bluuebunny/crossref_metadata_2025_split huggingface dataset:
The direct numerical integration of linear matrix differential equations using pade approximations
Authors: Trujillo D. M. 
Published: August 2005

AbstractA class of approximations to the matrix linear differential equation is presented. The approximations range, in accuracy, from the simplest forward difference scheme to the exact solution. The infinite series defining the exponential matrix is used to ascertain the accuracy of the various approximations. A clear distinction is made between approximations to the system equations and the forcing function, with the forcing term being represented by a piecewise linear function. Special application is given to the equations arising in structural dynamics of the form
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For these structural dynamic equations, the measure of the energy of the system is used to analyse the stability of the numerical approximations.
Uniform rational approximation of functions of several variables
Authors: Kaufman E. H. , Taylor G. D. 
Published: August 2005

AbstractWe present a program which has given excellent results for uniform approximation of functions by polynomials, rational functions, generalized polynomials, and generalized rational functions. The algorithm is described in detail and several examples are discussed. The approximation is done over a finite point set, which is commonly a set of real numbers or points in the plane (in the latter case we are doing what is often known as surface fitting). Input to and output from the program is in tabular form. The method used is a linear programming approach known as the differential correction algorithm, which has been shown by several authors to always converge in theory (quadratically in some situations). In practice, we have obtained convergence in nearly every case, and quadratic convergence in most cases. The program can also be used for simultaneous approximation of several functions.
Finite element analysis of the motion of a gas‐liquid interface in a forous medium
Authors: Lewis R. W. , Norris V. A. , France P. W. 
Published: August 2005

AbstractA numerical method is outlined for determining the movement of a gas‐liquid interface in a porous medium following the withdrawal of gas from an underground reservoir. The governing equations for the flow of both gas and the underlying liquid are formulated in terms of the finite element process using the Galerkin approach. The method consists of an iterative technique in which solution of the basic equations is dependent on the location of the interface. Cubic isoparametric elements are employed to allow accurate modelling of the curved boundary and to provide a relatively large number of interface points for a small number of elements. Extensions of the method are indicated in the text.
Power series expansion of the general stiffness matrix for beam elements
Authors: Paz Mario , Dung Lam 
Published: August 2005

AbstractThe general stiffness matrix for a beam element is derived from the Bernoulli–Euler differential equation with the inclusion of axial forces. The terms of this matrix are expanded into a power series as a function of the two variables: the axial force, and; the vibrating frequency. It is shown that the first three terms of the resulting series, which are derived in the technical literature from assumed static displacement functions, correspond respectively to the elastic stiffness matrix, the consistent mass matrix, and the geometric matrix. Higher order terms up to the second order terms of the series expansion are obtained explicitly. Also a discussion is presented for establishing the region of convergence of the series expansion for the dynamic stiffness matrix, the stability matrix, and the general stiffness matrix.
Minimization of load reduction in pipe networks subject to interrupted supply
Authors: Brameller A. , Li P. M. 
Published: August 2005

AbstractThe paper considers the question of reduction of loads on a pipe network, which may be necessary as a result of failure in supply or interruption of a pipe. The non‐linear relationship between pressure loss and flow along a pipe makes the problem of minimizing the reduction of loads also non‐linear. An iterative linear approximation technique is therefore adopted. When the question is formulated as a problem in linear programming, the constraints include nodal pressures as well as loads. It is shown how the number of these constraints may be reduced.
Optimal frequency‐weight computations for a disc
Authors: De Silva B. M. E. , Grant G. N. C. 
Published: August 2005

AbstractThis paper describes the computational aspects of an earlier analytical study1,2 of the problem of maximizing a linear combination of the natural frequencies of vibration of a turbine disc idealization subject to weight and fabrication constraints. The problem was formulated as an optimal control problem and solutions to the adjoint equations of the Pontryagin formalism obtained using perturbation techniques. These techniques transformed the problem to a non‐linear program. This paper gives detailed computational solutions to the non‐linear program which is characterized by pockets of relative optima. In addition, the dual problem of minimizing the weight subject to a frequency constraint is considered within the optimal control framework. The duality results are confirmed computationally for the two non‐linear programs.A description of some practical procedures for improving the convergence characteristics of these highly non‐linear programs is included.
Linear equality constraints in finite element approximation
Authors: Szabo Barna A. , Kassos Tony 
Published: August 2005

AbstractThe typical numerical problem associated with finite element approximations is a quadratic programming problem with linear equality constraints. When nodal variables are employed, the coefficient matrix of the constraint equations, [A], acquires a block‐diagonal structure. The transformation from polynomial coefficients to nodal variables involves finding a basis for [A] and computing its inverse.Simultaneous satisfaction of completeness and C1 (or higher) continuity requirements establishes linear relationships among the nodal variables and precludes inversion of the basis by exclusively element‐level operations.Linear dependencies among the constraint equations and among the nodal variables can be evaluated by the simplex method. The computational procedure is outlined.
Alternate hybrid stress finite element models
Authors: Wolf John P. 
Published: August 2005

AbstractAlternate hybrid stress finite element models in which the internal equilibrium equations are satisfied on the average only, while the equilibrium equations along the interelement boundaries and the static boundary conditions are adhered to exactly a priori, are developed. The variational principle and the corresponding finite element formulation, which allows the standard direct stiffness method of structural analysis to be used, are discussed. Triangular elements for a moderately thick plate and a doubly‐curved shallow thin shell are developed. Kinematic displacement modes, convergence criteria and bounds for the direct flexibility‐influence coefficient are examined.
An iterative improvement for non‐conforming bending elements
Authors: Crisfield M. A. 
Published: August 2005

AbstractA method is described whereby the formulation for non‐conforming bending elements includes the work dissipated across the inter‐element boundaries. For the examples considered, this correction is shown to lead to a significant improvement in accuracy at little extra cost. Since the solution procedure is based on an iterative technique, the method would be particularly suitable if applied to non‐linear problems.
A computational method for optimal structural design II: Continuous problems
Authors: Haug E. J. , Pan K. C. , Streeter T. D. 
Published: August 2005

AbstractA method for solving structural design problems that allows a continuous distribution of material along structural elements is presented. The method is an extension of the generalized steepest descent method presented in Reference 1. Inequality constraints on design variables, displacement, natural frequency, and buckling are explicitly treated and a minimum weight cost function is employed. A steepest descent method for boundary‐value state equations is developed and a computational algorithm is given. Several example problems in minimum weight structural design are solved and compared with results obtained by discretization techniques.
Solution of stiff boundary value problems by orthogonal collocation
Authors: Serth R. W. 
Published: August 2005

AbstractThe utility of the method of orthogonal collocation for solving stiff boundary value problems is investigated. To this end, the method is applied to a number of very stiff problems from the engineering and applied mathematics literature. The examples include both linear and non‐linear problems defined on both finite and infinite intervals, a singular perturbation problem, and an inherently unstable problem. The examples demonstrate the usefulness of the method for a wide variety of stiff problems, as well as some of its limitations.
Difference operator for variable stiffness plates
Authors: Chugh A. K. , Gesund H. 
Published: August 2005

AbstractA symmetric central finite difference operator is derived for the small deflection analysis of transversely loaded, ‘thin’, elastic plates, whose stiffnesses vary as functions of the in‐plane co‐ordinates. The operator is written here in Cartesian co‐ordinates for a square mesh, but the same technique can also be used to construct an operator for a rectangular mesh.
On implementation of the extended interior penalty function
Authors: Cassis Juan H. , Schmit Lucien A. 
Published: August 2005

AbstractThe extended interior penalty function formulation is implemented. A rational method for determining the transition between the interior and extended parts is set forth. The formulation includes a straightforward method for avoiding design points with some negative components, which are physically meaningless in structural analysis. The technique, when extended to problems involving parametric constraints, can facilitate closed form integration of the penalty terms over the most important parts of the parameter interval. The method lends itself well to the use of approximation concepts, such as design variable linking, constraint deletion and Taylor series expansions of response quantities in terms of design variables.Examples demonstrating the algorithm, in the context of planar orthogonal frames subjected to ground motion, are included.
On the use of isoparametric finite elements in linear fracture mechanics
Authors: Barsoum Roshdy S. 
Published: August 2005

AbstractQuadratic isoparametric elements which embody the inverse square root singularity are used in the calculation of stress intensity factors of elastic fracture mechanics. Examples of the plane eight noded isoparametric element show that it has the same singularity as other special crack tip elements, and still includes the constant strain and rigid body motion modes. Application to three‐dimensional analysis is also explored. Stress intensity factors are calculated for mechanical and thermal loads for a number of plane strain and three‐dimensional problems.
Panel flutter optimization—a refined finite element approach
Authors: Weisshaar Terrence A. 
Published: August 2005

AbstractThis paper presents the results of an aeroelastic optimization study. In this study the weight of a large aspect ratio panel immersed in high Mach number supersonic flow is minimized subject to the requirement that a critical aeroelastic parameter for flutter be held within specified limits. A refined finite element technique is used to model the panel flutter equilibrium equations, equations which act as constraints on the design search. The optimization mechanism itself is studied and discussed to provide qualitative results which may be useful to the solution of other aeroelastic optimization problems. The numerical results of this investigation are compared to converged numerical results to illustrate finite element accuracy. The results of the study show that the weight savings and material distribution found with an effective finite element model are comparable to those found by more complicated numerical methods.
A new finite element scheme for instability analysis of thin shells
Authors: Matsui Tetsuya , Matsuoka Osamu 
Published: August 2005

AbstractThis paper describes a new finite element scheme for the analysis of instability phenomena of arbitrary thin shells. A computationally efficient procedure is proposed for calculating the non‐linear stiffness and tangential stiffness matrices for a doubly‐curved quadrilateral element defined by co‐ordinate lines. The essential feature is the explicit addition of the non‐linear terms into the rigid‐body motion of the element. Thus the non‐linear and tangential element stiffness matrices can easily be generated by transforming the generalized element stiffness matrix for linear analysis, and the non‐linear terms of these matrices are separated into a number of component terms multiplied by the rigid‐body rotations. These component terms can be stored permanently and used to calculate efficiently the non‐linear and tangential stiffness matrices at each iteration. Illustrative examples are presented which confirm the validity of the present approach in the analysis of instability phenomena of thin plates and shells.
A computer solution for two‐dimensional fluid‐particle flows
Authors: Crowe C. T. , Stock D. E. 
Published: August 2005

AbstractA computer solution for two‐dimensional fluid‐particle flows using the cellular approach is presented. The euqations describing the flow of the continuous (fluid) phase are formulated using stream function, vorticity and enthalpy as the dependent variables. The effect of the disperse (particle) phase on the continous phase is represented by vorticity and energy sources in each cell. To illustrate the capability of the solution scheme, the flow of gas laden with hot particles issuing into a sudden expansion is analysed.
Inertia loading in finite element analysis of structures subject to compound motion
Authors: Barlow John 
Published: August 2005

AbstractThe problems associated with the stress analysis of structures subjected to body force loading due to compound motion are outlined. An economic method for calculating equivalent nodal loading, for use in a finite element displacement analysis, is proposed in which the element discretization and consistent mass matrices are used to advantage. The relevant equations, relating to the rigid body dynamics of compound motion, are appended in matrix notation. Validity of the method is demonstrated by an analysis of the stresses, due to gyroscopic and centrifugal forces, in an aero engine blade model.
Domain mappings for the numerical solution of partial differential equations
Authors: Oberkampf William L. 
Published: August 2005

AbstractIndependent variable transformations of partial differential equations are examined with regard to their use in numerical solutions. Systems of first order and second order partial differential equations in conservative and nonconservative form are considered. These general equations are transformed using generalized mapping functions and important computational features of the transformed equations are discussed. Examples of mappings which regularize domains are given involving various types of partial differential equations. These mappings are of particular importance in finite difference approximations because of the ease with which a mesh can be adapted to regions formed by co‐ordinate lines.
The incremental perturbation method for large displacement analysis of elastic‐plastic structures
Authors: Yokoo Yoshitsura , Nakamura Tsuneyoshi , Uetani Koji 
Published: August 2005

AbstractA procedure of applying the perturbation method is presented for the incremental numerical analysis of materially and combined non‐linear problems of discrete and discretized structral systems. Small but finite strain and stress increments are strictly distinguished from the strain rates and stress rates, respectively. It is shown that, by applying the perturbation procedure not only to the non‐linear strain‐displacement relations and equilibrium equations, but also to the constitutive equations in terms of rate quantities, all the governing equations can be satisfied to any desired accuracy at every instantaneous configuration in between the starting and terminal points of an incremental step. The proposed method provides also means of finding, to a desired accuracy, every point on an equilibrium path of a discrete system at which a new element will start yielding or unloading and possible critical points on the path. The significance of the proposed method is expected to be appreciated particularly in numerical investigations of critical behaviours and post‐buckling behaviours.
The solution of ill‐conditioned linear systems arising from Fredholm equations of the first kind by steepest descents and conjugate gradients
Authors: Squire William 
Published: August 2005

AbstractIt is shown that the methods of steepest descents and conjugate gradients give smooth solutions of the ill‐conditioned systems of linear equations obtained by the discretization of Fredholm equations of the first kind without the use of any regularization techniques. A modification of the usual method of steepest descents is described which is equivalent to applying two cycles of the usual method with very little additional work. A number of examples are worked including one with a degenerate kernel in which the algebraic system is singular.
On a numerical solution of the supersonic panel flutter eigenproblem
Authors: Gupta K. K. 
Published: August 2005

AbstractAn automated digital computer procedure is presented in this paper which enables efficient solution of the eigenvalue problem associated with the supersonic panel flutter phenomena. The step‐by‐step incremental solution procedure is based on an inverse iteration technique which effectively utilizes solution results from the previous step in determining such results during the current solution step. Also, the computations are limited to the determination of a few specific roots only, which are expected to contain the flutter mode, and this is achieved at each step without having to compute any other root.The structural discretization achieved by the finite element method yields highly banded stiffness, mass, and aerodynamic matrices; the aerodynamic matrix evaluated by the linearized piston theory is real but unsymmetric in nature. The solution algorithm presented in this paper fully exploits the banded form of the associated matrices, and the resulting computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most efficient and economical when compared to existing procedures of such analysis. Numerical results are presented for a two‐dimensional panel flutter problem.
A quadrature method for finite intervals
Authors: Squire William 
Published: August 2005

AbstractThe quadrature rule for a finite interval obtained by transforming to an infinite range and applying the midpoint rule is examined. It is found that the condition required to make the quadrature exact for a constant integrand imposes severe practical limits. The method is very good for integrands with singularities near the endpoints but ineffective for oscillatory integrands.
An iterative method for the design of symmetrical Joukowski airfoils of specified chord and maximum thickness
Authors: Pitoniak J. E. , Shanebrook J. R. , Lemmo A. C. 
Published: August 2005

AbstractAn iterative method is developed for designing symmetrical Joukowski airfoils of specified chord and maximum thickness. The method has been programmed for a digital computer and results for a particular airfoil design are given.
Efficient optimal design of structures by generalized steepest descent programming
Authors: Arora J. S. , Haug E. J. 
Published: August 2005

AbstractThe purpose of this paper is to present refinements in a steepest descent algorithm for optimal design of structures and numerical experience that demonstrates its numerical efficiency. The algorithm is based on a state space optimization technique that was initially developed and applied to optimal control problems. Design constraints are divided into four distinct subsets, the special characteristics of which are exploited to improve computational efficiency of the algorithm. Some further improvements in structural analysis, design sensitivity analysis, and constrained steepest descent programming calculations are presented. Optimum designs for three test problems are obtained and convergence rates are compared with results presented in the literature.
Rubber covered rolls—the thermoviscoelastic problem. A finite element solution
Authors: Batra R. C. , Levinson M. , Betz Eric 
Published: August 2005

AbstractThe coupled thermomechanical behaviour of a layer of thermorheologically simple material bonded to a uniformly rotating rigid cylinder and indented by another rigid cylinder is studied by the finite element method. The various approximations necessary to reduce the problem to one of tractable size and the computational methods used are discussed in some detail. The complete thermal, deformation and stress fields may be computed. Some results, computed for a grid using ‘rectangular’ elements, presented graphically include the temperature distribution, the stress distribution near the bond surface, the contact pressure distribution and the asymmetric surface deformation of the rubberlike layer.
A Poisson equation solver for rectangular or annular regions
Authors: King Hartley H. 
Published: August 2005

AbstractA FORTRAN subroutine is presented which solves the system of simultaneous linear equations associated with the finite difference representation of the Poisson equation for rectangular or annular regions. The code is arranged to require minimum storage, and all possible operations involving known zeros and ones are suppressed. Single subscripting is employed to minimize execution time.
Efficient least squares finite elements for two‐dimensional laminar boundary layer analysis
Authors: Lynn Paul P. , Alani Kawan 
Published: August 2005

AbstractThis paper presents the formulations of essentially one‐dimensional least squares and Galerkin‐least squares finite elements for the numerical solution of two‐dimensional laminar boundary layer equations. An iterative technique to cope with the non‐linearity of the boundary layer equations, in conjunction with the least squares finite element method, is proposed. Through exhaustive numerical investigations in the retarded flow over a plate, flow past a circular cylinder, the flow past an elliptic cylinder, the accuracy and applicability of the proposed method are demonstrated.
A numerical model for the simulation of two‐dimensional convective‐dispersion in shallow estuaries
Authors: Narayanan M. , Shankar N. Jothi 
Published: August 2005

AbstractA numerical model for describing two‐dimensional convective‐dispersive processes in tidally influenced shallow bays in given. The model uses a multi‐stage implicit technique with finite difference formulation, for solving the basic mass balance equation for a conservative constituent. The basic inputs to this model consist of instantaneous tidal velocities and depths obtained from an operational tidal hydrodynamic model.The sensitivity of the output concentrations to the variation of dispersion coefficients is investigated. Application of the model to a practical situation is demonstrated by considering Galveston Bay. Texas, U.S.A. The transport model is operated to generate results which are compared with measurements from dye release studies made in a physical model of Galveston Bay.