bluuebunny/crossref_metadata_2025 huggingface dataset:
Finite‐element analysis for immiscible two‐phase fluid flow in deforming porous media and an unconditionally stable staggered solution
Authors: Xikui Li
Published: August 2005

A finite‐element numerical model for immiscible two‐phase fluid flow in a deforming porous media is presented. The displacements, the pressures and the saturations of wetting phase are taken as primary unknowns of the model as the constraint about the capillary pressure between two fluid phases is applied. The governing equations and their finite‐element formulations are given in the paper. An unconditionally stable staggered solution procedure is devised for the integration of the formulations in the time domain. The stability analysis of the solution scheme is also carried out.
Substructure method for stress analysis of mass concrete structures
Authors: Bofang Zhu
Published: August 2005

In the finite‐element stress analysis of a mass concrete structure, owing to the effect of age of the concrete, it is necessary to compute a stiffness matrix and its inverse for every time increment. The computation is quite lengthy. In this paper a generalized substructure method is offered. It is assumed that the structure, consisting of m zones of different materials, is divided into m substructures, one for each zone. As every substructure is a homogeneous solid, the computation relevant to the substructure is required at the beginning only, and can be utilized repeatedly thereafter. Thus the computation is simplified remarkably.
On the numerical solution of a model air pollution problem with non‐smooth intial data
Authors: Seward W. L. , Kasibhatla P. S. , Fairweather G.
Published: August 2005

While one of the distinguishing features of air pollution problems is the presence of a large number of randomly scattered discrete soucrces, little attention has been devoted to the proper treatment of such souces in standard numerical techniques. In this paper we consider a model air pollution problem in two space variables which can be transformed to the one‐dimensional diffusion equation with a Dirac delta function as the initial conditon. the primary purpose of this study is to investigate the effect of two ways of representing thishighly singular initial condition, namely by L2 projection and by mollification, in commonly used numerical methods basedc on a Galerkin semi‐discretization together with the θ method in the marching direction. We report the results of extensive numerical experiments which demonstrate, for example, that in general the numerical solution obtained with mollified initial data is more accurate near the intial point than that obtained using projected initial data. Moreover, it is verified that the‘smoothed’ Crank‐Nicolson method, in which the first two Crank‐Nicolson steps are replaced by four steps of the backward Euler method, is the most effective marching technique.
An easily implemented static condensation method for structural sensitivity analysis
Authors: Gangadharan S. N. , Haftka R. T. , Nikolaidis E.
Published: August 2005

In many situations, the sensitivity of the response of a structure to parameters affecting only a small part of the structure is desired. In such cases, it is efficient to use substructuring or static condensation approaches. However, static condensation is not available in all finite‐element codes, and its implementation requires access to and familiarity with the source code of the program. The present paper suggests an alternative version of static condensation for sensitivity calculations which is easy to implement without access to the source code of the finite‐element program. The proposed approach (black‐box method) is demonstrated by applying it in system identification of joint parameters of 3D frame structures using a direct method for evaluating the sensitivity derivatives of the structural response with respect to the joint parameters.
A curved triangular plate bending element for Kirchhoff plates using a C0 coharmonic mixed two‐field formulation
Authors: Campbell John S. , Horgan Bernice
Published: August 2005

A curved triangular element is presented for thin Kirchhoff plates. A mixed, two‐field formulation is used, based upon the Marcus decomposition, in which the familiar biharmonic equation is supplanted by a pair of coupled Poisson‐type equations. Several examples of simply supported plates are given to illustrate the behaviour of this new formulation.
Finite‐element method for elastic wave propagation
Authors: Serón F. J. , Sanz F. J. , Kindelán M. , Badal J. I.
Published: August 2005

The object of this work is to analyse the computational aspects of the finite‐element method for the elastic wave equations. The necessary numerical techniques are analysed from the point of view of accuracy, performance and storage requirements when implemented in scalar and vector processors with large storage capacity. The method is implemented on an IBM 3090 with vector facility.

For this implementation we consider five different time integration schemes (explicit and implicit central difference, Houbolt, constant average acceleration and Wilson), and in the implicit case, both direct (Gaussian decomposition) and iterative (successive over‐relaxation, Jacobi semi‐iterative, Jacobi conjugate gradient) sparse linear systems solvers. These solvers are taken from the ITPACK2C and ESSL libraries using in each case the adequate representation scheme; skyline, row‐wise and compressed diagonal.

From our results it is concluded that constant average acceleration and explicit central difference are the most adequate integration methods and Jacobi conjugate gradient is the most efficient solver.
Experiments on iterative solution for the semi‐implicit characteristic–Galerkin algorithm
Authors: Bottura L. , Zienkiewicz O. C.
Published: August 2005

The 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

A 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.
Perturbed general eigensolutions
Authors: Leung A. Y. T.
Published: August 2005

The most general case of perturbation of a repeated eigenvalue of a derogatory eigenproblem is considered. It is shown that Puiseux expansions of the perturbed eigensolutions are inevitable in the degenerated case where the Taylor expansions are erroneous.
Weighting functions in single‐step algorithms for a non‐linear equation
Authors: Salamon N. J. , Xiang Jiannan
Published: August 2005

For 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

A 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

Given 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

An 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

A 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

The 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.
Benchmark of UTCHEM reservoir simulator on various Cray computers
Authors: Shiles G. , Pope G. A. , Sepehrnoori Kamy
Published: August 2005

The results of a benchmark on five Cray computers for a highly vectorized chemical flooding reservoir simulator are reported in this paper. The models used are a standard benchmark set used to compare the performance of various computing systems.
Nonlinear dynamic buckling of thin‐walled beam‐columns under ground excitations
Authors: Ali Ashraf , Yunus Shah M. , Sridharan S.
Published: August 2005

A 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

An 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

The 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

Non‐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

An 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

A 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

Chebȳshev 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

Refinement 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

A 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

The 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

In 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

A 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

An 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

This 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

An 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.
Incorporation of strain‐hardening in the implicit elasto‐viscoplasticity algorithm
Authors: Reed M. B.
Published: August 2005

An algorithm is presented for the inclusion of general strain‐hardening/softening behaviour into the direct method of finite‐element analysis of elasto‐viscoplasticity using implicit time discretization.
An algorithm for the numerical inversion of a tridiagonal matrix
Authors: Kumar Surendra , Shashi  , Pethö Árpad
Published: August 2005

This paper presents an algorithm for obtaining the inverse of a tridiagonal matrix numerically. The algorithm does not require diagonal dominance in the matrix and is also computationally efficient.
Adaptive refinement criterion for elliptic problems discretized by FEM
Authors: Storti M. , Nigro N. , Idelsohn S.
Published: August 2005

In 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

The 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

An 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

The 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

The 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.
Computation of isotropic tensor functions
Authors: Miehe C.
Published: August 2005

An explicit formulation and a procedure for the computation of isotropic tensor‐valued tensor functions is discussed. The formulation is based on a spectral decomposition in terms of second‐order eigenvalue bases, which avoids the costly computation of eigenvectors. As an important result a compact structure of the fourth‐order derivatives of general second‐order isotropic tensor functions is presented.
Use of load‐dependent vectors for dynamic analysis of large space structures
Authors: Ricles J. M. , Léger P.
Published: August 2005

Structural models of large space structures have a substantial number of degrees of freedom (DOF) and possess semi‐positive‐definite stiffness matrices. The paper presents an efficient co‐ordinate reduction procedure for structural dynamic analysis of large space structures. The method is based on the superposition of load‐dependent Ritz vectors, which are computed in block form using a shifted stiffness matrix. Comparative transient dynamic analyses are performed on a 2803 DOF model of the space station Freedom using the load‐dependent method (LDM) and the mode‐displacement method (MDM) based on the superposition of eigenvectors. It is shown that the LDM is able to provide convergence of displacements with a small number of vectors. The acceleration response is found to be more sensitive to vector truncation than the displacement response. Error norms based on the representation of the dynamic load by the vector basis are developed to provide an indication of the effect of vector truncation on the structural response.
Mapping of finite elements around corner singularities of the quasi‐harmonic equation
Authors: Aalto Jukka
Published: August 2005

The paper deals with the solution of the quasi‐harmonic equation by the finite element method in a domain with corners on its boundary. A mapping technique, which can be used for locating the nodes of standard isoparametric elements in a subgrid (patch) of finite elements in the vicinity of a corner singularity point, is presented. The equations of the mapping are based on the analytical singular solution of the problem. Some analytical and numerical results to show the efficiency of the technique are presented.
New assumed natural strain formulation of the shallow shell element
Authors: Muhanna Rafi L.
Published: August 2005

A new efficient formulation of the 36 degree‐of‐freedom conforming shallow shell element of an arbitrary triangular shape is presented. This formulation is based on natural co‐ordinates and independently assumed natural strain fields, and applied to shallow shell analysis. The 3‐node element incorporates the normal displacement and its first and second derivatives plus the tangential displacements and their first derivatives at each vertex. A closed form of the element stiffness matrix is achieved. The form of the stiffness matrix derived in this formulation explicitly reveals the essence of the shallow shell theory.

The presented approach results in avoiding definite integrals and matrix inversions, and permits operation with lower‐order numerical matrices, which are the same for all elements. The example applications presented demonstrate that accurate predictions of stresses as well as displacements are obtained with only a few elements.
Compound difference schemes for time‐dependent equations on non‐uniform nets
Authors: Charakhch'Yan A. A.
Published: August 2005

A new approach to constructing monotonous second‐order‐accurate schemes for time‐dependent Navier‐Stokes equations in the compressible case is suggested. Flows with shock waves and thin viscous boundary layers are considered. The approach joins two different schemes while each of them is appropriate for its own type of flow. The resulting scheme is constructed as a splitting one, and the approach is applied at the stage governed by the Euler equations in Lagrangian variables. The approach turns out to be fruitful also for parabolic equations with ‘viscous’ terms. The method is illustrated by the problem on compression of deuterium in a conical solid‐body target with viscous heating of deuterium.
Accuracy and efficiency of multivariant finite elements for three‐dimensional simulation of viscous incompressible flows
Authors: Gupta Mahesh , Kwon Tai H.
Published: August 2005

The performance of the univariant finite element Q1P0 and the multivariant finite elements QP0 and RP0 are compared for simulation of three‐dimensional incompressible viscous flows. Incompressible flow vortices for the RP0 element are presented. For the two flows simulated, the RP0 element is found to be not only the most accurate but also computationally the most efficient of the three types of finite element used. For one of the two flows simulated, the pressure distribution obtained by using the Q1P0 element is found to be afflicted with the checker‐board spurious pressure mode. For the uniform finite‐element mesh used, the checker‐board pressure mode is eliminated by taking a weighted average of the pressure over the neighbouring Q1P0 elements.
A 3D element for non‐linear analysis of solids
Authors: Radovitzky Raúl A. , Dvorkin Eduardo N.
Published: August 2005

An 8‐node element (HMITC) for 3D non‐linear analysis of solids is presented. The new element is based on an element developed by Wilson and Ibrahimbegovic, that incorporates incompatible modes, and on the method of mixed interpolation of tonsorial components. The HMITC element does not contain spurious zero energy modes and satisfies Irons' Patch Test. The numerical experimentation indicates that the HMITC has good performance even with distorted meshes.
Neural‐network‐based approximations for solving partial differential equations
Authors: Dissanayake M. W. M. G. , Phan‐Thien N.
Published: August 2005

A numerical method, based on neural‐network‐based functions, for solving partial differential equations is reported in the paper. Using a ‘universal approximator’ based on a neural network and point collocation, the numerical problem of solving the partial differential equation is transformed to an unconstrained minimization problem. The method is extremely easy to implement and is suitable for obtaining an approximate solution in a short period of time. The technique is illustrated with the aid of two numerical examples.
Superconvergent patch recovery of finite‐element solution and a posteriori L2 norm error estimate
Authors: Wiberg N.‐E. , Li X. D.
Published: August 2005

In the paper we present a superconvergent patch recovery technique for obtaining higher‐order‐accurate finite‐element solutions and thus a postprocessed type of L2 norm error estimate. Two modifications make our procedure different from the one proposed by Zienkiewicz and Zhu (1992), in which higher‐order‐accurate derivatives of the finite‐element solution at nodes are determined. Firstly, the recovery process is made for element, not for nodes. An ‘element patch’, which represents the union of an element under consideration and the surrounding elements, is introduced. Secondly, the local error estimate is calculated directly from the improved solution for this element. Numerical tests on both 1D and 2D model problems show that this method can provide an asymptotically exact a posteriori L2 norm error estimate if the used element possesses superconvergent points for the solutions.
Universal matrices with new infinite elements for quasiharmonic equation
Authors: Raghavarao C. V. , Sanyasiraju Yvss
Published: August 2005

A new approach to developing serendipity quadrilateral infinite elements is presented. Using these elements universal matrices for quasiharmonic equation are developed. For a particular member of the family these matrices are independent of the size and shape of the element. Using these matrices the element stiffness matrix can be generated in a simpler manner by taking into account the size and shape of the element.
Improvement on dual reciprocity boundary element method for equations with convective terms
Authors: Zhu Songping , Zhang Yinglong
Published: August 2005

The dual reciprocity boundary element method, first proposed by Nardini and Brebbia (1982, 1985), is a powerful technique for solving elliptic partial differential equations. Adopting this approach, a singular volume integral, which needs to be evaluated with a traditional boundary element method, can be converted into a boundary integral. However, when the governing equation is of a certain type, this conversion fails due to the singularities being introduced inside the physical domain and on the boundary arising by differentiating distance functions. We avoid these artificially created singularities by constructing a transformation which leads to improved numerical results.
Method to generate complex computational meshes efficiently
Authors: Landertshamer F. , Steffan H.
Published: August 2005

The paper demonstrates an approach to generate three‐dimensional boundary‐fitted computational meshes efficiently. One basic idea underlying the present study is that often similar geometries have to be meshed, and therefore an efficient mesh‐adaption method, which allows adaptation of the topological mesh to the specific geometry, would be more efficient than generating all new meshes. On the other hand the mesh generation for Cartesian topologies has been shown to be a very simple task. It can be executed by connecting and removing brick elements to a basic cube. In connection with a so‐called ‘Macro Command Language’, a high degree of automation can be reached when adapting topologically defined meshes to a surface. Furthermore, a high mesh quality has proved to be the key to good simulation results. During the mesh generation it is important to provide the possibility of modifiying the mesh quality and also the mesh density at any time of the meshing process. Using this generation method the meshing time is reduced—e.g. a computational mesh for a two‐valve cylinder head can be generated within a few hours.
The effects of a discontinuity in the forcing function of a singular integral equation
Authors: Mannix C. E.
Published: August 2005

A note on the effects of a weak discontinuity in the forcing function g(x) of a singular, integral equation of the first kind and the resulting strong discontinuity that can appear in the solution f(x) is presented.
Optimal uniform finite difference schemes of order two for stiff initial value problems
Authors: Selvakumar K.
Published: August 2005

The paper presents finite difference schemes of order two for stiff initial‐value problems, with a small parameter ε multiplying the first derivative. The schemes are a modified form of the classical trapezoidal rule. They are both optimal and uniform with respect to the small parameter ε, that is, the solution of the difference schemes satisfies error estimates of the form

Where C is independent of i, h and ε. Here h is the mesh size and ti in any mesh point. The schemes presented in this paper are different from the scheme of order two avaiable in the literature. Finally, numerical experiments are presented.
An alternative approach for large deflection analysis of axisymmetric plates on elastic foundation
Authors: Ye Jianqiao
Published: August 2005

The geometric non‐linear behaviour of thin axisymmetric circular plates on an elastic foundation is studied in the paper by using a boundary integral equation approach. A plate analogue procedure is suggested to simplify the solution. With such simplification, the foundation reaction can be arbitrary functions of plate deflection, rotation and curvatures. The boundary integral equation of thin plates and the fundamental solution of a biharmonic equation are employed for both bending and plane stress analysis. A number of numerical examples are given in the paper to show the effectiveness of the proposed method.
Conjugate gradient based projection: A new explicit computational methodology for frictional contact problems
Authors: Tamma Kumar K. , Li Maocheng , Sha Desong
Published: August 2005

With special attention towards the applicability to parallel computation or vectorization, a new and effective explicit computational approach for linear complementary formulations involving a conjugate gradient based projection methodology is proposed in this study for contact problems with Coulomb friction. The overall objectives are focused towards providing an explicit methodology of computation for the complete contact problem with friction. In this regard, the primary idea for solving the linear complementary formulations stems from an established search direction which is projected to a feasible region determined by the non‐negative constraint condition; this direction is then applied to the Fletcher‐Reeves conjugate gradient method resulting in a powerful explicit methodology which possesses high accuracy, excellent convergence characteristics, fast computational speed and is relatively simple to implement for contact problems involving Coulomb friction. Numerical test cases are also included to demonstrate the proposed methodology for contact problems with friction.
A time‐splitting finite difference method for two‐dimensional diffusion with an integral condition
Authors: Noye B. J. , Dehghan M.
Published: August 2005

A new fourth‐order locally one‐dimensional (LOD) finite difference scheme based upon the Noye‐Hayman method for one‐dimensional diffusion is used to solve a two‐dimensional time‐dependent diffusion equation with an integral condition replacing one boundary condition. Numerical testing shows this gives better results than a locally one‐dimensional scheme based on the classical forward‐time centred‐space (FTCS) method for one‐dimensional diffusion except when the diffusion number is 1/6 and the methods are identical. Results from some numerical experiments are presented.
A fourth‐order difference scheme for quasilinear poisson equation in polar co‐ordinates
Authors: Jain M. K. , Jain R. K. , Krishna Meera
Published: August 2005

We present in this paper a nine‐point, fourth‐order difference scheme for the numerical solution of the quasilinear Poisson equation in polar co‐ordinates,

with appropriate boundary conditions. A separate difference scheme of order four valid at r = 0 has also been obtained. The method is based on five evaluations of the function f. The numerical results of two problems obtained using this scheme are listed. The numerical results demonstrate the fourth‐order accuracy of the scheme.
Integral transform solution of eigenvalue problems
Authors: Mikhailov M. D. , Cotta R. M.
Published: August 2005

The generalized integral transform technique is used to reduce eigenvalue problems described by partial differential equations to algebraic ones, that can be solved by existing codes for matrix eigensystem analysis. The method is illustrated for the operators that correspond to heat and mass diffusion, but can be employed in different fields. Three examples demonstrate the potential of the method.
An adaptive time‐stepping algorithm for quasistatic processes
Authors: van den Boogaard A. H. , De Borst R. , van den Bogert P. A. J.
Published: August 2005

A scheme is presented that automatically determines the magnitude of the time step in quasistatic boundary value problems discretized via some customary method (finite elements, finite differences). The basic idea stems from the path‐following techniques widely employed in purely static analyses in the sense that the incremental displacements, measured in some suitable norm, are constrained to a prefixed value. Examples of trusses composed of a viscoelastic material are included to demonstrate the effectiveness of the method.
A new algorithm for finding a pseudoperipheral vertex or the endpoints of a pseudodiameter in a graph
Authors: Paulino Glaucio H. , Menezes Ivan F. M. , Gattass Marcelo , Mukherjee Subrata
Published: August 2005

Based on the concept of the Laplacian matrix of a graph, this paper presents the SGPD (spectral graph pseudoperipheral and pseudodiameter) algorithm for finding a pseudoperipheral vertex or the end‐points of a pseudodiameter in a graph. This algorithm is compared with the ones by Grimes et al. (1990), George and Liu (1979), and Gibbs et al. (1976). Numerical results from a collection of benchmark test problems show the effectiveness of the proposed algorithm. Moreover, it is shown that this algorithm can be efficiently used in conjunction with heuristic algorithms for ordering sparse matrix equations. Such heuristic algorithms, of course, must be the ones which use the pseudoperipheral vertex or pseudodiameter concepts.
Local‐global analysis on localized non‐linear shells of revolution
Authors: Harintho H. , Gould P. L.
Published: August 2005

A finite element program is developed as a tool to analyse shells of revolution with local non‐linearities. In reality, shells of revolution often exhibit local deviations, like a cut‐out, a junction and/or an imperfection. The stress concentration around a local deviation may produce plasticity and/or geometric non‐linearities in the surrounding region. The analytical model consists of three different types of elements: rotational, transitional and general. The rotational shell elements are used in the region where the shell is axisymmetrical and linear, while the two‐dimensional general shell elements are deployed in the deviation region where non‐linearities may occur. Transitional shell elements connect the two distinctively different types of elements to achieve displacement field continuities. The solution using the local‐global system with appropriate condensation and a predicted stress incremental procedure is suggested. It is shown that the technique is a very attractive alternative to the entirely general element style analysis for axisymetric shell structures with local deviations.