bluuebunny/crossref_metadata_2025_split huggingface dataset:
An algorithm for the solution of very large banded unsymmetric linear equation systems
Authors: Stabrowski M. M. 
Published: August 2005

AbstractThis paper presents an algorithm and corresponding FORTRAN program for the solution of unsymmetric banded linear equation systems. The algorithm is based on the Crout method. A special technique, called double windowing, enables the solution of very large equation systems with a total equation number reaching 30,000 and a full bandwidth in excess of 1,000. Special attention was devoted to minimization of peripheral processor time (communication with backing disc memory). An appendix lists the complete program for Cyber series computers (CDC).
Stint/CD: A stand‐alone explicit time integration package for structural dynamics analysis
Authors: Underwood Philip , Park K. C. 
Published: August 2005

AbstractThis paper is a user's guide for the stand‐alone explicit direct time integration package STINT/CD for structural dynamics analysis. STINT/CD uses an automatic variable time increment central difference method. The purpose, function, limitations and usage of the package are described. A FORTRAN listing of STINT/CD is given along with a sample problem which illustrates its usage and performance.
Quadratic and cubic transition elements
Authors: Hussain M. A. , Vasilakis J. D. , Pu S. L. 
Published: August 2005

AbstractQuadratic and cubic quadrilateral isoparametric elements are investigated for use as transition elements for use a crack tip elements. Computations for a single element are explicitly carried out using a symbolic algebraic manipulation program and in addition to the desired square root singularity, additional singularities are revealed. Cubic transitional elements were used for a double‐edge crack problem and only marginal improvement is found for a well‐laid out grid.
Eigensolution using lagrangian interpolation
Authors: Iyer M. S. 
Published: August 2005

AbstractA computationally efficient and accurate solution technique for large‐order eigenvalue problems with small to medium bandwidth is presented. The algorithm—called the Sub‐Polynomial Iteration (SPI) method—solves for the eigenvalues and corresponding eigenvectors. directly without any transformation to the standard form. The method is an efficient combination of several separate techniques including Sturm sequence, Lagrangian polynomial interpolation, inverse iteration with shift and Gram‐Schmidt orthogonalization. Computer run times for a set of sample solution indicate the efficiency of the SPI method.
Plane isoparametric hybrid‐stress elements: Invariance and optimal sampling
Authors: Spilker R. L. , Maskeri S. M. , Kania E. 
Published: August 2005

AbstractFormulation and applications of the hybrid‐stress finite element model to plane elasticity problems are examined. Conditions for invariance of the element stiffness are established for two‐dimensional problems, the results of which are easily extended to three‐dimensional cases. Next, the hybrid‐stress functional for a 3‐D continuum is manipulated into a more convenient form in which the location of optimal stress/strain sampling points can be identified. To illustrate these concepts, 4‐ and 8‐node plane isoparametric hybrid‐stress elements which are invariant and of correct rank are developed and compared with existing hybrid‐stress elements. For a 4‐node element, lack of invariance is shown to lead to spurious zero energy modes under appropriate element rotation. Alternative 8‐node elements are considered, and the best invariant element is shown to be one in which the stress compatibility equations are invoked. Results are also presented which demonstrate the validity of the optimal sampling points, the effects of reduced orders of numerical integration, and the behaviour of the elements for nearly incompressible materials.
Stereo decomposition subroutines for three‐dimensional plotter programs
Authors: Pammer Z. , Szabo L. 
Published: August 2005

AbstractTwo‐dimensional distributions and three‐dimensional element meshes are usually plotted in axonometric projection. Stereo decomposition can make the plots of complicated functions and structures more synoptical; the object appears in three dimensions. The method can be useful for the display of displacements and model shapes of three‐dimensional structures as well.
Mixed interpolation in primitive variable finite element formulations for incompressible flow
Authors: Jackson C. P. , Cliffe K. A. 
Published: August 2005

AbstractThis paper shows that mixed interpolation is required because of the nature of the pressure terms in the equations. These lead to finite element equations which in many circumstances do not uniquely determine the pressure, if the same interpolations are used for pressure and velocities.Several new combinations of pressure and velocity interpolation are analysed with the aid of a novel diagrammatic technique. In particular we consider some very interesting combinations in which, over nearly all the flow, the pressure and velocity are approximated on elements by biquadratic polynomials which are continuous across element boundaries.The theory of this paper is shown to be in complete agreement with numerical experiment.
Elastic‐plastic analysis of plates by the hybrid‐stress model and initial‐stress approach
Authors: Spilker R. L. , Munir N. I. 
Published: August 2005

AbstractTwo alternative hybrid‐stress‐based functionals are examined for the incremental elastic‐plastic static analysis of single layer plates. Material nonlinear effects are incorporated via the initial‐stress approach so that an equivalent nodal force vector is defined and the stiffness remains constant throughout the incremental loading. The alternative functionals differ in the incremental stress which is assumed to satisfy equilibrium; in the first, it is the actual stress increment, and in the second it is the elastic stress increment. Results are presented for two example problems, and comparisons of the alternative functionals and plausible iteration schemes are given. The effects of variation of pertinent solution parameters are also shown. A 4‐node hybrid‐stress plate element based on a Mindlin‐type displacement field is used for most cases; however, limited results are also presented using an 8‐node plate element, thus permitting comparisons of the relative efficiencies of the two elements.
Calculation of sensitivity derivatives in thermal problems by finite differences
Authors: Haftka Raphael T. , Malkus David S. 
Published: August 2005

AbstractThe transient thermal analysis of large aerospace vehicles such as the space shuttle requires models with thousands of degrees‐of‐freedom. The design of thermal protection systems for such vehicles requires the repetitive thermal analysis of the vehicle and the calculation of sensitivities—derivatives of the transient response with respect to design parameters. When the number of design parameters is large, the cost of the sensitivity calculations may become prohibitive. The present work is concerned with reducing the computational cost and errors in sensitivity calculations with one of the simplest available methods—the finite difference approach. A technique for calculating simultaneously the nominal and perturbed solutions required for the finite difference derivative is proposed. An expression for the optimum value of the perturbation parameter is obtained which permits reducing the computational error. An insulated cylinder is used as an example which demonstrates that significant improvements in accuracy and efficiency may be obtained.
On the accuracy of polynomial finite elements for crack problems
Authors: Johnson A. R. 
Published: August 2005

AbstractA square tensile sheet with symmetric edge cracks is analysed by the finite element method to demonstrate the accuracy obtained with polynomial elements when the mesh patterns are chosen on the basis of the element's interpolation functions. Numerical results are provided for the accuracy of the total strain energy, the stress intensity factor, and the numerical condition of the global stiffness matrix. The stress intensity factor is determined to within 1.0 per cent accuracy using quadratic (linear strain) triangular elements with only 138 degrees‐of‐freedom.
Discrete and non‐discrete mixed methods for plate bending analysis
Authors: Fujii Fumio 
Published: August 2005

AbstractFor plate bending analysis, both discrete and non‐discrete mixed methods are presented by using spline functions in the Hellinger‐Reissner variational principle. Piecewise spline interpolation with local supports and overall spline interpolation with boundary knots are applied to each of two mixed functionals. The prescribed boundary conditions can be considered by multiple boundary knots. The convergence behaviour of the mixed methods presented is studied. Numerical examples show that a high degree of accuracy can be obtained due to continuous properties in the high derivatives of the employed shape functions. The proposed mixed methods are found to be very competitive with other numerical methods for plate bending problems.
Dispersion analysis of finite element semidiscretizations of the two‐dimensional wave equation
Authors: Mullen Robert , Belytschko Ted 
Published: August 2005

AbstractThe dispersive properties of finite element semidiscretizations of the two‐dimensional wave equation are examined. Both bilinear quadrilateral elements and linear triangular elements are considered with diagonal and nondiagonal mass matrices in uniform meshes. It is shown that mass diagonalization and underintegration of the stiffness matrix of the quadrilateral element markedly increases dispersive errors. The dispersive properties of triangular meshes depends on the mesh layout; certain layouts introduce optical modes which amplify numerically induced oscillations and dispersive errors. Compared to the five‐point Laplacian finite difference operator, rectangular finite element semidiscretizations with consistent mass matrices provide superior fidelity regardless of the wave direction.
Finite element operators: Inexpensive evaluation of upwind schemes
Authors: Hansen J. S. , Von Flotow A. H. 
Published: August 2005

AbstractThis paper introduces the notion of the finite element operator, and shows its application to the evaluation of several upwind finite element schemes. It is demonstrated that these operators supply good qualitative information on the performance of these schemes in an inexpensive as well as visual manner. In addition, this method gives insight into grid dependent effects which often characterize finite element solutions.
Solving the model of isothermal reactors with axial mixing by the differential ouadrature method
Authors: Wang Kuo‐Ming 
Published: August 2005

AbstractThe numerical solution of nonlinear partial differential equations plays a very important role in may areas of physics, engineering and biology. In many cases all that is desired is a moderately accurate solution at a few points whcih can be calculated rapidly.In this work, we present a simple and direct technique, the differential quadrature method, which can be applied in various classes of partial differential equations. It produces moderately accurate results for the points of interest, generally few in number, and eliminates the difficulties of programming complex algorithms for the computer, as well as excessive use of storage and computer time. We illustrate this technique with the solution of the model of isothermal reactors with axial mixing. The results are compared with the results obtained by using the finite difference method. It is shown that differential quadrature of order 9 (9 points) provides approximately the same accurate results as the finite difference method (480 points) does.
Effects of internal finite element node placement on field problem solutions
Authors: Kraus Hal G. 
Published: August 2005

AbstractGiven herein, in abbreviated form, is a discussion of the effects of element internal and edge node location in the finite element‐Galerkin method. The solution dependencies on node placement of many numerical schemes are reviewed. Then, a transient linear one‐dimensional heat conduction problem, solved using the finite element‐Galerkin method, is used for illustration. Results show that, in contrast to many other numerical techniques, if the finite element‐Galerkin method is strictly adhered to with respect to spatial integrations for a given number of nodes in an element, the solution is unaffected by shifting node locations as long as the specific shape of any given element remains unaltered. The reason for this invariance becomes readily apparent upon examining the orthogonality requirements imposed by this method.
An analysis of alternatives for computing axisymmetric element stiffness matrices
Authors: Palacios Jose Antonio , Henriksen Mogens 
Published: August 2005

AbstractThis note compares the use of numerical and closed form integration in computation of element stiffness matrices for axisymmetric finite element analysis. Only constant strain elements are considered. Results obtained with Gaussian quadrature and closed form integrators are compared mutually and with an exact solution obtained from classical methods. The FEM global equations estimate the force‐displacement behaviour of an elastic continuum with an accuracy that depends on the integration method used. Selection of an integration order minimizing error is particularly critical in the presence of high stress gradients. Best results in the vicinity of the axis of revolution may be obtained with single‐point integration rather than higher order approximations or exact integration of the element stiffness matrix. This phenomenon and its consequences are subsequently discussed.
Direct‐iterative solution of ill‐conditioned finite element stiffness matrices
Authors: Gen‐Hua Shi 
Published: August 2005

AbstractIn this paper we discuss and expand the direct‐iterative method proposed originally by Wilson.1 First we introduce several simple numerical examples to illustrate the basic idea of this method before we proceed to prove the convergence of the direct‐iterative method. We then discuss the methods for selecting the transformative matrix (Q) to be used in transforming an ill‐conditioned matrix into a well‐conditioned matrix in the direct‐iterative method. There are two methods used to choose the matrix Q, namely the rigid body movement method and the imaginary element method. From examples 1‐3 we can see that the imaginary element mesh is optional, and the finite element mesh is not necessary. The imaginary element method is a generalization of the mesh refinement method development in Reference 3. Because instead of local rotation angle we only choose displacements of nodes to represent rigid body movement, the rigid body movement method is an improvement of the method in Reference 2. The advantage of these two methods is that, in order to obtain well‐conditioned matrices, only a few changes in the stiffness matrices are required even with general ill‐conditioned stiffness matrices, and then convergency is achieved rapidly under SOR iteration. Finally, the examples for computing each type of the ill‐conditioned matrix in three‐dimensional finite element analysis are presented to demonstrate the effectiveness of the direct‐iterative method in solving the large bandwidth problems.
A finite element model for plane elasticity problems using the complementary energy theorem
Authors: Vallabhan C. V. Girija , Azene Muluneh 
Published: August 2005

AbstractA finite element stress analysis capability for plane elasticity problems, employing the principle of stationary complementary energy, is developed. Two models are investigated. The first is a 24 d.o.f. rectangular finite element. The second model consists of an 18 d.o.f. triangular element. In order to allow for self‐equilibrating stresses which are continuous within the element, the well‐known Airy stress function ø is used. The function ø is represented by means of quintic Hermitian polynomials within the finite element. The values of the ø function and its derivatives up to order two are used as nodal parameters. For matching the stress function with the prescribed boundary tractions, additional equations are developed considering the force and moment equilibrium equations on the boundary consistent with the assumed stress function. These additional boundary equations are incorporated into the system equations using the Lagrangian multiplier technique. Excellent results are obtained for linear elastic problems even with coarse finite element discretization. Some examples of plane elasticity problems are solved and results compared.
A warning against misuse of quarter‐point elements
Authors: Peano A. , Pasini A. 
Published: August 2005

AbstractQuarter‐point elements are used very frequently for fracture mechanics computations, because the quarter‐point technique yields the required singular interpolation without any modification to existing software. This advantage is particularly significant for three‐dimensional stress intensity factor computations because of the difficulty of implementing other techniques. However, in practical 3‐D applications, the crack front is usually curved, and this note proves that a crack front distortion leads to a negative Jacobian in the region surrounding the crack front. The numerical difficulties to be expected depend on the aspect ratio of the elements.
On a finite element model for solving Dirichlet's problem of Laplace's equation
Authors: Yi‐Heng Chen 
Published: August 2005

AbstractThis paper is a sequel to the author's previous paper. 1In soliving Dirichlet's problem of Laplace's equation by the finite element method, we can subdivide the original region into many elements, which in general are chosen to be triangular or rectangular. Customarily, 2,3,7 polynomial trial functions are chosen as the basis of the finite element model.In this paper we divide the original region into rectangles and choose a particular series for the finite element model. This model is shown to be very efficient in obtaining the analytical solution of Laplace's equation over complex regions. From some computer trials it is demonstrated that this finite element model can be used to reduce the main memory storage and computer time requirements.
Some vector expansion functions for quadrilateral and triangular domains
Authors: Okon E. E. 
Published: August 2005

AbstractVector functions having a constant or zero divergence over a quadrilateral domain are derived using a parametric co‐ordinate formulation. Expansion functions with a constant curl, defined over parallelograms and triangles, which can be used in moments‐based investigations of electromagnetic wave interactions with surfaces and apertures, are then obtained. Finally, two basis functions, which have appeared in the literature and have been used to solve field problems associated with rectangular apertures and arbitrary surfaces, are identified as special cases of these expansion functions.
Hybrid‐stress eight‐node elements for thin and thick multilayer laminated plates
Authors: Spilker R. L. 
Published: August 2005

AbstractHybrid‐stress eight‐node isoparametric multilayer plate elements are developed for the analysis of thin to thick fibre‐reinforced composite plates. Transverse shear deformation effects are incorporated by allowing a linear through‐thickness displacement variation for in‐plane displacements in each layer, with displacement continuity enforced along interlayer surfaces. An alternative, kinematically constrained through‐thickness displacement distribution is also studied, characterized by laminate reference plane displacements and non‐normal rotations. All stress components are included and are interpolated independently within each layer; interlayer surface traction continuity and laminate upper/lower surface traction‐free conditions are satisfied exactly. Alternative forms of in‐plane stress distributions are examined and the best is shown to be based on a rationale used previously for single layer hybrid‐stress plate elements to avoid locking in the thin plate limit. Selected example problems are used to demonstrate the convergence and effects of plate thickness for each of the elements, and limited stress results serve to verify the expected optimal sampling points.
Interactive computer graphic preprocessing for three‐dimensional finite element analysis
Authors: Perucchio Renato , Ingraffea Anthony R. , Abel John F. 
Published: August 2005

AbstractAn interactive computer graphic system has been developed for generating and editing three‐dimensional finite element meshes. The various difficulties inherent to the generation of solid three‐dimensional geometries through an effective use of computer graphic techniques are examined to explain the advantages of this system. The method is a combination of discrete transfinite mapping and cubic spline blending algorithms, used, respectively, to create plane cross‐sectional meshes, and to generate the three‐dimensional geometry by interpolaring between the cross‐sections. The communication between analyst and machine is based on a digitizing tablet and a refresh vector scope. The dynamic viewing capabilities and depth cueing of the vector display greatly enhance the perception of the mesh three‐dimensionality. Multi‐view dynamic display is also employed to facilitate node or element selection. The flexibility and usefulness of the system are illustrated with the help of three examples of practical interest.
Estimating stress intensity factors with singular components of the total finite element solution
Authors: Staab G. H. 
Published: August 2005

AbstractDisplacement formulated singular elements are compared to isoparametric quarter‐node elements. The total stress and displacement solution for each element is decomposed into singular and regular components for evaluating stress intensity factors. Specific relationships between nodal displacements and the singular component of stress are presented for the isoparametric element at selected locations within the element. Numerical results for KI and KII in the slant crack problem are presented. The singular components are shown to produce superior results when considering crack opening displacements.
Minimum weight design of a spherical shell under a concentrated load at the apex
Authors: Thevendran V. 
Published: August 2005

AbstractThe minimum weight design of a spherical shell under a concentrated load at the apex is presented in this paper. The usual restrictions of statical equilibrium and various yield criteria have been utilized. The finite element method is used to discretize the design parameters and the resulting nonlinear minimization problems are solved using the modified Rosenbrock's optimization method.
The optimum size of quarter‐point crack tip elements
Authors: Harrop L. P. 
Published: August 2005

AbstractIngraffea and Manu1 and Lynn and Ingraffea2 have shown that the size of the quarter‐point elements can affect the computed elastic stress intensity factor. The nature of the effect is such that, all other details remaining constant, there is a particular crack tip element size which minimizes the error in the computed stress intensity factor. Here, size of element means the radial edge length. The reasons for this size dependence are discussed below. It will be seen that the discussion is in terms of the need to simultaneously represent the singular and finite stress terms in a given problem. The discussion has relevance to other formulations of crack tip elements.