bluuebunny/crossref_metadata_2025 huggingface dataset:
Behaviour of five solution algorithms on turbulent calculations
Authors: Chao Y. C. , Ho W. C.
Published: August 2005

The relative performances of five pressure‐velocity coupling solution algorithms, SIMPLE, CTS SIMPLE, SIMPLER. SIMPLEC and FIMOSE, are evaluated for three turbulent flow problems. The characteristics of these methods are investigated based on the computational effort required to reach certain levels of residuals in mass, momentum and turbulent kinetic energy. Comparisons of these methods used to solve turbulent flows in the present study and laminar calculations in previous literature are made to reveal the characteristic behaviour of these algorithms in the computation of these two flow regimes. It is found that SIMPLEC is the most efficient and stable method for solving the complex turbulent flows and its performance is not always identical to CTS SIMPLE. SIMPLER needs the fewest iterations.
A method for smoothing derivatives of multilinear finite element fields
Authors: Langtangen H. P.
Published: August 2005

An improved method for calculating smooth derivatives of multilinear finite element fields is presented. The method is also applicable to finite difference schemes. A simple one‐dimensional model problem is discussed analytically, and the new method shows superior behaviour compared to existing popular smoothing techniques. Two‐ and three‐dimensional problems involving isoparametric elements are tested, and the results show improvements over the widely used global least‐squares method, with lumped mass matrix, especially at the boundaries and for non‐uniform meshes.
A fast numerical algorithm for calculating electromagnetic waves in an inhomogeneous slab
Authors: Winter D. F. , Bosley D. L.
Published: August 2005

Consider a plane monochromatic electromagnetic wave normally incident on an absorbing dielectric slab, bounded by z = 0 and z = L, and whose electrical parameters ε, μ and σ are arbitrary functions of z. The media on either side of the slab have constant but generally different electrical properties. This paper describes an efficient numerical algorithm for calculating the electromagnetic field within the slab, as well as its absolute reflection and transmission coefficients. The waveform within the slab is represented by a new complex dependent variable satisfying a modified (complex) Helmholtz equation to be solved subject to mixed inhomogeneous conditions at the boundaries of the slab. If derivatives are replaced by nth‐order centred differences, the difference equation set is linear, sparse and efficiently solved by direct recursion. In this paper, complex arithmetic is avoided by replacing the complex Helmholtz equation with two coupled, real, second‐order ordinary differential equations. An algorithm of second‐order accuracy is developed which leads to a bitridiagonal difference equation set. Calculations are carried out for a variable‐property slab problem which can also be solved analytically. Numerical comparisons indicate that the method is accurate and efficient enough that a desk‐top computer is a practical computational machine.
Anomalous convection at low Prandtl number
Authors: Winters K. H. , Jack R. O.
Published: August 2005

The steady‐state natural convection of a fluid of low Prandtl number contained within a two‐dimensional rectangular box is simulated for conditions of an imposed horizontal temperature gradient and conducting horizontal surfaces. By the application of numerical bifurcation and continuation techniques combined with the finite‐element method the solution structure of the steady state equations is determined and a stable anomalous bicellular flow is found. In contrast to the normal unicellular flow that develops smoothly for increasing Prandtl number, the anomalous flow is associated with a disconnected branch that arises at a limit point. The derived solution structure clarifies certain phenomena observed in recent time‐dependent simulations of this problem.
Isentropic flow with cylindrical or spherical symmetry
Authors: Glaister P.
Published: August 2005

A numerical scheme is presented for the solution of the equations of isentropic flow in a single spatial co‐ordinate. This includes flow in a duct of variable cross‐section as well as flow with cylindrical or spherical symmetry, and can prove useful when testing codes for the two‐dimensional equations governing isentropic flow. The scheme is applied with success to a problem involving a converging cylindrical shock and to a problem involving the interaction of converging and diverging cylidrical shocks.
A higher‐order method for computing eigenvalues of two‐point boundary‐value problems
Authors: Chawla M. M. , Subramanian R.
Published: August 2005

We present a new finite‐difference method of order h5 for computing eigenvalues of two‐point boundary‐value problems. Our method leads to a generalized seven‐diagonal symmetric and positive‐definite matrix eigenvalue problem.
A variable‐density mesh generation for planar domains
Authors: Cescotto S. , Wu Zhou Ding
Published: August 2005

This paper describes an orginal method to generate a finite‐element mesh in a planar domain of arbitrary shape. The mesh density can be varied arbitrarily, not only on the contour but also inside the domain. The number of elements generated can be imposed approximately.
A unified formulation of two existing time‐domain boundary‐element approaches
Authors: Gallego R. , Dominguez J.
Published: August 2005

Two apparently different time‐domain boundary‐element formulations for plane‐stress/plane‐strain elastodynamic problems exist in the literature. The present paper shows why one of the formulations, which is valid for a particular type of interpolation function, forms part of the other, which can be used with any interpolation function. The main differences presented in the past between the two existing time‐domain boundary‐element methods were based on an incorrect expression of the tractions in the complete plane due to the rectangular impulse load. Results obtained in the past which were presented to evaluate the differences between the two formulations are shown to be incorrect. A compact expression for the fundamental solution integrated along a time step when the time interpolation functions of all the boundary variables are assumed to be piecewise constant is presented. This integral gives the same tractions as those corresponding to a rectangular impulse load.
A variational inequality principle in solid mechanics and application in physically non‐linear problems
Authors: Desong Sha , Huanchun Sun , Zhongding Zhang , Fuxin Yin
Published: August 2005

A variational inequality principle which is suitable for various constitutive laws of elasto‐plasticity is given in this paper. Then the variational inequality is reduced to a linear complementary problem by using incremental theory and the finite‐element methods.
The integrity of geometrical boundaries in the two‐dimensional delaunay triangulation
Authors: Weatherill N. P.
Published: August 2005

The Delaunay triangulation has recently received attention as a viable method for construction computational meshes. However, an arbitrary boundary definition which must be preserved in the triangulation process will not, in general, satisfy the geometrical definition on which the Delaunay construction is founded. The effect of this is that the integrity of the given boundary edges will be violated and the computational mesh will not conform to the applied geometrical shape. A method is proposed whereby boundary data are supplemented with points to ensure that imposed boundary edges are preserved during the Delaunay triangulation. The method is illustrated on a geometry of an estuary which exhibits highly complex geometrical features.
Comments on a simple algorithm for the plotting of contours
Authors: Singh Chandan
Published: August 2005

We consider a paper by Stelzer and Welzel (1987) about a new contour lines algorithm. Because of its exactness and its convincing straightforwardness we have tested it and incorporated it into our post‐processing software. This paper describes some aspects we experienced during the numerical experimentation which may be helpful for people considering using the method. Although the cited paper deals with both linearly interpolated isoparametric elements and quadratic ones we have restricted ourselves to the linear type to keep the relationships as simple as possible.
Study of 20node solid element
Authors: Kim Y. H. , Jones R. F. , Lee S. W.
Published: August 2005

The 20node three‐dimensional solid element based on the assumed displacement model was compared with the 18node solid element based on the assumed strain model. The kinematic stability associated with different integration rules was investigated for the 20node element.
Numerical modelling of crack propagation using multi‐variable and breakable finite elements
Authors: Zhang J. Y. , Hsu T. R. , Wang I. Q.
Published: August 2005

In this study, the advantage of the multi‐variable finite‐element model based on the generalized virtual work principle is described. The model has been applied to the elasto‐plastic fracture analysis with finite deformations. Using the multi‐variable finite‐element model with a‘breakable finite‐element’ concept, the authors proposed an algorithm which can more accurately simulate the crack growth. Numerical examples illustrate that the algorithm presented can be successfully used to predict whether the crack growth is stable or unstable. The rupture effective strain is considered as a fracture criterion, and some comparisons between various criteria are also provided.
Using preconditioned conjugate gradient for solving consecutive linear systems
Authors: Blanc J. Y. , Comon P. , Trystram D.
Published: August 2005

One can point out several applications to the solution of consecutive linear systems with symmetric positive‐definite matrices. Such problems arise, for instance, in signal processing, modellization of grid systems, stress analysis and automatic control. We describe in this paper an efficient and robust method based on an original preconditioned conjugate gradient algorithm, and compare it with the usual methods (Cholesky, modified Cholesky when successive systems are modified by an update of given rank, and incomplete Cholesky factorization) in terms of computational complexity.
Estimating the form of some three‐dimensional singularities
Authors: Abdel‐Messieh Y. S. , Thatcher R. W.
Published: August 2005

The method of infinite grid refinement is used to estimate the analytic form of some point singularities in three‐dimensional Laplacian and elasticity problems.
Generalized variational principles
Authors: Mikhailov M. D.
Published: August 2005

Equivalent variational formulations are found for a generalized linear boundary‐value problem which covers a wide class of engineering applications. The results presented yield as special cases the well‐known elasticity variational principles.
A fundamental solution for a plate on an elastic half‐space
Authors: Stolle Dieter F. E.
Published: August 2005

This contribution deals with the development of a fundamental solution for an elastic plate supported by an elastic half‐space. The author briefly discusses problems associated with using an existing fundamental solution, and then develops an alternative solution using an approximate foundation reaction function which is obtained from the concept of equivalent thickness and Boussinesq's solution for an elastic half‐space. The singular solution can be easily incorporated into existing boundary‐element codes, and makes use of material parameters which are directly related to the material properties of each layer. An approximation to the fundamental solution is also suggested. Comparisons between approximate and exact solutions are presented, and limitations are discussed.
An isoparametric finite‐element stokes flow test problem
Authors: Maslanik Miriam K. , Sani Robert L. , Gresho Philip M.
Published: August 2005

Two‐dimensional Stokes flow of an incompressible Newtonian fluid about a horizontal cylinder situated next to a moving wall is presented and suggested as a non‐trivial benchmark problem. Both the primitive variable Galerkin finite‐element and the exact solutions are generated on a sequence of refined meshes; error norms and convergence rates are presented for the C0 bilinear‐velocity/C−1 piece‐wise constant‐pressure and the C0 biquadratic‐velocity/C−1 linear‐pressure quadrilateral elements.
The Jacobian derivative method for three‐dimensional fracture mechanics
Authors: Barbero E. J. , Reddy J. N.
Published: August 2005

This paper presents a new algorithm to compute the distribution of the strain energy release rate along the crack front for three‐dimensional cracks (e.g. surface cracks). The algorithm is economical and accurate. The algorithm is illustrated via two‐dimensional and three‐dimensional examples including a surface crack in a cylinder under internal pressure and side‐grooved compact‐test specimens. It is shown, via specific examples, that only a single, self‐similar virtual crack extension is necesary to accurately compute the strain‐energy release‐rate distribution along the crackfront.
A selective reduced integration triangular plate element
Authors: Ferahi M. , Tabarrok B. , Cleghorn W. L.
Published: August 2005

A triangular plate element, allowing transverse shear deformations, is developed in this paper. The element is compatible and employs rotations and slopes as well as lateral deflection as degrees of freedom. Through static condensation it is possible to remove the slopes and form a less complex, incompatible element, involving only the lateral deflection and rotations. Illustrative examples are presented to demonstrate the performance of the element before and after condensation.
Unsteady thermal stress analysis in three‐dimensional problems by means of boundary‐element method
Authors: Ochiai Y. , Ishida R.
Published: August 2005

The boundary integral formulation for unsteady thermal stresses in three‐dimensional quasi‐static problems is proposed. It is shown that three‐dimensional unsteady thermal stress problems can be solved easily without the volume integral by means of the thermoelastic displacement potential and the boundary‐element method. It is also shown that the time integral can be easily carried out analytically. In order to investigate the accuracy of this method, unsteady thermal stress distributions for a cube are obtained.
Combining material and element rotation in one formula
Authors: Pedersen Pauli
Published: August 2005

The paper shows a combined transformation for material and element rotation, related to the finite‐element method. With this, the simplest co‐ordinate systems can be chosen individually for structure/solid, element and material. A corrected criterion for a material to be orthotropic is also included.
Location and structure of the nearest singularity of a perturbation series
Authors: Kwok Yue‐Kuen
Published: August 2005

The incompressible potential flow over a perturbed body is used as a model to shed light into the nature of the nearest singularity of a perturbation series. The solutions for various physical quantities are developed as a formal perturbation expansion in powers of a parameter up to 30 terms. The tedious computation is relegated to a computer. The calculations reveal that the location and structure of the nearest singularity of a pertubation series do change with the field point at the which the series is evaluated. Also the radius of convergence and behaviour of the perturbation series do depend significantly on the choice of the physical quantities. These results may provide salutary information for the analysis of computer extended pertubation series.
Space–time partial hybrid stress element for linear elastodynamic analysis of anisotropic materials
Authors: Jing Hung‐Sying
Published: August 2005

The variational basis and finite‐element implementation for the space‐time partial hybrid stress element is presented in this paper. Through convolution integration and dividing the six stress components into flexural (σx,σy,σz,τxy) and transverse shear (τxz, τyz) parts, the Hellinger‐Reissner functional or the total potential energy functional can be modified as the basis for constructing the space‐time partial hybrid stress element. By assuming Hermitian interpolation functions in time, displacement field for flexural stresses, and hybrid stress for transverse shear, the space‐time partial hybrid stress element can be established for linear elastodynamic analysis consistently without any contradiction.
Low‐order mixed method finite elements in non‐linear elasticity
Authors: Goleniewski G.
Published: August 2005

A mixed method finite‐element formulation for non‐linear plane‐strain elastic deformations is described. Incompressibility is built in explicitly. All fields have piecewise linear approximants over triangles except pressure, which is taken to be constant over matched pairs of triangles. The code is used in an investigation of the tilting mode of deformation of bonded rubber blocks. In particular the variation of tilting moment with aspect ratio is focused on for a range of tilting angles.
Numerical comparison of momentum interpolation methods and pressure—velocity algorithms using non‐staggered grids
Authors: Kobayashi M. H. , Pereira J. C. F.
Published: August 2005

Finite‐volume calculations of laminar separated flow around a fence are presented using a non‐staggered grid system. Using the pressure‐weighted interpolation method (PWIM), the role of the under‐relaxation factor in this method has been studied. The performance of two pressure‐velocity coupling algorithms, viz. SIMPLE and PISO, have been compared as well as the solution fields obtained using non‐staggered and staggered grids. A detailed study has been conducted to investigate the occurrence of physically unrealistic convective velocities in the solution fields.

The numerical results show that solutions obtained using non‐staggered grids are as accurate as those obtained using staggered grids. The presence of very small under/overshoots in the estimated convective fluxes is related to the simultaneous presence of high Péclét numbers and rapidly varying pressure gradients. However, for the complex separated flow investigated, no induced errors were detected in the solution field.
A comparison of gradient recovery methods in finite‐element calculations
Authors: Hawken D. M. , Townsend P. , Webster M. F.
Published: August 2005

In this paper we consider methods of gradient recovery in the context of primitive‐variable finite‐element solutions of viscous flow problems. Two methods are considered: a global method based on a Galerkin weighted residual procedure, and a direct method where gradients are recovered directly at individual nodes. The direct method has the benefit of utilizing the property of superconvergence as a natural consequence of its formulation, and furthermore requires no smoothing matrix to obtain the gradients at the nodal points. The two recovery schemes are considered with respect to two benchmark viscous flow problems of differing complexity. Both schemes are shown to produce comparable results, although the direct recovery method is found to be significantly more cost‐effective than the global method.
A numerical approach to find parameters using experimental data
Authors: Qamar Ihtzaz , Husain S. Wilayat
Published: August 2005

A numerical technique is presented to determine the unknown parameters in a given relationship using the experimental data. In this technique we formulate the required number of independent relationships by integration applied to various parts of the data along with the criterion of the least‐squares error with respect to one parameter. The results for two sample systems, one with two parameters and the other with three parameters, are presented. Comparison with the published work shows that the proposed method is less sensitive to the inaccuracies in the experimental data and generates a better fit than the existing methods such as the ordinary least‐squares technique. The method can easily be extended to systems with any number of parameters.
Finite‐element analysis of wrinkling membranes
Authors: Roddeman Dennis G.
Published: August 2005

A theoretical model for wrinkling membranes is used to develop a membrane element. Instead of deriving explicit expressions for the nodal forces and the stiffness matrix, the equivalent nodal forces are obtained by numerically simulating the virtual change of the element internal energy; the stiffness matrix follows from numerical differentiation of the nodal forces. Two examples illustrate the capabilities of the element.
An inverse finite‐element technique to determine the change of phase interface location in two‐dimensional melting problems
Authors: Ruan Yimin , Zabaras Nicholas
Published: August 2005

This paper is concerned with a two‐dimensional inverse phase change problem of particular importance to the analysis and design of welding processes. Specifically, a deforming finite‐element technique is proposed to calculate the change of phase interface location in two‐dimensional melting problems from temperature measurements at points inside the solid phase. The method is based on a minimization of the error between the measured and modelled temperatures at the sensor locations. It contains smoothing in time by utilizing future temperature data to calculate current values of the interface location as well as spatial smoothing. Several two‐dimensional examples are presented to illustrate the effectiveness of the proposed numerical model.
Exact discretization of an Euler beam element at specific frequencies corresponding to selected element boundary conditions
Authors: Downs B.
Published: August 2005

The exact discretization of simply supported rectangular thin plate elements for transverse vibration analysis, using the product of simply supported Euler beam properties, justifies this further study of Euler beams having a variety of end conditions. Five sets of boundary conditions, including the simply supported case, are examined and the theory for exact discretization is developed. Satisfactory verification of the discretization is obtained by eigenvalue analysis in all five cases. Applying the discretized properties to multi‐element beam analysis reveals an ill‐conditioning problem, present also in the conventional static matrices, for most combinations of end conditions. This problem does not occur for the simply supported element, whose discretized properties are then used to develop a highly accurate, frequency‐dependent mass matrix for use with the static stiffness matrix. Several comparisons are made of the results of eigenvalue error analysis.
On fitting stability regions of second derivative multi‐step methods
Authors: De Oliveira Paula , Patrício Fernanda
Published: August 2005

A class of second‐derivative two‐step methods, S(2), with order 5 and depending on two parameters – which are used to adapt the stability region while minimizing the truncation error coefficient – is constructed. An analysis of two subclasses of S(2)–A(0) stable methods and methods with finite stability interval ‐ with their stability and accuracy properties is presented. Numerical examples are also included.
A generalized finite‐difference solution of parabolic 3‐D problems on multi‐connected regions
Authors: Pennati V. , De Biase L. , Feraudi F.
Published: August 2005

A method for the solution of 3‐D parabolic problems on multi‐connected regions is presented. The domain discretization is automatic: at first the boundary is approximated by means of polyhedra; subsequently a Cartesian orthogonal non‐uniform grid is generated. The differential operator is discretized by a Crank‐Nicolson scheme, coupled with general finite‐difference formulae (GFDF).

Some test problems are presented to show the efficiency of the method.
Observations on numerical method dependent solutions of a modified Duffing oscillator
Authors: Addison P. S. , Chan A. H. C. , Ervine D. A. , Williams K. J.
Published: August 2005

Numerical solutions of a non‐linear oscillator have been produced by various methods. Some unexpected discrepancies have been found in the solutions obtained. This behaviour is reported herein, and the implications to the application of numerical methods to non‐linear dynamical systems are discussed.
A set of three drivers for BOXMG: A black‐box multigrid solver
Authors: Bandy Victor , Sweet Roland
Published: August 2005

In this paper we present three drivers for the Fortran software packages BOXMG and BOXMGP. They both act as black‐box matrix solvers for symmetric positive‐definite matrices using a multigrid method. There are two drivers, BBMG and BBMGP, that simplify the interface to BOXMG and BOXMGP, respectively. The other driver, DIVMG, provides a user‐friendly driver to both BOXMG and BOXMGP for a special class of problems. The DIVMG driver solves a two‐dimensional second‐order partial differential equation in divergence form on a rectangular domain with any combination of the following boundary conditions: Dirichlet, Neumann, Robin and periodic. The BBMG and BBMGP drivers, like the BOXMG solvers, still require the user to define the system of equations, while on the other hand the DIVMG driver also performs the discretization and only requires the user to define the problem.
The time‐parallel multigrid method
Authors: Horton Graham
Published: August 2005

We consider the problem of solving time‐dependent partial differential equations on an MIMD computer. Conventional methods for the solution of this type of equation when discretized by an implicit method such as backward Euler proceed by solving a sequence of problems iteratively. It is shown that, despite the sequential nature of this process, several processors may be employed to solve at several time steps simultaneously, a technique which we shall refer to as time‐parallelism. Details of a time‐parallel multigrid method based on the parabolic multigrid method due to Hackbusch and of a smoothing technique applicable to the two‐dimensional unsteady incompressible Navier‐Stokes equations are given. The parallel complexity of the method is shown to be qualitatively superior to that of previous parallel algorithms. Efficiencies obtained by an implementation of the method on a parallel Transputer system are presented.
On permanent capillar‐heavy waves in infinite channels
Authors: Moussa Nabil
Published: August 2005

This work is based on the constructive existence proof of solutions of a comprehensive class of non‐linear free boundary‐value problems of plane hydrodynamics by E. Zeidler (1971) and a general computational method for constructing the solutions numerically given by the author (1991). The case of permanent capillar‐heavy waves in infinite channels will be considered.
Quickly convergent integration methods for plane stress plasticity
Authors: Schoenfeld Scott , Benson Dave
Published: August 2005

Explicit finite‐element programs, such as DYNA3D, are frequently used to solve large structural problems, such as automobile impacts, that involve tens of thousands of shell elements. Since the explicit finite‐element programs do not use a stiffness matrix, the major cost of the calculation is the evaluation of the force vector. A significant part of that cost is the evaluation of the constitutive models. The standard algorithm for integrating J2 plasticity at the stress points is the radial return method. An iterative variation of radial return is commonly used to impose the zero normal stress condition within the shell elements. In this paper we explore several different non‐iterative methods that impose the zero normal stress condition in an approximate manner. We show that the cost of the constitutive evaluation can be reduced by 25 per cent without introducing significant errors.
On bicubic transformation for the numerical evaluation of Cauchy principal value integrals
Authors: Chen T. Charles
Published: August 2005

Recently a bicubic transformation was introduced to numerically compute the Cauchy principal value (CPV) integrals. Numerical results show that this new method converges faster than the conventional Gauss–Legendre quadrature rule when the integrand contains different types of singularity. Assume η is the singular point of a CPV integral. The point η divides the interval [−1, 1] into two parts: [−1, η] and [η, 1]. The bicubic transformation maps the intervals [−1, η] and [η, 1] to the interval [−1, 1] with the following constraints: it maps the point η − ϵ to μn, and η + ϵ to −μn, where μn is the largest Gaussian point of an n‐point Gauss–Legendre quadrature rule, and ϵ is a user‐supplied constant. The n‐point Gauss–Legendre quadruture rule is then applied. In contrast to ordinary expectation, further numerical experiment shows that smaller ϵ does not always produce better results. In this paper we are concerned with the selection of ϵ to yield rapid convergence of numerical integration when the bicubic transformation method is applied.
Suitability of three‐dimensional finite elements for modelling material incompressibility using exact integration
Authors: Bell R. W. , Houlsby G. T. , Burd H. J.
Published: August 2005

This paper examines the suitability of three‐dimensional finite elements to model accurately problems involving material incompressibility, using the displacement finite element method and exact numerical integration. The previously used method for classification of element suitability is presented and extended to the three‐dimensional case. However, an alternative approach for examining suitability, quantified in terms of free degrees of freedom (equal to the degrees of freedom minus the incompressibility constraints), is introduced. This is used to examine Lagrangian cubic, serendipity cubic and tetrahedral three‐dimensional elements configured in a regular cubic arrangement. The findings of this paper are substantiated by a number of three‐dimensional numerical experiments and comparison with a separate two‐dimensional study.

All serendipity cubic elements are found to be unsuitable. The linear strain tetrahedron is on the borderline of suitability in a 6‐tetrahedra‐per‐cube arrangement, and is thought to be only suitable if the mesh boundary nodes are not over‐constrained. The same element in a 5‐tetrahedra‐per‐cube arrangement, and higher order tetrahedra (quadratic strain etc), are suitable. The Lagrangian cube elements of higher order than the 27‐node cube are suitable, but are probably not as efficient computationally as the tetrahedral elements of the same order.
Evaluation of field singularities by an iterative boundary‐element method
Authors: Heyliger P. R. , Rudolphi T. J.
Published: August 2005

A numerical method is presented for the evaluation of field singularities of the type (1/r1‐λ) using iterative solutions of standard boundary‐element analyses in a region surrounding the origin of singularity. Results for λ are presented for both two and three‐dimensional problems, and representative asymptotic fields for these examples are discussed.
Direct method for a class of symmetric linear systems
Authors: Onana Awono , Mbala H. A.
Published: August 2005

A direct method is proposed for the numerical solution of a wide class of symmetric block‐tridiagonal systems of linear equations resulting from a finite‐difference or finite‐element discretization of elliptic boundary‐value problems with Dirichlet boundary‐value conditions on rectangular domains. The method is based on a result which generalizes the classical Cramer rule and on extensive use of the modified Chebȳshev polynomials for the formulation of the algorithm. A numerical example is provided to illustrate the validity of the proposed approach.
Solar pressure evaluation on large reflectors for space applications
Authors: Brunello P.
Published: August 2005

The evaluation of solar pressure effects over the antenna reflectors for communication satellites is becoming more and more important, since the diameters of such devices tend to be increased. For this purpose, a statistical approach based on the Monte Carlo method has been developed, as described in this paper, within a research project of the European Space Agency (ESA). In this way, detailed simulations can be carried out easily, thus allowing for analysing different geometrical and technological solutions and for defining an adequate compromise between antenna gain and pointing control capability of the satellite.
Application of augmented Lagrangian techniques for non‐linear constitutive laws in contact interfaces
Authors: Wriggers P. , Zavarise G.
Published: August 2005

The use of micromechanically based constitutive equations for contact interfaces leads to technically relevant parameters to ill‐conditioned finite‐element equations. In the paper an augmented Lagrangian technique is employed to overcome this difficulty and to provide a good converging algorithm.
Comparison of the BEM and FEM approach for the electromagnetic field analysis in a zoned medium
Authors: Krajewski Wojciech , Salon Sheppard J.
Published: August 2005

In the paper the BEM and FEM results have been compared in the context of 2D electromagnetic field analysis in a zoned medium with eddy current subregions. The practical problem concerning the turbogenerator end region has been discussed. The magnetic flux density over the surface of the end package and the current density in the non‐magnetic pressure plate have been analysed.
Finite‐element analysis of elastic contact between a shell of revolution and a rigid plate
Authors: Gautham B. P. , Ganesan N.
Published: August 2005

Elastic contact between a thick shell of revolution and a rigid plate in the case when the plate is brought into contact with the shell by giving a finite displacement to the plate is analysed by the finite‐element method. Field‐consistent higher‐order strain‐displacement relations with vanishing shear stresses on the surfaces are used. A finite element based on these relations is developed and used for the analysis. The contact conditions are imposed by use of the Lagrangian multipliers method, and the resulting minimization problem is solved iteratively. This procedure will lead to reduced memory requirements and computation time.
Comparison of strain recovery techniques for the mixed iterative method
Authors: Červenka Jan , Keating Scott C. , Felippa Carlos A.
Published: August 2005

Three strain recovery techniques are investigated in the framework of the mixed iterative method. The need for appropriate strain recovery for low‐order elements is shown. The three techniques compared are: C‐lumping, strain‐smoothing and a new technique called C‐splitting. It is shown that the use of C‐lumping has negative effects on the convergence of the mixed iterative method. Both strain‐smoothing and C‐splitting deliver convergent results, but the new technique converges faster.
Optimization analysis of the three‐level time schemes
Authors: Shayya Walid H. , Segerlind Larry J. , Bralts Vincent F.
Published: August 2005

A procedure was implemented to determine the optimum values for the two parameters of the Zienkiewicz three‐level time schemes which could be utilized for the numerical solution of a system of ordinary differential equations. A multivariable search method was implemented to estimate optimum values for these parameters. The resultant optimum three‐level time scheme produced very accurate results, satisfied physical reality, and did not produce any oscillations for the various problems that were investigated. The optimum values for the two parameters β and γ in the three‐level scheme were β = 0·50005 and γ = 1·0007. A comparison was made between this optimum scheme and other existing three‐level time schemes. The optimum scheme demonstrated superior results for all the problems that were analysed. However, the results of the optimization analysis produced a set of optimum parameters that were identical to the values that would reduce the general three‐level time scheme into a central‐difference two‐level time scheme, i.e. β = 1/2 and γ = 1.
Arbitrary Lagrangian‐Eulerian thermomechanical finite‐element model of material cutting
Authors: Rakotomalala R. , Joyot P. , Touratier M.
Published: August 2005

An arbitrary Lagrangian‐Eulerian model is described for the prediction of metal flow in a steady‐state forming process. The formulation is shown to be capable of dealing with free surface and boundary friction; the coupling with thermal effects is also considered. The numerical techniques are based on the finite elements for spatial discretization of the momentum equation and on an explicit integration scheme for discretization relative to time. The mass and energy equations are integrated by a finite‐volume method. Details on the application to an orthogonal cutting process are given in the final Section of the paper.
Eigensolution reanalysis of modified structures using perturbations and Rayleigh quotients
Authors: Chen Su‐Huan , Song Da‐Tong , Ma Ai‐Jun
Published: August 2005

A new eigensolution reanalysis method for modified structures is developed and presented based on the usual first‐order perturbation scheme and the Rayleigh quotients. By this method, the accuracies of the eigensolutions of the modified structures computed by perturbation methods are improved. A numerical example is presented and the accuracies of the usual first‐order perturbation method, second‐order perturbation method, William B. Bickford method and the proposed method are compared.
Truncated envelope peconditioning technique
Authors: Júdice J. J. , Patrício J. M.
Published: August 2005

In the paper the use of a truncated envelope technique is discussed as a preconditioning for the conjugate gradient method for solving large linear systems of equations with symmetric positive‐definite matrices. An algorithm to generate a truncated envelope is introduced. Computational experience with systems of linear equations from the Harwell‐Boeing collection is presented to highlight the efficiency of this approach.
Accurate finite element method for steady and quasisteady lifting aerofoil
Authors: Shi Jun , Hitchings D.
Published: August 2005

A finite element formulation based on superposition is proposed for a lifting aerofoil in incompressible potential flow. An accuracy improvement technique for the singularity at the aerofoil trailing edge is discussed. It is shown that the quarter‐node quadrilateral element can be readily employed to simulate this singularity. It is also demonstrated that the circulation in the flow field can be easily represented by a single constraint equation rather than introducing an artificial cut line in the mesh. The influence of finite‐element mesh size on solution accuracy and the correct form of the boundary condition have been investigated as well. Numerical examples are given for both steady and quasisteady Joukowski aerofoils of various thicknesses and at a range of incidences. In all test cases, good agreement is observed between the analytical solution and the numerical result.
Explicit variable time‐step method for implicit moving boundary problems
Authors: Zerroukat M. , Chatwin C. R.
Published: August 2005

The diffusion of oxygen into an absorbing medium as an example of an implicit moving boundary problem has been dealt with by a number of authors using various numerical techniques, and, where appropriate, approximate analytical expressions. To evaluate the time for complete absorption, extrapolation is usually employed. An unconditionally stable explicit numerical scheme that avoids the limitations of such methods is presented and tested herein. Unlike existing schemes this method is fully numerical; it avoids the large array size, generally required for existing methods, by using a variable‐length time step. The time for complete absorption emerges from the final step in the normal computing procedure with no recourse to extrapolation. Furthermore, owing to the implicit condition prevailing at the moving boundary, no iterations are needed to evaluate the time step required for the moving boundary to move a single space increment. The numerical results obtained compare very favourably with those due to earlier authors.
Boundary‐element solution of some structural‐acoustic coupling problems using the multiple reciprocity method
Authors: Sladek V. , Sladek J. , Tanaka M.
Published: August 2005

In the paper we have developed a new formulation for solution of structural‐acoustic coupling problems by boundary elements using the multiple reciprocity method. It is assumed that the structure is composed of plate components and is excited by the external or the internal noise source. The efficiency of the proposed formulation becomes especially remarkable if the boundary‐value problem is to be solved repeatedly for different values of frequency. The accuracy of the numerical computations has been compared with the analytical solution in a test example.
Lagrange multiplier approach for evaluation of friction in explicit finite‐element analysis
Authors: Zhong Zhi‐Hua , Nilsson Larsgunnar
Published: August 2005

An algorithm for evaluation of friction in general contact‐impact interfaces is described. The algorithm is based on an explicit finite‐element method. Coulomb's friction law is assumed. The defence node algorithm is used such that the sticking condition can be imposed with the Lagrange multiplier method even in explicit dynamic analysis. The algorithm is supposed to be applicable in general situations, including large deformations of the contact‐impact bodies and large relative sliding between the contact‐impact boundaries. Numerical results are presented to demonstrate the performance of the algorithm.
Homogenization and effective elastoplasticity models for periodic composites
Authors: Swan Colby C. , Cakmak Ahmet S.
Published: August 2005

Techniques for stress‐ and strain‐controlled in situ homogenization of inelastic periodic composites are presented. The results of homogenization computations on a specific elastoplastic composite solid are then employed to validate the form of an orthotropic elastoplasticity model with a tensorial kinematic hardening law.
General forming of transition elements
Authors: Horváth Ágnes
Published: August 2005

A generalization of the r(1−m)/m strain singularity of higher‐order isoparametric elements is presented. It is shown that, by variable placement of the side nodes between their original and singular positions, the point of singularity sensed by the element can be controlled. The transition elements have a strain singularity outside their domain. The singular and non‐singular elements are elements are special cases of the general mapping. The transition elements, together with the singular isoparametric elements, can be used for solving crack problems.
Fourth‐order difference method for quasilinear Poisson equation in cylindrical symmetry
Authors: Jain M. K. , Jain R. K. , Krishna Meera
Published: August 2005

We propose in this paper a nine‐point, fourth‐order difference method for the numerical solution of the quasilinear Poisson equation

with appropriate boundary conditions. The method is based on five evaluations of f. The numerical results of four problems obtained using this method are listed. The results demonstrate the fourth‐order accuracy of the method.
Modified simplex optimization program
Authors: Pedersen Pauli
Published: August 2005

A simple, yet storage‐effective ‘linear’ programming code is given. The assumption of non‐negative variables is bypassed without increasing the size of the problem. Furthermore, the objective is allowed to be summed over not just linear, but also concave, functions. A specific truss topology optimization example is shown.
Accelerated modified Newton‐Raphson iteration‐based finite‐element solution of structural problems involving non‐linear deformation behaviour
Authors: Chen Chang‐New
Published: August 2005

A new global secant relaxation (GSR)‐method‐based improvement procedure is used to improve the overall convergency performance of the modified Newton‐Raphson iteration in carrying out the solution of discrete systems resulting from the finite‐element discretization of a certain class of structural problems involving non‐linear deformation behaviour.
Addressing the corner problem in BEM solution of heat conduction problems
Authors: Kassab Alain J. , Nordlund R. S.
Published: August 2005

A numerical problem which features prominently in the implementation of the boundary‐element method (BEM) for the solution of heat‐conduction problems arises from double‐valued heat fluxes at boundary corners. This problem is readily dealt with by explicitly treating nodal heat fluxes as double‐valued prior to assembly of the nodal equations. This formulation is very flexible as it also permits imposing discontinuous thermal conditions at any boundary node. However, at corner nodes where temperature only is prescribed, the scheme leads to two unknowns, while only one nodal BEM equation is available there. An additional equation which closely follows the previous work of Walker and Fenner is derived for these nodes, and this provides sufficient information to resolve the upstream and downstream values of the heat flux at the temperature node. The additional equation is general, is free of heuristic constraints, and is applicable through the wide range of acute, shallow, obtuse and re‐entrant angles encountered in practice. Numerical examples are used to compare the present method with the Walker and Fenner approach and with analytical solutions. Results indicate both improved accuracy and generality, thus validating the present method.
Variational formulation for Timoshenko beam element by separation of deformation mode
Authors: Lee Seok‐Soon , Koo Jeong‐Seo , Choi Jin‐Min
Published: August 2005

A variational formulation for a Timoshenko beam element is derived by the separation of the deformation mode into the bending deflection and shear deflection. Shear deflection is projected into bending deflection and the projection matrix is constructed by using the equilibrium equation and the relation of force and displacement. The exact stiffness matrix of the Timoshenko beam element can be obtained by the present method. Examples are solved in order to show the effectiveness of the beam element in comparison with other elements.
Approximate solution of the Fokker‐Planck‐Kolmogorov equation by finite elements
Authors: El‐Gebeily Mohamed A. , Shabaik Hosam E. Emara
Published: August 2005

The paper considers the solution of the Fokker‐Planck‐Kolmogorov equation by the finite element method (FEM). The problem is set in a variational formulation suitable for the FEM. Some theoretical aspects related to applying the method are discussed. Discretization of the problem is carried out and questions of convergence and order of the method are also addressed. A numerical example is given to verify the validity of the approach.
Application of direct boundary integration method to wave diffraction by submerged bodies
Authors: Shankar N. Jothi , Cheong Hin‐Fatt , Nallayarasu S.
Published: August 2005

The diffraction of waves due to the presence of submerged objects in the ocean environment is solved by a relatively novel approach involving the direct boundary integration method (DBIM). Firstly, the method is tested for the case of a submerged circular cylinder and compared with the conventional boundary element method (BEM) results. The agreement between the results using this method and the BEM is good. Further, the DBIM has been applied to the case of a submerged horizontal plate for which the horizontal and vertical force coefficients are computed and compared with a semi‐analytical solution using the matched eigenfunction expansion method (EFEM). It is found that the computed results using DBIM are in good agreement with those of EFEM and BEM. Further, the DBIM is found to be computationally more efficient than the BEM for the water wave diffraction problems presented in this paper.