bluuebunny/crossref_metadata_2025_split huggingface dataset:
Improved strain interpolation for curved C° elements
Authors: Park K. C. 
Published: August 2005

AbstractThe strain energy of straight beam members derived from the isoparametric shape functions is known to be invariant with respect to the number of integration points as long as they exceed a minimum number. However, this invariant property is generally lost for curved members. For example, the two‐point integrated, membrane strain energy of curved beams by employing the quadratic shape functions is different from the three‐point integrated one. This paper presents an invariant strain interpolation scheme for quadratic curved beam elements, which can lead to improved membrane representations in curved shell elements, thus resolving the perplexing membrane‐bending coupling difficulties in thin shell analysis.
An inverse method for the design of axisymmetric optimal diffusers
Authors: Ahmed N. M. A. , Myring D. F. 
Published: August 2005

AbstractAn inverse inviscid–boundary‐layer interaction scheme is presented for the optimal design of axisymmetric ducts for subsonic, rotational flows. Distribution of the shape factor H on the duct wall, giving minimum total pressure loss and maximum static pressure rise, is used as boundary condition for the inverse integral boundary‐layer solution, to obtain the velocity and displacement thickness distributions on the wall. Vector addition of the inviscid core radius, derived from the solution of the inverse inviscid flow equations, and the displacement thickness produces the desired duct shape.
A new method for solving aerodynamic hybrid problem of profile cascade on S1 stream surface of revolution by employing stream‐function equation expressed with non‐orthogonal co‐ordinate system
Authors: Naixing Chen , Weihong Li 
Published: August 2005

AbstractA new method is developed in this paper for solving an aerodynamic hybrid problem of profile cascade on the S1 stream surface of revolution by employing a stream‐function equation on the non‐orthogonal co‐ordinate system. For this kind of problem, the shape of a portion of the blade profile is unknown. The remainder is determined by a given prescribed velocity distribution. Three examples, including two turbine cascades and a compressor cascade, have been carried out to examine this method. It is shown that the calculation method presented herein can be used as a powerful tool, together with the aerodynamic optimization method, for blade cascade design.
Thickness effects of CCT specimens
Authors: Miyamoto Hiroshi , Machida Kenji , Kikuchi Masanori 
Published: August 2005

AbstractFirst, the three‐dimensional elasto‐plastic analyses of 1CT and 18 mm thick CCT specimens are carried out by using the finite element method, and the thickness effects of both specimens are studied. In elastic states, there is no significant difference between the CT and CCT specimen in the distribution of theJ‐integral along the straight or curved crack front. However, in elasto‐plastic states, quite the contrary tendency is obtained in the distributions ofJ xand COD along the curved crack front for both specimens. Secondly, elasto‐plastic analyses are carried out for CCT specimens of four kinds of thickness (B= 200, 18, 6 and 4 mm). The distributions of theJ‐integral along the crack front are obtained and compared. Finally, the availability of theJRvalue is examined, which is evaluated from the load versus displacement curve by using Rice's formula.
A formulation of general shell elements—the use of mixed interpolation of tensorial components
Authors: Bathe Klaus‐Jürgen , Dvorkin Eduardo N. 
Published: August 2005

AbstractWe briefly discuss the requirements on general shell elements for linear and nonlinear analysis in practical engineering environments, and present our approach to meet these needs. We summarize and give further insight into our formulation of a 4‐node shell element using a mixed interpolation of tensorial components, and present a new 8‐node element using this approach. Specific attention is given to the general applicability of the elements and their efficient use in practice.
Numerical technique in plasticity including solution advancement control
Authors: Runesson Kenneth , Samuelsson Alf , Bernspång Lars 
Published: August 2005

AbstractNumerical techniques applied to the consistent formulation of plasticity, which is based on convex analysis, are investigated. For each time step the stress is found as the projection in complementary energy of the elastic stress onto the set of plastically admissible stresses, while the velocity field is the extremal of a non‐quadratic functional. Explicit formulas for von Mises' yield criterion with mixed hardening are developed and the nonlinear equations arising from finite element discretization are solved, for comparison, by a number of Newton‐type iteration procedures with line search and are‐length control. A few numerical examples with proportional and non‐proportional loading are analyzed.
Hybrid finite difference/finite element solution method development for non‐linear superconducting magnet and electrical circuit breakdown transient analysis
Authors: Kraus H. G. , Jones J. L. 
Published: August 2005

AbstractThe problem of non‐linear superconducting magnet and electrical protection circuit system transients is formulated. To enable studying the effects of coil normalization transients, coil distortion (due to imbalanced magnetic forces), internal coil arcs and shorts, and other normal and off‐normal circuit element responses, the following capabilities are included: temporal, voltage and current‐dependent voltage sources, current sources, resistors, capacitors and inductors. The concept of self‐mutual inductance, and the form of the associated inductance matrix, is discussed for internally shorted coils. This is a Kirchhoff's voltage loop law and Kirchhoff's current node law formulation. The non‐linear integrodifferential equation set is solved via a unique hybrid finite difference/integral finite element technique.
Incomplete factorization for finite element methods
Authors: Zyvoloski George 
Published: August 2005

AbstractAn incomplete factorization iterative scheme with ORTHOMIN acceleration is evaluated for three‐dimensional finite element applications. Both heat conduction and combined heat and fluid flow are investigated. Computational efficiency is investigated for both linear (8 node) and quadratic (27 node) elements as well as for various degrees of LU Decomposition. The factorization schemes worked well with both types of elements, and a variable factorization scheme, which distributes the level of factorization, performed well on difficult heat and fluid flow problems.
An efficient algorithm for the optimum design of trusses with discrete variables
Authors: Sepúlveda A. , Cassis J. H. 
Published: August 2005

AbstractA method to efficiently solve the problem of minimum weight design of plane and space trusses with discrete or mixed variables is developed. The method can also be applied to continuous variables. The original formulation leads to a non‐linear constrained minimization problem with inequality constraints, which is solved by means of a sequence of approximate problems using dual techniques. In the dual space, the objective function is to be maximized, depends on continuous variables, is concave and has first and second order discontinuities. In addition, the constraints deal simply with restricting the dual variables to be non‐negative. To solve the problem an ad hoc algorithm from mathematical programming has been adapted.Some examples have been developed to show the effectiveness of the method.
A ‘characteristic’ finite element scheme for convective‐dispersive transport with non‐equilibrium reaction
Authors: Fujinawa K. 
Published: August 2005

AbstractA finite element method coupled with the method of characteristics is applied to the problem of convective‐dispersive transport with non‐equilibrium reaction. Convective terms are calculated using moving particles together with influence element meshes for particle tracking, whereas dispersion terms are calculated by means of finite element techniques. The contribution from the term of non‐equilibrium reaction is incorporated into the algebraic equations by the use of analytical solutions to the equation of non‐equilibrium reaction for each time step and extended Simpson's numerical integrations.Comparison of the numerical results from the proposed procedure with analytical solutions to the simultaneous partial differential equations shows good agreement for the wide spectrum ranging from dispersion‐ to convection‐dominated transport with various reaction parameters.
Three‐dimensional analysis of magnetic field distortion of ferromagnetic beam‐plates by the boundary element method
Authors: Minato A. , Tone T. , Miya K. 
Published: August 2005

AbstractMagnetoelastic buckling of a ferromagnetic beam‐plate has been experimentally and theoretically studied by many investigators. A great discrepancy between the experimental results and the theoretical predictions has stimulated related studies. It has been supposed that the discrepancy could be attributed to the finite size of the test piece; this case has not yet been solved exactly, or even numerically.In this study the boundary element method is applied to solve for the magnetic field distribution around the finite specimen.
An adaptive finite element approach for the free surface seepage problem
Authors: Rank Ernst , Werner Heinrich 
Published: August 2005

AbstractA posteriori error estimates and adaptive mesh refinements are now on a rigorous mathematical foundation for linear, elliptic boundary‐value problems of second order. Yet, for non‐linear problems only a few results have been obtained till now. In this paper we consider as a non‐linear model problem the two‐dimensional fluid flow with free surface and show how results from linear a posteriori theory can be used to control the non‐linear iteration and to refine the mesh adaptively. A numerical example shows that, similar to linear problems, considerable improvement of the accuracy is obtained by an adaptive mesh refinement and that the influence of singularities on the order of convergence disappears.
A simple method for including shear deformations in thin plate elements
Authors: Fricker A. J. 
Published: August 2005

AbstractA method is described for including the effect of shear deformations in existing thin plate finite elements, and thereby extending their range of application to include moderately thick plates. The method does not add extra degrees of freedom to the final element, so the thick and thin plate elements can be used interchangeably, and the thick plate solution is not appreciably more expensive than the thin plate solution.It is assumed that the shear deformations are constant over the element and, to account for this, two extra internal shear strain variables are added to the element. Various methods for eliminating these internal variables are examined but it is shown to be impossible to simultaneously satisfy both the constant bending moment and constant shear patch tests, except for parallelograms. However, one method gives elements which pass the constant shear patch test and, although failing the constant bending moment patch test for arbitrary geometries, gives errors which are small enough to be neglected in most engineering applications.This method has been applied to a triangular plate element and it is shown that the results obtained with this element converge (for all practical purposes) to the correct thick plate results.
The method of lines and exponential fitting
Authors: van der Houwen P. J. , Wubs F. W. 
Published: August 2005

AbstractWhen the method of lines is used for solving time‐dependent partial differential equations, finite differences are commonly employed to obtain the semidiscrete equations. Usually, if the solution is expected to be smooth, symmetric difference formulae are chosen for approximating the spatial derivatives. These difference formulae are almost invariably based on Lagrange type differentiation formulae. However, if it is known in advance that periodic components of given frequency are dominating in the solution, more accurate difference formulae, based on exponentials with imaginary exponent, are available. This paper derives such formulae and presents numerical results which clearly indicate that the accuracy can be improved considerably by exploiting additional knowledge on the frequencies of the solution.
Transient analysis of three‐dimensional wave propagation using the boundary element method
Authors: Dohner Jeffrey L. , Shoureshi Rahmatallah , Bernhard Robert J. 
Published: August 2005

AbstractIn the past the time domain solution of the wave equation has been limited to simplified problems. This was due to the limitations of analytical methods and the capacity of computers to manipulate and store ‘large’ blocks of spatial information. With the advent of ‘super computers’ the ability to solve such problems has significantly increased. This paper outlines a method for transient analysis of wave propagation in arbitrary domains using a boundary element method. The technique presented will allow the definition of a domain, the input of impedance conditions on the domain's surface, the specification of inputs on the surface, and the specification of initial conditions within the domain. It will produce a complete solution of the wave equation inside the domain. The techniques are demonstrated using a program with a boundary element formulation of Kirchhoff's equation. The elements used are triangular and compatible.
A finite‐element–alternating technique for evaluating mixed mode stress intensity factors for part‐elliptical surface flaws
Authors: Simon H. L. , O'Donoghue P. E. , Atluri S. N. 
Published: August 2005

AbstractAn alternating method, in conjunction with the finite element method and an analytical solution for an elliptical flaw in an infinite solid, is used to determine the mixed mode stress intensity factors for surface flaws. This finite element alternating method leads to an inexpensive procedure for routine evaluation of accurate stress intensity factors in complex structural components containing surface flaws and subject to mixed‐mode loading. A variety of numerical examples is presented.
A new boundary finite element method for fluid–structure interaction problems
Authors: Mariem J. Ben , Hamdi M. A. 
Published: August 2005

AbstractIn order to study problems on fluid–structure interaction, we have used a mixed formulation which couples the classical functional of the structure with a new variational formulation by integral equations for the fluid. This formulation has the advantage over the finite element methods of avoiding the discretization of the fluid domain. Furthermore, unlike collocation methods, the explicit calculation of the Hadamard finite part of the singular integrals is avoided. This leads after discretization by boundary finite elements to a small and symmetrical algebraic system.Typical examples are presented that demonstrate the efficiency of this variational formulation by studying the sound transmission through a baffled plane structure and through a flexible panel backed by a rigid cavity. These include the calculation of the transmission loss factor and the determination of which modes dominate the noise transmission. Good agreement is obtained between numerical results and analytical results found in the literature.
A basis change strategy for the reduced gradient method and the optimum design of large structures
Authors: Joseph K. T. 
Published: August 2005

AbstractThis paper proposes a basis change strategy within the reduced gradient method for optimization under linear constraints. It ensures a non‐singular basis matrix at every iteration. The same strategy can reliably be used within the generalized reduced gradient method for optimization under non‐linear constraints. This method is applied to the minimum weight design of large structures under displacement and stress constraints, exploiting the sparsity of the constraint Jacobian matrix.
The comparative performance of some finite difference equations for transient heat conduction
Authors: Bhattacharya M. C. , Davies M. G. 
Published: August 2005

AbstractThe established finite difference equations to estimate one‐dimensional transient heat flow in solids are the ‘classical’ form (explicit), and the Crank–Nicolson and ‘pure‐implicit’ forms (both implicit). They are all based on finite difference approximation to the Fourier continuity equation. To these are now added three more explicit forms: exponential linear, exponential inverse cosine and polynomial, which are based on exact solutions to the Fourier equation. The performance of each of the six equations is tested against the exact results of a well known step excitations problem (the Groeber model). The tests consist of examining (i) finite difference errors arising from a single implementation of each form at different stages in the transient cooling process, (ii) the errors that accumulate during part or all of the cooling process (both as regards any bias that is introduced, and also a measure of variance) and (iii) the run times in executing the various forms. The nondimensional time step r was treated as the independent variable, and can be made arbitrarily large, by use of a simple time‐division procedure (otherwise r < ½ for use with the classical form). It is shown that having regard to both error and run time, the polynomial form appears to be the most efficient estimator.
An analysis of solidification problems by the boundary element method
Authors: Zabaras Nicholas , Mukherjee Subrata 
Published: August 2005

AbstractThe problem of interest in this paper is the calculation of the motion of the solid–liquid interface and the time‐dependent temperature field during solidification of a pure metal. An iterative implicit algorithm has been developed for this purpose using the boundary element method (BEM) with time‐dependent Green's functions and convolution integrals.The BEM approach requires discretization of only the surface of the solidifying body. Thus, the numerical method closely follows the physics of the problems and is intuitively very appealing.The formulation and the numerical scheme presented here are general and can be applied to a broad range of moving boundary problems. Emphasis is given to two‐dimensional problems. Comparison with existing semi‐analytical solutions and other numerical solutions from the literature reveals that the method is fast, accurate and without major time step limitations.
A finite element for edge‐cracked beam columns
Authors: Tharp Thomas M. 
Published: August 2005

AbstractThe stiffness matrix is derived for a finite element representing a beam column with rectangular cross section and a single edge crack. The element has zero length, and the standard nodal degrees of freedom associated with beam‐column elements. To illustrate its capabilities, the element is used to model propagation of multiple cracks in a self‐loaded fixed beam.
A finite element model for column‐supported shells of revolution
Authors: Han Kye J. , Tu Wen W. 
Published: August 2005

AbstractA finite element model suitable for the analysis of column‐supported shells of revolution is presented. This model combines in a single analysis axisymmetric shell elements with nodal circles and column elements with nodal points. Thus, it takes advantage of the axisymmetry of the shell, while the non‐axisymmetric nature of individual columns is fully accounted for. The compatibility between the two different types of elements is achieved through the use of a co‐ordinate transformation. The accuracy of the solutions is demonstrated through numerical examples. When a shell of revolution supported on equispaced columns of the same stiffness is subjected to a harmonically varying load in the circumferential angle, it is found that the resulting displacements are associated with selective harmonic terms. An equation which precisely defines this coupling mechanism is also derived.
Self‐adaptive stress analysis based on stress convergence
Authors: Roberti Paolo , Melkanoff Michel A. 
Published: August 2005

AbstractA new algorithm for self‐adaptive stress analysis is presented. The algorithm is based on h‐convergence and uses the measured stress convergence rate as an error indicator. A theoretical relation between stress convergence rate and pointwise error of stresses is derived for both the 1‐D and 2‐D case. Some examples are presented to illustrate the behaviour of the algorithm.
Equilibrium considerations of the updated Lagrangian formulation of beam‐columns with natural concepts
Authors: Gattass Marcelo , Abel John F. 
Published: August 2005

AbstractBathe and co‐workers'1,2 updated Lagrangian formulation is reviewed for a two‐dimensional beam‐column element. From this review a physical interpretation and properties are derived for the matrices of the method. A variant of Argyris and co‐workers'4,5 natural concept is introduced in the updated Lagrangian formulation, and a new method to derive element matrices arises. A detailed derivation of the matrices of the twodimensional beam‐column element is presented to clarify further the UL formulations. Explicit expressions for these matrices, computed with the use of symbolic manipulation,17 are also presented to illustrate the concepts discussed. Finally, numerical results are shown to compare and evaluate different methods and matrices.
A Legendre spectral element method for the Stefan problem
Authors: Rønquist Einar M. , Patera Anthony T. 
Published: August 2005

AbstractIn this paper we present a Legendre spectral element method for solution of multi‐dimensional unsteady change‐of‐phase Stefan problems. The spectral element method is a high‐order (p‐type) finite element technique, in which the computational domain is broken up into general (curved) quadrilateral macroelements, and the solution, data and geometry are expanded within each element in terms of tensor‐product Lagrangian interpolants. The discrete equations are generated by a Galerkin formulation followed by Gauss–Lobatto Legendre quadrature, for which it is shown that exponential convergence to smooth solutions is obtained as the polynomial order of fixed elements is increased. The spectral element equations are inverted by conjugate gradient iteration, in which the matrix‐vector products are calculated efficiently using tensor‐product sum‐factorization.To solve the Stefan problem numerically, the heat equations in the liquid and solid phases are transformed to fixed domains applying an interface‐local time‐dependent immobilization transformation technique. The modified heat equations are discretized using finite differences in time, resulting at each time step in a Helmholtz equation in space that is solved using Legendre spectral element elliptic discretizations. The new interface position is then computed using a variationally consistent flux treatment along the phase boundary, and the solution is projected upon the corresponding updated mesh. The rapid convergence rate and stability of the method are discussed, and numerical results are presented for a one‐dimensional Stefan problem using both a semi‐implicit and a fully implicit time‐stepping scheme. Finally, a two‐dimensional Stefan problem with a complex phase boundary is solved using the semi‐implicit scheme.
Adaptive mesh redistribution for a boundary element (panel) method
Authors: Carey G. F. , Kennon S. 
Published: August 2005

AbstractIn this paper, we extend the concept of a grading function, as introduced by Carey and Dinh2 in a one‐dimensional context, to curved contours. We then apply the idea to adaptive grid redistribution for a boundary element method to solve a model boundary value problem. Numerical results are included for a potential problem to demonstrate the effect of the redistribution scheme on the solution and the geometry of the domain.