bluuebunny/crossref_metadata_2025_split huggingface dataset:
Point matching computation of transverse resonances
Authors: Bates R. H. T. , Ng F. L. 
Published: August 2005

AbstractPoint matching (collocation) methods are reviewed and the conditions under which they break down are examined. The detailed treatment applies to complex‐valued solutions of the two‐dimensional Helmholtz equation with either Neumann or Dirichlet boundary conditions. Point matching methods (when they are valid) can have very real computational advantages. It is shown, by a combination of analysis and computational example, how to estimate whether the cross‐section of any particular resonant system is suitable for the application of an existing point matching method. An extended point matching method is introduced to handle cases for which previous methods fail. The method is illustrated with several computational examples. The discussion is specifically concerned with electromagnetic wave guides, but the results can be applied to a wide range of physical systems.
Solution methods for eigenvalue problems in structural mechanics
Authors: Bathe Klaus‐Jürgen , Wilson Edward L. 
Published: August 2005

AbstractA survey of probably the most efficient solution methods currently in use for the problems Kϕ = ω2Mϕ and KΨ = λKGΨ is presented. In the eigenvalue problems the stiffness matrices K and KG and the mass matrix M can be full or banded; the mass matrix can be diagonal with zero diagonal elements. The choice is between the well‐known QR method, a generalized Jacobi iteration, a new determinant search technique and an automated sub‐space iteration. The system size, the bandwidth and the number of required eigenvalues and eigenvectors determine which method should be used on a particular problem. The numerical advantages of each solution technique, operation counts and storage requirements are given to establish guidelines for the selection of the appropriate algorithm. A large number of typical solution times are presented.
A direct integral equation method for the potential flow about arbitrary bodies
Authors: Grodtkjær Erik 
Published: August 2005

AbstractThe velocity on the surface of an arbitrary three‐dimensional body in the potential flow of an ideal fluid is determined by means of an integral equation method. The equations to be solved are a pair of singular integral equations of the second kind, the unknowns being the desired velocity components. The integral equations are approximated by a set of linear equations, which are solved numerically. For ellipsoids the results are compared with the analytic solutions.
Criteria for finite element discretization of shells of revolution
Authors: Sen Subir K. , Gould Phillip L. 
Published: August 2005

AbstractA method is described whereby an efficient finite element discretization scheme for a shell of revolution can be predetermined and subsequently refined for successive analyses by considering the following criteria:

Stress intensification in the vicinity of a concentrated action.
Variation in the strain energy intensity function.

Several case problems have been studied to validate the procedure.
A computer program for filter design having arbitrary magnitude specifications in the frequency domain
Authors: Jullien G. A. , Sid‐Ahmed M. A. 
Published: August 2005

AbstractA general procedure is presented for the design of analogue or digital filters having arbitrary specifications in the frequency domain. The algorithm developed uses a simple technique for constraining the pole zero locations, for stability and minimum phase considerations, which is far more elegant than methods used by previous workers.1 This constraint procedure yields a unified approach to the design of both digital and analogue filters.The method employed is that of minimizing a square‐error criterion using the Fletcher–Powell2 conjugate gradient minimization routine.The programme is written in FORTRAN IV double precision complex arithmetic.
Flow of plastic and visco‐plastic solids with special reference to extrusion and forming processes
Authors: Zienkiewicz O. C. , Godbole P. N. 
Published: August 2005

AbstractWhen large, progressive, deformation occurs under plastic or visco‐plastic conditions, elastic deformations are negligible and the material flows in a viscous manner. The flow is non‐Newtonian and the viscosity is a function of the current strain rates. An effective numerical treatment of such non‐Newtonian flow by the finite element method is indicated here and is illustrated by examples of an extrusion process for which approximate slip line solutions are known.The methodology is extended to the solution of transient, quasi‐static situations and coupling with thermodynamic equations is discussed.A stream function formulation of the problem is used.
Application of finite element methods to thermohydrodynamic lubrication
Authors: Huebner Kenneth H. 
Published: August 2005

AbstractA finite element formulation is presented for the equations governing the steady thermohydrodynamic behaviour of liquid lubricated bearings. This formulation permits application of the iterative solution scheme to bearings of arbitrary geometry.A generalized Reynolds equation resulting from the combination of the mass and momentum conservation equations is cast into variational form and used to derive general finite element equations. The method of weighted residuals with Galerkin's criterion is used to generate finite element matrix equations for the thermal energy equation. In addition to the finite element formulation, a discussion of appropriate finite difference techniques is also given for problems without complex geometry.As an example, the formulations are applied to obtain numerical solutions for a three‐dimensional sector thrust bearing operating in the thermohydrodynamic regime. Pressure, velocity and temperature distributions are give, and the thermohydrodynamic solutions are compared with the results of classical isothermal theory.
Torsion of axi‐symmetric solids of variable diameter—including acceleration effects
Authors: Owen D. R. J. , Zienkiewicz O. C. 
Published: August 2005

AbstractA finite element method for the analysis of axisymmetric bodies in torsion is presented. The effects of an angular acceleration about the axis of symmetry is included. The accuracy of the method is tested against experimental results available for a stepped shaft and finally the problem of an accelerating shaft‐turbine disc system is considered.
Cubic spline Galerkin approximations to parabolic systems with coupled non‐linear boundary conditions
Authors: Murphy W. D. 
Published: August 2005

AbstractThis paper describes a practical implementation of the Galerkin finite element procedure for solving systems of parabolic partial differential equations with non‐linear boundary conditions. This technique consists of finding an approximation in the form of a finite sum of cubic B‐splines, which yield high‐order accurate results, and consequently, solutions can be developed with remarkable precision and speed up to the steady state region where conventional finite difference methods often fail. In addition, the choice of mesh width and nodal spacing can be automatically determined for a predictor‐corrector routine, thereby relieving the engineer of a great deal of ‘guess work’ that is normally characteristic of solving such problems.
Three‐dimensional elasto‐plastic finite element analysis
Authors: Owen D. R. , Salonen E. M. 
Published: August 2005

AbstractAdvances in technology and interest in limit state design have made the inclusion of non‐linear effects, such as elasto‐plastic behaviour, desirable in the analysis of many structures. Improvements in solution algorithms coupled with parallel developments in high speed digital computers have now made the practical solution of such problems possible. The paper presents numerical solutions to three‐dimensional elasto‐plastic problems illustrating the applicability of isoparametric elements and the order of computation times involved.
Panel flutter optimization by gradient projection
Authors: Pierson B. L. 
Published: August 2005

AbstractA gradient projection optimal control algorithm incorporating conjugate gradient directions of search is described and applied to several minimum weight panel design problems subject to a flutter speed constraint. New numerical solutions are obtained for both simply‐supported and clamped homogeneous panels of infinite span for various levels of inplane loading and minimum thickness. The minimum thickness inequality constraint is enforced by a simple transformation of variables.
Thermal deformation vector for a bilinear temperature distribution in an anisotropic quadrilateral membrane element
Authors: Wallerstein D. V. 
Published: August 2005

AbstractThis paper presents a thermal‐structural deformation vector for an anisotropic quadrilateral membrane element. The elastic properties of the element are based on linear stress assumptions and were developed by Robinson1. A general bilinear temperature field within the element is chosen in order to obtain a thermal deformation capability for the element commensurate with its elastic capability. A pseudo shear term is developed to account for part of the thermal deformation. The element is suitable for finite element analysis of advanced aircraft structures under elevated temperature environments and is particularly well suited for analysis of regions with severe temperature gradients such as occur in the vicinity of local heat sources and sinks. An example problem is included to demonstrate the behaviour of the element.
Crack tip finite elements are unnecessary
Authors: Henshell R. D. , Shaw K. G. 
Published: August 2005

AbstractIt is shown that a singularity occurs in isoparametric finite elements if the mid‐side nodes are moved sufficiently from their normal position. By choosing the mid‐side node positions on standard isoparametric elements so that the singularity occurs exactly at the corner of an element it is possible to obtain quite accurate solutions to the problem of determining the stress intensity at the tip of a crack. The solutions compare favourably with those obtained using some types of special crack tip elements, but are not as accurate as those given by a crack tip element based on the hybrid principle. However, the hybrid elements are more difficult to use.
Velocity potential computation by finite differences for compressible flow in ducts
Authors: O'Carroll M. J. 
Published: August 2005

AbstractPreliminary studies of computation with velocity potential are made with a view to the analysis of complex three‐dimensional flows. The methods used are applicable more generally to quasilinear elliptic problems with derivative boundary conditions on irregular domains. Second order finite difference approximations are constructed in simple form for plane ducts of general shape by using an irregular net. Derivative boundary conditions are handled quite easily. An iterative method is described which corresponds to freezing the coefficients in the quasilinear differential equation for velocity potential. The discretization is such that this is a ‘generalized Newton’ method for the non‐linear algebraic equations. Good convergence has been found in practice even when there are small supersonic zones. The discretization accuracy is tested by comparisons with the exact solution for incompressible flow between confocal hyperbolas.
Heat transfer during fluidized‐bed coating
Authors: Meyer Gunter H. 
Published: August 2005

AbstractA fully implicit numerical method for linear parabolic free boundary problems with coupled and integral boundary conditions is described. The partial differential equation and the boundary conditions are time discretized with the method of lines. An auxiliary function is introduced to remove the coupled and integral boundary conditions from the resulting free boundary problem for ordinary differential equations. Once separated boundary conditions are obtained, invariant imbedding is used to solve the free boundary problem numerically. The method is illustrated by solving the heat transfer equations for the fluidized‐bed coating of a thin‐walled cylinder.
A finite element method for the axisymmetric flow computation in a turbomachine
Authors: Hirsch Ch. , Warzee G. 
Published: August 2005

AbstractThe equations for the meridional through‐flow in a turbomachine are formulated as a quasi‐harmonic non‐linear equation. This equation is then solved iteratively by the finite element method and in order to obtain convergence an under‐relaxation factor has to be introduced. Comparisons with experimental results in single and multistage axial compressors show very good agreement. The finite element method is thus shown to be an efficient tool for this type of problem.
Theory and examples of partial approximation in the finite element method
Authors: Kikuchi Fumio 
Published: August 2005

AbstractThis paper presents theory and examples of partial approximation as a modification of the displacement method in the finite element analysis. This method requires different shape functions for different terms in the potential energy expression to curtail the processes in the standard displacement method. Explanation of the theory is given by use of a simple example for Poisson's equation. It can also be effectively utilized to give mathematical foundation to some finite element models based on physical reasonings, such as Melosh's rectangular element for plate bending and beam element approximation of circular arches.
Transformation of elliptic partial differential equations for solving two‐dimensional boundary value problems in fluid flow
Authors: Boadway J. D. 
Published: August 2005

AbstractIt is possible to transform elliptic partial differential equations to exchange the dependent with one of the independent variables. The Laplace equation for a stream function ‘Ψ’ over the X and Y co‐ordinate system, for example, can be transformed into a relationship expressing the Y position of streamlines in terms of strem function Ψ and X.Although the resulting new partial differential equation is much more complex it is much more convenient to use in a computer. An irregular Y boundary becomes, with the new relationship, merely the boundary values assigned to the outer streamlines and the computer always need only deal with a rectangular array. The resulting answer is in the form of the position of streamlines which is the information directly required for plotting flow maps.
Numerical techniques in probabilistic load flow problems
Authors: Allan R. N. , Grigg C. H. , Al‐Shakarchi M. R. G. 
Published: August 2005

AbstractThis paper describes numerical techniques which have been developed in order to solve the load flow problem of a power system network probabilistically instead of using normal deterministic methods. The aim in the development of these techniques has been to reduce the computational time and storage commensurate with maintaining a high degree of accuracy.
On the relationship between the finite element and finite difference methods
Authors: Gray William F. , Pinder George F. 
Published: August 2005

AbstractThe integral equations which arise from application of the Galerkin‐finite element scheme to the convective diffusion equation are examined to illustrate how this method represents differential equations. The formulae obtained are effectively spatial averages of standard finite difference equations written at a node. The truncation error in the finite element solution at a node is obtained for various nodal configurations.
Subspace iteration accelrated by using Chebyshev polynomials for eigenvalue problems with symmetric matrices
Authors: Yamamoto Yoshiyuki , Ohtsubo Hideomi 
Published: August 2005

AbstractBathe's algorithm of subspace iteration for the solution of the eigenvalue problem with symmetric matrices is improved by incorporating an acceleration technique using Chebyshev polynomials. This method of acceleration is particularly effective for this kind of iteration. The rate of convergence of the iteration scheme presented is considerably improved when compared with the original one, and satisfactory rates of convergence can be obtained for a wider range of eigenvalues.
Non‐linear programming—gradient projection via orthogonalization
Authors: Russell S. S. 
Published: August 2005

AbstractLarge scale non‐linear programming problems with non‐linear constraints are of practical concern in the areas of process control and system design. Although advances in computer technology address these problems, more efficient algorithms are needed. An algorithm currently used is Rosen's Gradient Projection Method. This note presents an alternative technique of performing the steps for finding the projected gradient used in Rosen's method, a technique that gives equivalent results with fewer computations.
A review of least‐squares methods for solving partial differential equations
Authors: Eason Ernest D. 
Published: August 2005

AbstractContinuous (integral) and discrete (point‐matching) least‐squares methods are presented for linear and non‐linear problems in boundary‐value, eigenvalue, and initial‐value form. The history is traced, and important theoretical and practical results are summarized. A comprehensive sample of the literature is presented, indexed to show type of application, version of least squares used, and results of comparison studies. The advantages of least‐squares methods are discussed, including convenience in formulation and error evaluation, generality of mixed and local (finite element) versions, and performance that is competitive with other methods.
A variable metric algorithm for constrained minimization based on an augmented Lagrangian
Authors: Gruver W. A. , Engersbach N. H. 
Published: August 2005

AbstractThis paper concerns the implementation of a recent idea, attributed to Hestenes and Powell, based on solving the equality constrained finite dimensional minimization problem

via the unconstrained problem

where ƒ is a non‐linear functional, g is a non‐linear mapping into Rp, K is a prescribed matrix of penalty constants and λ is the Lagrange multiplier. The computational algorithm is based on restoring active constraints to first order and adjusting x in the remaining necessary conditions by gradient projection. The minimization is performed by the variable metric rank‐two BGFS update with linear search by cubic interpolation. Computational results using the algorithm include two problems of minimum fuel trajectory optimization—two impulse rendezvous with Comet Encke and three impulse constrained positioning of a geostationary satellite.
A modification of the Monte Carlo method for steady heat conduction problems
Authors: Zinsmeister G. E. , Pan S. S. 
Published: August 2005

AbstractThe unique capability of calculating single points by Monte Carlo Methods is used in an attempt to develop an efficient Monte Carlo method for whole field calculations of heat conduction problems. Rather than calculate the whole field by Monte Carlo, only select points around the boundaries of inscribed figures of standard shapes are are so calculated. Interior points of the inscribed figures are then calculated by analytical (non‐numerical) techniques. The procedure is described and shown to be more efficient than previously published Monte Carlo modifications but not as efficient as the Gauss–Seidel method. This new procedure will most likely be competitive for subregion calculations rather than for whole field calculations (for which standard numerical procedures are most efficient) or for single point calculations (for which other Monte Carlo methods are most efficient).
Derivatives and their error bounds in second order problems by finite element
Authors: Mote C. D. , Young R. C. 
Published: August 2005

AbstractA previous paper by the authors presented a finite element technique for computing accurate and bounded solutions at arbitrary points in second order mixed boundary value problems. The technique is extended herein to the computation of accurate and bounded derivatives at arbitrary interior points. Numerical results are presented to illustrate both the strengths and limitations to the method.
Optimum structural design with stability constraints
Authors: Khot N. S. , Venkayya V. B. , Berke L. 
Published: August 2005

AbstractThis paper presents an optimization method based on optimality criterion for minimum weight of structures with stability requirements. A recurrence relation is derived and the method is explained in the context of the displacement method of finite element analysis. The incipient buckling of the structure is determined by a linear eigenvalue solution. The method is programmed for trusses and frames. Illustrative problems are given to show the applicability of the method of design of structures with a large number of design variables.
A new method of integration over polynomal finite element boundaries
Authors: Rodin E. Y. 
Published: August 2005

AbstractIn this note we are developing integration techniques for triangular regions in which one side is curved. Specifically, we are considering (a) general polynomial boundaries and (b) various combinations of elliptical boundaries. Integration is performed over all of these explicitly.One definite and considerable improvement achieved is the introduction of a new method of integration over polynomial type boundaries. This new method is not only exact for polynomials or other analytic functions, but also reduces the computing time considerably; for example, if for a sixth order polynomial the number of operations necessary (using previously available methods) to perform the integration was n, the method introduced here requires a number proportional to n1/6. Furthermore, coding time is also reduced considerably. It may be of value to mention that the availability of the results presented here could obviate the need for the use of isoparametric elements in some regions with curved boundaries.For completeness, explicit integration formulas for elliptic shaped regions are also listed.
A hybrid element method for steady linearized free‐surface flows
Authors: Mei C. C. , Chen H. S. 
Published: August 2005

AbstractIt is first shown that the two‐dimensional linearized ship wave problem can be recast as the sum of a radiation and a diffraction problem for simple harmonic waves. Each problem can be solved by a hybrid element method (HEM) where conventional finite elements are used near the body and analytical solutions are used in the remaining infinite regions (super‐elements). Variational principles which incorporate the matching conditions between regular and super‐elements as natural conditions are derived. Numerical examples are presented. The theoretical aspects for extending the above ideas to a three‐dimensional ship wave problems are also described.
PFVIBAT—a computer program for plane frame vibration analysis by an exact method
Authors: Åkesson Bengt Å. 
Published: August 2005

AbstractThe described program PFVIBAT uses the exact displacement method to perform free and forced vibration analysis entirely within the differential equation theory of beams thus avoiding assumed modes and lumped masses. The frame may contain rigid bodies. Clamped, hinged, guided and rolling connections are allowed for. Consideration of rotatory inertia, shear deformation and second‐order bending moments and shear forces as caused by static axial load is optional. Eigenfrequencies and modal masses are calculated with an accuracy that may be specified. Displacement and moment modes are plotted. Transient vibrations are studied.
The generation of elements with singularities
Authors: Akin J. E. 
Published: August 2005

AbstractA procedure is given for generating two‐dimensional conforming singularity elements from standard conforming elements. Three new elements with 0(r‐p) derivative singularities are introduced. The technique is based on the use of elements defined by numerically integrated shape functions. Special quadrature rules are suggested for triangular elements. The degeneration of these elements to crack tip elements and the direct evaluation near the singularity of element quantities, such as the stress intensity factors, is discussed.