bluuebunny/crossref_metadata_2025_split huggingface dataset:
A boundary integral solution to torsion of cylinders and solids of revolution
Authors: Battenbo H. , Banies B. H. 
Published: August 2005

AbstractThe boundary integral equation known as Green's Theorem has been solved to generate displacement and stress fields directly on the boundary for cylinders and solids of revolution in pure elastic torsion. The computer programs which effect the solution utilize conventional numerical methods and discrete analytical elemental integrations and are applicable to multiply‐connected shapes. The integral equation has been differentiated in each case, so that internal stresses may be generated directly, where required.Computed results are compared with analytical solutions and with experimental evidence produced by photoelastic techniques.
The application of node‐element rules for forecasting problems in the generation of finite element meshes
Authors: Fuhring H. 
Published: August 2005

AbstractThe number of equations which relate the mesh parameters (number of nodes, number of elements etc.) to each other is smaller than the number of unknowns contained therein. These rules are only applicable when several parameters of a defined mesh are known, but are unsuitable for use in the particularly interesting field of mesh projection unless additional inter‐relationships can be found. Such relationships are given for uniform meshes in which besides the characteristics of the element type the ‘solidity value’ of the structure plays an important role.The equations are derived for two‐dimensional triangular and quadrilateral elements and also for three‐dimensional tetrahedral and hexahedral elements. The fact that these relationships are also suitable for estimating the parameters of any non‐uniform mesh, discloses a wide field of application in the management of storage and in the control of programs for automatic mesh generation.
The calculation of branch flows in a directed network
Authors: Gay B. 
Published: August 2005

AbstractThis paper describes a procedure for the calculation of branch flows in a directed network in which the node‐to‐node flows are prescribed.The node‐to‐node paths of the network are enumerated using a combinatorial process. Procedures based on the path list are used to allocate the node‐to‐node flows to the alternative paths of the network according to Wardrop's first principle. The calculation, although necessarily iterative, is rapidly convergent.The method has been implemented as a computer program and the results obtained for a typical network are discussed.A linear relationship between branch potential and branch flow has been used, but the method can be extended to piece‐wise linear and non‐linear relationships.
Diagonal dominance and S.O.R. performance with skew nets
Authors: O'carroll M. J. 
Published: August 2005

AbstractAlternative finite difference formulations for elliptic equations on skew nets are investigated for suitability for rapid convergence of S.O.R. iterations. In dealing with the differential equation directly, diagonal dominance is a key property for convergence theorems. Mixed derivatives boundary conditions threatens this property, but formulas are presented which protect it as long as the net skewness is not too severe. Test calculations are reported showing convergence for these formulas to be as good as that of optimal S.O.R. theory, whereas other more direct formulas give a very inferior performance.
Transmission‐line matrix solution of waveguides with dielectric losses
Authors: Akhtarzad S. , Johns P. B. 
Published: August 2005

AbstractThe transmission‐line matrix method is a time‐domain numerical method for solving wave problems. This paper describes how a minor change in the computer program for loss‐free dielectrics extends the method to include dielectric losses. Results are given in terms of the wave impedance of a waveguide with losses, and also in terms of power decay due to losses in the dielectric of a resonant cavity.
A simple cubic displacement element for plate bending
Authors: Allman D. J. 
Published: August 2005

AbstractEarly attempts to construct a triangular finite element for plate bending problems from a compatible cubic displacement field are not entirely satisfactory. The present paper shows how an accurate plate element can be achieved using independent cubic polynomial assumptions for the internal and boundary displacements in conjunction with a modified potential energy principle. This approach yields a simple algebraic formulation with favourable connection quantities at the element vertices which will appeal to practical users of the conventional finite element displacement method. Moreover, in Appendix I it is shown that the cubic element is identical to a previous hybrid stress element with linear internal bending and twisting moments and cubic boundary displacements. The stresses obtained from the former hybrid finite element solution therefore satisfy the strain compatibility conditions exactly. This remarkable result has an important significance in the theory of hybrid finite elements.
Mathematical model and boundary conditions in stress analysis relating to steam turbine rotors, under transient operating conditions
Authors: Di Pasquantonio F. , Macchi A. 
Published: August 2005

AbstractAn appropriate mathematical model for calculation of thermoelastic stress in steam turbine rotors, under transient operating conditions, is developed in the framework of so called uncoupled quasi‐static theory. The numerical analysis has been carried out by means of the finite element code ANGUS, the accuracy of which has been evaluated by comparing it with an analytical solution given by one of the authors in Reference 2. It has been shown that, with an appropriate choice of thermal and elastic boundary conditions, it is possible to carry out stress transient analysis considering only a segment of the hottest zone of high or intermediate pressure body of rotors. The paper includes a comparison study of the influence of two types of thermal boundary conditions in the labyrinth glands.
Steady and unsteady finite element analysis of incompressible viscous fluid
Authors: Kawahara Mutsuto , Yoshimura Nobutoshi , Nakagawa Katsuya , Ohsaka Hajime 
Published: August 2005

AbstractFinite element procedures and related illustrative numerical examples for incompressible viscous fluid motion are discussed in this paper. The steady flow problem is solved by the Newton–Raphson method and the perturbation method. By numerical examples, it can be shown that the combined use of the Newton–Raphson method and perturbation method is suitable. For the analysis of unsteady flow, the perturbation method is employed. Assuming that the basic flow is known, unsteady flow is calculated by accumulating the solution of the linearized equation in which the boundary values are varied by small amounts. Steady flows of temperature dependent free convection are also discretized and analyzed by the same procedure as the conventional finite element Galerkin method. For shape functions, quadratic polynomials are used for velocity and temperature, and linear polynomials for pressure. It is to be noted that the selections of shape functions and solution method are the keys to the analysis of highly non‐linear fluid flow problems such as those discussed in this paper.
An ADI procedure suitable for virtual storage systems
Authors: Wang H. H. 
Published: August 2005

AbstractThe Peaceman–Rachford ADI technique is a well‐known iterative method for solving large systems of linear equations arising from finite difference methods of solution of partial differntial equations. The present note demonstrates how the algorithm can be conveniently rearranged for computation in a virtual storage system with paging. Timing results are given for a sample problem typical of those encountered in nuclear diffusion computation.
An automatic node relabelling scheme for minimizing a matrix or network bandwidth
Authors: Akhras Georges , Dhatt Gouri 
Published: August 2005

AbstractAn automatic algorithm is presented for reducing the bandwidth of symmetric sparse connectivity matrices. The procedure takes an arbitrary input sequence and creates an optimal bandwidth for complex network systems by renumbering the node labels. Thus, considerable improvement for computer storage and time is achieved in the solution of the systems.A large number of examples is presented to demonstrate the reliability and the efficiency of the method.
The analysis of rotational shells using a curved ring element and the mixed variational formulation
Authors: Barony S. Y. , Tottenham H. 
Published: August 2005

AbstractA finite element for the analysis of rotational shells using a mixed variational formulation is proposed. The element has arbitrary curvature in the meridional plane, its geometry being given by the values of the axial and radial co‐ordinates, slope and meridional curvature at the nodal circles. A linear variation in the thickness was included in the formulation as was an orthotropic material. Test cases of flat plates and spherical shells indicate that a high degree of accuracy is obtainable with relatively small number of elements.
A finite element Galerkin formulation and its numerical performance
Authors: Salaam U. , Sandhu R. S. 
Published: August 2005

AbstractA finite element Galerkin formulation admitting non‐homogenous boundary conditions and discontinuous approximants is derived from a variational principle. The procedure results in matrix equations explicitly allowing for jump discontinuties across interelement boundaries. As an illustration, a specialization of the procedure similar to a reduced integration technique is used to solve several problems in elastostatics. The improvement in accuracy in comparison with conventional methods is remarkable.
Comparative study of two and three level ADI methods for parabolic equations with a mixed derivative
Authors: Iyengar Satteluri R. K. , Jain M. K. 
Published: August 2005

AbstractADI difference schemes of two and three levels for the parabolic equations with a mixed derivative have been derived. Using the stability analysis and the principal part of the truncation error, a difference formula with minimum truncation error has been found. Comparative study of the two and three level formulas has been made through two examples, one with constant coefficients and another with variable coefficients.
Higher order difference formulas for a fourth order parabolic partial differential equation
Authors: Jain M. K. , Iyengar S. R. K. , Lone A. G. 
Published: August 2005

AbstractIn this paper, we have derived some new higher order difference formulas for the solution of a fourth order parabolic partial differential equation governing transverse vibrations of a uniform flexible beam in one and two space dimensions using Richtmyer's approach and a direct approach. Two examples illustrate the utility of the new difference methods.
Finite element methods for second order differential equations with significant first derivatives
Authors: Christie I. , Griffiths D. F. , Mitchell A. R. , Zienkiewicz O. C. 
Published: August 2005

AbstractGalerkin finite element methods based on symmetric pyramid basis functions give poor accuracy when applied to second order elliptic equations with large coefficients of the first order terms. This is particularly so when the mesh size is such that oscillations are present in the numerical solution. In the present note asymmetric linear and quadratic basis functions are introduced and shown to overcome this difficulty in an appropriate two point boundary value problem. In particular symmetric quadratic basis functions are oscillation free and highly accurate for a working range of mesh sizes.
Displacement incrementation in non‐linear structural analysis by the self‐correcting method
Authors: Haisler Walter E. , Stricklin James A. , Key John E. 
Published: August 2005

AbstractThe prediction of non‐linear structural behaviour by the finite element method wherein buckling does not occur has received considerable attention and, with it, reasonable success has been achieved. However, the post‐buckling problem has been less actively pursued probably because of the inherent numerical difficulties encountered. This Technical Note reviews very briefly the numerical methods currently being used for pre‐ and post‐buckling analysis and presents a self‐correcting approach based on load and displacement incrementation which is shown to be efficient, reliable, and easy to program. Numerical solutions are presented which demonstrate the effectiveness of the method.
A critical assessment of the Simplified Hybrid Displacement Method
Authors: Mang Herbert A. , Gallagher Richard H. 
Published: August 2005

AbstractThe Simplified Hybrid Displacement Method, an attractive modification of one of the principles of stationary value of modified potential energy, is examined critically and compared to another form of such variational principles and to the classical principle of minimum of potential energy. The three methods are studied from a theoretical vantage point and through the medium of numerical examples. A non‐conforming triangular finite plate bending element serves as the vehicle to solve a number of simple problems, utilizing the classical principle of minimum potential energy, a principle of stationary value of modified potential energy and the Simplified Hybrid Displacement Method.The attraction of this method derives from the fact that no additional independent unknown parameters—Lagrangian multipliers from a mathematical standpoint—enter into the modified energy functional, as is usually the case with hybrid methods.It is demonstrated numcrically that the Simplified Hybrid Displacement Method may become unstable. It is also shown that the stationary values of the modified energy functional for this method may be inconsistent with the corresponding minima of the classical potential energy. Furthermore, it is demonstrated that the Simplified Hybrid Displacement method is, in general, incapable of ‘restoring’ interelement slope continuity in the sense of a principle of stationary value of modified potential energy, that is, at least in an ‘integral sense’.
Mixed explicit‐implicit iterative finite element scheme for diffusion‐type problems: I. Theory
Authors: Neuman S. P. , Narasimhan T. N. 
Published: August 2005

AbstractA Galerkin finite element formulation of diffusion processes based on a diagonal capacity matrix is analysed from the standpoint of local stability and convergence. The theoretical analysis assumes that the conductance matrix is locally diagonally dominant, and it is shown that one can always construct a finite element network of linear triangles satisfying this condition. Time derivatives are replaced by finite differences, leading to a mixed explicit‐implicit system of algebraic equations which can be efficiently solved by a point iterative technique. In this work the accelerated point iterative method is adopted and is shown to converge when the conductance matrix is locally diagonally dominant. Several examples are included in Part II of this paper to demonstrate the efficiency of the new approach.
Mixed explicit‐implicit iterative finite element scheme for diffusion‐type problems: II. Solution strategy and examples
Authors: Narasimhan T. N. , Neuman S. P. , Edwards A. L. 
Published: August 2005

AbstractIn Part I1 of this paper we have established local stability and convergence criteria for the mixed explicit‐implicit finite element scheme and have shown that the proposed iterative method converges under certain conditions. Part II describes various practical aspects of the solution strategy such as convergence criteria for terminating the iterations, automatic control of time step size, reclassification of nodes from explicit to implicit during execution, estimation of time derivatives, and automatic adjustment of the implicit weight factor. Several examples are included to demonstrate certain aspects of the theory and illustrate the capabilities of the new approach.
A finite element collocation method for the exact control of a parabolic problem
Authors: Harley P. J. , Mitchell A. R. 
Published: August 2005

AbstractA finite element method is given for the problem of exact control of a linear parabolic equation. The basis functions consist of piecewise bicubic polynomials and the differential equation is satisfied at Gaussian collocation points within each element. The overdetermined system of equations obtained is solved by the method of least squares, and a convergence argument is given for the complete procedure. Numerical results are given for two problems of boundary control.
The coupling of the finite element method and boundary solution procedures
Authors: Zienkiewicz O. C. , Kelly D. W. , Bettess P. 
Published: August 2005

AbstractThe finite element method is now recognized as a general approximation process which is applicable to a variety of engineering problems—structural mechanics being only one of these. Boundary solution procedures have been introduced as an independent alternative which at times is more economical and possesses certain merits. In this survey of the field we show how such procedures can be utilized in conventional FEM context.
A homework exercise in finite elements
Authors: Strang Gilbert 
Published: August 2005

AbstractWe suggest an exercise which illustrates many of the fundamental ideas of finite elements, and is nevertheless easily programmed and quickly solved. It is governed by a partial differential equation on a circular region, but by maintaining symmetry the stiffness matrix becomes small and tridiagonal. The accuracy of linear elements can be studied in detail, and a straightforward extension leads to the eigenvalue problem, elements of higher degree, numerical integration, isoparametric elements, and a simple example in plasticity.
Numerical Fourier analysis in the range of higher frequencies
Authors: Ury J. F. 
Published: August 2005

AbstractA novel method is proposed for the numerical computation of Fourier coefficients in the range of higher frequencies for which hitherto no practical method was available. The accuracy of the results obtained by application of this method is discussed, and bounds of a correction term are determined accordingly. An example from the field of Diesel engine research is given, and the computed spectrum is compared with the spectrum recorded by an electronic harmonic analyzer.
A stability investigation of cable suspended pipelines
Authors: Contri Lorenzo , Schrefler Bernardo 
Published: August 2005

AbstractA postbuckling problem of continuous suspension bridges which are used for carrying pipelines is investigated. These are continuous over several bridge towers with pin connections at their base. A geometrically non‐linear analysis using the finite element method is performed to study the postbuckling behaviour under increasing loads (for instance by filling up the pipelines with fluid).Two examples are presented which investigate the aspect ratios of constructed continuous suspension bridges.
On computer‐aided analytic element analysis and the similarities of tetrahedron elements
Authors: Pedersen Pauli 
Published: August 2005

AbstractA complete analytical analysis of three‐dimensional, quadratic displacement tetrahedron elements is presented. The results show that the element stiffness can readily be obtained from the much simpler stiffness matrix of the linear displacement element. Thus, the task of obtaining the matrix of the quadratic displacement element is, in effect, reduced to finding that of the linear displacement element.The analysis has been made possible only by using a symbolic manipulation language (PL/I–FORMAC) on a computer. A rather general program for computer‐aided basic element analysis is presented. It seems that the extremely effective tool of symbolic manipulation has hardly been used until now in mechanics.
Solution of non‐linear boundary value problems by discrete least squares
Authors: Eason E. D. , Mote C. D. 
Published: August 2005

AbstractThis paper presents a new discrete (point‐matching) least squares method for solving general, non‐linear boundary value problems. The technique uses a mixed formulation and minimizes the sum of squared residuals by Powell's (1965) algorithm. The present method is compared with finite difference and weighted residual finite element methods in the examples and discussion. It shows considerable promise as a general differential equation solver for both large and small computer systems.
Error analysis of penalty function techniques for constraint definition in linear algebraic systems
Authors: Felippa Carlos A. 
Published: August 2005

AbstractThe penalty function approach has been recently formalized as a general technique for adjoining constraint conditions to algebraic equation systems resulting from variational discretization of boundary value problems by finite difference or finite element techniques. This paper studies the numerical behaviour of the penalty function method for the special case of individual equation constraints imposed on a symmetric system of linear algebraic equations. Constraint representation and computational roundoff error components are distinguished and asymptotically characterized in terms of the penalty function weight coefficients. On the basis of this study, practical rules for the automatic assignment of values to those coefficients within the linear equation solver are proposed. Numerical problems encountered in the case of more general constraints are briefly discussed, and procedures for circumventing such difficulties are suggested.
The numerical solution from measurement data of linear integral equations of the first kind
Authors: Radziuk J. 
Published: August 2005

AbstractThe problem considered in this paper is the solution of the Volterra integral equation of the first kind for the input function where we are given the impulse response or kernel and discrete, noise contaminated, observed values of the output function. The present method, introduced here, is based on assuming a multipolynomial form for the input function. Using the integral equation and the least squares method, the coefficients of all the terms in these polynomials are found simultaneously, in order to avoid bias toward any subset of the data. The solution is obtained in such a way that successive polynomials are continuous in function value and derivative at the points of juncture. Thus a smoothed estimate of the input function is generated. The development of the algorithm is presented and applied to two illustrative problems. Possible improvements and extensions of the method are also discussed.
FINITE: An approach to structural mechanics systems
Authors: Lopez L. A. 
Published: August 2005

AbstractFINITE is a general purpose structural mechanics system which runs under the POLO II supervisor. It is unique in that it provides users with a very flexible recursive structural modeling capability. Engineers can communicate with FINITE through a problem‐oriented language similar to STRUDL. Significant savings in computer and data entry times can be achieved when its recursive substructuring and condensation features are used appropriately. The structure of FINITE permits engineers to enter new elements with a minimal knowledge of the system operation. Nonsymmetric elements, hybrid elements, and elements with different degrees of freedom at the various nodes are all permissible. Various forms of linear constraints may be applied to the generalized displacements of a structure.The system runs under the POLO II supervisor and derives many of its attributes from the unique data base management facilities of this system. Among them are a limited working set size in a virtual memory environment and automatic restart capabilities.