bluuebunny/crossref_metadata_2025_split huggingface dataset:
Numerical computations of three‐dimensional thin panel structures
Authors: Růžičková H. , Ženíšek A. 
Published: August 2005

AbstractA finite element model for analysing static problems of three‐dimensional thin panel constructions is presented. The potential energy of stretching of each panel is represented by the classical Lagrange formulation of two‐dimensional elasticity and in the finite element discretization piecewise linear u, v displacements are used. The potential energy of bending of each panel is represented in the finite element discretization by Hellan and Herrmann's model, i.e. piecewise constant moments and piecewise linear w‐displacements are used. The physical appropriateness of the model is verified for different assemblages of panels, and in all cases good numerical results are obtained.
The elasto‐plastic analysis of plates using hybrid finite elements
Authors: Barnard A. J. , Sharman P. W. 
Published: August 2005

AbstractAn elasto‐plastic plate‐bending analysis is developed based on the finite element method and utilizing an assumed‐stress hybrid (Pian) element. Plasticity is incorporated using the Prandtl–Reuss relations and isotropic hardening theory together with an incremental residual force technique. Several example solutions are included to demonstrate the ability of this approach in elasto‐plastic plate‐bending problems.
Convergence problems in the asymptotic expansions for the Bessel functions of complex argument
Authors: Kausel Eduardo 
Published: August 2005

AbstractThe convergence of Hankel's asymptotic expansions for the Bessel functions of large complex argument are discussed, and a method is proposed to avoid numerical problems derived from their implementation in computer programs. Whiel the error tolerance cannot in all cases be controlled by the user, excellent results can indeed be obtained with application of the proposed method.
Numerical stability of dynamic relaxation analysis of non‐linear structures
Authors: Cassell A. C. , Hobbs R. E. 
Published: August 2005

AbstractThe estimation of the parameters (‘fictitious densities’) which control the convergence and numerical stability of a non‐linear Dynamic Relaxation solution is described. The optimal values of these parameters vary during the iterative solution and they are predicted from the Gerschgörin bounds, that is rowsums of the stiffness matrix, which are divided into constant and variable parts for computational convenience. The procedure is illustrated by reference to the analysis of an axially loaded beam on a non‐uniform elastic foundation.
Infinite elements
Authors: Bettess Peter 
Published: August 2005

AbstractA series of shape functions analogous to Lagrange polynomials, but including an exponential decay term, are suggested as appropriate for elements which extend to infinity. The shape functions are applied to a number of examples, mainly of viscous flow, where the domain extends to infinity. Both explicitly integrated and numerically integrated elements are described. The technique is applicable to many problems where the domain is supposed to extend to infinity.
Large displacement, transient analysis of space frames
Authors: Belytschko T. , Schwer L. , Klein M. J. 
Published: August 2005

AbstractA formulation is presented for the transient analysis of space frames in large displacement, small strain problems. For purposes of treating arbitrarily large rotations, node orientations are described by unit vectors and deformable elements are treated by a co‐rotational (rigid‐convected) description. Deformable elements may be connected either to nodes directly or through rigid bodies. The equations of motion are integrated by an explicit procedure. Sample results are presented on the snap‐through of an arch‐type structure and an idealization of a vehicle‐barrier impact.
A unidimensional convergence test for matrix iterative processes applied to Strapdown Navigation
Authors: Bar‐Itzhack Itzhack Y. 
Published: August 2005

AbstractThe investigation of the convergence properties of matrix iterative processes usually involves test matrices of high order. This fact may prohibit an analytic approach to the problem. In this paper a method is presented which converts the multidimensional test procedure into a scalar one. The method is presented in conjunction with the problem of matrix orthogonalization which exists in Strapdown Inertial Navigation. Three examples are presented in which the convergence of matrix orthogonalization techniques is investigated. The examples demonstrate the use of the unidimensional convergence test in determining the order of the processes and in finding sufficient conditions for convergence. Numerical results are presented.
Compact representation of triangular finite elements for Poisson's equation
Authors: Tsipouras Paul 
Published: August 2005

AbstractThe energy expression associated with Poisson's equation is written, for triangular domains, in a form invariant to translation and rotation. The element matrices derived from this depend only on the intrinsic parameters of the element, say the three sides. Considerable savings in storage can be achieved by storing the global stiffness matrix in terms of these element matrices.
An attenuation‐free upwind difference formula for analogue computation of charge flow in semiconductors
Authors: O'Carroll M. J. , Foster K. , McKay C. M. 
Published: August 2005

AbstractThe first order partial differential equations of charge flow are commonly differenced in the space co‐ordinate, with a view to analogue computation of the resulting ordinary differential equations in time. Defects of orthodox difference formulae are identified. In particular: (a) reversed waves and stability problems arise from central differences and (b) first order errors and a ‘pseudo‐viscous’ dispersion effect with accompanying false attenuation results from upwind differences. These difficulties are particularly serious in view of the coarse differencing required for practical analogue computation. A much superior formula is presented which is entirely free of attenuation and is easily implemented. Various other desirable features are reported.
Computable finite element error bounds for Poisson's equation
Authors: Barnhill R. R. , Brown J. H. , McQueen N. , Mitchell A. R. 
Published: August 2005

AbstractTheoretical error bounds of the form
equation image
are often available for finite element solutions U of elliptic problems. In this form the estimates give the order of convergence of the method but are of little practical value for estimating the size of the error because the magnitudes of the constant K and the theoretical solution u are unknown. An exception occurs in the case of the equation ∂2u/∂x2 + ∂2u/∂y2 + f = 0 in a rectangle where the Ritz–Galerkin finite element solution involves piecewise linears over a regular triangular grid. In this case where α = 1 and
equation image
Barnhill and Gregory1 have obtained the theoretical value 0·93√2 for K. In this note calculations are carried out for a variety of problems and the quantity K* = ∥u – U∥E/h∥f∥L2 measured and compared with K. The values of K* obtained fit into a well defined pattern from which we conclude that the theoretical constant K is of the correct order of magnitude.
A heuristic for root isolation
Authors: Jones Bush 
Published: August 2005

AbstractA heuristic for isolating the real roots of an equation involving a continuous function over a specified region is presented. Root isolation strategies are well known for polynomial and rational functions; however, there have been no really effective root isolation strategies for transcendental functions. For a transcendental function and a given interval, there has been no way to decide the existence of roots within the interval unless the function changed sign at the endpoints or unless evaluations were performed within the interval. This paper presents a new decision procedure using only interval endpoints. The methodology developed does not guarantee to detect real roots in an interval; however, the technique will effectively indicate real roots in a given interval unless the behaviour of the function is quite erratic.
Flexible finite‐difference stencils from isoparametric finite elements
Authors: Frey William H. 
Published: August 2005

AbstractA new finite‐difference technique for the numerical solution of boundary value problems for partial differential equations in two space variables is described. Isoparametric finite elements are used in a finite‐difference context to derive difference approximations to space derivatives on a locally curvilinear grid. The result is a generalization of a classical finite‐difference stencil which is ‘flexible’ in that it is adaptable to variable meshes, such as those arising from regions with curved boundaries. Numerical results presented for a test problem (potential flow past a circle) using a 9 × 10 grid agree with the analytic solution to within one per cent.
Stiffness matrix for a beam element including transverse shear and axial force effects
Authors: Chugh Ashok K. 
Published: August 2005

AbstractA simple and direct procedure is presented for the formulation of an element stiffness matrix on element co‐ordinates for a beam member and a beam‐column member including shear deflections. The resulting stiffness matrices are compared with those obtained using the alternative formulation in terms of member flexibilities: The relative effects of axial force and shear force on the stiffness coefficients are presented. The critical buckling loads, considering the effects of shear force, are computed and compared with those available in the literature. Only prismatic members are considered.
An advanced boundary integral equation method for three‐dimensional thermoelasticity
Authors: Rizzo F. J. , Shippy D. J. 
Published: August 2005

AbstractThe features of an advanced numerical solution capability for boundary value problems of linear, homogeneous, isotropic, steady‐state thermoelasticity theory are outlined. The influence on the stress field of thermal gradient, or comparable mechanical body force, is shown to depend on surface integrals only. Hence discretization for numerical purposes is confined to body surfaces. Several problems are solved, and verification of numerical procedures is obtained by comparison with accepted results from the literature.
Lagrange polynomials of a complex variable for two‐dimensional interpolation
Authors: Bates R. H. T. , Milner M. O. 
Published: August 2005

AbstractWe recognize that established techniques permit two‐dimensional interpolation to be accomplished efficiently as well as accurately when the grid of points, on which the data is available, is regular. Existing methods suitable for irregular grids are computationally protracted. We show that by using Lagrange polynomials of a complex variable we can interpolate, almost as conveniently as in one dimension, from an irregular grid onto particular points lying on parallel lines. Standard one‐dimensional interpolation schemes can then be used to complete the two‐dimensional interpolation. We discuss how, in any particular instance, the order of the Lagrange polynomials is chosen, and we present the results of a computational test of our method.
Some criteria for numerically integrated matrices and quadrature formulas for triangles
Authors: Laursen M. E. , Gellert M. 
Published: August 2005

AbstractFor a wide calss of finite element matrices integrated numerically rather than exactly, a definable number of sampling points is found to be sufficient for keeping their theoretical properties unchanged. A systematic criterion limiting the number of possible point configurations for numerical quadrature formulas on triangles is established. Some new high order formulas are presented. Tables containing optional formulas with respect to minimum number of sampling points and required degrees of accuracy are given. They are arranged so as to assist with selection of suitable quadrature formulas for finite element computer programming.
Blending interpolants in the finite element method
Authors: Marshall J. A. , Mitchell A. R. 
Published: August 2005

AbstractBlending function interpolants on rectangular elements are used to construct an overall interpolant which exactly matches function and normal derivative on the perimeter of a rectangular region. This overall interpolant is incorporated into the Ritz‐Galerkin version of the finite element method and a test problem involving the biharmonic equation is solved. The numerical results obtained demonstrate the considerable increase in accuracy of the exact boundary methods as compared with the usual method using interpolated boundary conditions. A similar investigation of second order elliptic problems with Dirichlet boundary conditions where the rectangular region is divided up into triangular elements yields the perhaps surprising result that blended interpolants on triangular elements do not necessarily improve the accuracy of the Ritz‐Galekin version of the Finite Element Method.
Modification to the Suhara‐Fukuda method of network generation
Authors: Shaw R. D. , Pitchen R. G. 
Published: August 2005

AbstractThis note describes improvements to the Suhara‐Fukuda method for generating a triangular finite element network. These are based on the use of a node generation procedure which distributes nodes is a regular pattern across the network area and is sufficiently flexible to permit any variation in element density. Because of the regular node distribution, poorly shaped elements will not arise and so the procedure for connecting the nodes to form elements can be simplified. Examples of networks generaed in this way are given.
Periodic Galerkin finite element method of tidal flow
Authors: Kawahara Mutsuto , Hasegawa Kenichi 
Published: August 2005

AbstractThis paper presents the finite element method of the analysis of tidal flow. Assuming that tidal flow is periodic, the Galerkin approach is employed as the numerical integration procedure in time using a trigonometric function as the interpolation function. The present method has shown to be suitable for computation especially from the point of computing time and numerical stability.
The solution of sparse linear equations by the conjugate gradient method
Authors: Jennings A. , Malik G. M. 
Published: August 2005

AbstractThe convergence properties of the conjugate gradient method are discussed in relation to relaxation methods and Chebyshev accelerated Jacobi iteration when applied to the solution of large sets of linear equations which have a sparse, symmetric and positive definite coefficient matrix. The conclusion is reached that its convergence rate is unlikely to be much worse than these methods, and may be considerably better. The conjugate gradient method may either be applied to the basic unscaled or scaled equations or alternatively to various transformed equations. Preconditioning, block elimination and partial elimination methods of transforming equations are considered, and some comparative tests given for six problems.
Finite difference approximation of boundary conditions along irregular boundaries
Authors: Hunt Bruce 
Published: August 2005

AbstractThe approximation of normal derivatives along a curved boundary becomes a major difficulty in obtaining finite difference solutions for irregular regions. A number of authors (for‐example, Allen,1 Fox,2 Greenspan3 and Parker and Ma4) have suggested various solutions to this problem. However, most of these suggested methods are fairly cumbersome to use since they require the use of different formulas for various combinations of mesh and boundary geometries. This note shows a different way to approximate a quite general boundary condition along curved boundaries. The method uses a uniformly spaced mesh, is simple, general, relatively easy to program and appears to give accurate results.
Construction of triangular finite element universal matrices
Authors: Silvester P. 
Published: August 2005

AbstractThe various ‘universal’ matrices from which finite element matrices for triangular elements are assembled in many electromagnetics and acoustics problems, can all be derived from a basic set of three fundamental matrices. These represent, respectively, the metric of the linear manifold spanned by the triangle interpolation polynominals, the finite differentiation operator on that same manifold, and a product‐embedding operator for the corresponding manifold for interpolation polynomials one order higher. Two of these have already been tabulated and published; the required method for computing the third is given in this paper, along with tables of low‐order matrices.
A partitioned parallel Runge‐Kutta method for weakly coupled ordinary differential equations
Authors: Mattione R. P. , Katz I. N. , Franklin M. A. 
Published: August 2005

AbstractIn many systems it is known a priori, that some states are ony weakly coupled with others. If such systems are solved on parallel processor it is possible to partition the states in such a way that one set of states is assigned to one processor and the other set of weakly coupled states to another. Computations can then be done in parallel. Because of the weak coupling it may not be necessary for information from the two sets to be communicated to each other for many integration steps. This can result in significant cost savings. In this paper, a partitined Runge—Kutta scheme is formulated for use on weakly coupleld systems of ordinary differential equations. An error expression is derived which provides a means for predicting the number of step sizes over which the partitioned formulas can be used in terms of a prespecified error tolerance. Numerical examples are presented both to verify the error expressions and to compare solutions using partitioned and unpartitioned schemes.
A starting algorithm for the numerical simulation of two‐phase flow problems
Authors: Lewis R. W. , White I. R. , Wood W. L. 
Published: August 2005

AbstractThe diferential equations governing two‐phase flow through a porous medium are derived and the space discretization is carried out by the Galerkin finite element method. An examination of the eigenvalues of the resulting system follows in order to decide on a suitable stability criterion to be satisfied by the time‐stepping algorithm. A class of time‐stepping schemes is introduced and their behaviour when applied to a specific problem is analyzed. The aim is to achieve an adequate modelling of the water‐oil interface and to preserve reasonable values of the capillary pressure. A technique to clustering the mesh around the interface is used to improved the modelling, and a boundary condition based on the relative mobilities of the two fiuids is imposed to enable the program to calculate the water‐oil ratio after breakthrough. The effect of lumping the mass matrix is then examined with a view to reducting the surge in the values obtained for the capillary pressure. Finally an optimum method is suggested for use as a starting algorithm for more sophisticated time‐stepping schemes.
An advanced structural analysis/synthesis capability—ACCESS 2
Authors: Schmit L. A. , Miura H. 
Published: August 2005

AbstractAn advanced automated design procedure for minimum weight design of structures (ACCESS 2) is reported. Design variable linking, constraint deletion, and explicit constraint approximation are used to effectively combine approach to structral synthesis is extended to problems involving fibre composite structure, thermal effects and natural frequency constraints in addition to the usual static stress and displacement limitations. Sample results illustrating these new features are given.
Analysis of some dispersion corrected numerical schemes for solution of the transport equation
Authors: Van Genuchten Martinus T H. , Gray William G. 
Published: August 2005

AbstractIn the last decade or so finite element techniques have been applied with increased frequency to contaminant transport problems. Whereas most of the attention has focused on finite element approximations of spatial derivatives, standard finite difference techniques are generally used for approximation of the time derivative. Such an approach yields a scheme which is at best second order correct in time. In this study several higher order approximations of the time derivative are developed and analyzed using a finite difference approximation, and Galerkin‐type finite element approximations in conjunction with several sets of basis functions. Results obtained with the different schemes exhibit significant improvements in the numerical solution of the convective‐dispersive equation.
On least squares approximations to indefinite problems of the mixed type
Authors: Fix George J. , Gunzburger Max D. 
Published: August 2005

AbstractA least squares method is presented for computing approximate solutions of indefinite partial differential equations of the mixed type such as those that arise in connection with transonic flutter analysis. The mehod retains the advantages of finite difference schemes namely simplicity and sparsity of the resulting matrix system. However, it offers some great advantages over finite difference schemes. First, the method is insensitive to the value of the forcing frequency i.e., the resulting matrix system is always symmetric and positive definite,. As a result, iterative methods may be successfully employed to solve the matrix system, thus taking full advantage of the sparsity. Furthermore, the method is insensitive to the type of the partial differential equation, i.e., the computational algorithm is the same in elliptic and hyperbolic regions. In this work the method is formulated and numerical results for model problems are presented. Some theoretical aspects of least squares approximations are also discussed.
Added mass computation by the boundary integral method
Authors: Deruntz John A. , Geers Thomas L. 
Published: August 2005

AbstractComputational techniques for the treatment of fluid‐structure interaction effects by discrete boundary integral methods are examinde. Attention is focused on the computation of the added mass matrix by finite element methods for a structure submerged in an infinite, inviscid, incompressible fluid. A general computational procedure is presented that is based upon a variational approach involving the assumption of constant source strength over each surface element. This is followed by an analysis of the discretization error for a spherical body that is then used to develop a hierarchy of computational schemes. These schemes are than evaluated numerically in terms of ‘fluid boundary modes’ for a submerged spherical surface. One scheme has been found to be surprisingly accurate in relation to its computational demands.
Node Reordering algorithms for water network analysis
Authors: Gay R. K. L. , Chin K. K. , Chua S. H. , Chan C. H. , Ho S. Y. 
Published: August 2005

AbstractThe node Admittance matrices for Water Networks are normally sparse and symmetrical. Advantage may be taken of these properties to reduce the amount of computational time and memory required to solve them. Two node reordering algorithms and an economic system of storing input data are described. The node reordering algorithms minimize the number of fill‐ins which would occur in the solution of the node admittance matrix. Only non‐zero elements are stored and operated on. Subroutines for the node reordering algorithms and storge of input data, written in FORTRAN IV are included.
Sor vs. conjugate gradients in a finite element discretization
Authors: Fried Isaac , Metzler Jim 
Published: August 2005

AbstractSucessive Overrlaxation and Conjugate Gradients are used to solve the linear algebraic system set up with finite elements for the discretization of a plane, linear, head conducting problem. It is numerically shown that even with the optimal overrelaxation factor SOR is hardly superior to CG which is decisively simpler to program.