bluuebunny/crossref_metadata_2025_split huggingface dataset:
Geometric idealizations in finite element computations
Authors: Szabó Barna A. 
Published: August 2005

AbstractCommonly used geometric idealizations in finite element analyses introduce errors which require either a large number of degrees of freedom or the use of special procedures to correct. In this paper the effect of geometric idealizations on computed data is examined through the example of a spherical shell with an edge ring. This example demonstrates that in typical structural problems it is better to avoid the use of sharp reentrant corners than to compensate for them by mesh refinement. The effect of different mapping techniques is also examined.
Linear and nonlinear finite element analysis on multiprocessor computer systems
Authors: Wilson Edward L. , Farhat Charbel H. 
Published: August 2005

AbstractSeveral general purpose computer systems with multiple processors operating concurrently are currently being commercially produced. Most of the present generation of finite element software was not designed to take advantage of this new technology. The purpose of this paper is to present the advantages of a new architecture for finite element programs which will operate efficiently on computer systems with any number of processors. Also, the basic approach is effective for multiprocessor computers with local or shared memory.The new computer program architecture is based on an initial application of a simple algorithm which automatically subdivides the complete finite element domain into a number of subdomains equal to the number of available processors. The resulting data structure requires a minimum of communication between processors during the formation of basic element matrices, reduction of subdomain matrices and the postprocessing of element results. The assembly and solution of the global system of subdomains can be accomplished directly or iteratively, and new concurrent solution algorithms can be introduced.Several of the ideas presented here have been tested on various types of computer. The new program architecture indicates that it is possible to obtain speed‐up times of over 90 per cent of the maximum theoretical values if appropriate numerical methods are employed.
Heat transfer analysis of structures containing phase‐change material
Authors: Loyd D. , Fröier M. 
Published: August 2005

AbstractA method is presented for analysing industrial heat transfer problems in which there is a transition. The finite element method is used, and for the calculations the special‐purpose heat transfer program THAFEM is utilized. The latent heat of a region with phase‐change material (PCM) is concentrated at the nodes of the elements in the region. The method is rapid and gives the necessary agreement between calculations and experimental results.As an example filling of explosives is considered. In order to avoid the formation of closed volumes of melted material surrounded by solidified explosive, it is necessary to control the cooling of the high‐explosive shell. The PCM is mainly trinitrotoluene with a melting point of 80.3°C. Another example that shows the applicability of the method is a fire‐proof floppy‐disk cabinet with walls made from layers of Glauber's salt, a PCM with a melting point of 32°C. The cabinet should withstand a fire, without the inside temperature exceeding the maximum allowed value of 52°C, for a prescribed time.
An isoparametric boundary solution for thermal radiation
Authors: Keavey M. A. 
Published: August 2005

AbstractIn order to solve problems of re‐radiation and reflection in finite element thermal analysis, a discretization consisting of flat isothermal surfaces is usually assumed. Such an approximation is clearly inconsistent if an isoparametric model is used for any surrounding solid. In addition, geometric view‐factors are often required explicitly, but their calculation is generally considered to be tedious and error prone. The representation of radiative exchange by a boundary integral equation is a standard analytical technique. The use of such a representation in conjunction with finite element analysis, however, appears to be quite recent. The present work describes a scheme whereby standard finite element/boundary element coupling theory may be applied to yield a method which is both simple and consistent. The use of isoparametric elements allows varying temperatures and curved surfaces to be modelled. For an empty enclosure the kernel of the integral equation is simply related to the differential geometric view‐factor. Re‐radiation and reflection are implicit.
Tracking the transient phase‐change front using the temperature of the convectively cooled surface
Authors: Choi Heon‐Oh 
Published: August 2005

AbstractThe coupled conduction‐convection problems which results from the solidification of a convective liquid are transformed into an equivalent minimization problem using an additional boundary condition which can be obtained from experiments. This transformed problem eliminates the necessity of solving the dynamic and energy equations of the liquid phase. Numerical simulations are performed to examine the applicability of the present method. Comparisons are made between the transient positions of the phase‐change front obtained from the present method and the steady‐state solutions. Sensitivity analysis of 10 per cent variations of the cooling rate are made.
Parametrized multifield variational principles in elasticity: I. Mixed functionals
Authors: Felippa Carlos A. 
Published: August 2005

AbstractA one‐parameter family of mixed variational principles for linear elasticity is constructed. This family includes the generalized Hellinger‐Reissner and total potential energy principles as special cases. The presence of the free parameter offers an opportunity for the systematic derivation of energy‐balanced finite elements that combine displacement and stress assumptions. It is shown that Fraeijs de Veubeke's stress‐assumption limitation principle takes a particulary elegant expression in terms of the parametrized discrete form. Other possible parametrizations are briefly discussed.
A single‐step algorithm for oscillatory problems
Authors: Thomas R. M. , Evans S. J. 
Published: August 2005

AbstractWe consider a class of multistage single‐step methods introduced by Zienkiewicz et al.1 and developed by Thomas and Gladwell.2 From this class, we derive methods which are particularly suitable for the numerical solution of oscillatory problems. We propose a particular pair of methods which permit local error estimation while retaining a ‘one‐step’ mode of operation. We discuss the implementation of this pair for both linear and nonlinear problems, and illustrate the discussion with numerical results.
Numerical analysis of transient states in one‐dimensional non‐linear systems
Authors: Jordan A. J. , Aniserowicz K. 
Published: August 2005

AbstractAn algorithm for the analysis of non‐linear partial differential equations describing transient states of one‐dimensional physical problems with boundary conditions given on the opposite ends of the analysed domain is presented. The algorithm makes use of the Runge‐Kutta and bisection methods used in space ℝ1 and the forward finite difference method for the time domain. The algorithm is illustrated by one‐dimensional analysis of a temperature field in a transient state.
A simulation of seasonal temperature and moisture content changes in the ground
Authors: Thomas H. R. , Owen R. C. 
Published: August 2005

AbstractThe paper describes the application of a numerical model to the prediction of seasonal temperature and moisture content changes in the ground. The results are compared with measured values taken over a two year period at the site of a monitored field experiment. Blind predications have been carried out on the basis of assumed material parameters. It is concluded that the analysis is largely capable of modelling the phenomena observed. Certain limitations are, however, exposed.
Numerical determination of the stress intensity factor KI in transient thermal state: Application to the cooling of a ‘penny shaped crack’
Authors: Berthomieu G. , Jouanna P. , De Langres E. 
Published: August 2005

AbstractThis study describes the evolution of the stress intensity factor KI for fissures in brittle elastic materials subjected to transient thermal actions. The case studied is a ‘penny shaped crack’ located in a rock mass and through which runs a fluid whose temperature falls in time.Computation was carried out using the CASTEM finite element method and its subprograms. The four steps are described: mesh elaboration, calculation of temperature field, thermo‐mechanical computations and estimation of KI by displacements or the J integral method. The results are given for various transient thermal conditions and for a steady state case for reference. Cooling spreads very slowly in the rock mass and there are steep temperature gradients in the first few millimetres.
Local boundary integral equation analysis of 2‐dimensional potential problems using Fourier series
Authors: Askin S. , Fenner R. T. 
Published: August 2005

AbstractLocal boundary integral equation (boundary element) methods make it possible to determine the variables of interest in a small pre‐selected region of a solution domain, without the need to determine the unknowns over the rest of the boundary. A method of this type based on Fourier series is developed for two‐dimensional potential problems governed by Laplace's equation. Very accurate values of the function and its derivatives can be obtained.
A finite‐element technique for coupled reaction and heat transfer analysis with negligible mass diffusion
Authors: Lee Ching‐Chih 
Published: August 2005

AbstractA technique is developed for solving a coupled reaction and heat transfer problem in which mass diffusion is negligible. The energy equation is solved by the conventional finite‐element method with temperature unknowns at the nodes, while the reaction kinetics is incorporated with reaction variables at the Gauss points in each element. As examples, cure of SMC (sheet moulding compound) in a cylinder and cure of rubber in an engine mount are analysed using a mechanistic and a phenomenological reaction model, respectively.
On the principle of cyclic symmetry in machine dynamics
Authors: Ramamurti V. , Seshu P. 
Published: August 2005

AbstractCyclic symmetric structures are those that posses a circumferentially periodic geometry, e.g. gear wheels, bladed discs, etc. Accurate prediction of their static and dynamic characteristics is essential to ensure optimum design. An analysis of the entire structure is often prohibitively costly. Through illustrative examples, the essential features of an analysis scheme exploiting the geometric periodicity are brought out. Avoiding much of the mathematics, the underlying principle (termed the‘eiψ relationship’) for both static and dynamic analysis is explained. The parallel to the special case of axisymmetric structures is drawn.
A new third‐order finite‐difference method for transient one‐dimensional advection—diffusion
Authors: Noye B. J. 
Published: August 2005

AbstractThe accuracy of some first and second‐order methods for solving the time‐dependent one‐dimensional constant‐coefficient advection‐diffusion equation are compared theoretically on the basis of the dominant error terms in their modified equivalent partial differential equations. A new very stable three‐point (in space) third‐order implicit method is then developed by combining two second‐order methods. The accuracies of the various methods are then compared by means of numerical tests.
Boundary‐element analysis of wave scattering from cracks
Authors: Jia Z. H. , Shippy D. J. , Rizzo F. J. 
Published: August 2005

AbstractA multi region boundary‐element method is employed to study the scattering of time‐harmonic waves by cracks in a three‐dimensional elastic solid. Special shape functions are employed to model the near‐crack singularity. The multi region formulation enables removal of singularities from all boundary integral equations. The matter of fictitious eigenfrequencies is discussed and resolved. Values of dynamic stress intensity factors for three problems involving penny‐shaped cracks are compared with results of other investigators.
On buckling mode superposition in non‐linear analysis of shells
Authors: Flores Fernando G. , Godoy Luis A. 
Published: August 2005

AbstractThis paper is concerned with the numerical solution of kinematically non‐linear shell problems using approximate techniques. The interest is focused on shells of revolution, for which a technique proposed by Nagy and König has been implemented and assessed by means of numerical studies. The non‐linear path is approximated using a reduced basis of buckling modes. The results illustrate that reasonable estimates of moderately non‐linear paths can only be expected for cases in which the fundamental path is governed by membrane action.
On relaxation of jacobi iteration for consistent and generalized mass matrices
Authors: Wathen A. J. 
Published: August 2005

AbstractIn time‐dependent finite‐element calculations a ‘mass matrix’ arises. It is thus necessary to solve or approximate a matrix system at each step even for ‘explicit’ time integration methods. In this manuscript we analyse the efficiency of Jacobi‐like iteration for solving such matrix equations which arise when the Galerkin or Taylor‐Galerkin methods are used.
Free‐vibration analysis of cyclic symmetric structures
Authors: Balasubramanian P. , Jagadeesh J. G. , Suhas H. K. , Ramamurti V. 
Published: August 2005

AbstractA subspace iteration scheme for the Hermitian eigenvalue problem arising from analysis of cyclic symmetric structures is presented. This operates in the semi‐complex domain and its computational efficiency is demonstrated. A modified convergence checking criterion which gives better error estimates, and a new trial vector selection scheme which accelerates convergence for the Hermitian eigenvalue problem based on the Ritz method, are presented.
Control‐volume energy‐balance fe formulation of the 8‐node hexahedron element
Authors: Abboud J. B. , Hardisty H. 
Published: August 2005

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

AbstractA finite‐element computer program consists of four basic modules, namely, computation of element stiffness matrices, assembly of the global stiffness matrix, solution of the system of linear simultaneous equations, and calculation of stresses. Vector algorithms consisting of direct vector Fortran code and the Engineering and Scientific Subroutine Library (ESSL) routines are presented for these modules. Numerical investigations were conducted using the IBM 3090–600E VF computer.For element stiffness matrix calculation, using a vector length equal to the number of elements produced speed‐up in the range of 3·2 to 3·7 over the corresponding scalar code. The vectorized global element stiffness matrix assembly was accomplished with the help of an INDEX array and the ESSL routine DAXPYI that resulted in the speed‐up of 2·6 to 4·3. The ESSL routines DPBF and DPBS gave speed‐up of 7·7 to 53·6 over a scalar Gaussian solver. The scalar‐to‐vector speed‐up for the stress calculation ranges from 2·2 to 5·33. The speed‐up of the totally vectorized program over the scalar program is from 7·4 to 51·9.As would be expected, the equation solution takes up the most computational effort in a finite‐element analysis. For the models we analysed the equation solution consumed 93 per cent to almost 100 per cent of the total CPU time in the scalar computations. Vectorizing the equation solver only reduces the percentage of its share to the range of 63 per cent to 88 per cent. In a totally vectorized program, the share of the equation solver effort is 85 per cent to 97 per cent. For the models analysed, the additional speed‐up accomplished by vectorizing the whole program over the one with a vectorized equation solver only was from 10 per cent to 40 per cent.
Surface pressure solution for boundary‐element analysis of stokes flow
Authors: Ingber Marc S. , Li Jing 
Published: August 2005

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

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

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

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

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

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

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

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

AbstractA common approach for solving initial value problems representing algebraic differential equations is to formulate the solution as a polynomial function. This paper presents predictor based integration formulae by formulating the solution function as a vector valued Bernstein polynomial, namely a Bézier function. The Bézier function subdivision theorem leads to a predictor evaluation algorithm for the next solution point using de Casteljau's iterative control vertex generation technique. It is shown that the convergence of the algorithms is a consequence of the use of the Bernstein uniform approximation basis and that the de Casteljau predictor evaluation scheme leads to a computationally simple estimate of the local truncation error.