bluuebunny/crossref_metadata_2025_split huggingface dataset:
A systematic procedure for generating useful conformal mappings
Authors: Caughey D. A. 
Published: August 2005

AbstractA Procedure is presented for generating a class of conformal mappings useful in the formulation of finite−difference problems involving curved boundaries. The method provides a systematic approach that is capable, in principle, of reducing the geometry to a nearly−rectangular domain for a wide variety of partical problems. The introduction of sheared co−ordinates in this computational domain then provides for solution of the problem in a nearly−orthogonal (in fact, nearly−conformal) co−ordinate system, with its boundaries corresponding to co−ordinate lines. The method is based upon the Schwarz−Christoffel transformation and is quite simple to apply. Several examples illustrating the types of geometries which can be treated in this manner are presented.
Upwinding of high order Galerkin methods in conduction−convection problems
Authors: Christie I. , Mitchell A. R. 
Published: August 2005

AbstractUpwinded parabolic and cubic elements are derived on a uniform grid of size h for the finite element Galerkin method applied to the solution of the model conduction−convection problem εu″ — Ku′ = 0, ε, K > 0, subject to the boundary conditions u(0) = 1, u (1) = 0. Extension of the results to more complicated problems is indicated. Finally numerical results are given comparing some of the methods derived for a range of L(=Kh/2ε), the grid Peclet number.
An elasto‐viscoplastic thermal stress model with applications to the continuous casting of metals
Authors: Williams J. R. , Lewis R. W. , Morgan K. 
Published: August 2005

AbstractA finite element model is presented for the analysis of the thermal stress development in a body with temperature dependent material properties. The thermal model allows a change of phase to occur within the body and an elasto‐viscoplastic constitutive relationship is used for the stress analysis. An example is given of the applicability of the technique to the analysis of continuous casting in metals.
A simply implemented two dimensional Shockley–Poisson solver with applications to CCD
Authors: Fortino Andres G. , Nandan Joseph S. 
Published: August 2005

AbstractA numerical method for the solution of the two dimensional Shockley–Poisson equation is presented and applied to the analysis of MOS devices. This SOR–Newton method is compared to Gummel's algorithm in two dimensions and shown to be more easily implemented. Application of the resulting code to interelectrode effects in charge coupled devices is given as an example.
Restricted range adaptive curve fitting
Authors: Hull J. A. , Taylor G. D. 
Published: August 2005

AbstractIn this paper we present an algorithm for adaptively computing smooth piecewise polynomial approximations using restricted range uniform approximations on a finite point set. We also present several numerical examples and offer suggestions for the effective use of this algorithm. We have found the algorithm to be effective for approximating a wide class of functions, either with or without significant levels of noise. Furthermore, since the user of this algorithm actually defines tolerance bands within which the approximation will lie, the algorithm allows the user a great deal of flexibility and control over the shape of the resulting approximations.
On the use of the total scalar potential on the numerical solution of fields problems in electromagnetics
Authors: Simkin J. , Trowbridge C. W. 
Published: August 2005

AbstractThe paper summarizes the formulation of a set of computer algorithms for the solution of the three‐dimensional non‐linear Poisson field problem. Results are presented that were obtained by applying algorithms to the analysis of two‐dimensional magnetostatic fields. Scalar and vector potentials were used, and it is shown that the convenient single valued scalar potential associated with the induced sources gives severe accuracy problems in permeable regions. The results become as good as those obtained using vector potential if the scalar potential associated with the total field is used for permeable regions. The combination of two scalar potentials has a significant advantage for three‐dimensional problems.
An algorithm for automatically tracking ablating boundaries
Authors: Weeks George E. , Cost Thomas L. 
Published: August 2005

AbstractAn algorithm has been developed which automatically calculates the time‐dependent positions of points on the ablating boundaries of two‐dimensional continuum structures with geometrially complex shapes. The structural boundary may consist of ablating and non‐ablating parts. The initial ablating and non‐ablating boundaries are defined by the disjoint union of piecewise linear arcs passing through a finite set of nodal points on the boundary, each defined by a pair of rectangular Cartesian co‐ordinates. For a specified ablation rate, the algorithm calculates successive positions of the boundary points at times specifiec by the user. The algorithm is designed such that it may be easily incorporated, along with an automated mesh generation procedure, into existing finite element codes for transient thermal or stress analysis of structures with ablating boundaries. Two examples are presented from the field of solid rocket analysis.
An improved method for contouring on isoparametric surfaces
Authors: Gray W. H. , Akin J. E. 
Published: August 2005

AbstractA general non‐linear interpolation procedure for contouring on any isoparametric surface was presented in a previous article. The method used standard isoparametric interpolation functions and a predictor method for tracing element contour lines. The method presented here extends the previous work by using a predictor‐corrector method to trace element contour lines, thereby making the contouring algorithm more accurate.
Frequency analysis of thick orthotropic plates on elastic foundation using a high precision triangular plate bending element
Authors: Babu P. V. Thangam , Reddy D. V. , Sodhi D. S. 
Published: August 2005

AbstractA high precision triangular thick orthotropic plate bending element on an elastic foundation is developed for the free vibration analysis of thick plates on elastic foundation. The element has three nodes with twelve degrees‐of‐freedom per node, and takes into account the shear deformation and rotatory inertia. The accuracy of the element is established by comparison of the natural frequencies of certain thick and thin plates, determined from a consistent mass matrix formulation, with available results.
The evaluation of improper integrals encountered in the use of conformal transformation
Authors: Binns K. J. , Rees G. R. , Kahan P. 
Published: August 2005

AbstractMethods are described and reviewed for the accurate numerical evaluation of improper integrals encountered in conformal transformation solutions involving boundaries of relatively complicated shape. Four methods are reviewed for the solution of integrals containing end‐point singularities. Two new methods are discussed for the solution of integrals containing both end point singularities and simple poles within the range of integration. One method uses a combination of a simple recursive formula and the coefficients of a Chebyshev series and a second method involves subtracting out the singularity and the use of Gauss–Jacobi quadrature. Both methods can give results of high accuracy and an upper limit of the error is readily found. A numerical example is taken which is typical of the application to practical problems and this brings out a comparison of the two methods.
Finite elements for an optimal control problem governed by a parabolic equation
Authors: Meric R. A. 
Published: August 2005

AbstractA stationary variational formulation of the necessary conditions for optimality is derived for an optimal control problem governed by a parabolic equation and mixed boundary conditions. Then a mixed finite element model with elements in space and time is utilized to solve a simple numerical example whose analytical and finite difference solutions are given elsewhere. Numerical results show that the proposed method with C° continuity elements constitutes a powerful numerical technique for solution of optimal control problems of distributed parameter systems.
Piecewise linear elastic–plastic analysis
Authors: Kaneko Ikuyo 
Published: August 2005

AbstractThe purpose of this paper is to show that a mathematical programming method, due to Maier and his co‐workers, of nonlinear structural analysis can be rerformulated so that greater computational efficiences are achived. The methods are designed for a class of elastic–plastic structures under ‘piecewise linear’ assumptions and solve among others the problem of determining the stresses and strains in the structure. The reformulation gives rise to a class of mathematical programming problems calles a ‘n by dn linear complementarity problem’, for which the author has developed an efficient algorithm. It will be explained why and by how much the proposed method (the reformulation and its solution by the author's algorithm) solves the structural problems more efficiently than the existing one. Results of a systematic computer experiment supporting the efficiency of the proposed method are also presented.
Representation and discretization of arbitrary surfaces for finite element shell analysis
Authors: Wu Sheng‐Chuan , Abel John F. 
Published: August 2005

AbstractAn interactive computer graphics system has been developed for generating the geometric description of an arbitrary shell surfface. The various difficulties facing the user of sophisticated, doubly‐curved shell finite elements and the inefficiency of preprocessing for shell analysis are discussed to explain the benefits of this system. The method is a synthesis of spline theory and algorithms, and an interactive means for man–machine communication. The basic technique employed is a modified lofting method in which cardinal splines. An inversion procedure is incorporated which increases significantly the efficiency of the B‐spline approximation process. Static and dynamic graphic displays greatly enhance visualization at any stage of the procedure. Two examples of practical interest are presented in some detail to demonstratge the flexibility and usefulness of this approach. Some natural extensions of this system for interactive mesh generation on the surface are also demonstrated.
Strees analysis of variable cross‐section indeterminate beams using reopeated integration
Authors: Wilson Howard B. , Farrior Donna S. 
Published: August 2005

AbstractA simple computer method is presented for analysing statically indeterminate beams having sectionally constant EI values and loads consisting of any number of arbitrarily placed concentrated forces and couples as well as any number of uniform and ramp loads. Unknown reactions are treated as parameters which are determined by simulataneous imposition of end conditions and interior constraints. Support locations are specified independently of any discontinuites of load or cross‐section. A computer program implementing this method is described which has very concise data input considerably shorter than tupically required in programs based on the stiffness method.
Adaptive l1–l2 curve fitting
Authors: Avila P. G. , Taylor G. D. 
Published: August 2005

AbstractIn References 1 and 2, algorithms were introduced for adaptively computing smooth piecewise polynomial approximations using uniform, least‐squars (l2) and restricted‐range uniform approximations. This present paper introduces a FORTRAN program for computing smooth piecewise polynomial approximations to data and/or precise mathematical functions (in discrete form) which allows the user the option of using best l1 of best l2 approximations. (The l2 option of this newly developed l1–l2 adaptive curve‐fitting package supersedes the code listed in Reference 1 for the old least‐squares program.) In this paper, adaptive curve‐fitting algorithm used in this l1–l2 package is described in detail, the FORTRAN program is the given (in the Appendix) and discussed, the numerical results are presented in an effort to illustrate how the l1 and l2 versions of this algorithm may be used most effectively.
Errors arising from irregular boundaries in ADI solutions of the shallow‐water equations
Authors: Weare T. J. 
Published: August 2005

AbstractTruncation errors introduced by operator splittingtechniques, such as the ADI scheme, are discussed in the contextof the two‐dimensional shallow‐water equations. Numericalexamples of flow along a uniform channel, with and withoutfriction, illustrate the practical significance of these errors when the boundary is not aligned with the computational gridaxes. With irregular boundaries the maximum time step aceptable ismore severely restricted than has been realized hitherto. The problem, which is shown to stem from the treatment of the boundary conditons, is inherent in any splitting scheme and is difficult to circumvent.
A new numerical method for transient thermal stress problems
Authors: Takeuti Y. , Tanigawa Y. 
Published: August 2005

AbstractA new numerical method of calculating unsteady‐state heat conduction and thermal stresses by using improved coefficient matrix patterns on the nodal points of a structure is given. Good agreement is obtained between our results and the rigorous results, and this method seems to yield better accuracy than other well‐known approximate methods for two‐dimensional transient thermal stress problems.
A class of preconditioned conjugate gradient methods for the solution of a mixed finite element discretization of the biharmonic operator
Authors: Axelsson Owe , Munksgaard Niels 
Published: August 2005

AbstractThe homogeneous Dirichlet problem for the biharmonic operator is solved as the variational formulation of two coupled second‐order equations. The discretization by a mixed finite element model results in a set of linear equations whose coefficient matrix is sparse, symmetric but indefinite. We describe a class of preconditioned conjugate gradient methods for the numerical solution of this linear system. The precondition matrices correspond to incomplete factorizations of the coefficient matrix. The numerical results show a low computational complexity in both number of computer operations and demand of storage.
Description of a curved boundary shape without first derivative discontinuities
Authors: Redmer J. , Kuehne K. , Dahl W. 
Published: August 2005

AbstractFor the two‐dimensional isoparametric 8‐node element an additive condition is formulated, so that the function describing the domain boundary is continually differentiable at the common nodes on the boundary. This condition will be satisfied by moving the mid‐side nodes into a special position. The advantage in using this modified element will be shown by an example of the elasto‐plastic calculation of a double‐edge notched specimen.
On the approximation of incompressible materials in the displacement method
Authors: Debongnie J. F. 
Published: August 2005

AbstractA mathematical description of the numerical approximation to incompressibility with nearly incompressible displacement finite elements is presented. By the way of functional analysis, it leads to a condition of convergence to the incompressible problem when v is increased up to 0.5, which can be identified with Fried's K1 criterion.
On modified incomplete cholesky factorization methods for the solution of problems with mixed boundary conditions and problems with discontinuous material conefficients
Authors: Gustafsson Ivar 
Published: August 2005

AbstractIn Reference 1 a class of first‐order factorization methods for the solution of large, sparse systems of equations, of which the coefficient matrix is a symmetric M‐matrix, was introduced. Asymptotic results for the computational complexity was proved in the case of systems arising from finite difference approximation of second‐order self‐adjoint elliptic partial differential equation problems in two dimensions with Dirichlet boundary conditions. In this paper the result is extended to cover even mixed boundary conditions and problems with discontinuous material coefficients. Results from numerical experiments with various finite difference and finite element approximations are presented and comparisons with direct and other interative methods are made.
Orthogonal base functions and consistent diagonal mass matrices for two‐dimensional elements
Authors: Schreyer Howard L. , Fedock Joseph J. 
Published: August 2005

AbstractOrthogonal base functions that are complete first‐order polynomials but contain higher order terms are developed for normalized rectangular and triangular elements. To obtain exact expressions for kinetic energy under rigid body rotation, an internal node is introduced at the centroid of each element. Then the corresponding mass matrix is both diagonal and consistent. A mixed variational formulation is used in the derivation of spatially discretized field equations. Central Difference time integration is utilized to provide sample results which are compared with other numerical or analytical solutions.
Exterior flow with an isoparametric Hermite cubic element
Authors: Williams B. R. , Morton K. W. 
Published: August 2005

AbstractAn isoparametric Hermite cubic element is developed for calculating compressible flows past complex aerofoils in two dimensions. A simple intermediate transformation is used to derive an isoparametric transform whose Jacobian is always non‐zero and which attains very high accuracy on the boundary. Application of the method and assessment of the error is illustrated by flow past a circular cylinder.
The finite element method in problems of nonlinear optics
Authors: Chesnokov S. S. , Egorov K. D. , Kandidov V. P. , Vysloukh V. A. 
Published: August 2005

AbstractThe Possibility of the application of the finite element method to some problems of nonlinear optics is investigated in this paper. The self‐action of a light beam in a nonlinear medium is considered. The general approach to the cretion of conservative computation schemes is presented, based on varitional principles. Definite schemes, which are applicable for the problem of thermal self‐action, are described in detail both in the case of cylindrical and or rectangular co‐ordinates. The accuracy and convergence of the models are analysed. The results of computation of the self‐action problems in motionless and moving media are presented.
Weight functions from virtual crack extension
Authors: Parks D. M. , Kamenetzky E. M. 
Published: August 2005

AbstractThe stiffness‐derivative method of Parks1 for calculating the linear elastic crack tip stress intensity factor for any symmetric crack configuration and a particular loading is extended to calculate the weight function vector field2,3 which serves as a Green's function for the stress intensity factor. The method, which combines the observations of Rice3 on the weight function and of Zienkiewicz4 on the differential stiffness method, permits very efficient determination of the weight function, requiring only one additional back‐substitution on the already‐factored stiffness matrix. Thus, the stress intensity factor for arbitrary loading of this configuration can subsequently be determined by quadrature alone. The promising extension of the method to three‐dimensional configurations is outlined.While this manuscript was under review, the authors became aware of the recent work of Vanderglas,21 in which the same approach as ours is used to extend the stiffness derivative method. The present work was then voluntarily revised in order to address further certain aspects of the topic of shape function perturbation, which Vanderglas noted.
Structural weight optimization by dual methods of convex programming
Authors: Fleury C. 
Published: August 2005

AbstractThis paper is mainly concerned with a new structural optimization method based upon the concept of duality in convex programming. This rigorous formulation permits justification of many intuitive procedures which are used in the classical optimality criteria approaches. Furthermore, the dual algorithms proposed in this paper do not suffer from the drawbacks inherent to the optimality criteria approach. The selection of the set of active constraints does not introduce any difficulty and is achieved correctly in all cases. The subdivision of the design variables in an active and passive group is intrinsically contained in the dual formulation. The efficiency of the dual algorithms is shown with reference to some problems for which the classical methods do not lead to satisfactory results.
Finite element and conjugate gradient methods for a nonlinear optimal heat transfer control problem
Authors: Meric R. A. 
Published: August 2005

AbstractThe boundary control problem of optimal heating of an infinitely long slab with tempertue‐dependent thermal conductivity, subjected to a convection and radiation boundary condition, is analysed by numerical methods.In order to reformulate the optimal control problem of distributed parameter systems as a mathematical programming problem of finite dimension, a space, co‐ordinate is discretized by use of the finite element method, while the Runge–Kutta method is utilized for time integrations. Finally, the performance index of the optimal control problem is minimized by the conjugate gradient method of optimization.
On the analysis of accuracy for two‐equation transient problems
Authors: Lynch Daniel R. , Gray William G. 
Published: August 2005

AbstractFourier analysis of numerical accuracy has traditionally concentrated on the propagation behaviour of various methods. When systems of equations in more than one unknown are involved, analysis of propagation accuracy alone is shown to be incomplete. A distribution factor is introduced to complement the Fourier analysis in these cases, and application of the concept to two problems commonly encountered in the water resources field is demonstrated. The distribution factor is shown to provide important information which cannot be obtained from the customary analysis of propagation accuracy.
Improved boundary–integral equation method for time‐dependent inelastic deformation in metals
Authors: Morjaria Mahes , Mukherjee Subrata 
Published: August 2005

AbstractEfficient solution of boundary value problems for time‐dependent inelastic deformation in metallic structures is of great practical importance. These problems are generally solved by finite element methods and separate descriptions for time‐independent plasticity and time‐dependent creep are normally used. The boundary–integral equation method was recently applied for the first time to such problems. This paper presents a very efficient numerical implementation of the method with a linear description of the relevant variables over each boundary element and a newly developed Euler‐type time‐integration scheme with automatic time‐step control for time integration. Numerical results for plates in plane stress with and without cutouts, under different loading histories, are presented. A combined creep–plasticity constitutive theory with state variables is used to model material behaviour. The results are more accurate and are obtained with much less computational effort compared to a previous attempt with an uniform description of variables over each boundary element and a predictor–corrector scheme for time integration. The computer program developed is quite general and can handle plane stress problems for plates of arbitrary shapes subjected to arbitrary time‐histories of loadings. The numerical results presented in the paper are for certain illustrative problems.