical approximation of the boundary condition generates a celerity error, a reflected wave with amplitude proportional to the size of the celerity error is produced; (b) if the numerical approximation of the boundary condition generates a numerical diffusion and hence an amplitude damping error, a reflected wave with amplitude proportional to the magnitude of the numerical diffusion is produced. A modification of the Sommerfeld radiation boundary condition to account for the linear bottom friction effect is investigated. Numerical experiments show that the use of the backward characteristics scheme with quadratic interpolation is able to reduce significantly the reflection of the wave at the outflow boundary and that the scheme is unconditionally stable.
Method to determine optimum number of knots for cubic splines
Authors: Qamar Ihtzaz
Published: August 2005

In this paper a new method has been presented to determine the optimum number of knots for cubic splines. The knot‐finding process is based on the numerical integration of the input curve. The number and the location of the knots is determined automatically. The method has been applied to a test case and the performance has been compared with two other existing methods. It is shown that fewer knots are retained for the portions of the curve having small curvature whereas a larger number of knots is retained for highly curved portions. The computer time required by our method depends only upon the number of points in the input curve and does not depend upon the shape of the curve or the desired accuracy.
Appropriate boundary conditions for FE‐modelled elastic half‐plane
Authors: Bjarnehed Hans L.
Published: August 2005

The completely adhesive contact between an FE‐modelled orthotropic half‐plane and a vertically loaded rigid flat punch is studied. Interface normal and shear‐stress distributions between the punch and half‐plane are FE‐calculated and compared for some sets of half‐plane boundary conditions frequently used in the literature for contact problems with friction. These results are compared with analytical solutions, and appropriate half‐plane boundary conditions are recommended for frictional contact problems.
Flow development in entrance region of ducts
Authors: Carvalho T. M. B. , Cotta R. M. , Mikhailov M. D.
Published: August 2005

The integral transform method is used to compute numerically the development of the velocity profile in the hydrodynamic entrance region for laminar flow inside a parallel plate channel. The results have user‐prescribed accuracy and can be used to test other numerical methods.
Corrective technique for numerical prediction of liquid flow rate in annular flow study
Authors: Tso C. P. , Sugawara S.
Published: August 2005

The computer code FIDAS‐3DT, developed by Power Reactor & Nuclear Fuel Development Corporation of Japan, has been used to solve by the finite‐difference method an air‐water horizontal annular flow problem based on two‐phase, three‐fluid and two‐component velocity modelling. In an attempt to improve the water flow rate results, as compared with those of a reported experiment, several corrections applied to the code are investigated, and the recommended technique is presented.
Mesh enrichment against mesh regeneration using quadrilateral elements
Authors: Zhu J. Z. , Hinton E. , Zienkiewicz O. C.
Published: August 2005

An adaptive refinement procedure using a new automatic quadrilateral element mesh generator is presented. The performance of the adaptive procedure in achieving a given accuracy with different mesh refinement strategies is compared. It is found that when using bilinear or biquadratic quadrilateral elements refinement strategies of both mesh enrichment and mesh regeneration can lead to a prescribed accuracy being achieved by the Zienkiewicz–Zhu adaptive procedure1 with the optimal rate of convergence. However, fewer mesh refinement steps are needed if the strategy of mesh regeneration is employed with the newly developed automatic quadrilateral element mesh generator2.
Geometrically based, automatic generator for irregular triangular networks
Authors: Henry R. F. , Walters R. A.
Published: August 2005

The network generation method described herein produces two‐dimensional irregular triangular grids in which element area is proportional to some scalar density function defined over the domain. This density function can reflect arbitrarily chosen properties of the geometry or flow. After the initial generation, various adjustment utilities and an interactive (graphic‐based) editor ensures that the resultant triangular elements are well shaped. Some of these utilities can be used with adaptive refinement schemes.
Stability analysis of three‐level difference schemes for initial‐boundary problems for multidimensional convective–diffusion equations
Authors: Kwok Yue‐Kuen , Tam Kin‐Kiu
Published: August 2005

A systematic procedure is presented to derive stability conditions for leap‐frog‐type finite‐difference schemes for the multidimensional constant‐coefficient convective‐diffusion equation. The treatise includes von Neumann stability analysis for pure initial‐value problems and matrix stability analysis for Dirichlet boundary‐value problems. Discrepancies on time‐step restriction between von Neumann stability analysis and matrix stability analysis are observed.
Some aspects in the calculation of transverse shear stresses in Mindlin plates
Authors: Canisius T. D. Gerard , Foschi Ricardo O.
Published: August 2005

Calculation of transverse shear stresses in Mindlin plates by the use of the equilibrium equations and the displacement solutions from either finite‐strip or finite‐element analyses is considered. It is shown that at least quadratic interpolation of displacements should be used for this purpose. Also, a difference in the shear stress distributions obtainable across the plate thickness under linear and geometrically nonlinear analyses is explained.
Semi‐Loof element for plate instability
Authors: Jønsson J. , Krenk S. , Damkilde L.
Published: August 2005

In the formulation of the semi‐Loof element the rotation of the tangent plane is derived from the interpolation of the transverse displacement, while the rotation of the normal is interpolated separately by another set of shape functions. The geometric stiffness matrix can be formulated by use of either of the two rotation representations. It is demonstrated that the use of the tangent plane representation in the geometric stiffness matrix is far superior to the common form at present.
Generalized finite‐differences solution of 3D elliptical problems involving Neumann boundary conditions
Authors: Pennati V. , Corti S.
Published: August 2005

A method is presented for the solution of elliptical problems defined on general‐shape multiconnected three‐dimensional domains approximated by means of polyhedra. The boundary conditions may be of the Neumann type. The differential operator and the normal derivative are discretized by generalized finite‐difference (GFD) methods using an orthogonal non‐uniform Cartesian grid. The convergence properties are analysed and the solutions of some Poisson and biharmonic problem are presented.
Heuristic optimization of a laminated composite plate and its comparison with a minimization method
Authors: Morton S. K. , Webber J. P. H.
Published: August 2005

A heuristic optimization design methodology based on redesign rules for composite laminated plates is presented. It is modelled on the cyclic approach to the design process observed in designers of structural components using composites. In comparison with a simple weight minimization algorithm it gives quasioptimal ply thicknesses, but takes under ten iterations. It is thereby shown to be most suitable for initial design studies. Multiaxial combinations of in‐plane loads and bending moments are considered in the design procedure.
Method of iterative linearization to solve non‐linear stochastic vibration problems
Authors: Gao Shiqiao , Niemann H.‐J.
Published: August 2005

In this paper, an iterative method of statistic linearization (IMSL) is presented to solve non‐linear stochastic vibration equations. This method represents an improvement over the classical linearization method. The method uses the solution of the corresponding linear vibration equation as an initial value in an iterative procedure. To obtain information about essential statistical average values, the method uses a ‘boot‐strapping’ procedure, which defines a pseudorandom process based on the statistical characteristics of the linear solution and then uses samples from the process to estimate them. For Gaussian input excitation, the statistical average values are obtained by theoretical analysis.
Higher‐order singular isoparametric elements for crack problems
Authors: Horváth Ágnes
Published: August 2005

Standard isoparametric finite elements can be used as singular crack‐tip elements in fracture mechanical computations by placing the middle nodes in the neighbourhood of the crack tip. Such elements have already been applied to several plane and three‐dimensional problems, so this method can be considered as commonly well accepted. The paper shows that singularity of order r(1 − m)/m is obtained with an nth‐order isoparametric element.
Unconditionally stable FEM for transient linear heat conduction analysis
Authors: Qin Q. H.
Published: August 2005

The paper presents a new method for the numerical solution of transient linear heat conduction problems. In the proposed method, the transient linear heat conduction equation is first integrated with respect to time over subsequent intervals. Then the resulting set of elliptic equations is discretized in space according to a finite‐element procedure. The method is unconditionally stable. At the end of the paper, the effectiveness of the proposed method is assessed through some numerical examples.