bluuebunny/crossref_metadata_2025_split huggingface dataset:
A choice of interpolation schemes for the boundary‐element method in elastodynamics
Authors: Wu T. W. , Lee L. 
Published: August 2005

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

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

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

AbstractThe virtual contact loading method (VCLM), a highly efficient numerical method to solve elastic contact problems, is proposed in this paper. Having applied virtual loads on the possible contact region (PCR) of a structure system, we carried out the usual finite‐element calculations only once and made a local iteration analysis in PCR then the contact region (shape and size), contact state (stick, slide or mixed), contact normal and shear stress distributions, and the stress and displacement fields in contact bodies were all obtained simultaneously. This method is very simple and easy to use.The elastic contact problems for cylinder–cylinder are solved in this paper and the results agree well with those in previous work.
Validation of finite‐element codes for prediction of machining distortions in forgings
Authors: Chandra U. 
Published: August 2005

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

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

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

AbstractThe completely adhesive contact between an FE‐modelled orthotropic half‐plane and a vertically loaded rigid flat punch is studied. Interface normal and shear‐stress distributions between the punch and half‐plane are FE‐calculated and compared for some sets of half‐plane boundary conditions frequently used in the literature for contact problems with friction. These results are compared with analytical solutions, and appropriate half‐plane boundary conditions are recommended for frictional contact problems.
Corrective technique for numerical prediction of liquid flow rate in annular flow study
Authors: Tso C. P. , Sugawara S. 
Published: August 2005

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

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

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

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

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

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

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

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

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

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

AbstractThe paper presents a new method for the numerical solution of transient linear heat conduction problems. In the proposed method, the transient linear heat conduction equation is first integrated with respect to time over subsequent intervals. Then the resulting set of elliptic equations is discretized in space according to a finite‐element procedure. The method is unconditionally stable. At the end of the paper, the effectiveness of the proposed method is assessed through some numerical examples.
Critical look on new approach for geometrically evolving domains in geomechanics
Authors: Modaressi H. , Roux F. 
Published: August 2005

AbstractNumerical modelling of geometrically evolving domains, such as multistep construction, accretion and excavation, has always been of great interest to geotechnical engineers. Stress, strain and pore‐pressure changes depend on hydromechanical properties and the loading process. Several techniques are proposed in the literature for numerical simulation of excavation or backfilling processes. These are mostly based on a natural methodology that consists in dividing the problem into several time steps, each coinciding with the addition or removal of one layer which is then modelled by means of several elements. Unfortunately, as in these methods the evolving parameters and their relative influence are not explicit, it is not possible to determine their accuracy. A more rigorous approach lies in the geometrical transformation of the studied domain, depending on the time variable for a reference domain in which the conservation equations are verified. The application of this methodology implies a great number of calculations. By using limited development techniques of the Jacobian of transformations it is possible to reduce the volume of computations. Such a technique results in approximations which can be evaluated.
Finite‐element method for EHL analysis of spherical bodies
Authors: Karami G. , Zarinchang J. , Eraghi R. Satourians , Kazeminejad H. 
Published: August 2005

AbstractA finite‐element solution for elastohydrodynamic lubrication (EHL) of spherical bodies undergoing elastic deformation is presented. The Galerkin finite‐element approach is employed and the domain under investigation is discretized using isoparametric quadrilateral elements. Isothermal conditions are assumed and the generation of the pressure is assumed to be governed by the Reynolds equation. The viscosity and the density of the oil are assumed to be functions of the pressure. It is assumed that the underlying surface deforms elastically under the hydrodynamic pressure distribution. The accuracy of the technique is illustrated in particular examples.
Empirical way to improve stress accuracy at stress concentrations in finite element analysis
Authors: Tenchev R. T. 
Published: August 2005

AbstractThe nodal stresses in a finite element may be calculated in two ways: (a) directly at the nodes; (b) by bilinear extrapolation from the stresses at the 2 × 2 Gauss points. In both cases the von Mises stress is computed from the averaged nodal stresses. In areas of stress concentration, when the mesh is not adequately refined, there is a significant difference between the maximum von Mises stresses when methods (a) and (b) are used. By means of numerical examples it is shown that method (a) is superior to (b). Using both stress values an empirical formula, based on numerous FEM results, is presented for improving the accuracy of the maximum von Mises stress. The error reduction is considerable. Only plane stress problems with 8‐node quadrilateral isoparametric elements are considered.
Applying dispersion correction to numerical approximations of the two‐dimensional wave equation ‐ eigenproblems
Authors: Mackie R. I. 
Published: August 2005

AbstractA technique is presented whereby numerical calculations of vibration modes can be improved. The paper looks at the classical two‐dimensional wave equation using finite difference approximations. Analysis of the numerical dispersion of the approximations is used to develop a correction method. In general the numerical dispersion is dependent upon both the frequency and the direction of a wave, but if a 9‐point formula is used the directional dependence is much reduced. This enables correction factors to be obtained using only the frequency of a vibration mode. The method was tested on the vibration of a square membrane and of an L‐shaped region; in both cases a marked improvement in accuracy was obtained, at very little computational cost.
A direct solver for the least‐squares problem arising from GMRES(k)
Authors: Galán Manuel J. , Montero Gustavo , Winter Gabriel 
Published: August 2005

AbstractThis is a study about one of the core questions in the GMRES(k) method regarding the obtaining of vector yk for the least‐squares problem, argminy |Hky ‐ β(n)e1|2 (see Saad and Schultz1). We propose a simple but efficient approach to the resolution of this problem and a low cost computation of the residual and the residual norm, including both in a complete and detailed FGMRES(k) algorithm. The whole algorithm of minimization only involves two backward substitutions with triangular matrices and a dot product. The residual and the residual norm are computed, making use of results in the least‐squares problem.
Semi‐discretization method for the heat equation with non‐local boundary conditions
Authors: Araújo A. L. , Oliveira F. Aleixo 
Published: August 2005

AbstractSemi‐discretization methods with iterated corrections are considered for solving the heat equation with boundary conditions containing integrals over the interior of the interval. The given problem is transformed into an ordinary differential system of equations, when we substitute the spatial derivative by finite differences. Such a system is then solved with an implicit integrator together with a quadrature method for the boundary integrals and, for each time step, the numerical scheme ‐ implicit integrator and quadrature method ‐ is repeated iteratively in order to achieve a given accuracy. The extra work we need with the iterated corrections enables us to take care of the interrelation of the solution u(x, t) at the interior and at the boundary points and also to start the numerical process with rough approximations of u(0, t) and u(1, t).An improvement of the results is achieved when we estimate the local spatial truncation error and make the injection of that estimation into the ordinary differential system. Numerical experiments are presented.
Dispersion properties of simple 3D finite elements
Authors: Johnson Erland 
Published: August 2005

AbstractThe dispersion properties of plane waves, propagating in an infinite uniform mesh with linear cubic 3D finite elements, are investigated. Time discretization is performed with the central‐difference time‐stepping scheme in combination with lumped mass matrices. The stiffness matrices are integrated analytically with different integration schemes, and dispersion relations are derived. The results show that the stiffness integration scheme can be chosen to reduce dispersion and improve the isotropy of wave propagation. It is also observed that the numerical wave speed becomes zero along certain wave propagation directions for specific wave numbers.
On the pseudomaterial approach for the analysis of transient forming processes
Authors: Cruchaga M. , Oñate E. , Idelsohn S. 
Published: August 2005

AbstractA fixed‐mesh method for the analysis of transient forming processes is presented. The mesh covers material regions and zones through which the material may flow. These last zones are identified by a pseudomaterial with relatively small physical parameters. During time processing, the interface between both materials is followed by an arbitrary Lagrangian mesh. This technique appears to be suitable for the treatment of moving surfaces with sharp corners. A particular boundary condition for the Navier‐Stokes equations is also introduced in order to model a porous wall.
A note on FEM buckling analysis
Authors: Wagner W. 
Published: August 2005

AbstractThe investigation of the non‐linear response of shell‐like structures requires insight into stability behaviour. In the paper we compare two strategies to compute singular points based on different eigenvalue problems. We show a simple algorithm to calculate critical load factors A used in engineering buckling analysis from the eigenvalues of the standard eigenvalue problem (KT – ω1) φ = 0. Some numerical examples illustrate the derived results and algorithms.
On the assumed displacement fields of a shallow curved shell finite element
Authors: Allman D. J. 
Published: August 2005

AbstractAn essential requirement for a satisfactory curved shell finite element is a capability for exact representation of rigid body movements: otherwise serious difficulties can occur, as is well known from early developments in shell finite element analysis. It is shown in this paper that appropriate assumed displacement fields for a particular shallow curved shell finite element with 18 degrees of freedom can be obtained in a very simple, yet apparently novel, way which permits the exact recovery of all rigid body movements. The shallow curved shell finite element considered here is constructed on a triangular flat facet approximation to a general thin elastic shell; it has quadratic middle surface geometry to allow for accurate modelling of arbitrary curvatures.
A posteriori finite element method error estimates for fourth‐order problems
Authors: Pomeranz Shirley B. 
Published: August 2005

AbstractA posteriori error estimation for typical Euler‐Bernoulli beam bending problems is developed using a recovery operator based on a smoothing technique that is applied in the context of one‐dimensional fourth‐order problems. The development exploits a discrete superconvergence property of the ‘bending moments’ of the trial space interpolant of a polynomial solution of sufficiently low degree at certain Gauss points, and the superconvegence property of the energy norm difference of the trial space interpolant (of the weak solution) and the finite element approximation. An asymptotically exact error estimator is developed.