bluuebunny/crossref_metadata_2025_split huggingface dataset:
An accurate scalar potential finite element method for linear, two‐dimensional magnetostatics problems
Authors: McDaniel T. W. , Fernandez R. B. , Root R. R. , Anderson R. B. 
Published: August 2005

AbstractWe have assessed the accuracy of a commercially available computer software package for finite element method calculations of magnetostatic fields. The computer program, MSC/NASTRAN,Available from the MacNeal‐Schwendler Corporation, Los Angeles, CA 90041, U.S.A.
is well known for its wide applicability in structural analysis and heat transfer problems. We exploit the fact that the differential equations of magnetostatics are identical to those for heat transfer if the magnetic field problem is formulated with the reduced scalar potential.1 Consequently, the powerful, optimized numerical routines of NASTRAN can immediately be applied to two‐ and three‐dimensional linear magneto‐statics problems. Application of the NASTRAN reduced scalar potential approach to a ‘worst case’ two‐dimensional problem for which an analytic solution is available has yielded much better accuracy than was recently reported2 for a reduced scalar potential calculation using a different finite element program. Furthermore, our method exhibits completely satisfactory performance with regard to computational expense and accuracy for a linear electromagnet with an air gap. Our analysis opens the way for large three‐dimensional magnetostatics calculations at far greater economy than is possible with the more commonly used vector potential and boundary integral methods.
Boundary element analysis of nonlinear water wave problems
Authors: Nakayama Tsukasa 
Published: August 2005

AbstractA new boundary element technique based on Green's formula is applied to the analysis of nonlinear water wave problems. The problems are formulated mathematically as two‐dimensional nonlinear initial‐boundary value problems in terms of a velocity potential, assuming the fluid to be inviscid and incompressible, and the flow to be irrotational.In the present paper, two kinds of wave‐making problems are analysed: (1) a tsunami generated by sea bed elevation; (2) generation, propagation and run‐up on a vertical wall of a solitary wave. Numerical results obtained by the present method are compared with available experimental data and analytical solutions. Excellent agreements are obtained.
Number of non‐zero blocks in the stiffness matrix of the finite element network
Authors: Feng Zhenxing 
Published: August 2005

AbstractIn Reference 1 a series of general formulae for evaluating the total number of non‐zero blocks in the stiffness matrix, both of two‐dimensional and three‐dimensional (arbitrary polygonal/polyhedral) finite element networks, was presented. In this paper, an alternative, more direct and efficient method for deriving such formulae is presented. In addition, this new method can be used for more complex situations. In fact, it may be used for almost all kinds of finite element networks.
A numerical analysis of time‐dependent two‐dimensional magnetic fields
Authors: Macbain John A. 
Published: August 2005

AbstractThe nonlinear diffusion equation as applied to two‐dimensional time‐dependent magnetic fields is solved with a finite element algorithm. This algorithm permits the analysis of problems possessing complex geometries, induced eddy currents, permanent magnets, and nonperiodic excitation currents. The numerical procedure utilizes implicit time stepping with an iterative scheme to solve the resulting set of equations. Two examples of applications of this program are presented.
Implementation of an improved bisection algorithm in buckling problems
Authors: Evans D. J. , Shanehchi J. 
Published: August 2005

AbstractAn improved bisection strategy is presented to determine the eigenvalues of a real symmetric tridiagonal matrix which occurs in a simple column buckling problem. The new strategy, which involves only a minor modification, utilizes incomplete Sturm sequences only as long as relevant information on the next and following eigenvalues is obtained resulting in a minimization of the computational work. The strategy is particularly effective if only a few eigenvalues are required. The technique can be used for a wider class of eigenvalue problems than the illustrative one presented here.
AGTHOM—automatic generation of triangular and higher order meshes
Authors: Moscardini A. O. , Lewis B. A. , Cross M. 
Published: August 2005

AbstractThe development and implementation of a comprehensive interactive computer package for the generation of finite element meshes for two‐dimensional problems is described. The package, AGTHOM, minimizes the user defined input and attempts to maximize the flexibility for the user with regard to modifying the mesh. An important feature of AGTHOM is its independence of expensive graphics hardware by using approximate terminal plots. Versions are available in both extended BASIC and FORTRAN.
An engineers' defence of the patch test
Authors: Irons Bruce , Loikkanen Matti 
Published: August 2005

AbstractThis convergence criterion is proved for any ‘legalizable’ finite element formulation, i.e. any model for which a conforming displacement version is possible, using the same nodal variables. Engineers may therefore take control of (and responsibility for) convergence, for most of the elements in service today. Stummel's counter‐example is explained as a technical misunderstanding, due to inadequate documentation of the patch test. It is suggested, without proof, that the test (properly applied) is universal, provided that it is always combined with an adequate test of stability.
Simplified finite element mesh for dynamic analysis of a nuclear reactor building
Authors: Bakeer Reda M. , Mandel James A. 
Published: August 2005

AbstractThe design of nuclear facilities requires dynamic analysis to evaluate their performance during an earthquake. In modal analysis, a method recommended for dynamic analysis by the Nuclear Regulatory Commission, the natural frequencies and mode shapes of the structure are commonly calculated using a stiffness matrix computed using the finite element method.A primary goal of this study was to design a finite element mesh, capable of modelling a reactor structure, with a minimum number of nodes and elements. This is necessary since analysis using a mesh fine enough to include all of the structural elements is not feasible because of exorbitant computer time and storage requirements. It was found that for lateral motion, a representative reactor structure could be accurately modelled using a simplified mesh with only one isoparametric quadratic quadrilateral element per floor. In this mesh essentially infinite springs must be placed between the masses at each floor level to prevent internal movements of the lumped masses within the quadratic quadrilateral elements.It was also found that a structure with rigid heavy bottom floors and a light top floor can be subjected to large displacements in the top floor during earthquakes. It was concluded that the properties of that light top floor (especially shear area) controls the value of the fundamental frequency of the building.
Unified finite element analysis
Authors: Mikhailov Mikhail Dimitrov 
Published: August 2005

AbstractA special matrix is introduced, the elements of which are zero or first‐order differential operators. This matrix is used to define a boundary value problem which covers a wide class of engineering applications. An equivalent variational formulation is found using an extension of the Gauss theorem. From this variational principle the equations of the elements are derived. The unified formulae presented here can be useful for educational purposes and for the design of a finite element system for total analysis.
Indentation of a half‐space with a rigid indentor
Authors: Voyiadjis George Z. , Buckner N. Ellis 
Published: August 2005

AbstractIn this work the problem of indentation of a half‐space by a spherical rigid indentor is investigated using the finite element method.A system of constitutive equations applicable to elasto‐plastic materials subjected to large deformations is used to determine the deformations and stresses for the contact problems. These equations represent the simplest generalization for the large‐deformation conditions of the classical theory of plasticity of metals based on the von Mises yield condition and the associated flow rule. The material formulation of the kinematical and dynamical relations will be used. These equations combine the kinematic and the isotropic strain‐hardening models.The results obtained from this work are compared with existing solutions for this problem that are confined to small strains and elastic, ideal‐plastic materials.
Boundary integral equation solution of moving boundary phase change problems
Authors: O'Neill Kevin 
Published: August 2005

AbstractBoundary integral equation methods are presented for the solution of some two‐dimensional phase change problems. Convection may enter through boundary conditions, but cannot be considered within phase boundaries. A general formulation based on space‐time Green's functions is developed using the complete heat equation, followed by a simpler formulation using the Laplace equation. The latter is pursued and applied in detail. An elementary, noniterative system is constructed, featuring linear interpolation over elements on a polygonal boundary. Nodal values of the temperature gradient normal to a phase change boundary are produced directly in the numerical solution. The system performs well against basic analytical solutions, using these values in the interphase jump condition, with the simplest formulation of the surface normal at boundary vertices. Because the discretized surface changes automatically to fit the scale of the problem, the method appears to offer many of the advantages of moving mesh finite element methods. However, it only requires the manipulation of a surface mesh and solution for surface variables. In some applications, coarse meshes and very large time steps may be used, relative to those which would be required by fixed grid domain methods. Computations are also compared to original lab data, describing two‐dimensional soil freezing with a time‐dependent boundary condition. Agreement between simulated and measured histories is good.
Optimum design sensitivity based on approximation concepts and dual methods
Authors: Schmit L. A. , Chang K. J. 
Published: August 2005

AbstractAn optimum design sensitivity analysis capability is reported which exploits the approximation concepts‐dual method formulation of the minimum weight structural sizing problem. An efficient iterative solution technique is used to facilitate determination of sensitivity derivatives for both primal and dual variables. Estimates on the useful range of parameter perturbations, over which the optimum design sensitivity projections can be expected to yield satisfactory revised optimum designs, are also obtained. Numerical results for several example problems will be presented to illustrate the effectiveness of the capability reported.
Numerical solutions to some free surface flows through nonhomogeneous media
Authors: Remar J. , Bruch J. C. , Sloss J. M. 
Published: August 2005

AbstractSteady‐state, free surface seepage through a heterogeneous porous medium underlain by a drain at a finite depth is solved using a fixed domain solution technique. The problems investigated are axisymmetric seepage from a circular pond and plane seepage from a symmetric channel. These ponds and channels may have variable shaped bottoms. Since the Baiocchi transformation was used to define a new dependent variable, the form of the permeability function was restricted to a product of functions of the independent variables. Herein the permeability was chosen to be a function of the depth only. For certain forms of this function, namely those having negative gradients, part of the flowfield becomes unsaturated and this violates the assumed saturation of the flowfield in the flow theory. The governing differential equation, which holds in the sense of distributions, is derived for a fixed solution domain and a simple algorithm (a finite difference successive over‐relaxation scheme with projection) is given to obtain the solution to these free surface problems. Numerous comparisons are made with published results. Rigorous mathematical justification of the methods used herein can be found in the references cited.
Chebyshev filtering Lanczos' process in the subspace iteration method
Authors: Loh Chee Hoong 
Published: August 2005

AbstractBathe's basic algorithm of subspace iteration for the solution of the symmetric eigenvalue problem is improved by including a Chebyshev filtering mechanism. To obtain satisfactory convergence for the largest eigenvalues, a shifting strategy is adopted. The shift factor is approximately computed by the Lanczos process.
Finite elements with increased freedom in choosing shape functions
Authors: Bergan P. G. , Nygård M. K. 
Published: August 2005

AbstractStarting with a mathematical statement of the convergence requirements for an element stiffness matrix, the paper discusses displacement shape functions that may be used in connection with the potential energy principle. In short, these functions must be force orthogonal and energy orthogonal, but they need not be conforming (satisfy interelement compatibility). It is shown that the requirements to the displacement functions may be greatly relaxed through slight modifications of the coupling stiffness between fundamental and higher order displacement modes. Several alternative formulations are examined. In particular, a new ‘free formulation’ is suggested. Using this form, which is very simple, the only requirement to the displacement patterns used is that they should contain the fundamental deformation modes and be linearly independent. Applications of the theory to triangular and rectangular plate bending elements are shown; the simple stiffness matrix for the latter is given explicitly. The numerical results compare favourably with other types of finite elements.
Scalar potentials in multiply connected regions
Authors: Brown M. L. 
Published: August 2005

AbstractAn algorithm, for use on a digital computer, is explained for cutting multiply connected regions in three‐dimensional space. The algorithm is suitable for complex electromagnetic field problems where a magnetic scalar potential, affected by current loops, is to be calculated in a multiply connected region. Problems in fluid dynamics with vorticity affecting a scalar potential, could also be attacked with this algorithm. Since finite element methods are ubiquitous in field calculations, the cuts of the space constructed by the algorithm should ideally correspond to the given discretization; this can be arranged by an application of the Lebesgue Covering Theorem, for which a second algorithm is provided.
The application of shape‐preserving splines for the solution of differential equations
Authors: Shoucri Magdi M. , Shoucri Rachad M. 
Published: August 2005

AbstractThis paper investigates the use of shape‐preserving interpolants based on Bernstein polynomials for the numerical solution of differential equations. A simple and accurate algorithm is presented for the integration of the initial value ordinary differential equation, as well as for the partial differential equation of the Burger type.
Minimum‐weight design of trusses by an optimality criteria method
Authors: Allwood R. J. , Chung Y. S. 
Published: August 2005

AbstractThis work presents an optimality criteria method which accurately and efficiently solves the structural optimization problem of trusses subject to deflection and stress constraints. The method is based upon the Newton–Raphson method and a first‐order approximation both for deflection and stress constraints using the method of virtual work. It solves the problem rigorously and no serious difficulties have yet been encountered in spite of the drawbacks inherent in the Newton–Raphson method. Worked examples show its superiority to other methods and its ability to cope with trusses with many members and subject to multiple constraints.
A memory‐economic frontwidth reduction algorithm
Authors: Silvester Peter P. , Auda Hesham A. , Stone Geoffrey D. 
Published: August 2005

AbstractA simple element numbering algorithm is described which yields near‐minimal frontwidths for two‐ and three‐dimensional finite element assemblies. Renumbering of E elements requires an immediate‐access computer memory size which is proportional to the square root of E in two‐dimensional problems, and to the two‐thirds power of E in three dimensions. This very small memory requirement allows processing of large problems in minicomputers. When used in large computers, page‐swapping operations are minimized.
A recursive quadratic programming method with active set strategy for optimal design
Authors: Belegundu Ashok D. , Arora Jasbir S. 
Published: August 2005

AbstractRecursive quadratic programming methods have become popular in the field of mathematical programming owing to their excellent convergence characteristics. There are two recursive quadratic programming methods that have been published in the literature. One is by Han and the other is by Pshenichny, published in 1977 and 1970, respectively. The algorithm of Pshenichny had been undiscovered until now, and is examined here for the first time. It is found that the proof of global convergence by Han requires computing sensitivity coefficients (derivatives) of all constraint functions of the problem at every iteration. This is prohibitively expensive for large‐scale applications in optimal design. In contrast, Pshenichny has proved global convergence of his algorithm using only an active‐set strategy. This is clearly preferable for large‐scale applications. The method of Pshenichny has been coded into a FORTRAN program. Applications of this method to four example problems are presented. The method is found to be very reliable. However, the method is found to be very sensitive to local minima, i.e. it converges to a local minimum nearest to the starting design. Thus, for optimal design problems (which usually possess multiple local minima) it is suggested that Pshenichny's method be used as part of a hybrid method.
A robust incomplete Choleski‐conjugate gradient algorithm
Authors: Ajiz M. A. , Jennings A. 
Published: August 2005

AbstractWhen applied to large sparse sets of simultaneous equations, classical iterative methods may yield very poor convergence rates. This paper gives an incomplete Choleski‐conjugate gradient algorithm (ICCG) which has reliably good convergence rates at the expense of computing and using at each iteration an incomplete Choleski factor of the coefficient matrix. The method is applicable to any problems in which the coefficient matrix is symmetric positive definite and is likely to be advantageous with respect to elimination when it is not possible to represent the equations in a dense band form.
A discrete singularity formulation for solving steady, fully developed duct flows
Authors: Yano H. , Fukutani S. , Kieda A. , Oshima T. 
Published: August 2005

AbstractA very effective numerical formulation is proposed to solve approximately the problem of steady, fully developed laminar flows of incompressible fluids in straight ducts of arbitrary, simply connected cross‐sections. The method is an application of the discrete singularity technique, with a finite number of singularities located outside the domain concerned. To illustrate the usefulness of the method, some examples of computations are also presented.
Finite layer analysis of layered elastic materials using a flexibility approach. Part 1—Strip loadings
Authors: Small J. C. , Booker J. R. 
Published: August 2005

AbstractIt is well known that the analysis of a horizontally layered elastic material can be considerably simplified by the introduction of a Fourier or Hankel transform and the application of the finite layer approach. The conventional finite layer (and finite element) stiffness approach breaks down when applied to incompressible materials. In this paper these difficulties are overcome by the introduction of an exact finite layer flexibility matrix. This flexibility matrix can be assembled in much the same way as the stiffness matrix and does not suffer from the disadvantage of becoming infinite for an incompressible material. The method is illustrated by a series of examples drawn from the geotechnical area, where it is observed that many natural and man‐made deposits are horizontally layered and where it is necessary to consider incompressible behaviour for undrained conditions.
The post‐processing approach in the finite element method—part 1: Calculation of displacements, stresses and other higher derivatives of the displacements
Authors: Babuška I. , Miller A. 
Published: August 2005

AbstractThis is the first in a series of three papers in which we discuss a method for ‘post‐processing’ a finite element solution to obtain high accuracy approximations for displacements, stresses, stress intensity factors, etc. Rather than take the values of these quantities ‘directly’ from the finite element solution, we evaluate certain weighted averages of the solution over the entire region. These yield approximations are of the same order of accuracy as the strain energy. We obtain error estimates, and also present some numerical examples to illustrate the practical effectiveness of the technique. In the third paper of this series we address the matters of adaptive mesh selection and a posteriori error estimation.
Incremental shakedown analysis in the case of thermal effects
Authors: Kleiber M. , König J. A. 
Published: August 2005

AbstractA new method of performing the shakedown analysis of structures subjected to variable repeated loads and temperature fields is presented. The method employs the standard incremental elastic‐plastic finite element algorithm and is based upon a cyclic repetition of piecewise‐proportional paths that contain all the vertices of the load‐temperature variation domain. A numerical example illustrates the approach.
A partial‐boundary element approach to the elastic torsion problem of a prismatic beam with a cracked rectangular cross‐section
Authors: Shangchow Chang 
Published: August 2005

AbstractUsing the partial‐boundary element approach, in which only a part of the boundary in problem is discretized, the elastic torsion problem of a prismatic beam of a cracked rectangular cross‐section has been solved in this brief paper, together with a numerical example to show the accuracy and versatility of the approach.
The design of a variable‐step integrator for the simulation of gas transmission networks
Authors: Chua T. S. , Dew P. M. 
Published: August 2005

AbstractThe simulation of a large‐scale gas transmission network involves the numerical solution of a large system of initial valued, stiff algebraic/differential equations. Rapid changes in the solution are present due to the disturbances generated by the varying consumer demand and the operation of network controlling devices such as compressors. This paper discusses the design of an efficient variable‐step integrator for the solution of the problem. Two sets of strategies are presented for implementing the variable‐step integrator; one for the implicit numerical method such as the diagonally implicit Runge–Kutta methods, and the other for the linearly implicit Rosenbrock‐type method. The performance of the numerical methods implemented are compared with the British Gas simulation program PAN on a number of large, realistic transmission networks.