bluuebunny/crossref_metadata_2025_split huggingface dataset:
Experiments on iterative solution for the semi‐implicit characteristic–Galerkin algorithm
Authors: Bottura L. , Zienkiewicz O. C. 
Published: August 2005

AbstractThe performance of the iterative procedure used for the explicit characteristic—Galerkin method in the solution of advection‐dominated problems is investigated here in the implicit case. The procedure is conditionally stable, and here its stability limit is compared to that of time stepping. It is shown that in a limited range of values of the implicitness parameter θ it is possible to generate explicit methods by use of the iterative solution procedure. This is true, in particular, at θ = ⅓; with this choice the algorithm generated is more accurate, has a wider stability margin and lower cost (for linear problems) than the usual choice θ = 0. Because of these properties, this algorithm might be used for further improvement of the performance of fluid‐dynamics codes.
An efficient algorithm for generating B‐spline interpolation curves and surfaces from B‐spline approximations
Authors: Wang Hui Ping , Hewgill Denton E. , Vickers Geoffrey W. 
Published: August 2005

AbstractA useful and simple algorithm is presented for interactively generating B‐spline interpolation curves and surfaces from B‐spline approximation solutions. The difference between the data points and the B‐spline approximation is used to modify the control vertices in order to generate a succession of B‐spline approximations which converge rapidly to the interpolation solution. The intermediate B‐spline approximations can be viewed interactively and the most appropriate solution selected for a particular application.
Weighting functions in single‐step algorithms for a non‐linear equation
Authors: Salamon N. J. , Xiang Jiannan 
Published: August 2005

AbstractFor the single‐step time‐integration algorithm formulated by Zienkiewicz et al., a weight function of the form tr is posed. The weight parameters θ are found through a simple formula for a range of values r. These are used to integrate three numerical formulations of the non‐linear dynamics equation for a planar pendulum. Comparisons with existing integration methods show that, for r non‐positive, the r‐methods are accurate, stable and very competitive. Results are dependent both upon r and the formulation. Useful ranges for r are discussed.
The spline finite‐strip method in the buckling analyses of thin‐walled structures
Authors: Van Erp G. M. , Menken C. M 
Published: August 2005

AbstractA spline finite‐strip method capable of analysing the buckling of prismatic thin‐walled structural members under arbitrary loading is presented. It utilizes cubic B3splines as displacement functions in the longitudinal direction and polynomials in the transverse direction. Numerical integration is used to determine the geometric stiffness matrix of the strips. Two examples which demonstrate the accuracy and versatility of the method are presented.
A note on the boundary layer in the sixth‐order theory of transverse bending of anisotropic shear‐deformable elastic plates
Authors: Reissner Eric 
Published: August 2005

AbstractGiven the existing interest, from a computational point of view, in the boundary layer aspects of the theory of thin shear‐deformable plates, we undertake an asymptotic analysis of the stress boundary problem for a semi‐infinite anisotropic plate. Our principal conclusion is that the effect of anisotropy can result in order of magnitude changes for the quantities of interest, relative to the corresponding quantities for orthotropic and isotropic plates.
Sparse matrix approximation to an integral equation of scattering
Authors: Canning Francis X. 
Published: August 2005

AbstractAn integral equation formulation of scattering of waves obeying Helmholtz's equation is considered in two dimensions, along with a standard discretization that generates a full matrix equation. A transformation involving banded matrices is introduced that (for most large problems) replaces this full matrix by one which, although full, has nearly all of its elements reduced in size by many orders of magnitude. Sample calculations show that in many cases these small elements may be approximated by zero with little loss in accuracy, thereby generating a sparse matrix equation. This transformation is effective whenever much of the scatterer(s) is somewhat smooth, although isolated discontinuities are allowed. It is speculated that with minor changes this transformation will also be effective for three‐dimensional problems and for a variety of integral equations of wave motion.
A non‐iterative technique for design of aerofoils in incompressible potential flow
Authors: Barron Ronald M. 
Published: August 2005

AbstractA new method is proposed for designing aerofoils in potential flow, based on the von Mises co‐ordinate transformation. This formulation has the advantages of eliminating the numerical grid generation process and providing a design method which does not require iteratively adjusting the aerofoil shape. The method has been tested for symmetric and non‐symmetric aerofoils at several angles of attack, and the results show excellent agreement with the exact profiles.
A unified formulation for triangular and quadrilateral flat shell finite elements with six nodal degrees of freedom
Authors: Ibrahimbegovic Adnan , Wilson Edward L. 
Published: August 2005

AbstractThe flat shell elements presented herein are obtained by superposing discrete Kirchhoff plate bending elements and the membrane elements with drilling degrees of freedom. A simple formulation is presented which allows a 4‐node quadrilateral thin shell element to degenerate into the 3‐node triangular element. Therefore it can easily be used in mesh refinement and to solve other modelling problems. With a trivial modification, the discrete Kirchhoff quadrilateral plate bending element reduces to the standard discrete Kirchhoff triangular element when two nodes are coalesced. For the membrane elements this modification need not be performed, since we use reduced quadrature to avoid membrane locking. The shell elements possess six degrees of freedom per node, which allows easy modelling of complex shell surface intersections and compatibility with other elements with rotational degrees of freedom. Both the quadrilateral and triangular elements produce a 24 × 24 stiffness matrix. The direct stiffness addition of the terms associated with the coalesced nodes, performed in the finite‐element assembly process, produces the 18 × 18 triangular element stiffness. Several numerical examples are presented which illustrate the accuracy of the element.
Nonlinear dynamic buckling of thin‐walled beam‐columns under ground excitations
Authors: Ali Ashraf , Yunus Shah M. , Sridharan S. 
Published: August 2005

AbstractA new analysis technique has been developed to study the non‐linear elastic mode interaction in thin‐walled beam columns under ground excitation. The technique is capable of handling arbitrary cross‐sectional shapes and end conditions. In the analysis of P ‐ Δ effects in the building frames, the technique incorporates the instantaneous loss of stiffness due to local buckling of the individual plates in a rational and convenient manner. The latter is achieved via use of the finite‐strip technique which is found to be extremely efficient in the local and post‐local buckling analysis of prismatic plate structures. The overall behaviour is modelled by a one‐dimensional finite element in which the effects of local buckling are appropriately incorporated. It is observed that moment frames lose stability at an axial load significantly lower than the static buckling load, even for moderate levels of earthquake.
On the boundary‐reducing approximate technique for solving finite‐element elliptic problems
Authors: Bulgakov V. E. 
Published: August 2005

AbstractAn approximate technique has been developed for solving elliptic boundary‐value problems. It is based on reducing finite‐element systems of equations to the boundary which divides the domain into subdomains. The system of equations obtained after reduction admits an approximate solution due to neglecting small coefficients of the boundary matrix constructed by means of an auxiliary coarse grid division over the boundary. The series of numerical examples for theory of elasticity problems presented in the paper demonstrates the method's applicability.
Comparison of numerical solutions of a one‐dimensional non‐linear heat equation
Authors: Burger J. , Machbub C. 
Published: August 2005

AbstractThe aim of this communication is to compare different algorithms for the solution of the 1‐D non‐linear heat equation. A standard finite‐element method is implemented for the space discretization which transforms the initial problem into a non‐linear ordinary differential system. This new system is then solved by means of seven classical algorithms included in the ACSL software (advanced continuous simulation language). Three test cases are considered, and results are compared with available analytical solutions.
Application of the Laplace transform to one‐dimensional non‐linear transient heat conduction in hollow cylinders
Authors: Chen Han‐Taw , Lin Jae‐Yuh 
Published: August 2005

AbstractNon‐linear transient heat conduction in a hollow cylinder with temperature‐dependent thermal conductivity is investigated numerically by using the hybrid application of the Laplace transform technique and the finite‐element method (FEM) or the finite‐difference method (FDM). The governing equation is discretized in the space domain using the FEM or the FDM, and then the non‐linear terms are linearized by using the Taylor series expansion. The time‐dependent terms in the linearized equations are removed by the Laplace transform technique. The numerical inversion of the Laplace transform is used to invert the transformed temperature to the result in the physical quantity. Since the present method is not a time‐stepping procedure, the results at a specific time can be calculated in the time domain without step‐by‐step computations. The computational results at a specific time are convergent over the entire space domain at about the fourth or fifth iteration. To show the accuracy of the present method, a comparison of the present results and those using the FDM in conjunction with the Crank—Nicolson algorithm is made.
Inverse analysis of axisymmetric ducts for compressible swirling flows
Authors: Ahmed N. 
Published: August 2005

AbstractAn inverse design method for the prediction of compressible rotational flow and wall shape of axisymmetric ducts is presented. The method is aimed at the treatment of high Reynolds number flows in which insignificant regions of boundary layer flow exist. The flow is assumed to be inviscid and shock‐free, such that total temperature and pressure remain constant along the flow stream lines. The analysis is derived from the continuity, momentum and perfect gas relationships in curvilinear co‐ordinates. The resulting differential equations are solved by using a numerical algorithm based on the iterative solution of finite‐difference equations in a curvilinear grid. The method is tested by using a simple smooth wall velocity profile, and a reasonable duct shape is obtained.
A boundary‐element method with mesh refinement for a weakly singular integral equation
Authors: Ervin V. J. , Stephan E. P. 
Published: August 2005

AbstractA weakly singular integral equation of the first kind on an open, smooth surface piece Γ in ℝ3is solved approximately via the Galerkin method. Owing to the singular behaviour of the solution of the integral equation near the edge of Γ, the Galerkin approximations converge only with orderO(h½ − ε), ε > 0, if a quasiuniform mesh is used on Γ. We show how to compensate the effect of the edge singularities by using an appropriately graded mesh. Numerical experiments for the Galerkin method, using piecewise constant and piecewise linear functions on triangles, demonstrate the effect of graded meshes and show experimental rates of convergence which underline the theoretical results.
Chebyshev approximations to stress intensity factors: An application of ‘DERIVE’
Authors: Ioakimidis N. I. 
Published: August 2005

AbstractChebȳshev polynomials have been used extensively for the approximation of functions. Here we apply this approach (together with two Gauss‐Chebyshev numerical integration rules) to the case of stress intensity factors. The problem of a simple straight crack under exponential loading is used as the vehicle for the illustration of this semi‐analytical/numerical (SAN) approach. The computer algebra system DERIVE was found to be appropriate and was used in the present application. Sufficient SAN results (from DERIVE) are displayed. The present results are numerically superior to the corresponding results based on Taylor (or Maclaurin) polynomials.
On mesh refinement methods of mixed‐hybrid finite elements for revealing the nature of the singularity in the free edge of a composite laminated plate
Authors: Bar‐Yoseph Pinhas , Ben‐David Daniel 
Published: August 2005

AbstractRefinement methods were applied in order to find the form of singularity in the free edge of a composite laminated plate. The application of a logarithmic stretched mesh in the past has led to problems by the creation of needle elements. Another disadvantage of this method has been the inability for self‐adaptation. In this work, two mesh‐refinement methods, employing rectangular elements, were applied in order to solve these problems. The first is the ‘interface constraints’ method, and the second is based on the use of a ‘new mixed‐hybrid transition element’. Although the first method is much simpler and almost no changes are needed in existing programs, it has a severe problem in that there is a shortage of degrees of freedom within the singularity zone. In our case this caused a totally incorrect solution. The second method needed a conceptual change in both program and analysis, but it gave accurate results.
An efficient equation solver for frictional contact problems using the boundary integral equation formulation
Authors: Dandekar B. W. , Conant R. J. 
Published: August 2005

AbstractA solution algorithm is developed for frictional contact problems solved using the boundary integral equation method when the loading is proportional. The algorithm takes advantage of certain characteristics of the boundary integral equation formulation of contact problems and of proportional loading. These characteristics lead to a solution process requiring that the incremental‐iterative procedure commonly used in solving contact problems numerically be applied only to a reduced set of equations representing points within the potential contact zone.
Eigenvalues and eigenmodes of 8‐node brick elements
Authors: Kidger D. J. , Smith I. M. 
Published: August 2005

AbstractThe modes of deformation attainable by 8‐node brick elements are isolated. Explicit eigenvalues can be associated with most of these modes (and in special cases with all of them). The effects of ‘reduced’ and ‘selective reduced’ integration are clearly illustrated.
On invariance of isoparametric hybrid/mixed elements
Authors: Sze K. Y. , Chow C. L. , Wanji Chen 
Published: August 2005

AbstractIn this paper the issue of invariance for various hybrid/mixed models with and without incompatible displacement modes is addressed. Special emphasis is directed to assumed spaces of the primary variables which are based on the natural co‐ordinates. It is found that if the assumed spaces of all primary variables are invariant to orthogonal transformations, any derived models would automatically be invariant. In contrast to the traditional concept of choosing the starting stress/strain interpolants based on either global or local co‐ordinate systems, it is shown that it is not necessary to employ either complete or balanced polynomial expansions of natural co‐ordinates in order to preserve the element invariance. Based on one of the newly proposed classes of stress/strain interpolants, 8–node invariant‐assumed stress brick elements are proposed which are close to Loikkanen and Irons' assumed stress counterpart of Wilson's Q6 brick element.
Plate quadrilateral finite element with incompatible modes
Authors: Ibrahimbegović Adnan 
Published: August 2005

AbstractA four‐node quadrilateral plate element with a set of incompatible modes is presented in this work. In an analysis of thin plates, the element exhibits a similar performance as the well known discrete Kirchhoff plate element. The computational effort associated with the element is also comparable to that associated with the discrete Kirchhoff element. However, as opposed to the discrete Kirchhoff plate element, the presented plate element is based on the Reissner–Mindlin plate theory and can be used in a thick plate analysis as well.
An implicit multigrid scheme for hypersonic strong‐interaction flowfields
Authors: Thomas James L. 
Published: August 2005

AbstractAn implicit multigrid method for the compressible Navier–Stokes equations is applied to a series of two‐dimensional, steady, laminar hypersonic flows over a compression ramp, including both attached and separated flow conditions. The algorithm uses upwind‐biased differencing for the convective and pressure terms and central differencing for the shear‐stress and heat‐transfer terms. An implicit spatially factored scheme is used to advance the solution in time on a given mesh, and a V‐cycle multigrid strategy is used to accelerate convergence. The multigrid algorithm provided an order of magnitude decrease in the computational time required to obtain a converged position of the separation location and enabled a substantially grid‐independent result to be obtained for each of the flows considered.
Reanalysis of static response and its design sensitivity of locally modified structures
Authors: Liu Zhong‐Sheng , Chen Su‐Huan 
Published: August 2005

AbstractThis paper proposes a reanalysis method of static response and static response design sensitivity of locally repeatedly modified structures. By partitioning global stiffness matrix K(b) in terms of degrees of freedom affected directly by modification of structural parameters and matrix triangle factoring, the dimension of the equilibrium equation for reanalysis is decreased. The static response and static response design sensitivity of locally modified structures can be solved rapidly and simultaneously.
Compound matrix method for eigenvalue problems in multiple connected domains
Authors: Anturkar N. R. , Papanastasiou T. C. , Wilkes J. O. 
Published: August 2005

AbstractAn algorithm based on a compound matrix method is presented for solving difficult eigenvalue problems of n equation sets in connected domains that are coupled through (n – 1) sets of interfacial boundary conditions, when n is an arbitrary number. As an example, a linear stability problem of n‐layer plane Poiseuille flow is formulated. The resulting Orr–Sommerfeld equations form a set of stiff differential equations at high wavenumbers, which are solved accurately for various combinations of parameters.
Adaptive refinement criterion for elliptic problems discretized by FEM
Authors: Storti M. , Nigro N. , Idelsohn S. 
Published: August 2005

AbstractIn a recent paper1 we presented a data structure to be used with multigrid techniques on non‐homogeneously refined FEM meshes. This paper focuses on the adaptive refinement techniques used there. The error estimate is obtained from standard Taylor series. For each element we compute its efficiency in terms of the size, the norm of the second derivatives of the unknown and the parameter p, where Lp is the chosen norm. The way the norm influences the optimal mesh is studied. The number of elements to be refined at each step is such to produce a fast convergence to the optimal mesh, followed by successive homogeneous refinements. We hope that the analysis of these two subjects could be of value for people working with other (perhaps very dissimilar) adaptive refinement techniques (error estimate and data structure, for instance).
Two problems with GGP generalized geometric programming algorithm
Authors: Yeh Alexander 
Published: August 2005

AbstractThe generalized geometric programming algorithm GGP has been found to be one of the better algorithms for optimizing algebraic functions subject to algebraic constraints. The paper discusses two problems with the GGP algorithm presented by Avriel et al. (1980). The first problem is that, because of the way that constraint tolerances are checked, the checks may pass even when a constraint is violated beyond the acceptable tolerance. This problem can affect an acceleration technique suggested for the algorithm. This paper presents two possible solutions to this problem. The second problem is the algorithm's weakness in handling equality constraints. This problem seems to especially affect the ‘Phase I’ part of the algorithm, which finds a feasible solution from a random starting point. While extensions have been made to get around this limitation, no discussion on why the original algorithm has problems with equality constraints has been made. This paper discusses why the problems exist.
Two‐dimensional transient dynamic analysis with adaptive mesh refinement
Authors: Selman A. , Hinton E. 
Published: August 2005

AbstractAn adaptive finite‐element (FE) method for the solution of two‐dimensional transient dynamic problems is described. The computational domain is represented by an unstructured assembly of linear triangular elements, and the mesh adaption is achieved by regenerating the grid using an error indication procedure coupled with an automatic mesh generator. Problems involving shock and wave propagation are solved to illustrate the numerical performance of the method.
Variational formulation of two complementary hybrid‐Trefftz FE models
Authors: Jirousek J. 
Published: August 2005

AbstractThe paper presents two complementary variational formulations of Trefftz‐type elements wherein the piece‐wise assumed displacement approximations a priori fulfil the governing differential equations over the element subdomain. The two formulations are such that either the displacement conformity or the reciprocity of the conjugate tractions is enforced at the element interfaces, one more strongly than the other. This is achieved through linking the piece‐wise approximations either through an auxiliary displacement or a boundary traction frame. The two formulations concern solid mechanics and structures.Although for hybrid elements monotonic convergence in energy cannot be warranted, in practice the two presented formulations yield opposite bounds on the energy provided that the number of internal Trefftz functions is sufficiently large.
Optimum design of composite laminates with STROPT
Authors: Belsare S. , Haririan M. 
Published: August 2005

AbstractThe design of a composite laminate involves the determination of layer thicknesses and orientation angles. The problem is posed as the optimum weight (or volume) design of composite laminates which withstand the specified loads without failure. The modified Hill‐Mises or Tsai‐Wu failure criterion is taken as a constraint, each layer being subjected to this criterion. The design variables considered are the layer thicknesses and orientation angles. Based on the finite‐element analysis capability of composite laminates provided by NISA II, a composite laminate optimization procedure has been developed. Nonlinear optimization techniques are used to approach the optimum design of the composite laminates. Efficient design sensitivity analysis procedures are implemented based on the direct differentiation and adjoint variable methods. Example problems illustrate that the program offers an efficient and practical design tool for composite laminates.