bluuebunny/crossref_metadata_2025_split huggingface dataset:
Quality of trial functions in quadratic isoparametric representation of an arc
Authors: Morley L. S. D. 
Published: August 2005

AbstractAn examination is made of displacement trial functions found in the quadratic isoparametric representation of an arc. Special attention is given to the quality of curvature change description and to effective manipulation of the trial functions. Various interpolation formulae are derived which have relevance to curved shell finite element design under Love‐Kirchhoff assumptions.
A comparative study on three boundary element method approaches to problems in elastodynamics
Authors: Manolis George D. 
Published: August 2005

AbstractIn this study, three boundary element method approaches are compared by solving a typical problem in linear elastodynamics. The first approach formulates and solves the problem in the real time domain in conjunction with a time‐stepping algorithm. The other two approaches formulate and solve the problem in the Laplace and the Fourier transformed domains, which necessitates a numerical inversion of the results to the time domain. The results obtained compare favourably with available analytic solutions. A detailed tabulation of the computer time and memory requirements of each approach is presented.
Finite element method for unbounded field problems and application to two‐dimensional taper
Authors: Orikasa Teruaki , Honma Toshihisa , Fukai Ichiro , Washisu Shin 
Published: August 2005

AbstractTreatment of the finite element method for an unbounded field problem was proposed by McDonald and Wexler in 1972. Their method is superior to others, because it can exclude the singularities of Green's functions. This paper explains the treatment of the method in our 1979 letter which had some revisions of McDonald and Wexler's and calculated the time‐harmonic field problems. Examples presented are electromagnetic fields of two‐dimensional tapers which are open‐ended. Electromagnetic waves propagate in the taper and radiate from the taper to free space. In this case, the exact solutions for radiation from tapers are not available because of the complicated shape, and so the finite element method is useful in solving these problems. Electromagnetic fields of tapers involving dielectric slabs are also calculated as examples of inhomogeneous problems.
A study of nonlinear periodic systems via the point mapping method
Authors: Flashner Henryk , Hsu C. S. 
Published: August 2005

AbstractIt is well known that one way to treat nonlinear periodic dynamical systems governed by ordinary differential equations is to find first the corresponding point mappings. This approach has many advantages but it has a main obstacle in that it is difficult to obtain the exact mapping except in very special cases. Presented in this paper is a procedure which allows us to determine the point mapping in a polynomial form up to any specific degree of accuracy. The procedure when applied to linear periodic systems reduces to the one proposed by Friedmann et al.22 After presenting the algorithm for finding the point mappings, the method is applied to several problems in order to study the dynamical properties of the systems and to demonstrate the usefulness of the method.
Structural optimization to include material selection
Authors: Imai Kanji 
Published: August 2005

AbstractThe mini‐max dual method ia applied for solving the material selection structural optimization problems. A somewhat general objective function is introduced to consider structural weight and material cost simultaneously. It is expressed by the sum of scaled structural weight and material cost. The present formulation can yield minimum cost and minimum weight designs as two distinct special cases. It is shown that practically useful intermediate optimal designs can exist between the two extremes. Only truss structures are considered as a representative example. One numerical example is provided to illustrate the change in optimal material distribution when various objective functions are employed. A particular advantage in using the dual method for the material selection problem is also described.
Comparison of magnetic fields computed by finite element and classical series methods
Authors: Baker F. E. , Brown S. H. , Brauer J. R. , Gerhardt T. R. 
Published: August 2005

AbstractThe finite element reduced scalar potential method of calculating magnetic fields is investigated by comparing it with a classical series method. Both methods are applied to two problems having a current band surrounding a ferromagnetic shell. The magnetic field distributions obtained by both methods are shown to be in generally good agreement.
Damping and phase analysis for some methods for solving second‐order ordinary differential equations
Authors: Gladwell I. , Thomas R. M. 
Published: August 2005

AbstractWe consider numerical methods for initial value problems for second‐order systems of ordinary differential equations, analysing them by applying them to the test equation We discuss conditions which ensure an oscillatory numerical solution and the desirability of such a property. We also use a slightly more general test equation to derive conditions which ensure that the numerical forced oscillation is in phase with the true forced oscillation.To illustrate the theory, we consider the damping and phase properties of some frequently used methods.
A non‐conforming piecewise quadratic finite element on triangles
Authors: Fortin M. , Soulie M. 
Published: August 2005

AbstractIt is shown in this paper that non‐conforming finite elements on the triangle using second‐degree polynomials can be easily built and used. Indeed they appear as an ‘enriched’ version of the standard piecewise quadratic six‐node element. This work is divided into two parts. In the first we present the basic properties of the element, namely how it can be built and basic error estimates. We also show that this element exhibits a very peculiar regularity property. In the second part we apply our element to the approximation of viscous incompressible flows and more generally to the approximation of incompressible materials.
Geometrically nonlinear formulation for the curved shell elements
Authors: Surana Karan S. 
Published: August 2005

AbstractThis paper presents a geometrically nonlinear formulation using total lagrangian approach for the three‐dimensional curved shell elements. The basic element geometry is constructed using the coordinates of the middle surface nodes and the mid‐surface nodal point normals. The element displacement field is described using three translations of the mid‐surface nodes and the two rotations about the local axes. The existing shell element formulations are restricted to small nodal rotations between two successive load increments. The element formulation presented here removes such restrictions. This is accomplished by retaining nonlinear nodal rotation terms in the definition of the displacement field and the consistent derivation of the element properties. The formulation presented here is very general and yet can be made specific by selecting proper nonlinear functions representing the effects of nodal rotations. The element properties are derived and presented in detail. Numerical examples are also presented to demonstrate the behaviour and the accuracy of the elements.
A note on universal matrices for triangular finite elements for the quasi‐harmonic equation
Authors: Subramanian G. , Bose C. Jeyachandra , Babu C. Ramesh 
Published: August 2005

AbstractAn algorithm to generate universal matrices for plane triangular finite elements for the general ‘quasi‐harmonic’ equation is presented. For every member of the triangle family three numerical universal matrices are obtained which are independent of the size, shape and ‘material’ properties of the element. Of these, two are basic and the third can be generated from one of these two. The element ‘stiffness’ matrix is conveniently generated by manipulating these two basic matrices taking into account the size, shape and material properties of the element in a simple manner.
Dynamic elasto‐plastic response of shells in an acoustic medium—EPSA code
Authors: Atkatsh Robert S. , Bieniek Maciej P. , Baron Melvin L. 
Published: August 2005

AbstractA nonlinear, large deflection, elasto‐plastic finite element code (EPSA) has been developed for the analysis of shells in an acoustic medium subjected to dynamic loadings. The nonlinear equations of shells are discretized with the aid of a finite difference/finite element method based upon the principle of virtual work. The resulting system of equations contains the nodal displacements as the generalized co‐ordinates of the problem. The integration in time of the equations of motion is done explicitly via a central difference scheme.Shell strain‐displacement relations are established by a two‐dimensional finite difference scheme. The shell constitutive equations are formulated in terms of the shell stress resultants and the shell strains and curvatures. The fluid‐structure interaction is accounted for by means of the doubly asymptotic approximation (DAA) expressed in terms of orthogonal fluid expansion functions. The analytically produced results satisfactorily reproduce available experimental data for dynamically loaded shells.
A decomposition procedure for large‐scale optimum plastic design problems
Authors: Kaneko Ikuyo , Ha Cu Duong 
Published: August 2005

AbstractA decomposition procedure is proposed in this paper for solving a class of large‐scale optimum design problems for perfectly‐plastic structures under several alternative loading conditions. The conventional finite element method is used to cast the problem into a finite dimensional constrained nonlinear programming problem. Structures of practically meaningful size and complexity tend to give rise to a large number of variables and constraints in the corresponding mathematical model. The difficulty is that the state‐of‐the‐art mathematical programming theory does not provide reliable and efficient ways of solving large‐scale constrained nonlinear programming problems. The natural idea to deal with the large‐scale structural problem is somehow to decompose the problem into a collection of small‐size problems each of which represents an analysis of the behaviour of each finite element under a single loading condition. This paper proposes one such way of decomposition based on duality theory and a recently developed iterative algorithm called the proximal point algorithm.
An infinite element and a formula for numerical quadrature over an infinite interval
Authors: Pissanetzky Sergio 
Published: August 2005

AbstractIn this publication we present a new infinite element and discuss a formula for numerical quadrature over infinite regions. Both the element and the formula are based on the properties of a set of orthonormal functions, obtained by mapping the Legendre polynomials on the infinite interval. The element can represent any (physical) function over the entire infinite region, and the formula can integrate most integrands over the infinite interval. They are thus very convenient for implementation in a general computer program, which could then be used to solve different problems with no restrictions concerning the asymptotic behaviour of the solutions or the form of integrands to be integrated over the infinite interval. However, the element and the formula will perform at their best when used in conjunction, and for problems of electrostatic, magnetostatic, etc., potential.The formula was compared with other existing formulae and found to be either superior or satisfactory in practically all cases, as shown by the results of many numerical experiments.Expressions of shape functions are given for the element. A test problem was solved using the element and the formula, and the results are shown to be more accurate than those obtained when solving the same problem using infinite elements with exponential decay and Gauss‐Laguerre numerical quadrature.
A boundary element solution to elasto‐plastic torsion of solids of revolution
Authors: Zhen‐Sheng Chen 
Published: August 2005

AbstractA boundary element method for the solution of problems of elastic and elasto‐plastic torsion of solids of revolution is proposed. The displacement and stress field produced by a circumferential ring load in an infinite elastic body are derived and used as the fundamental solution to establish the governing integral equations. For the elasto‐plastic case, linear boundary elements and bilinear quadrilateral internal cells are used for discretization of these equations. In order to carry out Gaussian integrations along boundary elements and over internal cells, a method ensuring sufficient accuracy for the calculation of singular integrals is proposed. Numerical results for several problems are given.
General derivative approximations for finite different schemes
Authors: Patterson J. C. 
Published: August 2005

AbstractA general expression for finite difference approximations for all derivatives up to the (N − 1)th order on a finite difference mesh with N‐nodes is established. The mesh may be non‐uniform and the derivative evaluated at any of the N‐nodes. An estimate for the truncation error is obtained and shown to depend on the nonlinearity of the mesh as well as on the mesh diameter. Specific formulae for first‐ and second‐order derivatives are given as examples.
On extrapolation boundary conditions for the numerical solution of hyperbolic difference schemes
Authors: Jamieson S. M. , Sloan D. M. 
Published: August 2005

AbstractAn analysis is presented for the stability of an initial and boundary value difference scheme arising from the solution of a two‐dimensional hyperbolic equation by the Lax‐Wendroff method. The positive and negative characteristic speeds of the linear equation are not necessarily equal in magnitude. Supplementary boundary conditions required for the finite difference solution are obtained using extrapolation for a linear combination of the dependent variables. The analysis produces stability intervals for the parameter which describes this linear combination of variables. Numerical experiments are described which support the theoretical analysis.
A posteriori error analysis and adaptive processes in the finite element method: Part II—adaptive mesh refinement
Authors: De S. R. Gago J. P. , Kelly D. W. , Zienkiewicz O. C. , Babuska I. 
Published: August 2005

AbstractThis is a paper presented in two parts dealing respectively with error analysis and adaptive processes applied to finite element calculations. Part I contains the basic theory and methods of deriving error estimates for second‐order problems. Part II of the paper deals with the strategy for adaptive refinement and concentrates again on the p‐convergent methods. It is shown that an extremely high rate of convergence is reached in practical problems using such procedures. Applications to realistic stress analysis and potential problems are presented.
A finite element for the analysis of reinforced concrete structures
Authors: Gupta Ajaya K. , Akbar Habibollah 
Published: August 2005

AbstractFormulation of a four‐node isoparametric element suitable for modelling cracks in reinforced concrete structures is presented. The standard isoparametric element is known to give spurious shear stresses. The conventional remedy of selective integration breaks down in a ‘cracked’ element. It is shown that the proposed formulation gives superior results as compared to both the standard isoparametric element and the conventional selectively integrated element.
Reparametrization and its application in computer‐aided geometric design
Authors: Ball A. A. 
Published: August 2005

AbstractThe paper develops the theory of reparametrization within the context of computer‐aided geometric design. It is established that the parametrization plays a positive role in the numerical description of curves and surfaces and it is proposed that the parametrization should be controlled, independently from the shape, via reparametrization. A general approach to reparametrization is adopted in which a function to change the parametrization is modelled in addition to the basic parametric equation. Examples are given for parametric polynomial curves, probably the most commonly used curve segments in computer‐aided geometric design. Finally it is shown how reparametrization might be applied to enhance existing surface definition procedures. A surface equation is developed based on the parametric cubic segment that can define shapes virtually independent of the parametrization.
Modelization of phase changes by fictitious‐heat flow
Authors: Roose J. , Storrer O. 
Published: August 2005

AbstractThis paper presents an efficient algorithm to solve phase change problems. The first part gives the definition of the problem and mentions some practical applications. The second part analyses how to deal with phase changes by means of concentrated fictitious heat flows. The principles of the method are described and compared to those of other methods. The concept of ‘the area associated with a node’ is developed and some practical values for the weight coefficients are recommended. Conclusions are given about the convergence and the stability of the algorithm, and about the improvements obtained by prescribing the temperatures and using relaxation techniques. Theoretical and practical examples illustrate the validity and efficiency of the proposed method.
Boundary integral equation method for linear porous‐elasticity with applications to fracture propagation
Authors: Cheng Alexander H‐D. , Liggett James A. 
Published: August 2005

AbstractFor the semi‐infinite crack propagating quasi‐statically in a porous‐elastic medium, the boundary integral equation method (BIEM), based on a reciprocal principle, is formulated for the governing equations of the Biot model of linear porous‐elasticity. The resulting numerical scheme is efficient since the discretization of the solution unknowns is required only along the axis of symmetry of a fracture. Fracture propagation criteria based on both elastic and plastic constitutive relations are investigated. Practical applications of the model are expected in the failure of overconsolidated clay, earthquake prediction and underground hydraulic fracturing for energy exploration.
Non‐iterative solution of a tridiagonal‐type matrix coupled by diagonal submatrices
Authors: Deshpande M. D. 
Published: August 2005

AbstractA non‐iterative method is presented for solving a system of algebraic equations forming a banded matrix with each diagonal submatrix being tridiagonal and all other submatrices being diagonal. A recursion relation is assumed between successive elements of the solution vector. This relation is determined by equating a linearly combined form of it with the original set of equations also being linearly combined. The solution vector is determined by back‐substitution of elements in the recursion relation. Since the method takes advantage of the banded structure of the matrix, it is more efficient than the conventional methods. A FORTRAN program that incorporates the present method is included.
An optimized solution for the diffusion equation on a non‐uniform grid
Authors: Sobey R. J. 
Published: August 2005

AbstractA lowest order difference scheme has been developed for a spatially non‐uniform grid such that the integrated square error is a minimum. This algorithm accommodates grid asymmetry and maintains reasonable accuracy without recourse to higher order approximations. Numerical experiments and computations of the Fourier response factor confirm the performance of the optimized asymmetric algorithm.
Deflection of thick beams of multimodular materials
Authors: Bertm C. W. , Gordaninejad F. 
Published: August 2005

AbstractA transfer‐matrix analysis is presented for determining the static behaviour of thick beams of ‘multimodular materials’ (i.e. materials which have different elastic behaviour in tension and compression, with nonlinear stress–strain curves approximated as piecewise linear, with four or more segments). To validate the transfer‐matrix method results, a closed‐form solution is also presented for cases in which the neutral‐surface location is constant along the beam axis. Numerical results for axial displacement, transverse deflection, bending slope, bending moment, transverse shear, axial force and location of neutral surface are presented for multimodular and bimodular models of unidirectional aramid cordrubber. The transfer‐matrix method results agree very well with the closed‐form solutions.
Numerical solution of a parabolic system with coupled nonlinear boundary conditions
Authors: Liu Ta‐Jo 
Published: August 2005

AbstractA numerical technique has been developed to solve a system that consists of m linear parabolic differential equations with coupled nonlinear boundary conditions. Such a system may represent chemical reactions, chemical lasers and diffusion problems. An implicit finite difference scheme is adopted to discretize the problem, and the resulting system of equations is solved by a novel technique that is a modification of the cyclic odd–even reduction and factorization (CORF) algorithm. At each time level, the system of equations is first reduced to m nonlinear algebraic equations that involve only the m unknown grid points on the nonlinear boundary. Newton's method is used to determine these m unknowns, and the corresponding Jacobian matrix can be computed and updated easily. After convergence is achieved, the remaining unknowns are solved directly. The efficiency of this technique is illustrated by the numerical computations of two examples previously solved by the cubic spline Galerkin method.
An invariant eight‐node hybrid‐stress element for thin and thick multilayer laminated plates
Authors: Spilker R. L. 
Published: August 2005

AbstractA hybrid‐stress eight‐node isoparametric element is developed for the analysis of thin or thick multilayer fiber‐reinforced composite plates. Transverse shear deformation effects are included by allowing for individual layer cross‐section warping for thick laminates, or alternatively, laminate non‐normal cross‐section rotations for thin to moderately thick laminates. All stress components are included and are interpolated independently within each layer. Interlayer surface traction continuity and appropriate upper/lower surface traction‐free conditions are exactly satisfied. The layer stress field is selected on the basis of earlier single‐layer element studies so that the resulting element is naturally invariant with respect to co‐ordinate translation or rotations, is non‐locking in the thin‐plate limit, and the element stiffness is of correct rank. An example for which an elasticity solution is available is used to demonstrate the element performance. Schemes for reduction of element stiffness computation time are also presented.
Analysis of multi‐layer laminates using three‐dimensional super‐elements
Authors: Jones R. , Callinan R. , Teh K. K. , Brown K. C. 
Published: August 2005

AbstractAnalysis of multi‐layer composite laminates using three‐dimensional finite element models often results in high computational cost. This communication reports a three‐dimensional super‐element scheme which can reduce the computational cost.
Finite element analysis of wave motion
Authors: Kawahara Mutsuto , Miwa Toshihiko 
Published: August 2005

AbstractTo estimate wave motion, the finite element method is presented based on the linear interpolation function and two‐step explicit numerical integration in time. For the determination of free surface position, the two‐step scheme based on the Eulerian technique is usefully employed. Travel and run‐up of solitary wave have been analysed and compared with the analytical solution. Both results are reasonably well in agreement. This method is applied to estimate the wave force on the practical breakwater to show the validity of the method.