bluuebunny/crossref_metadata_2025_split huggingface dataset:
Finite element method in magnetohydrodynamic channel flow problems
Authors: Singh Bani , Lal Jia 
Published: August 2005

AbstractThe finite element method has been applied to the steady‐state fully developed magnetohydrodynamic channel flow of a conducting fluid in the presence of transverse magnetic field. Simple elements have been used to obtain the numerical values of velocity and induced magnetic field. To test the efficiency of the method, three different geometries, viz., rectangle, circle and triangle, are taken as the section of the pipe whose walls are non‐conducting. Comparison is made with those cases in which exact solutions are available. Apart from giving good results, the FEM makes it possible to solve the problem for a pipe with arbitrary cross‐section which was not possible by the other methods.
A finite strip method for the geometrically nonlinear analysis of plate structures
Authors: Lengyel P. , Cusens A. R. 
Published: August 2005

AbstractA finite strip method is presented for the geometrically nonlinear analysis of prismatic structures under arbitrary loading. The method employs an iterative finite element approach but replaces numerical integration by an explicit formulation. A computer program has been developed and is described in the paper; a numerical example is given.
Variable upwinding and adaptive mesh refinement in convection‐diffusion
Authors: Carey G. F. , Plover T. 
Published: August 2005

AbstractAn analysis of the stability and oscillation properties of upwind finite element methods for convection‐diffusion is given and used to develop a variable upwinding formulation. This formulation is particularly well suited to problems with nonconstant coefficients, nonlinearity or non‐uniform meshes. We present the theoretical analysis and numerical studies for a standard steady‐state and transient model one‐dimensional convection‐diffusion problem. The variable upwind strategy can also be used to significant advantage in conjunction with adaptive mesh refinement. Numerical results for the steady‐state case in which convection dominates and the mesh is adaptively refined into a boundary layer confirm the efficacy of the scheme.
Nonlinear flow analysis in pipe networks
Authors: Ohtmer O. 
Published: August 2005

AbstractPipe networks are computed in an analogous mannner to frameworks in structural mechanics loaded only by moments. The mesh method (force method) is applied. Due to the boundary layer effects in special pipe members, the flow problem is in general nonlinear. Therefore, the Newton‐Raphson iteration procedure is used to solve the nonlinear system of equations. Using the computed flow rates in the TREE structure (determined by graph theory) as initial values, the iteration procedure converges rapidly to a user specified tolerance value. The loss coefficients of pressure for different pipe members (TUBE, VALVE, BOW, TEE, PUMP, KNEE, ±CONTR, ±DIFSR) need only be given in diagrams. These diagrams are used in digitalized form. In the back‐substitution phase with known flow rates in all members, the pressure at the joints is computed.The main advantages of the analysis as outlined are that no initial values for the member flow rates need be known, the iteration procedure converges rapidly, and within each iteration step only small systems of linear equations need to be solved. Due to the fact that the loss coefficients of pressure need only be given in diagrams, arbitrary nonlinear networks can be analysed by the unchanged program system. A flow rate assumption may be specified in the input for a member of a mesh.The pressures at the joints are defined as unknowns (displacement method) in References 7, 8 and 10. The flow rates in the members are defined as unknowns (force method) in Reference 9. The nonlinear system of equations is always solved by the Newton‐Raphson procedure. In Reference 10 a strategy is presented to take into account different pipe members, but in a different way from that outlined in this paper. The members BOW, TEE, KNEE, CONTR, DIFSR are not examined in Reference 10.
Predictor‐corrector methods for parabolic partial differential equations
Authors: Jacques I. B. 
Published: August 2005

AbstractIn this paper we extend predictor‐corrector methods, commonly used for the numerical solution of ordinary differential equations (o.d.e.s), to parabolic partial differential equations (p.d.e.s), typically of the form ut = auxx + ƒ(u, ux, x, t).We describe linear multistep methods for p.d.e.s, the nonlinear algebraic equations arising from implicit formulae being solved using a corrector analogous to those used for o.d.e.s. A sufficient condition for convergence of the iteration is then derived and is found, in most cases, to be far less restrictive than that obtained from the usual method of lines approach. Numerical results are presented to investigate the necessity of this condition. They also indicate that we can accelerate convergence by reducing the time increment. This allows us to achieve convergence within a prescribed number of iterations and so to construct PCm methods corresponding to P(EC)m methods for o.d.e.s. Numerical results are also given to test the absolute stability of the Crank‐Nicolson corrector for various predictors P, and iterations, m.
Spurious reflection of elastic waves due to gradually changing finite element size
Authors: Celep Zekai , Bažant Zdeněk P. 
Published: August 2005

AbstractWhen a homogeneous elastic continuum is modelled by a non‐uniform finite element grid, the differences in the size of adjacent finite elements can cause a spurious wave reflection which does not exist in the continuum. Extending previous studies in which the spurious wave reflection was investigated for the case of two uniform grids with a sudden element size change from one grid to the other, the present study deals with the case when the two uniform grids of different element sizes are separated by a transition zone through which the element size varies gradually, either by a geometric progression or by an arithmetic progression. The solution is carried out in complex variables and numerical plots of the results are given. When the ratio of wavelength to the largest element size is as low as 4 : 1, the spurious wave reflection is very significant, while for the ratios over 10 : 1 it is insignificant. Inserting a transition zone with gradually varying element size between the two uniform parts of the grid somewhat mitigates the phenomenon of spurious reflection, but this is significant only when the ratio of element sizes in the uniform grids is small (less than about 1·5 : 1). Varying the element size throughout the transition zone in an arithmetic progression seems slightly better than in a geometric progression. The spurious wave reflection is less pronounced for higher‐order elements, in particular for linear strain elements as compared to constant strain elements. The spurious reflection is also less severe for consistent mass than for lumped mass.
Numerical methods for partial differential equations based on power series
Authors: Small Robert D. 
Published: August 2005

AbstractStable difference schemes that approximate partial differential equations to any desired order are generated by means of power series. The method is demonstrated on the one‐dimensional heat equation and the stability is studied in detail. Stability analyses are then presented for parabolic linear equations with constant coefficients. A nonlinear example is presented which indicates the efficiency of the higher ordered schemes.
Elements for the numerical analysis of wave motion in layered strata
Authors: Tassoulas John L. , Kausel Eduardo 
Published: August 2005

AbstractA technique is developed for the numerical analysis of wave motion in layered strata. Semidiscrete particular solutions satisfying inhomogeneous boundary conditions are calculated by the finite element method. These solutions are combined with semidiscrete modes of an appropriate eigenvalue problem. The boundary conditions corresponding to rigid and rough footings on a layered stratum are treated in detail. Applications are considered which demonstrate the validity of the technique.
Numerical solution of nonlinear quasi‐stationary magnetic fields
Authors: Melkes Frantis̃ek , Zlámal Milos̋ 
Published: August 2005

AbstractThe problem of quasi‐stationary nonlinear magnetic fields is formulated in a variational form. A Galerkin finite element solution is constructed. Discretization in time is carried out by means of one‐ and two‐step linear A‐stable schemes. The resulting system of nonlinear equations is solved by Newton's method. A numerical example is given.
Finite element analysis of sinusoidal small‐amplitude vibrations in deformed viscoelastic solids. Part I: Theoretical development
Authors: Morman K. N. , Nagtegaal J. C. 
Published: August 2005

AbstractA general method is presented for the isothermal mechanical analysis of incompressible material solids in which a small‐amplitude time harmonic oscillation is superposed on a static finite deformation field. Material behaviour is assumed to be of the ‘fading memory’ type describable by the finite linear viscoelasticity theory of Coleman and Noll.4 Existing finite element codes, that treat finite elasticity material behaviour, can be extended with minor modifications to treat the subject problem. A specialized form of the finite linear viscoelasticity constitutive equations proposed by Morman8 has been implemented in the MARC nonlinear finite element program for predicting the response of statically deformed elastomeric components to small amplitude vibrations. Numerical results obtained with MARC for the static force‐deflection behaviour and dynamic (complex) stiffness for a viscoelastic cylinder subject to combined axial and twisting pre‐loads, are in excellent agreement with corresponding analytical results.
Design of a recursive, shape controlling mesh generator
Authors: Bykat A. 
Published: August 2005

AbstractA recursive, shape controlling triangulation method is described. The method is designed to produce a labelling which implies reduced fill in the solution of (finite element) equations assembled from such a triangulation and allows simple implementation of a nested disection algorithm for irregular domains. This approach saves a substantial amount of time usually spent on discovering a suitable relabelling of the triangulation. In addition, the matrix of the resulting system is then endowed with a recursive doubly bordered block diagonal form. This allows us to develop a recursive parallel bisection method for the solution of the system of equations.
A stream function‐vorticity finite element formulation for Navier‐Stokes equations in multi‐connected domain
Authors: Mizukami Akira 
Published: August 2005

AbstractIn this paper we present a stream function‐vorticity finite element formulation for Navier‐Stokes equations which does not require an iterative procedure for satisfying the boundary conditions, and show that this formulation is of great advantage in solving the flow problems in a multi‐connected domain.
Accurate Petrov‐Galerkin methods for transient convective diffusion problems
Authors: Dick Erik 
Published: August 2005

AbstractThe Petrov‐Galerkin method is applied to transient convective diffusion problems with convection dominance. Weighting functions are used which differ from the shape functions by both symmetric and non‐symmetric modifications. It is proved that the symmetric modifications largely influence the accuracy. By a one‐dimensional and a two‐dimensional example it is shown how to choose this modification to maximize accuracy.
Fast modal response method for structures
Authors: Leung Y. T. 
Published: August 2005

AbstractRegardless of their simplicity, all structures have an infinite number of degrees‐of‐freedom (d.o.f.) when subjected to dynamic loading. The usual finite element method reduces the infinite d.o.f. system to a model with a limited d.o.f. while capturing the significant physical behaviour. The modal analysis reduces the number of d.o.f. further to a limited number of modal co‐ordinates. However, accurate results comparable to the original finite element model may not be possible unless higher modes are included. The present paper is to recommend a response analysis which makes use of both the natural modes and the mass and stiffness matrices of the system to improve the convergence with respect to the number of modes. While the effects of lower modes are analysed similar to the modal analysis, the effects of higher modes are included in the system matrices and the information for higher modes is not needed.
A two‐dimensional finite element idealization for thermo‐elastic deflection in beams
Authors: Abouaf Marc , Chenot Jean‐Loup , Marcelin Jean‐Luc 
Published: August 2005

AbstractThis paper addresses the problem of thermo‐elastic deflection in beams using a two‐dimensional finite elemement idealization of the cross‐section. Bending effects are introduced in a gerneralized plane strain formulation assuming that constant curvature dominates the flexural deformation. The method leads to a plane strain calculation which is very interesting from the computational point of view; thermal deendence of the physical properties can be taken into account, which would be inconceivable in a three‐dimensional problem.
High‐accuracy product integration methods for the Abel equation, and their application to a problem in scattering theory
Authors: Cameron R. F. , McKee S. 
Published: August 2005

AbstractIn this paper we present orsder three, four and five backward product integration methods for the generalized Abel equation

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We illustrate their use by silving the small angle deflection problem, and show computationally that these methods are convergent for all ϵ ϵ(0,1). The coefficients of order three and four methods are given in Applenidx I.
Optimum synthesis of linkages with autocorrelation concept (modified least squares technique)
Authors: Lapalikar S. R. , Rao A. C. 
Published: August 2005

AbstractCorrelation is a measure of similarity between two functions. When two functions are exactly similar and equal, the correlation between them is maximum. The correlation concept can be used for system design, e.g. the four‐bar mechanism, the slider crank mechanism, etc. The motion generated by four‐bar linkage can be expressed as a function of link dimensions, input and output angles. The product of generated function and desired function gives correlation. The best possible design would be when the deviation of actual correlation from its maximum value (i.e. 100 per cent correlation) is least. This concept, in fact, leads to a modified least squares approach and based on this an objective function is formulated and minimized to give link dimensions. The results obtained are better than the least squares technique, and this is illustrated through different numerical examples.
Numerically efficient procedures for dynamic contact problems
Authors: Madsen Nels 
Published: August 2005

AbstractThe solution of dynamic contact (elastic impact) problems is complicated by the changing nature of the contact area. If a finite element approach is used, the system matrices vary with the contact area. If the problem is properly formulated, such changes are rank one. Rank one changes produce easily determinable changes in the LDLT decompositions of the system matrices. This renders a class of dynamic contact problems soluble with the same accuracy and computational effort as is associated with the solution of any dynamic problem using finite element procedures. Consideration of an example problem involving the impact of spring–mass systems confirms this claim.
A complex variable boundary element method: Development
Authors: Hromadka T. V. , Guymon G. L. 
Published: August 2005

AbstractA generalized boundary integral equation method for the solution of the Laplace equation is developed based on the Cauchy integral theorem for analytical complex variable functions. Although the approach is complicated by the utilization of complex variable theory, the resulting model involves direct integration along straight‐line boundary segments (elements) rather than using quadrature formulae that are required in current real variable boundary element formulations. Previously published boundary integral equation methods based on the Cauchy integral theorem are shown to be a subset of the generalized model theory developed in this paper.
The numerical solution of two generalizations of the neumann moving interface problem into two dimensions
Authors: Schulze H. J. , Howarth J. A. , Poots G. 
Published: August 2005

AbstractWe present numerical solutions for the following Stefan problems. The half‐space z > 0 is initially filled with liquid at its fusion temperature. The boundary z = 0, taken to be the x axis, is maintained at a constant temperature, less than the fusion temperature, for x < 0. For x > 0, the first problem considers the case of an insulated boundary, and the second problem considers the case of the boundary maintained at the fusion temperature. This gives rise to a solid‐liquid interface curved in the (x, z) plane.
Optimal control finite element approximation for penalty variational formulation of three‐dimensional Navier–Stokes problem
Authors: Kai‐Tai Li , Ai‐Xiang Huang , Yi‐Chen Ma , Du Li , Zhi‐Xing Liu 
Published: August 2005

AbstractAn optimal control finite element approximation of the penalization type for the solution of incompressible viscous Navier–Stokes equations is presented. This paper has proved the convergence of its minimizing sequence and the existence of the solution for the optimal control problem corresponding to the penalty variational problem of the Navier–Stokes equations. Based on this method and the conjugate gradient algorithm, the program for solving the three‐dimensional Navier–Stokes problem has been developed, and some numerical results have also been provided.
Compact analytic expressions of two‐dimensional finite difference forms
Authors: Reali M. , Rangogni R. , Pennati V. 
Published: August 2005

AbstractIn this paper a straightforward derivation of one‐ and two‐dimensional finite difference forms for general cartesian networks is given. General analytic compact expressions up to third order for first derivatives are specifically derived. General cartesian networks with locally telescoping subnetworks are also introduced and the basic problem of approximating derivative boundary conditions is clarified. The applicability of these general finite difference forms is shown by solving numerically the Laplace problem with mixed Dirichlet–Neumann boundary conditions for an elliptic domain.
A shear‐flexible triangular finite element model for laminated composite plates
Authors: Lakshminarayana H. V. , Murthy S. Sridhara 
Published: August 2005

AbstractFormulation and numerical evaluation of a shear‐flexible triangular laminated composite plate finite element is presented in this paper. The element has three nodes at its vertices, and displacements and rotations along with their first derivatives have been chosen as nodal degrees‐of‐freedom. Computation of element matrices is highly simplified by employing a shape function subroutine, and an optimal numerical integration scheme has been used to improve the performance. The element has satisfactory rate of convergence and acceptable accuracy with mesh refinement for thick as well as thin plates of both homogeneous isotropic and laminated anisotropic materials. The numerical studies also suggest that reliable prediction of the behaviour of laminated composite plates necessitates the use of higher order shear‐flexible finite element models, and the proposed finite element appears to have some advantages over available elements.
Algorithms for refining triangular grids suitable for adaptive and multigrid techniques
Authors: Rivara M. Cecilia 
Published: August 2005

AbstractTwo general algorithms for refining triangular computational meshes based on the bisection of triangles by the longest side are presented and discussed. The algorithms can be applied globally or locally for selective refinement of any conforming triangulation and always generate a new conforming triangulation after a finite number of interactions even when locally used. The algorithms also ensure that all angles in subsequent refined triangulations are greater than or equal to half the smallest angle in the original triangulation; the shape regularity of all triangles is maintained and the transition between small and large triangles is smooth in a natural way. Proofs of the above properties are presented. The second algorithm is a simpler, improved version of the first which retains most of the properties of the latter. The algorithms can be used either for constructing irregular computational meshes or for locally refining any given triangulation. In this sense they can be adequately combined with adaptive and/or multigrid techniques for solving finite element systems. Examples of the application of the algorithms are given and two possible generalizations are pointed out.
Hellinger–Reissner principles for plate and shell finite elements
Authors: Morley L. S. D. 
Published: August 2005

AbstractThe Hellinger–Reissner generalized variational principle is used to deduce further principles directed especially towards formulation of high integrity finite elements for plates and curved shells in polynomial parametric representation. Assumed stresses in these principles are derived from displacements and supplemented with stresses derived from stress functions.
A C0 triangular plate element with one‐point quadrature
Authors: Belytschko T. , Stolarski H. , Carpenter N. 
Published: August 2005

AbstractA triangular plate element of the Mindlin type, which uses linear fields for rotations and transverse deflections, is developed. Success is achieved, in contrast to previous failures with this element, by decomposing the displacements into well‐defined bending and shear modes which are associated with bending and shear energies, respectively. The element only requires a single quadrature point, which is very attractive for nonlinear analysis. Results are presented for a variety of plate problems; the accuracy is similar to the 4‐node bilinear Mindlin plate and its rate of convergence is approximately of order h2.
Surface integral finite element hybrid (SIFEH) method for fracture mechanics
Authors: Annigeri Balkrishna S. , Cleary Michael P. 
Published: August 2005

AbstractAn effective surface integral and finite element hybrid (SIFEH) method has been developed to model fracture problems in finite plane domains. This hybridization by (incrementally) linear superposition combines the best features of both component methods. Finite elements are used to model the finite domain (and eventually nonlinearity), while continuous distributions of dislocations (resulting in surface integral equations) are used to model the fracture (i.e. displacement discontinuity). This method has been implemented in a computer program and results of representative problems are presented: these compare very well with known solutions and they demonstrate the computational advantages of SIFEH over other numerical methods (including the individual components).
Path independent integrals for computing stress intensity factors at sharp notches in elastic plates
Authors: Sinclair G. B. , Okajima M. , Griffin J. H. 
Published: August 2005

AbstractA set of path independent integrals is constructed for the calculation of the generalized stress intensity factors occurring in elastic plates having sharp re‐entrant corners or notches with stress‐free faces and subjected to Mode I, II or III type loading. The Mode I integral is then demonstrated to enjoy a reasonable degree of numerical path independence in a finite element analysis of a test problem having an exact solution. Finally, this integral is used on the same problem in conjunction with a regularizing, finite element, procedure or superposition method. The results indicate that sufficiently accurate estimates of these stress intensity factors for engineering purposes can be achieved with little computational effort.