bluuebunny/crossref_metadata_2025 huggingface dataset:
2‐D transient interior flux by time‐domain boundary‐element method
Authors: Israil A. S. M. , Banerjee P. K.
Published: August 2005

In this paper, interior flux calculations for two‐dimensional transient scalar wave propagation are developed and presented for the first time in the BEM literature. There are some severe analytical difficulties in the derivation of these kernels which have been circumvented through physical interpretation. Moreover, an apparent singularity at the wave‐front of these kernels has been reduced to an integrable one through some convenient condensation. These kernels have been implemented in the time‐domain BEM algorithm with linear temporal variation and quadratic spatial variation for the field variables. Some numerical examples are presented to demonstrate the accuracy of the implementation.
Strategies for large scale structural problems on high‐performance computers
Authors: Noor Ahmed K. , Peters Jeanne M.
Published: August 2005

Novel computational strategies are presented for the analysis of large and complex structures. The strategies are based on generating the response of the complex structure using large perturbations from that of a simpler model, associated with a simpler structure (or a simpler mathematical/discrete model of the original structure). Numerical examples are presented to demonstrate the effectiveness of the strategies developed.
The extension boundary‐element method for 2‐D potential problems
Authors: Yihua Yan , Huli Shi
Published: August 2005

In the paper, a new BE formulation is introduced so that we can adopt nearby adjacent nodes to improve the trial functions on each boundary element. The extension element approximation is derived and implemented, and the accuracy of the solution is, therefore, raised without increasing the total number of nodes (or the dimension of the system). The proposed method preserves all the advantages of conventional BEM. Furthermore, it may improve the higher‐order variations. Numerical examples demonstrate the validity and prospect of the extension‐BEM (EBEM).
Unified numerical treatment of hyperelastic and rubber‐like constitutive laws
Authors: Gadala M. S.
Published: August 2005

A unified numerical treatment for handling various forms of constitutive relations for hyperelastic and rubber‐like materials is presented. A general form for the stress and the constitutive tensors is derived. The form requires the calculation of certain tensors and matrices which are presented. Application examples are given for generalized Mooney–Rivlin, generalized Mooney–Rivlin with modified invariants, Swanson, Blatz‐Ko and Hart‐Smith constitutive models.
Defining residual stresses by applying the fem
Authors: Flašker Joze , Aberšek Boris
Published: August 2005

This paper deals with the influence of residual stresses on the total value of loading for calculation of the stresses of a gear. We develop a computer program RESMET which serves as a pre‐processor, calculates the residual stresses by the application of different FE programs or can be used in simple cases as an independent program. The results obtained by RESMET are in good agreement with those obtained by the experiments.
Grid control for non‐orthogonal elliptic grids
Authors: Vreugdenhil C. B.
Published: August 2005

A relation is given between grid properties such as grid angle and aspect ratio and the metric coefficients of the transformation from the physical to the computational domain. A transformation is proposed in which these grid properties occur explicitly, such that the resulting grid will have the required grid angle and aspect ratio. This leads to an elliptic grid‐generation procedure with non‐linear coefficients. Some examples are given which illustrate that the properties can be predicted.
Padé and upwinding finite difference schemes for the quantum mechanical equation of motion
Authors: Kwok Yue‐Kuen , Barthez Daniel
Published: August 2005

A systematic approach is presented to search for a two‐level six‐point finite difference of Padé type for the numerical solution of the quantum mechanical equation of motion. A family of second order accurate Pade schemes is obtained and the stability properties are analysed by the von Neumann and matrix methods. Also, a similar stability analysis is also performed for a family of two‐level first order accurate upwinding difference schemes by the von Neumann and matrix methods. Discrepancies between the stability results obtained by the von Neumann and matrix methods are observed.
Numerical methods applicable to laser refraction through a caustic
Authors: Pearson Carl E. , Christiansen Walter H.
Published: August 2005

Numerical computation of laser beam refraction may involve difficulties associated with ray paths through a caustic, where first‐order amplitude values become infinite. We choose the special test case of a stratified gas, and compare the results obtained by numerical integration of the ray differential equations with both asymptotic results and direct numerical solution of the exact wave equation. A final section evaluates the numerical solution of a parabolic approximation to the Helmholtz equation, with particular reference to the effect of the caustic. The final conclusion is that, with appropriate safeguards, any of these methods can effectively deal with the presence of a caustic surface.
A subspace iteration for eigenvector derivatives
Authors: Ting T.
Published: August 2005

An iterative procedure for calculating eigenvector derivatives has been developed based on the subspace iteration concept. The basic formulation is derived directly from the first variation of the resulting equations of subspace iteration for solving eigenvalue problems. Since the basic formulation conserves the convergence properties of the original subspace iteration for eigen‐problems, an overrelaxation scheme similar to Bathe's approach is employed to accelerate the subspace iteration process for calculating eigenvector derivatives.
An auxiliary equation method for obtaining superconvergent finite‐element approximations
Authors: Johnson Richard W. , MacKinnon Robert J.
Published: August 2005

A finite‐element method is developed which improves accuracy and yields superconvergent approximations to two‐dimensional elliptic boundary‐value problems on a union of square bilinear elements. This method employs an auxiliary equation which is derived using a Taylor series analysis on the discrete formula obtained from a Galerkin finite‐element formulation. Application of the finite‐element method to the auxiliary equation results in O(h4) convergence for problems with constant coefficients and improved accuracy for problems with variable coefficients. Supporting numerical examples are given.
Cubic spline technique for solution of Burgers' equation with a semi‐linear boundary condition
Authors: Jain P. C. , Shankar Rama , Singh T. V.
Published: August 2005

By using the splitting‐up technique and cubic spline method, numerical solutions of Burgers' equation ut = uxx + ϵuux, 0 < x < 1, t > 0 and u(x, 0) known, are obtained constructively by taking either of the two pairs of the semi‐linear boundary conditions: (i) u(0, t) = 0, ux(1, t) = aup(1, t), t > 0; (ii) u(1, t) = 0, ux(0, t), = ‐ aup(0, t), where 0 < p < ∞. The stability analysis of the proposed method is discussed.
Adaptive mesh refinement for faceted shells
Authors: Bonet J. , Pica A. , Peiró J. , Wood R. D.
Published: August 2005

The application of the Zienkiewicz and Zhu error estimator to three‐dimensional faceted shells presents some difficulties which arise from the lack of C1 continuity of the geometry. This paper presents a method to circumvent such difficulties based on the existence of a mapping from a flat reference configuration to the actual shell. This mapping is used not only to enable meshes to be generated in a two‐dimensional space, but also to define a stress measure – similar to the first Piola–Kirchhoff stress used in large deformation mechanics – which can be consistently smoothed over the reference configuration. A preliminary investigation of the method is provided by three simple examples.
Exploiting the physical symmetry of regular mesh in substructuring analysis
Authors: Lam Y. C. , Xiao‐Lin Liu
Published: August 2005

A new technique of multi‐level substructuring based on a regular mesh is presented. The technique takes advantage of the physical symmetry and repetitivity generated by the regular mesh. A special node‐numbering/addressing system is developed to exploit the symmetry which results in the stiffness matrices not only being symmetrical about the leading diagonal, but a regular pattern emerging with respect to the other diagonal. The same pattern exists for their inverses. A new condensation scheme is used to take full advantage of the regular patterns. As a result, only about a quarter of the stiffness matrices and their inverses need to be processed, as compared to half when using the conventional method.

Based on the technique, a two‐dimensional finite‐element analysis program FEMSUB has been implemented in the University's VAX network. Through a number of numerical tests, it is discovered that the new technique can result in savings of both core storage and computing time. The savings become more significant when the scale of a problem increases. The investigation indicates that the core storage requirement decreases when using substructures of higher levels. However, for computational efficiency, both the level of substructuring and the number of repeated substructures have an effect. Thus, a dimensionless parameter R (number of substructures used/maximum number of substructures) has been introduced to correlate the effect of the technique on computational efficiency.
A mapping of multi‐level problems to multi‐dimensional crossbar networks
Authors: Kolp Otto
Published: August 2005

Mappings are discussed from m‐dimensional process spaces to n‐dimensional crossbar networks which preserve the nearest‐neighbour relation between processes, i.e. neighboured processes are mapped to processors connected by a common crossbar. Even in the case of multi‐level process structures, a neighbouring relation between processes can be derived such that the neighboured processes can communicate directly.
Fast adaptive composite grid methods on distributed parallel achitectures
Authors: Lemke Max , Quinlan Daniel
Published: August 2005

The fast adaptive composite grid method (FAC) is an algorithm that uses uniform grids, both global and local, to solve partial differential equations. This method is known to be highly efficient on scalar or singe‐processor vector computers, due to its effective use of uniform grids and multiple levels of resolution of the solution. On distributed memory multiprocesssors, such methods benefit from their tendency to create multiple isolated refinement regions, which may be effectively treated in parallel. However, they suffer from the way in which the levels of refinement are treated sequentially in each region. Specifically, the finer levels must wait to be processed until the coarse‐level approximations have been computed and passed to them; conversely, the coarser levels must wait until the finer level approximations have been computed and used to correct their equations.

The asynchronous fast adaptive composite method (AFAC) eliminates this bottleneck of parallelism. Through a simple mechanism used to reduce interlevel dependence, individual refinements levels can be processed by AFAC in parallel. The result is that the convergence rate of AFAC is the square root of that for FAC. Therefore, since both AFAc and FAC have roughly the same number of floating‐point operations, AFAC requires twice the serial computational time as FAC, but AFAC, may be much more efficiently parallelized.

This paper presents a comparison of FAC and AFAC under a variety of conditions, including vectorization and parallelization. Results are presented for distributed memory multiprocessor architectures (SUPRENUM, Intel iPSC/2 and iPSC/860). The most crucial factor for the evaluation of both algorithms is the different computation/communication cost ratios of these architectures. It is shown that, under many circumstances, AFAC is superior to FAC in a parallel environment.
An efficient multigrid scheme for elliptic equations with discontinuous coefficients
Authors: Liu C. , Liu Z. , McCormick S.
Published: August 2005

An efficient multigrid scheme for elliptic equations with jump discontinuous coefficients is presented. It is based on a cell‐centred grid and finite‐volume method, with the diffusion coefficients at the jump interface being determined by a flux conservation condition. The diffusion coefficients on coarse grids are calculated by a simple restriction of the coefficients from the fine grid. An efficient interpolation operator, which is constructed by the so‐called effective area law, is developed. Computational results for a two‐dimensional scalar elliptic equation and for two‐phase porous media flow show that the new scheme achieves multigrid efficiency typical of the constant‐coefficient case.
Resolution of moving fronts using the self‐adaptive time‐dependent fast adaptive composite grid method
Authors: McKay S. M. , Thomas J. W.
Published: August 2005

The fast adaptive composite grid method (FAC) is a discretization and solution method design to achieve efficient local resolution by constructing the discretization based on various regular grids and using these grids as a basis for fast solution. FAC is designed so as to share all of the attributes of the composite grid and multigrid methods. As is the case for most mesh refinement schemes, it is advantageous to optimally choose the grids so as to save both storage and computational costs. The FAC method has previously been shown to be an effective tool in obtaining numerical solutions of many types of steady problems. In addition time‐dependent problems with stationary fronts or singularities have also been resolved efficiently with FAC. An adaptive scheme has been developed and implemented that, based on given error tolerances, calculates the optimal time discretization and locates the spatial regions where more resolution is needed. Patches are set up to be used by the various FAC algorithms. The spatial refinement scheme is able to track areas of resolution which move across the domain, allowing for small composite grids at each time step.
Numerical investigation of convection/diffusion phase change of a metal with temperature‐dependent viscosity
Authors: Esikova N. B. , Iliev O. P. , Vabishchevich P. N.
Published: August 2005

Heat and mass transfer during crystallization in a square cavity, involving natural laminary convection of liquid metal with temperature‐dependent viscosity, are investigated numerically on a grid with 51 × 51 nodes. A brief survey of existing techniques for convection/diffusion phase change problems is given. A fixed grid numerical methodology, based on the fictitious regions method, is used for solving the 2‐D Stefan problem coupled with the Navier–Stokes equations in the Boussinesq approximation. The viscosity variation is modelled by an exponential form, ν/ν0 = exp ( – α(T – 1)). The influence of the Grashof number and of the parameter α on heat and mass transfer are investigated.
A higher‐order accurate Petrov–Galerkin finite‐element method for elliptic boundary‐value problems
Authors: MacKinnon R. J. , Johnson R. W. , Langerman M. A.
Published: August 2005

We formulate a higher‐order (superconvergent) Petrov–Galerkin method by determining, using a finite‐difference approximation, the optimal selection of quadratic and cubic modifications to the standard linear test function for bilinear elements. Application of this method to linear elliptic problems results in improved accuracy and higher rates of convergence for problems with constant coefficients and improved accuracy for problems with variable coefficients. Supporting numerical examples are given.
Compressible duct flow of a real gas in a Lagrangian frame
Authors: Glaister P.
Published: August 2005

An approximate Riemann solver is presented for the compressible flow equations with a general (convex) equation of state in a duct of variable cross‐section and within a Lagrangian frame of reference. The scheme is applied to a well‐known shock tube problem.
Generalized conforming triangular elements for plate bending
Authors: Zhifei Long
Published: August 2005

Based on the modified principle of potential energy, three triangular thin‐plate elements with nine degrees of freedom (LZ1, LZ2 and LZ3) are derived by using compatibility conditions for nodal deflection at each node and generalized compatibility conditions for average deflection and average normal slope along each side of the element. These generalized conforming elements are low‐order and high‐precision elements which pass the patch test. When overall considerations of accuracy, simplicity and reliability are taken into account, these new elements are the best 9‐DOF triangular thin‐plate elements currently available.
Modified Lanczos method for solving large sparse linear systems
Authors: Mai Tsun‐Zee
Published: August 2005

Generalized conjugate gradient methods are often used to solve large sparse non‐symmetric linear systems. Such systems often arise in the numerical solution of convection–diffusion problems. The Lanczos/Orthodir method proposed by Jea and Young suffers the roundoff error problem. In this paper a modified Lanczos/Orthodir method is considered. The modifications are based on Paige's computational procedure and on the adaptive restarting procedure. Numerical results showed that the modified Lanczos/Orthodir method is more stable than the original version. Furthermore, with the adaptive restarting scheme the method performed much better than the Lanczos/Orthomin method.
Crack propagation in tooth root with variable loading
Authors: Flašker Jože , Pehan Stanislav
Published: August 2005

The paper describes the numerical method for calculating the crack propagation in the tooth root of a case‐hardened and hardened gear. The method is based on the linear elastic fracture mechanics taking into account the total values of loadings and properties of the individual layers of the gear material. The main points are the determination of the stress intensity factor and the numerical calculations of the crack propagation, crack speed and path1.
A boundary‐element method for the solution of a class of time‐dependent problems for inhomogeneous media
Authors: Clements David L. , Larsson Ashley
Published: August 2005

A boundary‐element method is derived for determining the anti‐plane displacement and stress in an inhomogeneous elastic material subjected to a time‐dependent load.
A comparison of TVD Lax–Wendroff methods
Authors: Rider William J.
Published: August 2005

This paper compares two formulations of Lax–Wendroff TVD methods. The basis of comparison is to the results of several test problems providing both qualitative and quantitative results. Results show that using an upwind biased limiter provides higher resolution of both smooth and discontinuous solutions from a lower amount of induced numerical viscosity. The conclusion is that a limiter should have as small a support as possible in order to limit its effects if high resolution is the object.
On a numerical solution of a class of partial differential equations of mixed type, not adding artificial terms
Authors: Pogu M. , De Cursi J. E. Souza
Published: August 2005

A relaxation‐like method for the numerical solution of a class of partial differential equations of mixed type is presented. The equations of this class have not yet been solved by functional outlines. The numerical method does not add artificial terms to the original equation.
How to deal with hypersingular integrals in the symmetric BEM
Authors: Holzer S.
Published: August 2005

The symmetric boundary‐element method for mixed boundary‐value problems is currently gaining increasing interest as it permits the derivation of symmetric matrices. It is even possible to obtain positive‐definite finite‐element stiffness matrices for BEM subregions, and therefore the method provides a very straightforward coupling to the finite‐element method (FEM). The BEM subregions can be handled like FEM substructures in a domain decomposition context. The symmetric BEM uses the full set of integral representations for the 2n types of boundary data for self‐adjoint problems of order 2n and solves them in a weighted residual (Galerkin) sense. The main difficulty of the method is caused by the need to compute hypersingular integrals arising from the integral representations of the Neumann boundary data. It is the object of the paper to show that, for 2‐D problems on polygonal domains, these hypersingular integrands pose no problem at all, even for higher‐order approximations. The present approach makes use of analytical integrations as far as possible. The integrals of the hypersingular expressions are derived completely within the framework of simple engineering mathematics. The problem is reduced to the computation of weakly singular integrals even for C0 continuous approximations.
Self‐adaptive finite‐element simulation of bipolar, strongly reverse‐biased pn‐junctions
Authors: Kornhuber Ralf , Roitzsch Rainer
Published: August 2005

The potential distribution of bipolar, strongly reverse‐biased pn‐junctions can be described by a double obstacle problem for the Laplacian. The problem is solved by a self‐adaptive finite‐element method involving automatic termination criteria for the iterative solver, local error estimation and local mesh refinement. Special attention is paid to the efficient resolution of the geometries typically arising in semiconductor device simulation. The algorithm is applied to a reverse‐biased pn‐junction with multistep field plate and stop electrode to illustrate its efficiency and reliability.
A simple local error estimator and an adaptive time‐stepping procedure for direct integration method in dynamic analysis
Authors: Li X. D. , Zeng L. F. , Wiberg N.‐E.
Published: August 2005

A simple a posteriori local error estimator for time discretization in structural dynamic analysis is presented. It is derived from the difference of the solutions between an ordinary integration method (the Newmark scheme) and another higher‐order one which assumes that the derivatives of accelerations vary linearly within each time step. It may be obtained directly without resolving new equations, so the additional computational cost is small and the implementation is convenient. Furthermore, it is shown that this error estimator may also be obtained by Taylor expansion or by a post‐processing technique. Accordingly, an adaptive time‐stepping procedure, which automatically adjusts the time‐step size so that the local error at each time step is within a prescribed accuracy, is described. Numerical examples, including two single‐DOF problems, a two‐DOF problem and a multi‐DOF model, are presented. The results show that the presented local error estimator is simple, reliable and accurate.
Numerical solution of Burger's equation
Authors: Mittal R. C. , Singhal Poonam
Published: August 2005

In the present paper numerical solutions of the one‐dimensional Burger equation are obtained. The technique of finitely reproducing non‐linearities introduced by Bazley is used. This technique when applied to Burger's equation gives a method where a system of non‐linear ordinary differential equations is to be solved. The present method produces very accurate results in comparison to finite‐difference of finite‐element methods.
Standard eigenvalue analysis by boundary‐element method
Authors: Kamiya N. , Andoh E.
Published: August 2005

A method for analysing eigenvalues of the Helmholtz equation using a standard existing subroutine for eigenvalue determination is developed in this paper. It is based on the boundary integral equation formulation known as the multiple reciprocity method (MRM). The above‐mentioned formulation, having polynomial matrices in terms of the eigenvalue as the coefficient matrices, is transformed into the standard‐type eigenvalue problem. The resulting formulation makes it possible to determine the required eigenvalues only by boundary discretisation without any initial rough estimation.
A posteriori error bounds for numerical solutions of regularized compressible flow problems
Authors: Niijima Koichi
Published: August 2005

We give a posteriori error bounds for numerical solutions of regularized compressible flow problems. To verify the efficiency of our method, numerical experiments are performed.
Trefftz‐like numerical method for linear boundary‐value problems
Authors: Khokhlov A. V.
Published: August 2005

A generalized Trefftz method for solution of linear boundary‐value problems for partial differential equation sets is presented. An approximate solution is constructed as a linear combination of basis functions satisfying the differential equations involved and forming a complete sequence. Unknown factors are determined through minimizing some norm of the approximate solution boundary‐value deviation from the current boundary data. A unified formulation constitutes the foundation for various modifications and particular applications.

The approach enables one to: reduce the problem geometrical dimensionality by one; construct a smooth approximate solution satisfying the governing differential equation; use a universal set of approximating functions for problems with identical equations and varying in boundary conditions; develop a closed, semi‐analytical computational algorithm requiring small input and producing extremely high output accuracy; obtain approximate solution error bounds in inner points via its deviation from prescribed values on the boundary and easily control the degree of accuracy of the numerical results by the residual values at boundary points; treat solution singularities caused by singular boundary conditions precisely.

The technique developed has proved to be effective in fluid mechanics, elastostatics, Saint‐Venant's theory for torsion and bending prisms, potential and elastic plate bending problems.
Efficient three‐dimensional model of rolling using an explicit finite‐element formulation
Authors: Edberg Jonas , Lindgren Lars‐Erik
Published: August 2005

Rolling is simulated by a three‐dimensional finite‐element model with elastoplastic constitutive equations. The use of an explicit finite‐element formulation, instead of the more commonly used implicit formulation, has reduced the required computing time. The larger of the models used is one step towards a general and complete computational model of rolling. Results from experiments and from two‐ and three‐dimensional calculations are compared.
Simple curved shear beam elements
Authors: Choi Jong Keun , Lim Jang Keun
Published: August 2005

We have developed two curved beam elements with two nodes, CSCC and CSLC, based on Timoshenko's beam theory and the curvilinear co‐ordinate system. These curved beam elements have been modified from the conventional strain element, which has been applied only to Euler beam analysis. Therefore they do not have any spurious constraints and locking characteristics. They also show rapid and stable convergence on the wide ranges of beam length to height ratio for linear and non‐linear analyses.
Some remarks on post‐processing and negative norm estimates for approximations to non‐smooth solutions of hyperbolic equations
Authors: Bales Laurence A.
Published: August 2005

Some formulae and an error estimate for post‐processing approximations to solutions of hyperbolic partial differential equations are derived. The post‐processing is applied to a fully discrete approximation of the discontinuous solution of an initial boundary‐value problem for the wave equation in one space dimension to reduce oscillations and construct a much more accurate approximation to the solution.
Application of iterative global/local finite‐element analysis. Part 1: Linear analysis
Authors: Whitcomb John D. , Woo Kyeongsik
Published: August 2005

Iterative global/local finite‐element stress analysis was used to perform linear analysis of two configurations with local damage. One was a tubular joint with local debonding; the other was a fibre matrix unit cell with debonding along part of the interface. The global/local procedure was shown to be both accurate and efficient for both configurations.
BEM analysis of reduced dynamic stress concentration by multiple holes
Authors: Providakis C. P. , Sotiropoulos D. A. , Beskos D. E.
Published: August 2005

The reduction of stress concentration around a circular hole in a dynamically loaded plate by introducing auxiliary holes around the original hole is studied numerically. The solution of this plane stress problem is carried out in the Laplace transformed domain with the aid of the boundary‐element method, and subsequently the time domain response is obtained by numerically inverting the transformed solution. Numerical examples are presented which demonstrate a stress reduction as high as 18 per pent by the introduction of two auxiliary holes in the loading direction for the uniaxial case.
Numerical procedure for calculation of temperature evolution in composite elements with internal cavities
Authors: Luyckx P. , Stienon P. , Franssen J‐M. , Dotreppe J‐C. , Hogge M.
Published: August 2005

In the paper a computation code based on the finite‐element method for temperature evolutions in composite elements with internal cavities is presented. It is suitable for the analysis of various thermal problems encountered in mechanical and civil engineering such as fire risk assessment. It is based on a plane isoparametric triangular element with six nodes allowing the modelling of curved boundaries. In order to analyse composite steel‐concrete elements and to take into account the non‐linearities coming from the temperature‐dependent material properties and from the boundary conditions, an implicit integration scheme is used. Another advantage of the program is the possibility of describing internal cavities with convection and radiation exchanges. In order to show the capacity of the program two examples are presented. Comparisons have been made with experimental and other numerical results, exhibiting very good agreement.
Criteria for eliminating oscillation in analysis of heat‐conduction equation by finite‐element method
Authors: Ouyang Huajiang , Xiao Ding
Published: August 2005

In finite‐element analysis of transient heat conduction, oscillatory results are quite common. Several criteria for eliminating oscillation which permit choice of time step length and/or element mesh and type are sensibly derived and proved with a different methodology from those of previous work. Numerical examples are presented to show their validity and usefulness.
Direct simulation of turbulent flow and heat transfer in a channel. Part II: A Green's function technique for wavy walls
Authors: Rutledge J. , Sleicher C. A.
Published: August 2005

The possibility of improving heat transfer rates by the imposition of a wavy boundary led to this extension of direct simulation of heat transfer in turbulent flow in a channel. This part of the paper shows how a pattern of micro‐riblets on the surface and parallel to the flow is incorporated into the solution of the Navier‐Stokes and temperature equations. The channel is two‐dimensional with walls at different but uniform temperatures, and the fluid properties are constant. The presence of the patterns presents a considerable computational problem that can be largely overcome by the use of a discrete Green function technique. The method is illustrated by making short‐time calculations of the velocity and temperature fields for a Prandtl number of 0.72, a Reynolds number based on channel half‐width and bulk velocity of 2800, and a sinusoidal pattern with a height of 5 wall units.
Numerical procedure for thermal creep stress in mass concrete structures
Authors: Du Chongjiang , Liu Guangting
Published: August 2005

In the paper the experimental results considering the effects of temperature on the elastic modulus and creep of concrete are introduced into the mathematical models of the three‐dimensional finite‐element method to improve the calculation of creep stresses in mass concrete structures. The finite‐element implementation of the exponential algorithm for concrete creep at variable temperatures is studied. The numerical solution procedure for thermal creep stresses in mass concrete structures with temperature effects is presented and a three‐dimensional finite‐element program is developed.
On the stabilization of the rectangular 4‐node quadrilateral element
Authors: Hueck U. , Reddy B. D. , Wriggers P.
Published: August 2005

The standard bilinear displacement field of the plane linear elastic rectangular 4‐node quadrilateral element is enhanced by incompatible modes. The resulting gradient operators are separated into constant and linear parts corresponding to underintegration and stabilization of the element stiffness matrix. Minimization of potential energy is used to generate exact analytical expressions for the hourglass stabilization of the rectangle. The stabilized element is shown to coincide with the element obtained by the mixed assumed strain method.
The unimportance of the spurious root of time integration algorithms for structural dynamics
Authors: Hulbert G. M. , Chung J.
Published: August 2005

Most commonly used second‐order‐accurate, dissipative time integration algorithms for structural dynamics possess a spurious root. For an algorithm to be accurate, it has been suggested that the spurious root must be small and ideally be zero in the low‐frequency limit. In the paper we show that good accuracy can be achieved even if the spurious root does not tend towards zero in the low‐frequency limit. This permits more flexibility in the design of time integration algorithms. As an example, we present an algorithm that has greater accuracy than several other dissipative algorithms even though for all frequencies its spurious root is non‐zero. We also show that the degraded performance of the Bazzi‐ρ algorithm is not due to its non‐zero spurious root.
Derivation of shape functions for an exact 4‐D.O.F. Timoshenko beam element
Authors: Eisenberger Moshe
Published: August 2005

Timoshenko beam elements have been the subject of numerous publications. The difficulty was that of arriving at a superconvergent element with four degrees of freedom, as is the case for the Bernuli‐Euler classical beam element. Two different approaches are presented here for the derivation of the shape functions. The first is based on the flexibility matrix, where utilizing the unit load method, including the term that accounts for the shear deformations in the virtual work expression, the stiffness matrix is derived. Then, a second method is presented to derive the exact shape functions, directly from the differential equations of the Timoshenko beam theory. The resulting shape functions are the same in both methods.
Convergence of stress maxima in finite element computations
Authors: Yosibash Zohar , Szabó Barna A.
Published: August 2005

The convergence of stress maxima, computed directly from finite element solutions, is investigated with respect to a family of exact solutions characterized by varying degrees of smoothness. The performances of h‐ and p‐extensions and the product and trunk spaces are evaluated and documented with respect to a family of benchmark problems. In uniform p‐extensions a characteristic pattern in the convergence of stress maxima was observed. There does not appear to be a clear‐cut advantage of the product space over the trunk space in this respect. The much faster convergence of stress maxima in the case of p‐extensions, as compared with h‐extensions, is evident from the results.
Enhanced 8‐node three‐dimensional solid and 4‐node shell elements with incompatible generalized displacements
Authors: Slavković Radovan , Živković Miroslav , Kojić Miloš
Published: August 2005

Enhanced 8‐node three‐dimensional solid and 4‐node shell elements are proposed in the paper. Improvement of the response of the 3‐D solid is achieved through additional strains corresponding to generalized displacements incompatible between elements. In the case of the 4‐node shell, the membrane behaviour is improved through addition of incompatible membrane strains.

Some linear and geometrically non‐linear examples demonstrate significant improvements of the elements. Results are compared with solutions obtained with the standard, displacement‐based elements and with results available in the literature.
A three‐dimensional symmetric linear equation solver
Authors: Gravvanis George A.
Published: August 2005

Factorization procedures for the efficient solution of large sparse linear finite difference systems have been introduced recently. In these procedures the large sparse symmetric coefficient matrix of a certain structure is factorized exactly, yielding a direct solution method. Furthermore, approximate factorization procedures yeild implicit preconditioning iterative methods for the finite difference solution. The numerical implementation of these algorithms is presented and Fortran subroutines for the efficient solution of the resulting sparse symmetric linear system of algebraic equations are given.
Note on finite element predictions of natural frequencies
Authors: Wood W. L.
Published: August 2005

It is well known that the finite element discretization with a distributed mass matrix gives overstimates of the natural frequencies of a system. The note shows that these do not necessarily become progressively worse as the frequency increases.
Discretization error dominance over subgrid terms in large eddy simulation of compressible shear layers in 2D
Authors: Vreman Bert , Geurts Bernard , Kuerten Hans
Published: August 2005

Second‐ and fourth‐order‐accurate spatial discretization methods give rise to discretization errors which are large than the corresponding subgrid terms in large eddy simulation of compressible shear layers in 2D, if the ratio between the filter width and the grid spacing is close to one. Even if an exact representation for the subgrid‐scale contributions is assumed, large eddy simulation is accurate only if this ratio is sufficiently larger than one. In that regime fourth‐order methods are more accurate than second‐order methods. An analysis of the data obtained from two‐dimensional direct numerical simulations of compressible shear layers substantiates these assertions.
Influence of contact area on service life of gears with crack in tooth root
Authors: Flašker J. , Glodež S. , Pehan S.
Published: August 2005

The paper describes the influence of contact area on the service life of dynamically loaded gears with a crack in a tooth root. Numerical results obtained with the finite element method using the program package BERSAFE are compared with the experimental results obtained on the universal testing machine INSTRON 1255. Numerical and experimental results are in good agreement. The analysis shows that the contact area directly influences the speed and direction of the crack propagation and the service life of the gear with a crack in a tooth root.
A numerical solution for dynamic interaction between rigid wheel and flexible beam
Authors: Lee Kisu
Published: August 2005

A numerical method is presented for the analysis of dynamic interaction between rigid wheel and flexible beam. In contrast to traditional approaches, the wheel nominal motion as well as the contact force are considered here as unknowns. The correct contact force between the wheel and the beam is computed by iteratively reducing the constraint error towards zero, and a simple time integration is employed for the solution of equations of motion. Convergence of the iterative scheme is analysed, and numerical simulations are conducted to demonstrate the accuracy of the solution.
On the eigenvalues basic to the analytical solution of convective heat transfer with axial diffusion effects
Authors: Oliveira M. C. , Ramos R. , Cotta R. M.
Published: August 2005

The integral transform method is employed in the analytical solution of the non‐classical eigenvalue problem that appears in connection with the analysis of forced convection in ducts, including the effect of fluid heat diffusion in the axial direction. The related eigenfunctions are expanded in terms of eigenfunctions from a simpler auxiliary eigenvalue problem, and the original eigenvalues are determined from the associated matrix eigensystem analysis. Convergence rates of the proposed solutions are illustrated and reference results established for different values of the governing parameters.
Permanent heavy waves in circular‐shaped channels
Authors: Moussa Nabil
Published: August 2005

Because of the earth's curvature, all existing channels have a curvature. E. Zeidler gave an existence and uniqueness proof for permanent heavy and capillar‐heavy waves in such circular shaped channels. Based on this proof and on a general computational method for constructing the solutions numerically, the case of permanent heavy waves in circular‐shaped channels is considered in this work.
On a novel mesh for the regular boundary layers arising in advection‐dominated transport in two dimensions
Authors: Hegarty Alan F. , Miller John J. H. , O'riordan Eugene , Shishkin G. I.
Published: August 2005

Upwind finite difference operators on uniform meshes are well known to be unsuitable for the numerical solution of singularly perturbed partial differential equations, in the sense that, in the neighbourhood of the boundary layers, the error in the numerical approximation may increase as the mesh is refined. Recently, on the other hand, it has been predicted theoretically that the use of upwind finite difference operators on specially designed piecewise uniform meshes guarantees the decrease of the nodal error to zero as the number of mesh elements increases. In the paper the general theorem is quoted and its prediction is validated by numerical experiment for a specific linear advection‐dominated transport equation in two dimensions. Experimental values of the convergence rate are obtained, which also agree with the theoretical estimates.
Generalized Laplacian smoothing of unstructured grids
Authors: Hansbo Peter
Published: August 2005

In this note we point out the natural choice of smoothing by use of a metric tensor to maintain control of the local element stretch. The extension to grids on surfaces in 3D is straightforward. Numerical examples are given.
Similarity of stiffness and mass matrices in plate bending elements
Authors: Krishnan A. , Krishnadasan C. K.
Published: August 2005

It has been noticed that the stiffness and mass matrices of a triangular plate bending element can be generated from the known stiffness and mass matrices of a similar triangular element making use of scaling matrices. This could be used to advantage in solving problems involving large degrees of freedom if the structure could be discretized into similar triangles. The idea is extended to study the free vibration of a square plate clamped on all edges with a square central cutout.
Dynamic stiffness matrix for variable cross‐section Timoshenko beams
Authors: Eisenberger Moshe
Published: August 2005

The Timoshenko beam model incorporates the effect of shear deformations and rotary inertia in the vibration response of beams. For constant cross‐section beams it was shown that the effect is dependent on the aspect ratio of the beams, and for beams with large ratio the effect is small. In this work exact vibration frequencies for variable cross‐section beams are found using the dynamic stiffness matrix approach. An example is given and compared with known results of beams with various taper ratios.
Non‐linear Wilson's brick element for finite elastic deformations of three‐dimensional solids
Authors: Ibrahimbegović Adnan , Kožar Ivica
Published: August 2005

A geometrically non‐linear version of the well known 8‐node Wilson brick element is presented. The element is based on a sound variational formulation and the modified method of incompatible modes, which are shown to render quite a satisfying, locking‐free performance in some challenging large displacement problems.
The new variational problem in three‐dimensional eddy‐current field computation
Authors: Jian Huang , Bangding Tan , Jihui Yu , Mingzhong Rao
Published: August 2005

A new variational problem corresponding to a three‐dimensional eddy‐current boundary‐value problem is treated in the paper. The equivalence between the variational problem and the boundary‐value problem is proved, and so is the uniqueness of the solution. These form the foundation of the H ‐ Ψ method.
Closed‐form derivation of an 8‐node hexahedral element stiffness matrix by the hybrid stress method
Authors: Saether Erik
Published: August 2005

A general methodology for deriving explicit element stiffness matrices in hybrid stress formulations has recently been developed by the author. The technique utilizes special stress field transformations to eliminate the complementary energy matrix inherent to hybrid formulations, thus simplifying the stiffness definition such that an explicit evaluation can be accomplished. The elimination of numerical integration and matrix inversion results in a substantial decrease in computational cost. The methodology is applied to derive explicit algebraic expressions for the Pian‐Tong hexahedral element stiffness matrix.
A statistical mechanical model of solidification
Authors: Yang Y. S. , Blake N. , Abbott T. B. , McCarthy J. F.
Published: August 2005

A model of solidification is developed from a statistical mechanics basis that incorporates nucleation of columnar and equiaxed grains, thermal and solute diffusion, and latent heat of the phase change. The model is applied to the solidification of austenitic steel. The dendritic growth of columnar and equiaxed grains is simulated, including the segregation of solute ahead of the solid‐liquid interface. The irregular branched morphology of the solid forms in a manner analogous to dendritic morphologies that arise from constitutional undercooling in real materials. There is competition between columnar and equiaxed growth. When growing grains approach, the solute layer and the thermal field act to prevent them overlapping.
Plotting of fringe contours from finite element results
Authors: Ramesh K. , Yadav A. K. , Pankhawalla Vijay A.
Published: August 2005

A novel and simple approach to plot fringe contours from finite element results that simulates the fringe thickness variation as observed in experiments is presented. The procedure does not require solution of any non‐linear equation. Shape functions are used as interpolation functions to plot fringe contours from the nodal values of fringe orders. The various fringe contours one usually comes across in stress analysis are also reviewed. The program code in Turbo‐Pascal employing the new algorithm is given. Stress and displacement contours at the tip of a crack in an SEN (single‐edge‐notched) specimen are plotted using the code developed. The fringe contours plotted correspond to those observed in experiments such as photoelasticity, holography and Moire.
An assumed strain approach avoiding artificial thickness straining for a non‐linear 4‐node shell element
Authors: Betsch P. , Stein E.
Published: August 2005

A quadrilateral degenerated C0 shell element is presented which relies on extensible director kinematics and which incorporates unmodified three‐dimensional constitutive models. It is shown that the direct interpolation of the extensible director field causes severe locking behaviour in the case of thin shell structures. An assumed strain interpolation is proposed to overcome the thin‐shell defect. Due to this modification the shell element is able to accommodate large rotations without a rotation tensor, even for very thin shells. Several large deformation examples confirm that the developed shell element is competitive with more elaborate formulations which use rotational degrees of freedom.