bluuebunny/crossref_metadata_2025 huggingface dataset:
A decoupling procedure for the modal analysis of structures in contact with incompressible fluids
Authors: Antoniadis I. , Kanarachos A.
Published: August 2005

A decoupling procedure is described for the modal analysis of structures in contact with incompressible fluids. According to this procedure, the problem can be decoupled in two main subproblems, each defined only on the structure or the fluid domain. First, a set of basis vectors for the structural displacements—and the corresponding ‘mass’ and ‘stiffness’ terms—must be computed. Then a set of potential (Laplacian) problems for the fluid must be solved, using the structural basis vectors in the place of the structural displacements at the normal pressure derivative (Neumann) boundary conditions on the fluid–structure interface. If the ‘in vacuum’ structural eigenmodes are used as basis vectors, some important computational and physical advantages result. Numerical examples verify the efficiency of the approach.
Toward expert systems in finite element analysis
Authors: Carey Graham F. , Patton Peter C.
Published: August 2005

The evolution of finite element programs and program systems for engineering analysis and the more recent pioneering development of expert systems are briefly described.

The literature is very extensive and only a small representative sample is indicated in this paper.

From these we proceed to develop some general principles and guidelines using expert systems with finite element techniques and novel computer architectures.
On nonlinear temperature‐dependence of thermal strain
Authors: Mulligan Gale P.
Published: August 2005

Finite element calculation and the nonlinear temperature‐dependence of thermal strain are reviewed using basic principles. An approach for thermal strain calculation based on an instantaneous coefficient of thermal expansion, material description, is presented for incremental finite element analysis. The approach is then related to the current calculation method which uses a reference‐dependent mean expansion coefficient. Implications of the alternative approaches are discussed, and the principles are applied to actual expansion data for an epoxy. The paper is written to aid finite element analysts and code developers on thermal strain calculation.
Singularities at angular points in elastic contact problems
Authors: Fabrikant V. I. , Sankar T. S.
Published: August 2005

A new procedure is suggested for numerical treatment of elastic contact problems for non‐classical domains. The numerical procedure is based on formulae derived for an accurate computer evaluation of singular integrals. These formulae define the value of the singular integral in the neighbourhood of the singularities, while the regular part of the integral can be evaluated by any standard subroutine. The method allows practically exact solution of elastic contact problems for punches of various plan forms like, for example, rectangle, rhombus, triangle, oval, etc. The nature of the stress singularity at the boundary of the domain of contact is clarified. Numerical results presented for a rectangle indicate that the assumption of a square root singularity is wrong, and that the power of the singularity is not constant along a rectangle edge.
Convergence of transverse shear stresses in the finite element analysis of plates
Authors: Hughes Thomas J. R. , Franca Leopoldo P.
Published: August 2005

If bending moments converge at a sufficiently fast rate, it is proved that transverse shear stress resultants calculated from the moment equilibrium equation also converge. The result holds independent of the plate theory or type of element employed.
Mesh‐refined computation of disordered vortex flow around a cranked delta wing: Transonic speed
Authors: Rizzi Arthur , Purcell Charles J.
Published: August 2005

A numerical method that produces a high‐resolution simulation by solving the Euler equations for compressible flow with mesh refinement is used to explore how a crank in the leading edge of a delta wing may excite short‐wave instabilities in the vortex sheet shed from the leading edge. The particular case simulated is transonic flow at M∞ = 0.9 α = 10 deg. around a twisted cranked‐and‐cropped TKF delta wing of MBB. Made possible by the recent increase in size of computer memory, the study consists of a grid‐refinement sequence that starts with a standard‐mesh discretization of 80,000 cells and ends with a fine mesh of over 600,000 cells. Instead of it spiralling into a second vortex at the crank, the usual event in low‐speed flow, the crank sets off standing‐wave oscillations over much of the sheet. Not seen in the standard‐mesh solution, the instability begins to appear in the fine‐mesh results. Therefore, it is the shortest waves resolved that are most unstable, but the energy contained in them comes from the large‐scale motion and seems to be small.
Periodic structure beyond a hope bifurcation
Authors: Mitchell A. R. , Stein G. , Maritz M.
Published: August 2005

A Hopf bifurcation where a stable fixed pointer bifurcates into a stable periodic orbit as a parameter passes through a critical value, occurs frequently in nonlinear problems. Here, the Maynard Smith nonlinear map in population dynamics involving a parameter k is analysed with the help of numerical experiments in order to determine the periodic structure of the map beyond the primary Hopf bifurcation of period 6 which occurs at k = 1. The interesting result obtained is that in the parameter range from k = 1 to the value for blow‐up of all initial conditions, there are successive windows of periods 7, 8 and 9, the last containing a secondary Hopf bifurcation of period 4.
Application of spline finite strip analysis to variable depth bridges
Authors: Uko C. E. A. , Cusens A. R.
Published: August 2005

A spline finite strip method capable of analysing variable thickness solid slab bridges is presented. It utilizes cubic B‐splines as displacement functions in the longitudinal direction, with third‐order polynomials as transverse displacement functions. Numerical integration is used to take account of variable thickness in the longitudinal direction of a strip. A numerical example based on a two‐span bridge deck is given.
Bibliography on finite elements and supercomputing
Authors: White Donald W. , Abel John F.
Published: August 2005

This bibliography of recent (generally since 1977) works on supercomputing and finite elements contains two principal sections: (1) a relatively comprehensive listing of publications specifically coupling finite elements and supercomputing, and (2) a cross‐reference compilation by topical category.
A finite element model for tides and currents with field applications
Authors: Walters Roy A.
Published: August 2005

A finite element model, based upon the shallow water equations, is used to calculate tidal amplitudes and currents for two field‐scale test problems. Because tides are characterized by line spectra, the governing equations are subjected to harmonic decomposition. Thus the solution variables are the real and imaginary parts of the amplitude of sea level and velocity rather than a time series of these variables. The time series is recovered through synthesis. This scheme, coupled with a modified form of the governing equations, leads to high computational efficiency and freedom from excessive numerical noise. Two test‐cases are presented. The first is a solution for eleven tidal constituents in the English Channel and southern North Sea, and three constituents are discussed. The second is an analysis of the frequency response and tidal harmonics for south San Francisco Bay.
Iterative algorithms and software for solving large sparse linear systems
Authors: Young David M. , Mai Tsun‐Zee
Published: August 2005

The paper is concerned with iterative algorithms for solving systems of linear algebraic equations where the coefficient matrix is large and sparse. Such systems often arise in the numerical solution of partial differential equations by finite difference or finite element methods. The algorithms considered include a basic iterative method, an acceleration procedure for speeding up the convergence of the basic iterative method and an adaptive procedure for determining any necessary iteration parameters. Algorithms are described both for the case where the coefficient matrix is symmetric and positive definite and for the nonsymmetrizable case. The ITPACK Project was established by the Center for Numerical Analysis at The University of Texas in 1974. The object of ITPACK was the study of iterative algorithms, using both theoretical and experimental methods. Several software packages are described which have been developed as part of the ITPACK project for carrying out experimental studies with a variety of algorithms over a wide range of problems. Recent work on the use of advanced computer architectures is briefly discussed.
Natural convection in an enclosure with a vertical baffle
Authors: Zimmerman E. , Acharya S.
Published: August 2005

A numerical study is made of natural convection in an enclosure with a vertical, finitely conducting baffle. The end‐wall is assumed to be either perfectly conducting or adiabatic. Predicted flow and isotherm patterns indicate the existence of strong thermal stratification in the baffle/cold wall region and are in qualitative agreement with reported experimental results. The baffle strongly influences the hot‐wall Nusselt number distribution, but has a weaker effect on the cold‐wall Nusselt number distribution. The predicted Nusselt numbers show satisfactory agreement with the high Rayleigh number based experimental correlation of Lin and Bejan in a partially divided enclosure of aspect ratio 0.3.
Predictions of the combustor coannular swirling flowfield using a modified turbulent kinetic energy equation
Authors: Chao Y. C. , Ho W. C. , Liu S. S.
Published: August 2005

A modified model based on the turbulent kinetic energy equation is used to predict the recirculating swirling flowfield. The model properly includes the wave and oscillation nature of the swirling flow and redefines the energy budget in the turbulent kinetic energy equation. This brings about significant improvements in the recirculation zone as well as the recovery region, as compared with the results from models used by Rodi and Launder et al. of the Richardson number type corrections in the dissipation equation.
A pressure cycle control algorithm for superplastic forming
Authors: Bonet J. , Wargadipura A. H. S. , Wood R. D.
Published: August 2005

The calculation of the pressure cycle is of crucial importance for the successful development of a thin sheet superplastic forming process. The pressure cycle must be such that the forming time is minimized while maintaining a strain rate that maximizes the strain‐rate sensitivity parameter, in order to reduce the propensity of the material to undergo localized necking. One way of dealing with this problem is to control the pressure by constraining the maximum equivalent strain rate. This paper presents a general numerical algorithm for achieving such control, in conjunction with a finite element analysis of the forming process. Three examples are given of strain‐rate controlled pressure cycles for the forming of a plane‐strain strip.
Thin plates of variable thickness with linear flexural rigidity
Authors: Jianqiao Ye , Haihong Xiao
Published: August 2005

A very simple method is suggested in this paper to analyse plates of variable thickness with linear flexural rigidity. Bi‐harmonic analysis is adopted to establish the boundary integral equation in the present study. Numerical examples are given to show that the approach developed in this paper is effective.
Lifting aerofoil calculations using von Mises variables
Authors: Naeem R. K. , Barron Ronald M.
Published: August 2005

A natural streamline coordinate system approach has been developed for steady two‐dimensional incompressible lifting flow problems. Flow equations with appropriate boundary conditions are presented in terms of von Mises coordinates (x, ψ), where ψ is the streamfunction for the flow. The finite difference method is used to discretize the non‐linear elliptic equation describing the flow. Favourable agreement with available results is obtained.
Optimal structural remodelling — simulation by virtual distortions
Authors: Holnicki‐Szulc Jan
Published: August 2005

A numerical method for simulation of optimal structural redesign by virtual distortions is presented. First, the idea of the simulation technique is discussed in the case of truss structures and then the application to the case of in‐plane loaded plates is made. The optimal results for the class of continuous solutions as well as for Michell's pseudocontinuums are reached.
Iterative improvement of eigensolutions from reduced matrices
Authors: Sauer G.
Published: August 2005

The Guyan method to reduce stiffness and mass matrices of linear structures is widely used in engineering practice. However, it introduces errors in the reduced mass matrix, and the eigensolutions based on this matrix are reliable only for the lowest modes. Additionally a certain skill is required to select appropriate analysis co‐ordinates. But the eigensolutions from the reduced matrices can easily be improved by a straightforward iteration procedure. This procedure is presented. The achievable improvements in accuracy are demonstrated by an example.
Five‐point FTCS finite‐difference methods for heat conduction
Authors: Noye B. J.
Published: August 2005

A family of five‐point second‐order forward‐time centrred‐space (FTCS) explicit finite‐difference equations for solving the one‐dimensional heat conduction (diffusion) equation with constant coefficients and Dirichlet boundary conditions is described. Some members have stability ranges larger than that of the standard three‐point FTCS equation, others are more accurate, and some are both more accurate and more stable. Values at grid points adjacent to boundaries are computed by means of an explicit procedure with stability and accuracy matching that of the equation used at interior grid points.
A model of one‐dimensional primary and secondary consolidation, based on flow channel considerations
Authors: Thomas H. R.
Published: August 2005

The possible influence of one aspect of flow channel characteristics on consolidation behaviour is addressed. In particular, the effect of potential distributions between particles forms the basis for the work. An attempt is made to represent this microscopic phenomenon, at the macroscopic level, by the mechanistic approach that the coefficient of permeability varies as a function of the remaining excess pore water pressure. It is shown that the approach proposed is capable of reproducing the classical experimentally observed one‐dimensional consolidation settlement curves of viscous clay. Primary and secondary compression behaviour is modelled.
Procedures for residual equilibration and local error estimation in the finite element method
Authors: Kelly D. W. , Isles J. D.
Published: August 2005

Procedures to enforce equilibration of residuals and determine complementary a posteriori error estimates for linear elasticity have been published elsewhere.1−4 Methods for determining the error in stress and displacement have also been proposed.3 Here we discuss an extension to the procedure for equilibrating the residuals and apply it to a simple example. Results for the error in stress and displacement are presented.
On the front‐tracking scheme for phase‐change problems
Authors: Askar Hasan G. , Abdul‐Latif Wisal
Published: August 2005

Phase‐change problems can be solved numerically for the temperature distribution when accompanied by explicit reference to the position of the front at each time interval. An improved front‐tracking scheme provides accurate determination of the phase front in the different stages of analysis. The front is made to coincide with a created grid node throughout the numerical analysis. The scheme utilizes a combination of the finite‐difference and finite‐element methods for obtaining the solution of the phase‐change problem.
A new boundary integral equation‐finite‐element method for clamped orthotropic plate bending problems
Authors: Shi G. , Bezine G.
Published: August 2005

In this paper, a simplified boundary integral equation‐‐finite‐element method is proposed for the bending analysis of thin clamped orthotropic plates according to Kirchhoff's theory. The solution procedure is based on the direct boundary element method earlier developed for isotropic plate bending problems. The integral equations necessary for solving the orthotropic plate bending problem are derived after transformation of such a problem into an equivalent isotropic plate bending problem by introducing an unknown transverse loading distributed in the interior domain of the plate. A simple discretization scheme is described in this paper for the plate boundary and its interior domain. Some computational examples are presented in this paper, and the numerical results illustrate a satisfactory accuracy of the method.
Spatially regularized solution of inverse elasticity problems using the BEM
Authors: Zabaras N. , Morellas V. , Schnur D.
Published: August 2005

This paper is concerned with solution by the boundary element method (BEM) of a certain class of inverse linear elastic problems using the spatial regularization method. More specifically, the problem of calculating the boundary and internal conditions on a deformed specimen given approximate information on the displacements at discrete ‘sensor locations’ in the specimen is discussed. The solution algorithm employs a sensitivity analysis and a least‐squares minimization of the difference between the calculated and measured displacements at each sensor location. The ideas presented here can be applied to contact problems where measurements of the deformation at the contact area are difficult.
Elastic‐plastic hybrid/mixed finite‐element method and its application to the non‐uniform tension of square sheet metal
Authors: Hu Ping , Zhou Dajun
Published: August 2005

A new elastic‐plastic hybrid/mixed finite‐element method, presented in this paper, is used for the numerical analysis of non‐uniform tension and buckling behaviour of square sheet metal under the diagonal tensile condition. The total displacement, stress and strain fields as well as their evolution up to a critical buckling condition are obtained for comparison with the experimental results by using the Moire method. It is found that the FEM can be a useful tool for studying the complex elastic‐plastic deformation problem in sheet‐metal forming processes.
On the construction of physical systems from spectral data
Authors: Zimoch R. Z.
Published: August 2005

This paper presents an algorithm for the solution of the inverse problem for a matrix differential equation of the form Aẍ + Bẋ + Cx = 0. In the method use is made of the Taylor formula for a matrix function of many variables. It is shown that the algorithm is always convergent. The paper includes a description of the appropriate algorithms and numerical examples.
On higher‐order asymptotic factorization of non‐linear operators
Authors: McMorran Andrew G. , Cooke Charlie H.
Published: August 2005

Operator splitting for evolution equations which involve non‐linear differential operators is investigated. The occurrence of third‐orderaccurate multifactor splittings which are characterized by all‐positive fractional steps and which involve at most four factors is discovered. This result is surprising, as a recent investigation by Sheng (1989), of evolution equations involving general linear operators, establishes that no third‐orderaccurate factional‐step splitting having all‐positive fractional steps exists, regardless of the number of factors attempted. However, the present investigation indicates it is unlikely that Sheng's result has much bearing on the existence of positive‐step splittings for non‐linear equations. In addition to the result mentioned above, with n = 3, 4, 5, another case is exhibited of a non‐linear equation which permits all‐positive step, n‐thorder splittings requiring only n + 1 factors. Indeed, a pathological case is examined of a partial differential equation with an annihilating operator which permits k‐factor, nth‐order splittings, for k > 1 and n > 1. Thus, for the non‐linear case, one should expect only the unexpected. Finally, the idea of equivalent splittings for linear aganist non‐linear equations is considered. For a particular equation, all splittings having five factors or less, which are obtained by considering a linearization are shown applicable also to the non‐linear case. However, there exists a four‐factor all‐positive step splitting of the non‐linear equation which is not discovered by the linearized approach.
Bifurcations of an oscillator to two‐harmonic excitation
Authors: Leung A. Y. T. , Fung T. C.
Published: August 2005

The incremental harmonic balance method has been successful for harmonic excitation. It is extended to determine the steady‐state solutions of a non‐linear oscillator subject to periodic (two‐harmonic) excitation. Higher‐order subharmonic solutions result from bifurcations. As the bifurcation process continues in an accelerated rate, chaotic solutions are obtained when no simple subharmonic solution coexists. When periodic solutions do coexist, the final steady‐state solution depends on the initial conditions. The evolution of the amplitude against the system parameters can be recorded on a bifurcation graph. An initial bifurcation graph is constructed when one of the system parameters varies. Neighbouring bifurcation graphs when other system parameters are changing are obtained in an incremental manner. If only the boundaries dividing the qualitatively different solutions are constructed, a parametric diagram is obtained. The characteristic of the solutions can be read directly from the diagram. For an oscillator subject to two‐harmonic excitation, the parametric diagram is found to be qualitatively different from those with one‐harmonic excitation. The parametric diagram is highly foliated when many stable and unstable higher‐order subharmonic solutions coexist at the same time under some combination of conditions. It is possible that the periodic solutions disappear suddenly and give way to chaotic solutions due to a small change in the system parameters without undergoing period doubling.
Non‐associative Drucker‐Prager plasticity at finite strains
Authors: Hofstetter G. , Taylor R. L.
Published: August 2005

A straightforward extension of the return mapping algorithm for J2‐plasticity at finite strains to a non‐associative Drucker‐Prager yield criterion, assuming elastic volumetric response, is presented. It is shown that the concept of plastic incompressibility, assumed at the outset, does not hold for a certain range of stresses.
Modelling of turbulent transonic flow around aerofoils and wings
Authors: Müller Bernhard , Rizzi Arthur
Published: August 2005

Turbulent flows around aerofoils and wings are simulated by solving the two‐and three‐dimensional Navier‐Stokes equations in quadrilaterals and hexahedrons, respectively. Turbulent flow is described by an algebraic eddy viscosity model. Boundary‐conforming O‐and O‐Otype meshes are generated by the transfinite interpolation method. The finite‐volume technique is employed for spatial discretization using two cells in each computational co‐ordinate direction more than the conventional approach to evaluate the viscous fluxes. An explicit three‐stage Runge–Kutta scheme is used for time integration. The method is applied to compute turbulent transonic flow over the NACA 0012 aerofoil and the ONERA M6 wing. The results are compared with experimental and computational data.
A simplified approach to calculate the damping ratio matrix for multiple degree of freedom vibration systems
Authors: Wilson J. M. , Man Liu
Published: August 2005

In modal analysis of damping systems, the criteria matrix of damping ratios is of importance for both experiments in identification of structure parameters and theoretical analysis of assessing dynamical response. In a single degree of freedom system, the damping ratio can be defined easily and obtained by some simple calculations. So the vibration response envelope can be predicted, which is important for passive isolation and active control of vibration in dynamical design. Likewise, in a multiple degree of freedom system, the concept can be defined similarly to the single degree of freedom,1 while it involves complicated manipulations and calculations to obtain the damping ratio matrix in terms of mass, damping and stiffness matrices. Some available stimulating references have discussed the damping ratio matrix and presented some alternative criteria matrices.1–4

However, the final formula to evaluate the damping ratios is quite complex and it needs several eigensolutions. If the mass matrix is formed by uniform interpolation to the stiffness, the calculations are even greater than that in the state space calculating eigensolutions directly. Regarding these, a new approach is presented in this paper in terms of modal parameters to calculate the damping ratio matrix. Therefore, the damping ratio matrix takes the parallel form to the single degree of freedom system, and the calculations are greatly reduced. Further, the paper also discusses the case of incomplete sets of eigenpairs, which is of practical importance since for most large structures the complete eigensolution is either unnecessary or computer‐timeconsuming and inaccurate for higher modes; in finite‐element modelling only lower‐order Ritz vectors or even static deformation modes in normal cases are employed.
Computational efficiency of p‐ and h‐ version elements
Authors: Gupta Ajaya Kumar , Fang Ting‐Hsiung , Chen Hong
Published: August 2005

The plate‐with‐a‐circular‐hole problem has been solved using p‐ and h‐version models. Both models give solutions of comparable accuracy in roughly the same amount of computer time. As p is increased from 8 to 10 in the p‐version models, and the number of 8‐node isoparametric elements is increased from 30 to 42 in h‐version models, the accuracy of stress values and distributions does not improve significantly in both versions. However, the computational effort in the p‐version models increases much more (200%) than it does in the h‐version models (40%). Because one of the edges in each of the two elements of the p‐version model is curved, the stiffness matrix cannot be evaluated in closed form and consumes a significant amount of computer time.
Extension and application of the QUICKER scheme to a non‐uniform rectangular grid system
Authors: Koo Hyeong‐Mo , Park Seung O.
Published: August 2005

The QUICKER formulation of the QUICK scheme is extended to a non‐uniform rectangular grid system that can be widely adopted for the calculation of the flow problems of engineering interest. This new formulation is applied to obtain solutions of a one‐dimensional non‐linear Burgers equation and a two‐dimensional lid‐driven cavity flow. The computational results show that the new formulation is superior to existing schemes such as hybrid and skew‐upwind‐differencing, especially when the grid Peclet (or Reynolds) number is high.
A parallel transient algorithm for structures with extended independent substructure computation
Authors: Bennighof Jeffrey K. , Wu Jiann‐Yuarn
Published: August 2005

A parallel algorithm for linear structure transient response problems is presented in which transient response is computed independently for substructures for extended periods of time, and these substructure responses are then corrected to obtain the response of the overall coupled structure. The correction of the uncoupled substructure responses only requires the interface portions of these responses sampled occasionally in time, and is done independently for different substructures in a streamlined procedure. A numerical example is presented to demonstrate the method and show its accuracy.
Geometrically non‐linear analysis of shell structures
Authors: Moy S. S. J. , Lam S. S. E.
Published: August 2005

The paper presents a finite element formulation for the geometrically non‐linear analysis of shells. The formulation is based on the Hellinger—Reissner approach and uses internal transverse shear stress unknowns to alleviate the problem of shear locking. A ring and a quadrilateral element are presented, together with three examples which demonstrate the accuracy of the elements.
Hierarchical hybrid rectangular finite‐element formulation for 2‐D elasticity problems
Authors: Perry B. , Bar‐Yoseph P. , Rosenhouse G.
Published: August 2005

A simple and efficient algorithm for the generation of hierarchical hybrid rectangular finite elements for two‐dimensional elasticity problems is presented. A significant saving in computational effort needed for calculating the stiffness matrices of the various finite elements is gained by using symbolic algebra for calculating exactly the necessary integrals. Hierarchical matrices G and H, corresponding to a stress field up to a cubic approximation and a displacement field up to a quadratic approximation, are detailed. The described method for generating hierarchical hybrid stress elements could easily be extended for higher‐order elements.
Quadrilateral isoparametric finite element with central node
Authors: Stefanov Ivo
Published: August 2005

The quadrilateral four‐node isoparametric finite element is transformed by adding a fifth node in its centre. The shape functions used are of relatively high degree and satisfy the requirements for compatibility and completeness. In the numerical examples the new five‐node finite element provides a better accuracy than the classic four‐node one.
Non‐linear terms in frame analysis using eulerian moving co‐ordinates
Authors: El‐Ghazaly Hany Ahmed
Published: August 2005

The effect of retaining the non‐linear term (½ u) in the strain‐displacement equations for frame analysis using Eulerian moving co‐ordinates is discussed. The resulting non‐linear equilibrium equations are solved using the energy search method of analysis. Two examples are discussed involving tension‐bending and compression‐bending coupling. It has been shown that the non‐linear term (½ u) may be omitted from the strain‐displacement relationship without sacrificing any significant accuracy. The finding agrees in substance with a conclusion reported in the literature which was limited to non‐linear stability analysis of truss structures.
Variational principles and hybrid approach for finite deformation analysis of shells
Authors: Qin Q. H. , Jin F. S.
Published: August 2005

A complementary Hu‐Washizu functional Γ3, based on formulae presented by Atluri (1984), is given in dyadic notation. By introducing Legendre transformation, the Heillinger‐Reissner functional Π2, Γ2 and the classic potential energy functional Π1 are obtained. An incremental modelling of functional Γ3 for the analysis of finite deformation and finite rotations of arbitrarily shaped shells is presented. The numerical results are shown to be in good agreement with those found in published literature.
A general computational method for solving non‐linear free boundary‐value problems of plane hydrodynamics
Authors: Moussa Nabil
Published: August 2005

This work is based on the constructive existence proof of solutions of a comprehensive class of non‐linear free boundary‐value problems of plane hydrodynamics by E. Zeidler (1971). A general computational method was developed and illustrated on the specific case of permanent heavy waves in infinite channels.
A compact unconditionally stable finite‐difference method for transient one‐dimensional advection‐diffusion
Authors: Noye B. J.
Published: August 2005

A new compact second‐order finite‐difference method for solving the time‐dependent one‐dimensional constant‐coefficient advection—diffusion equation is developed. It involves a spread of only two grid points in space and two levels in time. It may be evaluated in an explicit marching manner and requires the availability of only upstream boundary values. It is unconditionally stable and has the property of giving ‘non‐negative’ values for a large range of Courant and diffusion numbers. For all grid Reynolds numbers greater than 2 it is shown to be more accurate than commonly used second‐order methods, all of which involve a spread of three grid points in space.
Axisymmetric potential flow calculations. Part 2: Design mode
Authors: Zhang S. , Barron R. M. , Rudraiah N.
Published: August 2005

The pure inverse problem of designing a body with a prescribed surface pressure in incompressible axisymmetric potential flow is solved using the streamfunction as a co‐ordinate in the computational plane. The problem is formulated mathematically as a mixed boundary value problem and the solution is obtained using the finite‐difference technique. The body shape is computed simultaneously with the entire flow field and does not have to be iteratively adjusted to meet the target surface pressure. Results are presented for elliptical, NACA 0012 and minimum‐drag cross‐sections.
An improved mode superposition method for linear damped systems
Authors: Huiping Shao
Published: August 2005

In this paper a practical improved mode superposition method for linear damped systems is suggested. In this method, a recurrence formula, an exact answer can be obtained in terms of low‐degree modal information to fourth‐degree accuracy.
Improving the efficiency of incomplete Choleski preconditionings
Authors: Papadrakakis Manolis , Dracopoulos Michael C.
Published: August 2005

Techniques based on the idea of preconditioning have significantly improved the efficiency of classical iterative methods. In this work two preconditioning approaches based on incomplete Choleski factorization have been further refined, with the result that both storage requirements and solution times have been greatly improved. The first is based on the rejection of certain terms of the factorization process according to their magnitude. An efficient computational handling of the incomplete factorization is proposed which improves substantially the complicated addressings and the overall efficiency of the iterative method. The second preconditioning matrix is based on a rejection criterion relative to the position of the non‐zero terms of the coefficient matrix. Such preconditioners have been proposed in the past but experience with the application of the finite‐element method is not favourable since the factorization very often becomes unstable or the rate of convergence is not satisfactory. The modifications proposed here give this type of incomplete factorization both robustness and efficiency.
Beam cantilevered from elastic support: Finite‐element modelling
Authors: Cook Robert D.
Published: August 2005

A beam, modelled by standard beam elements, is to be connected to a plane, which is modelled by quadrilateral elements. Beam elements include rotational d.o.f. but quadrilateral elements do not. The connection is made by extending the beam into the plane by an additional beam element. Herein we present a formula for the stiffness of the additional beam element so that the elasticity of the support is properly represented.
A simple quadrilateral shear panel element
Authors: Chen Harn C.
Published: August 2005

A shear panel element of general quadrilateral shape is so formulated that it assumes a state of constant shear flow. This is achieved by using isoparametric shape functions to approximate the displacement field and then using the mean of the strain‐displacement matrix to evaluate shear strain and the resulting stiffness matrix. Numerical examples show that the element reproduces analytical solutions when its shape is rectangular and behaves satisfactorily when its shape is not rectangular.
On the relation of the cell discretization algorithm to the primal hybrid finite element method
Authors: Coffey Mark W.
Published: August 2005

We point out the connection between the cell discretization algorithm and the primal hybrid finite‐element method. There is a very close relationship between these two non‐conforming methods. In particular, an important result between Lagrange multipliers and normal derivatives obtains in both cases. Sample numerical evidence verifying this connection is presented for a simple two‐dimensional elliptic problem.
On shock capturing for pure water with general equation of state
Authors: Cooke Charlie H. , Chen Tze‐Jang
Published: August 2005

The numerical investigation of shock phenomena in gas or liquid media where enthalpy is the preferred thermodynamic variable poses special problems. When an expression for internal energy is available, the usual procedure is to employ a splitting scheme to remove source terms for the Euler equations, then upwind‐biased shock capturing algorithms are built around the Riemann problem for the conservative system which remains. However, when the governing equations are formulated in terms of total enthalpy, treatment of a pressure–time derivative as a source term leads to a Riemann problem for a system where one equation is not a conservative law. The present research establishes that successful upwind‐biased shock capturing schemes can be based upon the pseudoconservative system. The method is applied to numerical simulations of shock wave propagation in pure water.
Indefinite elliptic problem preconditioning
Authors: Vassilevski P. S.
Published: August 2005

Based on investigating the eigenvalue distribution of the preconditioned matrices that arise in the finite‐element discretization of indefinite elliptic problems with preconditioning matrices, constructed on the basis of the principal coercive part of the considered elliptic problems, it is proved that the Krylov subspace CG‐type methods like MINRES converge with a rate of convergence determined only by the stability properties of the discrete problem in terms of a priori estimates and the accuracy of the preconditioning matrix with respect to the principal coercive part of the considered finite‐element stiffness matrix. This is also demonstrated by numerical experiments. The method is of practical interest if there are only a few negative eigenvalues.
On the damping ratio of multi‐degree‐of‐freedom systems
Authors: Man Liu , Wilson J. M.
Published: August 2005

The damping parameter is commonly used when assessing a vibration system or analysing dynamical response, as well as reducing vibration levels. A basic step towards analysing a damped system is to solve its complex eigenvalues. However, the solution is computer‐time‐consuming. An alternative way is to get the damping ratio matrix so that the behaviour of the system in each mode can be determined. This paper presents a simple means of identifying the corresponding relation between the mode number and its damping ratio by a matrix perturbation method which leads to the transformation perturbation or TP method. The equivalence of the complex eigenproblem of damped systems and transformed damping matrix in calculating the damping ratios is also discussed.
On stress intensity factor computation from the quarter‐point element displacements
Authors: Lim I. L. , Johnston I. W. , Choi S. K.
Published: August 2005

In conjunction with the quarter‐point element, a wide range of stress intensity factor computation techniques may be employed. Of these, the displacement correlation technique (DCT) and the quarter‐point displacement technique (QPDT) have been in common use. It has been suggested by various investigators that the DCT is more rational in formulation and should therefore be more accurate than the QPDT. However, published numerical studies provide conflicting results on the relative performance of either technique. To resolve this anomaly, this study provides a detailed investigation on the DCT and QPDT performance. On the basis of considering the second term in Westergaard's expression and supported by numerical experiments, it is concluded that the QPDT would generally perform better than the DCT.
Note on sensitivity analysis to improve eigenvalue analysis
Authors: Chen Lien‐Wen , Ku Der‐Ming
Published: August 2005

The stability behaviour of a cantilever beam, carrying a concentrated mass at the free end and subjected to a uniformly distributed follower force, is studied by the finite‐element method. In the present finite‐element formulation, the Timoshenko beam theory is utilized to derive the governing equations of motion. In order to more quickly and efficiently obtain the critical load for such a non‐conservative system, a numerical technique which utilizes the eigenvalue sensitivity with respect to the follower force is introduced instead of the conventional trial‐and‐error technique. The high accuracy and rapid rate of convergence through the combination of the present finite‐element model and the numerical algorithm are demonstrated with the numerical example given.
Application of PLTMG to a stream function problem
Authors: Mooney J. R.
Published: August 2005

The finite‐element package PLTMG was designed to solve a wide variety of non‐linear, scalar elliptic PDEs. In this paper we examine the application of PLTMG to the solution of a potential flow problem using the stream function formulation. The flow problem is that of irrotational steady flow through a shallow lake with prescribed inflows and outflows. A two‐dimensional (vertically integrated) model is used. One or more islands may be present. The paper focuses on the advantages of the stream function formulation for obtaining accurate streamlines and partial residence times as opposed to using a potential function formulation. If islands are present the stream values at the island boundaries are unknowns which must be determined to fulfil a condition of zero circulation round each island. Thus, if N islands are present, an N‐fold linear continuation must be performed to determine the solution.
Hierarchical modelling of discontinuous fields
Authors: Fish J.
Published: August 2005

A methodology has been developed to hierarchically model discontinuous fields by means of the s‐version of the finite‐element method. This is achieved by overlaying portions of the finite‐element mesh where discontinuities need to be embedded with a finite‐element mesh which is discontinuous across the crack faces (containing unconstrained double nodes along the discontinuity). By this technique crack propagation can be simulated by advancing the crack front in the superimposed mesh only, keeping the base mesh fixed and unaware of the crack existence. The hierarchical structure of the method ensures computational efficiency, especially in linear systems. Numerical experiments for mode I and mixed‐mode problems are presented to validate the present formulation.
Contaminant infiltration into a pressurized tube with a fabric end cap with turbulent external flow
Authors: Robertson S. R.
Published: August 2005

A short pressurized tube with a fabric end cap is placed concentrically within a longer, larger tube with a contaminated, turbulent flow. The effects of external velocity and internal pressure on the infiltration of contaminant into the pressurized tube are studied. The SIMPLER finite‐difference method, together with the two equation model of turbulence, is used to model the flow.
A note on recurrence relations for simulating ODEs
Authors: Brown Kevin S.
Published: August 2005

A technique is described for using Newton's identities to compute the coefficients of multi‐step recurrence formulae for simulating ordinary linear differential equations of high order. This approach gives the exact root‐matched recurrence formula without having to determine the complex roots of the characteristic polynomials.
A new plate shell element of 16 nodes and 40 degrees of freedom by relative displacement method
Authors: Xu Xing , Cai Ruifeng
Published: August 2005

An isoparametric plate shell element of 16 nodes and 40 degrees of freedom is developed in this paper directly from 3‐D elastic theories. In order to overcome the difficulties caused by straightforward use of a 3‐D formulation, the relative displacement method is introduced. For curved shell elements, the use of the orthogonal curvilinear co‐ordinate system greatly reduces the computer effort. The new element can conveniently solve shell problems with variable thicknesses and also easily link with other finite elements using displacement d.o.f. such as 8‐node to 21‐node 3‐D elements. Numerical examples demonstrate the efficiency of the element.
Performance of a Hermitian element for a beam with rotational constraints
Authors: Wisniewski K. , Turska E. , Schrefler B. A.
Published: August 2005

The behaviour of a Hermitian two‐node element based on the Bernoulli beam equation is examined. The assumed constraints generate rotation‐dependent distributed moments. It is shown that for these moments a potential exists, and that a rigid translation is the only rigid body mode of the element. The analysis of the Bernoulli equation demonstrates that very large values of α= e/EI enforce the condition w,x = 0, resulting in displacements equal to zero. The element is examined for two types of constraints. The first type of constraint, diminishing rotations of a beam (α < 0), yields regular solutions which, however, seem to have a non‐differentiality near the end of the beam. A special procedure is developed to evaluate analytical solutions for long beams or stiff constraints, for which computer accuracy is exceeded. For the second type of constraint, enlarging rotations of a beam (α > 0), a highly oscillatory nature of the solution is proven.
Perturbation based on boundary‐element technique in structural vibration analysis
Authors: Liu Han‐Bing , Chen Su‐Huan , Liu Zhong‐Sheng
Published: August 2005

This paper, based on the boundary‐element technique, presents a perturbation method which can be applied to reanalysis of the eigenvalues and eigenvectors in an elastic structure. Regarding the shape changes of a structure as the perturbation of its surface nodes within the neighbourhood of the given values, this method uses the perturbation formula to obtain the eigensolutions of the modified system without solving the generalized eigenvalue problem. Finally, the authors give some sample examples to demonstrate the validity of the method.
The application of a numerical model of heat and mass transfer in unsaturated soil to the simulation of laboratory‐based experiments
Authors: Thomas H. R. , King S. D.
Published: August 2005

A numerical model of coupled heat and mass transfer in unsaturated soil, recently proposed by the authors, is used to simulate a laboratory‐based experimental test. The modelling approach adopted is based on the use of the capillary potential and the temperature as independent variables. The experimental results have recently been presented in the literature by other workers. Very good correlations are obtained of both steady‐state values of variables and the times required to reach steady‐state conditions. The results achieved lend confidence to the numerical modelling approach proposed and extend the range of applications of the model hitherto achieved to that of a further generic soil type, namely a silt.
Incompressible viscoplastic flow analysis using a quadrilateral 2‐D element based on mixed interpolation of tensorial components
Authors: Dvorkin Eduardo N. , Canga Marcelo E.
Published: August 2005

In the Eulerian description of metal forming operations usually rigid/incompressible viscoplastic material models are used. In this paper a quadrilateral 2‐D finite‐element formulation for incompressible viscoplastic flow analysis is developed. The element (QMITC) is based on mixed interpolation of tensorial components, and the incompressibility constraint is imposed via the penalty method. It is shown that the resulting element does not lock either in plane strain rate flows or in axisymmetric flows, that the oscillations in the pressure predictions (checkerboard) tend to zero when the mesh is refined and that the solutions for some typical benchmark problems are very accurate.