bluuebunny/crossref_metadata_2025_split huggingface dataset:
Solution of linear equations for small computer systems
Authors: Ida Nathan , Lord William 
Published: August 2005

AbstractA solution technique, based on Gauss elimination, is described which can solve symmetric or unsymmetric matrices on computers with small core and disk requirement capabilities. The method is related to frontal techniques in that renumbering of the nodes, such as in a finite element mesh, is not required, and the elimination is performed immediately after the equations for a particular node have been fully summed. Only two rows of the matrix need be on core at any step of the solution, but for more efficiency, the program presented here requires all the equations associated with two nodes to be on core. Minimum disk storage is achieved by storing only nonzero entries of the matrix, a single pointing vector for each node, regardless of the number of degrees‐of‐freedom, and the use of a single sequential file. Special care is taken of the boundary nodes where only the diagonal and the right‐hand‐side vector are stored. Assembly and elimination for these nodes are avoided completely. The performance of the program is compared with both symmetric and nonsymmetric frontal routines and is shown to be acceptable. The major merit of the method lies in the fact that it can be implemented on small minicomputers. The reduction of core and disk storage inevitably increases the solution time, but the decrease in the output file size also makes the back‐substitution and resolution processes more efficient. In some cases, the total solution time can be shorter than for the frontal method due to this property.
Minimum norm solutions to linear elastic analysis problems
Authors: Kaneko I. , Plemmons R. J. 
Published: August 2005

AbstractA basic problem in the linear elastic analysis is that of finding the vectors of stresses and strains, given a finite element model of a structure and a set of external loads. One purpose of this paper is to show that the problem is a special case of the minimum norm problem for underdetermined systems of linear equations. In this regard, the three conventional structural analysis approaches, i.e. the displacement method, the natural factor formulation and the force method, are unified and interpreted in the framework of the minimum norm problem, which is divided into two approaches—the primal formulation and the dual formulation. Numerical comparisons of several computational procedures capable of solving the minimum norm problem are given from computational efficiency and accuracy points of view. Included in the comparisons are the three conventional structural analysis approaches mentioned above, and several alternative approaches.
Numerical solution of nonlinear inverse heat conduction problem with a radiation boundary condition
Authors: Mehta R. C. 
Published: August 2005

AbstractA finite difference solution for the transient nonlinear heat conduction equation in a finite slab with a radiation boundary condition is proposed. An implicit finite difference approximation is used which enables accurate estimation of the surface temperature as well as prevention of oscillation of computed values at the surfaces. A two‐time level implicit method is used, while Taylor's forward projection method is employed for taking account of the nonlinearities. An iterative method is described which predicts unknown surface conditions. An example is illustrated which is typical of those that arise in practical applications. The results demonstrate that the method is remarkable in its stability to predict surface conditions without debilitation.
Reduction methods for nonlinear steady‐state thermal analysis
Authors: Noor Ahmed K. , Balch Chad D. , Shibut Macon A. 
Published: August 2005

AbstractHybrid analysis techniques based on the combined use of finite elements and the classical Bubnov–Galerkin approximation are presented for predicting nonlinear steady‐state temperature distributions in structures and solids. In these hybrid techniques the modelling versatility of the finite element method is preserved and a substantial reduction in the number of degrees‐of‐freedom is achieved by expressing the vector of nodal temperatures as a linear combination of a small number of global‐temperature modes, or basis vectors. The Bubnov–Galerkin technique is then used to compute the coefficients of the linear combination (i.e. the amplitudes of the global–temperature modes).The basis vectors chosen are the path derivatives commonly used in perturbation techniques, namely, the derivatives of the nodal–temperature vector with respect to a preselected control (or path) parameter(s). The vectors are generated by using the finite element model of the initial discretization. Also, the performance of alternate sets of basis vectors is investigated. In the alternate sets, only a few path derivatives are generated, and they are augmented by a constant vector representing a uniform temperature rise (or drop), and by reciprocal vectors with nonzero components equal to the reciprocals of the nonzero components of the path derivatives. A problem‐adaptive computational algorithm is presented for efficient evaluation of global approximation vectors and generation of the reduced system of equations and for monitoring the accuracy of the reduced system of equations.The potential of the proposed reduction methods for the solution of large‐scale, nonlinear steady‐state thermal problems is also discussed. The effectiveness of these methods is demonstrated by means of four numerical examples, including conduction, convection and radiation modes of heat transfer.This study shows that the use of the uniform‐temperature mode and the path derivatives as global approximation vectors significantly increases the accuracy of the solutions obtained by reduction methods, thereby enhancing the effectiveness of these methods for the solution of large‐scale, nonlinear thermal problems.
A general iterative method to design Kármán‐Trefftz and Joukowsky airfoils
Authors: Yükselen M. A. , Erim M. Z. 
Published: August 2005

AbstractA general iterative method is presented to design Kármán–Trefftz and Joukowsky airfoils of specified thickness and camber ratios and the location of the maximum thickness point. The method has been programmed for a digital computer and results of some applications are given.
An improved isoparametric transformation for finite element analysis
Authors: Celia Michael A. , Gray William G. 
Published: August 2005

AbstractThe standard isoparametric transformation for finite element analysis is shown to be only a special case of a more general transformation which allows for flexibility in locating side and interior element nodes. Side nodes positioned at the same relative distance from corner nodes in both local and global space, and interior nodes positioned such that they do not affect the Jacobian of the co‐ordinate transformation, provide improved accuracy over nodes positioned locally without regard for the global configuration. This concept is demonstrated in the context of two‐dimensional quadratic quadrilateral isoparametrics, but is also applicable to higher orders and dimensions. In the test cases examined, the new formulation provides a reduction in error of up to three orders of magnitude and also provides accurate solutions for nodal placements which are not allowed using the standard transformations.
A generalized finite difference scheme for convection‐dominated metal‐forming problems
Authors: Tseng Ampere A. 
Published: August 2005

AbstractA simple but versatile numerical technique using generalized finite difference discretization has been developed for heat transfer problems involving high convective heat flow, irregular geometry and high local thermal gradients. Upwind differencing is utilized to stabilize the numerical oscillations often induced in convection‐dominated heat transfer problems. An arbitrary irregular mesh scheme is adopted to treat the irregular geometry and to achieve high accuracy in zones having high thermal gradients. To demonstrate the validity of the formulation procedure, results predicted from the present scheme are compared with the analytical solution for a problem having a regular boundary. Application to a typical metal‐forming process having curved boundaries is then included.
Description of the orthogonal collocation method for modelling flames in furnaces
Authors: Chandrasekharan K. , Briffa F. E. J. 
Published: August 2005

AbstractThe orthogonal collocation method has been used to solve some of the governing equations encountered in modelling flames with the boundary layer approximation. A split trial function is used to permit greater resolution of the region close to the reactor inlet. The governing equations constituting a set of coupled parabolic partial differential equations are transformed to a set of ordinary differential equations and integrated numerically by an explicit marching method. The details of the numerical scheme are elaborated.
A conservative finite element method for heat conduction problems
Authors: Banaszek Jerzy 
Published: August 2005

AbstractThis paper is concerned with the development of a numerical model which is based on the direct integral balance of internal energy over an a priori defined subdomain, associated with any nodal point, and on the piecewise temperature and geometrical interpolation inherent in the isoparametric finite element concept. This discretization procedure, also called the conservative finite element method (CFEM), ensures local and global energy conservation, in spite of discretization errors, and preserves the major feature of the finite element technique, i.e. the versatility of its algorithm.The CFEM equations are first developed and then some features of the CFEM matrices and solutions are compared with relevant features of the finite element method based on the Galerkin orthogonalization process (GFEM).To confirm better accuracy of the numerical procedure thus developed, four examples of a comparative nature, dealing with simple configurations, are solved.Furthermore, the stability and oscillation characteristics of the CFEM and GFEM solutions are established by means of the von Neumann approach, in order to show less stringent stability requirements for the CFEM model.
Incremental finite element analysis of geometrically altered structures
Authors: Ghaboussi Jamshid , Pecknold David A. 
Published: August 2005

AbstractA conceptually simple, general method is described for the finite element simulation of multi‐stage construction and excavation processes, including recognition of nonlinear material behaviour. Anomalous results reported in the literature for simulation of excavation of elastic media are examined, and shown to result from the inconsistent determination of nodal excavation forces from element boundary stresses.
Stresses from arbitrary loads on a penny‐shaped crack
Authors: Smith R. N. L. 
Published: August 2005

AbstractAn implementation of a solution to the problem of a penny‐shaped crack in an infinite elastic solid with arbitrary normal and shear loads is described, and is used to generate the stresses corresponding to some simple crack loads. The program described is fast and stable, and is shown to give accurate results even if the crack loads are not of the desired polynomial form. Stress intensity factors are obtained directly from combinations of load constants.
An explicit conditionally stable finite difference equation for‐heat conduction problems
Authors: Bhattacharya M. C. 
Published: August 2005

AbstractThis paper reports a new explicit and conditionally stable finite difference equation for heat conduction. It predicts results with an accuracy comparable with or better than that obtainable by other methods. Stability of operation can be extended to any desired degree by subdividing the basic time step and increasing the number of nodes. Some existing difference equations are special cases of the new equation reported in this paper. The new solution has been tested by calculating the response of a slab to transient and progressive waves whose analytical solutions are known.
Structural design sensitivity analysis with general boundary conditions: Dynamic problem
Authors: Hsieh C. C. , Arora J. S. 
Published: August 2005

AbstractIn a previous paper1, design sensitivity analysis of static response of structural systems when general boundary conditions are imposed during the analysis phase was developed and presented. This paper presents methods for design sensitivity analysis of dynamic response of structural systems when general boundary conditions are imposed during the analysis phase: Eigenvalue as well as transient response problems are discussed. Design sensitivity expression for eigenvalue constraints is derived. For the transient problem, point‐wise as well as the integral‐type constraint functions are treated. Advantages of these design sensitivity analysis procedures for the dynamic problem are the same as for the static problem. Namely, they are compatible with any existing finite element analysis computer code. Also, they can handle general boundary conditions that are design independent or dependent. Three simple examples are presented to show use of the procedures. Based on these applications, general‐purpose numerical procedures can be developed and incorporated into existing computer codes.
Explicit expressions for energy release rates using virtual crack extensions
Authors: Haber Robert B. , Koh Hyun M. 
Published: August 2005

AbstractA new finite element technique for calculating energy release rates is presented. An explicit expression for energy changes due to virtual crack extensions is formulated based on a variation of isoparametric element mappings. Energy release rates are calculated directly from integral expressions evaluated over singular quarter‐point isoparametric elements surrounding the crack tip. Since the energy release rates are expressed in variational form, there is no need for the analyst to select a small finite crack extension to simulate a virtual crack extension. The method is shown to produce very accurate solutions even with fairly coarse element meshes. A similar technique for mixed‐mode fracture based on mutual potential energy release rates is described.
An apporach to automatic three‐dimensional finite element mesh generation
Authors: Caendish James C. , Field David A. , Frey William H. 
Published: August 2005

AbstractRecently developed solid modelling systems for the design of complex physical solids using interactive computer graphics offer the exciting possibility of an integrated design/analysis system. Called geometric modellers, these systems build complex solids from primitive solids (cubes, cylinders, spheres, solid patches, etc.) and macro solids (combination of primitives)3, 4, 8, 16, 18, 25, 38. To provide an effective structural analysis capability for these systems, methods must be devised to ease the burden of discretizing the solid geometry into a user controlled (usually locally graded) finite element mesh. The purpose of this paper is to describe an interactive solid mesh generation system capable of generating valid meshes of well‐proportional tetrahedral finite elements for the decomposition of multiply connected solid structures. The system uses a semi‐automatic node insertion procedure to locate element node points within and on the surface of a structure. An independent automatic three‐dimensional triangulator then accepts these nodes as input and connects them to form a valid finite element mesh oftetrahedral elements. Although this report makes use of a modeller based on a constructive solid geometry representation (a so‐called CSG modeller), the mesh generation strategy elaborated herein is completely general and makes no particular use of the CSG representation.
A four‐node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation
Authors: Bathe Klaus‐Jürgen , Dvorkin Eduardo N. 
Published: August 2005

AbstractThis communication discusses a 4‐node plate bending element for linear elastic analysis which is obtained, as a special case, from a general nonlinear continuum mechanics based 4‐node shell element formulation. The formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate (and shell) element.
A finite element for the three‐dimensional deformation of a circular ring
Authors: Lebeck A. O. , Knowlton J. S. 
Published: August 2005

AbstractA finite element is developed for the three‐dimensional deformation of a circular ring. The derivation is based on ring theory. The unique feature of the element is that it provides for coupling between the in‐plane and out‐of‐plane loads and deflections. The element is derived in terms of polar co‐ordinates so that no co‐ordinate transformation is needed to assemble the elements. Three ring deflection problems are solved using an assembly of the elements. Two of the solutions are compared with analytical results and one is compared with experimental results. The comparisons verify the theory.
Generalized co‐ordinate partitioning in static equilibrium analysis of large‐scale mechanical systems
Authors: Nikravesh Parviz E. , Srinivasan Manohar 
Published: August 2005

AbstractThis paper presents a computer‐based method for automatic formulation and efficient numerical solution of static equilibrium equations for nonlinear constrained mechanical systems with conservative forces. Nonlinear holonomic constraint equations and a potential energy function are written in terms of a maximal set of Cartesian generalized co‐ordinates. A stable static equilibrium configuration is found by minimizing the potential energy of the system, subject to the kinematic constraint equations, i.e. constrained optimization. A Gaussian elimination algorithm with full pivoting decomposes the constraint Jacobian matrix, identifies dependent and independent co‐ordinates and construct an influence coefficient matrix that relates variations in dependent and independent co‐ordinates. This information is employed to convert the constrained optimization problem to an unconstrained optimization problem. A simple example is presented to illustrate the method. An algorithm that may be used in analysis of large‐scale systems is presented.
Numerical analysis of damped transient beam vibrations by use of Fourier transforms
Authors: Karlsson Lennart 
Published: August 2005

AbstractAs an approximation for the mechanism behind noise emission from a rock drilling rod, the transient damped vibrations of a beam (the drilling rod) in bending and shear is studied. At one end the beam is supported by a distributed damped Winkler‐type foundation. In order to determine required transfer function from an applied moment at the other end of the beam, it is divided into two finite elements. Each element is treated as a uniform Rayleigh–Timoshenko beam in an ambient medium. The fast Fourier transform (FFT) technique is utilized. Good agreement between calculated and measured strains is obtained. A single‐figure measure which is approximately proportional to the sound power radiated from the vibrating beam is calculated for different damping materials at the supported end. It is found that a relatively high value of the stiffness of the Winkler‐type foundation is needed if a significant level of reduction in the sound power radiated from the beam is to be achieved.
The poor bending response of the four‐node plane stress quadrilateral
Authors: Prathap Gangan 
Published: August 2005

AbstractMany plane stress finite elements which can exactly represent rigid‐body and constant‐strain modes are too stiff in their response to the simple flexural action of a beam. This problem has received considerable interest. In this paper we explore a new interpretation of the problem and show that the poor bending response of the original 4‐node plane stress quadrilateral can be quantitatively predicted by an error model.
Free convection heat transfer to steady radiating non‐Newtonian MHD flow past a vertical porous plate
Authors: Bestman A. R. 
Published: August 2005

AbstractNon‐Newtonian fluid motion generated by a vertical porous hot plate in the presence of a transverse magnetic field is studied when viscous and ohmic dissipations are significant. When the temperature of the plate is very large, a general differential approximation for the radiative flux enables the asymptotic flow, valid far away from the tips of the plate, to reduce to a set of nonlinear and coupled ordinary differential equations. The solutions of these differential equations are studied for both small and large values of the absorption coefficient. The temperature, velocity and magnetic field distributions are discussed quantitatively. A primary conclusion of the analysis is that the distributions of temperature, velocity and magnetic field are much larger for a fluid with a large absorption coefficient than for a fluid with a small absorption coefficient.
Finite element solution for electromagnetic scattering from two‐dimensional bodies
Authors: Mason John L. , Anderson William J. 
Published: August 2005

AbstractThe problem of scattering from bodies in free space is formulated using a differential equation approach. The finite element mesh extends outward into the far field region of the scattering body, where the outer boundary condition is evaluated using the asymptotic expression for the scattered field. Numerical results for two scattering bodies are presented and discussed. Non‐physical, standing waves appear in the results due to the inadequacy of the outer boundary condition in fulfilling the radiation condition for the scattered field. The differential equation approach does not appear to be competitive with integral equation approaches for thin bodies, but seems promising for handling scattering from thick inhomogeneous bodies into which the field penetrates.
An additional stiffness parameter measure of error of the second kind in the finite element method
Authors: Prathap Gangan 
Published: August 2005

AbstractConventional error analyses norms in the finite element method are based on the percentage error or its equivalent in some computed value as compared to the theoretically predicted value. In problems where two or more field variables are coupled, it is possible that if the field interpolation functions do not ‘consistently’ reproduce limiting situations of physical behaviour, there may be very large errors which are exaggerated enormously when some structural parameters become indefinitely large in a penalty limiting sense. The percentage error norms therefore saturate quickly to a value approaching 100 per cent and do not sensibly reflect the relationship between error and the structural parameter, even on a logarithmic plot.Errors due to these spurious constraints have recently been recognized as belonging to a special class described as ‘errors of the second kind’. A new error norm, called the additional stiffening parameter, helps to recognize the manner in which errors of the second kind can be blown out, of propprtion by a large variation in some structural parameter. Recent investigations in some multi‐field problems are summarized here to demonstrate the usefulness of this concept.
Velocity–pressure distribution in grain bins—Brooker's model
Authors: Miketinac M. J. , Sokhansanj Shahab 
Published: August 2005

AbstractThe pressure pattern of nonlinear airflow through a filled grain bin is obtained by numerically solving the partial differential equation modelling the flow. The finite element method as implemented in an IMSL package—TWODEPEP—is used to obtain the numerical approximation to the solution. The predicted isopressure lines are compared with other published computational results and with the experimentally measured values. It is shown that some features of the experimental isopressure patterns can be obtained computationally by using solution techniques that are more accurate than the ones used so far.