bluuebunny/crossref_metadata_2025 huggingface dataset:
A fast implementation of explicit time‐stepping algorithms with the finite element method for a class of nonlinear evolution problems
Authors: Segal A. , Praagman N.
Published: November 2005

In this paper a class of nonlinear evolution problems is considered. It is shown that, under special conditions, the application of the product approximation method for nonlinear problems in the finite element method results in constant (i.e. time‐independent) matrices. In those cases the amount of computing required to solve these equations with an explicit time‐stepping algorithm is decreased considerably compared to the standard Galerkin formulation in which the matrices are time‐dependent. The method is applied to two practical two‐dimensional problems: the shallow water equations and a nonlinear heat conduction problem.
Simply supported plates by the boundary integral equation method
Authors: París F. , de León S.
Published: November 2005

Plates governed by Kirchhoff's equation have been analysed by the boundary integral equation method using the fundamental solution of the biharmonic equation. In the case of supported plates, the boundary conditions permit the uncoupling of the field equation into two harmonic equations that originate, due to the nature of the fundamental solution, easier integration kernels and a simpler system of equations. The calculation of bending and twisting moments and transverse shear force can be formed, combining derivatives of the integral equation which defines the expression of the deflection on any point of the plate. The uncoupling of the biharmonic equation into two Poisson's equations involves the discretization of the domain of the studied problems. Nevertheless, the unknown quantity of the problem does not appear in the domain integrations for which a refined discretization is unnecessary. In the paper, however, a numerical alternative is considered to express the domain integral by means of boundary integrals. In this way, we need only discretize the boundary of the plate, making it necessary to solve a supplementary system of equations in order to calculate the coefficients of the approximation carried out.
Performance of GEM2 on the ELLPACK problem population
Authors: Delves L. M. , McKerrell A. , Peters S. A. , Phillips C.
Published: November 2005

The Pilot global element program GEM2 MK1.0 has been used to solve the two‐dimensional problems in the ELLPACK population of partial differential equation test problems. The performance achieved is summarized in this paper; special attention is paid to those problems which are singular or near singular, and for which comparisons have been published by Houstis and Rice.12
Direct cubic spline approximation to integrals with applications in nautical
Authors: Phythian J. E. , Williams R.
Published: November 2005

A cubic spline is fitted directly to the integral function

where f is continuous in [a, b]. This method is applied, with the derivative boundary condition, to determine ship stability from a curve of righting levers (a curve relating a ship's righting lever to the angle of heel). This direct‐fit method is extended to two‐dimensional integrals and applied to obtain the buoyancy curve and hence the underwater ship volume.
Infinite ring elements
Authors: Cheung Y. K. , Guo Dajiang , Tham L. G. , Cao Zhiyuan
Published: November 2005

Seven infinite ring elements have been proposed for the stress analysis around opening in an infinite medium. All elements employ trigonometrical series for interpolation in the θ‐direction and decaying function in the r‐direction. Numerical results indicate that all of them can converge for self‐equilibrating force systems, but only the element which was derived from the stress function can converge in the non‐self‐equilibrating external loads. The present study clearly indicates the close relationship between the semi‐analytical element and closed‐form solution.
Elastoplastic BIE analysis of cracked plates and related problems. Part 2: Numerical results
Authors: Cruse T. A. , Polch E. Z.
Published: November 2005

Part 1 of this paper reports on the formulation of an advanced boundary—integral equation model for fracture mechanics analysis of cracked plates, subject to elastoplastic behaviour or other, related body force problems. The basis of this formulation contrasts with other BIE elastoplastic formulations in the use of the Green's function for an infinite plane containing a stress free crack. This Green's function formulation assures that the total elastic strain field for the crack problem is accurately imbedded in the numerical model. The second part of this paper reports on the numerical implementation of this algorithm, as currently developed. The anelastic strain field (residual strains, thermal strains, plastic strains, etc.) is approximated as piecewise constant, while the boundary data is modelled with linear interpolations. An iteration solution scheme is adopted which eliminates the need for recalculation of the BIE matrices. The stability and accuracy of the algorithm are demonstrated for an uncracked, notch geometry, and comparison to finite element results is made for the centre‐cracked panel. The data shows that even the crude plastic strain model applied is capable of excellent resolution of crack tip plastic behaviour.
Automatic adaptive remeshing for finite element simulation of forming processes
Authors: Cheng Jung‐Ho
Published: November 2005

An automatic remeshing scheme has been developed to enable finite element simulation of even complicated forming processes. It has been demonstrated that for many practical applications the incorporation of this technique in the existing computer codes is indispensable not only for more accurate solutions but sometimes just for striving to obtain solutions. In order to avoid the tedious procedures of, e.g. interrupting the analysis, performing rediscretization, mapping of current state variables and preparing the new set of boundary conditions, methods for automating the remeshing procedures and the related accuracy problems have been presented. Several examples, such as a heading process, an extrusion process through a square die, and a one‐blow impression‐die forging process with flash have been successfully tested out with this automatic remeshing scheme.
Non‐linear heat conduction in composite bodies: A boundary element formulation
Authors: Azevedo J. P. S. , Wrobel L. C.
Published: November 2005

The present paper discusses the numerical solution of steady‐state non‐linear heat conduction problems in composite bodies by using the boundary element method. Two kinds of non‐linearities are considered: the temperature dependence of the thermal conductivity and boundary conditions of the radiative type. By introducing the integral of conductivity as a new variable the governing equation of the problem becomes linear in the transform space. Transformed boundary conditions of the Dirichlet and Neumann types are also linear but convective boundary conditions become non‐linear. Also, discontinuities arise in the value of the integral of conductivity across the interface between materials with different properties since continuity of temperature is imposed. The problem is numerically solved by discretizing the external and interface boundaries of the region under consideration with constant boundary elements and applying an iterative scheme of the Newton–Raphson type.
Vector potential formulations and finite element trial functions
Authors: Ratnajeevan S. , Hoole H. , Rios Rafael , Yoganathan S.
Published: November 2005

In field systems containing a divergenceless vector, the problem may be posed in terms of a vector potential for convenience. For the solution of the magnetic vector potential in three dimensional problems with current sources, there exist three standard variational formulations in the literature. While all these are known to give verifiable physical solutions, there is some question as to which is to be preferred. Indeed, one of them is invalid for infinite dimensional fields in that, without the finite element trial functions, it will not give unique solutions since it does not explicitly impose the divergence of the vector potential.

In this paper, we look at the formulations in the light of the restrictions imposed by the finite element trial functions for tetrahedral elements and arrive at the curious result that that formulation which is totally invalid when the vector potential is unrestricted by trial functions, is in fact valid in finite element analysis and, at the same time, is the best. We further show that this formulation yields naturally non‐divergent vector potential solutions, strictly as a result of the trial functions.
Partial eigensolution of damped structures by non‐linear optimization
Authors: Marcos Bernard , Béliveau Jean‐Guy
Published: November 2005

The partial solution of damped structures involves the determination of only a few of the resonant frequencies and corresponding damping characteristics and mode shapes. The procedure outlined here uses a modification of the variable metric solution algorithm, in which the dicision variables are elements of the complex eigenvector and the eigenvalue. The quadratic eigenvalue problem is reformulated as a sequential unconstrained minimization problem. Both normality and orthogonality constraints are incorporated in the objective function. The method is compared to an adaptation of the subspace iteration technique, also applicable to the quadratic eigenvalue problem.
Generalized viscoelastic model for creep analysis coupled with plastic deformation
Authors: Lee Sang Hoon
Published: November 2005

A creep analysis capability, using a generalized viscoelastic model, is introduced to process the creep behaviour coupled with elastoplastic deformation. The formulation is based on the step‐by‐step time integration of the Kelvin‐Maxwell rheological model with non‐constant parameters.

The concept of a rheological model is extended to the multiaxial stresses by the Prandtl‐Reuss stress‐strain relationship, from which the tangential stiffness matrix is formed for Newton's iteration. If the plastic deformation is coupled with creep, the algorithm will seek a solution in two distinct steps. Various choices of empirical creep laws are available and small variations in temperature are allowed as implemented in the general purpose finite element analysis program.
Eigenvalue reanalysis by improved perturbation
Authors: Inamura Toyoshiro
Published: November 2005

A new efficient method of eigenvalue reanalysis has been developed based on the perturbation method such that first the differential equations which describe the change of the eigenvalues and eigenvectors of a system being modified are derived from the perturbation method and then the solutions of these equations are obtained by following them up with the solutions of more simple equations. The special features of this method are that it can give a clear correspondence between the eigenpairs before and after system modification, and that the computer run time spent by this method is far shorter than that of revised analysis by FEM when only a few selected modes are used in the form of an approximate computation. In addition, this approximate computation can give more accurate results than the perturbation method. The efficiency of the proposed method has been verified by applying it to a simple spring‐mass model as well as a 600 degrees‐of‐freedom model which receive structural modification.
Optimization of actively controlled structures using goal programming techniques
Authors: Rao S. S. , Venkayya V. B. , Khot N. S.
Published: November 2005

The problem of design of actively controlled structures subject to restrictions on the damping parameters of the closed‐loop system is formulated and solved as a multiobjective optimization problem. The purpose of control is to effectively suppress structural vibrations due to initial excitation. The cross‐sectional areas of the members are treated as design variables. The structural weight and the controlled system energy are considered as objective functions for minimization. The goal programming approach is used for the solution of the multiobjective optimization problems. The procedure is illustrated through numerical simulations using two‐bar and twelve‐bar truss structures.
Convergence of curved shell elements based on assumed covariant strain interpolations
Authors: Jang Junho , Pinsky Peter M.
Published: November 2005

A C0 9‐node shell element based on assumed interpolations of covariant strain components defined with respect to the element natural co‐ordinate system has recently been proposed. In this formulation, the covariant strains are obtained directly from the Cartesian strains by tensor transformation without any need to compute laminar co‐ordinate based strains. In the present work, the interpolated covariant strains used in this element are analysed to determine their satisfaction of the basic requirements for successful strain interpolation. These basic requirements are stated as invariance to rigid body motions and ability to represent constant and linear strain states. In the finite element formulation, the weak form of momentum balance is expressed in terms of covariant strains and contravariant stresses. The corresponding elasticity tensor is a function of the components of the metric tensor associated with the element natural co‐ordinate system. The invariance properties of the metric tensor in the context of the finite element approximation are also discussed.
Advanced elastic and inelastic three‐dimensional analysis of gas turbine engine structures by BEM
Authors: Banerjee P. K. , Wilson R. B. , Miller N.
Published: November 2005

The boundary element method (BEM) has been known for some time to be extremely useful for the solution of elastic stress analysis problems involving high stress/strain gradients. In particular, the method has been extensively used for the study of both two and three‐dimensional fracture mechanics problems. Recent analytical and numerical developments coupled with the general availability of greatly increased computing capacity have made both elastic and inelastic three‐dimensional stress analysis feasible for complex geometries such as those found in gas turbine engine components.

This paper summarizes the features of an advanced stress analysis method based on BEM for elastic and inelastic analyses of multizone or substructured three‐dimensional solids. The elastic analyses involve isotropic or cross anisotropic media with thermal and centrifugal loading. The inelastic analyses include isotropic plasticity with variable hardening and kinematic plasticity with multiple yield surfaces.
Analysis of steady free convection from an axisymmetric heat‐generating body embedded in a semi‐infinite porous medium
Authors: Lakshminarayana L. , Gopalakrishnan A.
Published: November 2005

An analysis is presented for the steady state free convective flow and heat transfer from an axisymmetric heat‐generating body that is embedded in a fluid‐saturated, semi‐infinite, porous medium. The porous medium is assumed to be rigid, homogeneous and isotropic, and be in thermal equilibrium with the fluid. The fluid is assumed to be incompressible, with the density changes contributing only towards the buoyancy forces via the Boussinesq approximation. The governing equations for the fluid consist of the equation of continuity, Darcy's law and the equation of energy. After introducing the stream function concept, the equations governing the stream function and pressure are derived. Using the non‐dimensional variables, the non‐dimensional equations governing the non‐dimensional forms of the temperature, stream function and pressure are dervied and the appropriate boundary conditions are stated. The mathematical formulation contains two parameters; D, the non‐dimensional depth of the body from the surface of the porous medium, and a product Raθs of Rayleigh number (Ra) and the non‐dimensional surface temperature of the body (θs). The Galerkin finite element method, with linear, isoparametric, quadrilateral elements, is used to reduce the mathematical formulation into a set of algebraic equations. The expressions to calculate the non‐dimensional surface temperature and Nusselt number of the body, and the non‐dimensional velocity of the fluid, are derived. A computer code has been developed to solve the algebraic equations, using Gauss elimination procedure, in a banded matrix form. The computer code, in addition to the non‐dimensional temperature, stream function and pressure, calculates the isothermal lines, non‐dimensional surface temperature of the body, Nusselt number of the body, velocity field and isobars.

To demonstrate the application of the code, a spherical heat‐generating body is considered as an example. Numerical results are obtained for D = 3 and 6, and Raθs = 0.001, 0.1, 1 and 5, and presented.
A decomposition method for the integration of the elastic–plastic rate problem
Authors: Matthies Hermann G.
Published: November 2005

The numerical integration of the rate equation of an elastic–plastic material is considered. Special attention is focused on the discretization via the fully implicit backward Euler method in the small strain case with linear elasticity and the yield function a general quadratic in stress space. Here the calculation of the plastic (Lagrange) multiplier reduces to the computation of the smallest positive root of a polynomial in one variable. Explicit formulae are given for some special cases.
Modal solution of transient heat conduction utilizing Lanczos algorithm
Authors: Coutinho Alvaro L. G. A. , Landau Luiz , Wrobel Luiz C. , Ebecken Nelson F. F.
Published: November 2005

In this work, a modal solution method for transient heat conduction utilizing a co‐ordinate transformation matrix generated by the Lanczos algorithm is presented. The special characteristics of this co‐ordinate transformation are also discussed. The comparisons made in the NASA Insulation Test problem analysis shown that this approach is more cost‐effective than direct solutions, without loss of accuracy.
Geometrically non‐linear formulation for three dimensional curved beam elements with large rotations
Authors: Surana Karan S. , Sorem Robert M.
Published: November 2005

This paper presents a geometrically non‐linear formulation (GNL) for the three dimensional curved beam elements using the total Lagrangian approach. The element geometry is constructed using co‐ordinates of the nodes on the centroidal or reference axis and the orthogonal nodal vectors representing the principal bending directions. The element displacement field is described using three translations at the element nodes and three rotations about the local axes

The element displacement field has also been described in the literature using Euler parameters, Milenkovic parameters, or Rodriges parameters representing the effects of large rotations.

. The GNL three dimensional beam element formulations based on these element approximations are restricted to small nodal rotations between two successive load increments. The element formulation presented here removes such restrictions. This is accomplished by retaining non‐linear nodal terms in the definition of the element displacement field, and the consistent derivation of the element properties. The formulation presented here is very general and yet can be made specific by selecting proper non‐linear functions representing the effects of nodal rotations. The details of the element properties are presented and discussed. Numerical examples are also presented to demonstrate the behaviour and the accuracy of the elements. A comparison of the results obtained from the present formulation with those available in the literature using a linearized element approximation clearly demonstrate the superiority of the formulation in terms of large load steps, large rotations between two load steps and extremely good convergence characteristics during equilibrium iterations. The displacement approximation of these elements is fully compatible with the isoparametric curved shell elements (with large rotations), and since the elements possess offset capability, these elements can also serve as stiffeners for the curved shells.
A cubic triangular finite element for flat plates with shear
Authors: Yuan Fuh‐Gwo , Miller Robert E.
Published: November 2005

This paper presents the development of a straightforward displacement type triangular finite element for bending of a flat plate with the inclusion of transverse (or lateral) shear effects. The element has twenty two degrees of freedom consisting of ten for the lateral displacement of the midplane and six for rotations of the normal to the undeformed midplane of the plate. The latter are taken as independent of the slopes of the deformed midplane in order to include deformation due to transverse shear. The element is fully conforming and may be orthotropic. At interelement boundaries, the element matches adjacent elements both with respect to lateral displacement of the midplane and the rotations of the normal. The result is an efficient ‘linear moment’ triangular element but with transverse shear deformation included. Numerical computations for a number of examples are presented. The results show the element to be more flexible than most other finite element models and agree closely with those from a numerical solution of the three dimensional elasticity equations. The results also converge to those from thin plate theory when the thickness to length ratio becomes small or when the transverse shear moduli are artificially increased.
Benchmark computation and performance evaluation for a rhombic plate bending problem
Authors: Babuška Ivo , Scapolla Terenzio
Published: November 2005

The paper addresses the question of the accuracy and reliability of the computational analysis of the rhombic plate problem. The Kirchhoff model has a large error (measured in the energy norm) in comparison with the three dimensional solution with a soft simple support; also for very thin plates (t = 1/100a) and all angles (up to α = 90°). The Reissner–Mindlin model gives results 3–5 times better and is less sensitive to the change of the plate angle. The Kirchhoff model is a relatively good approximation of three dimensional setting for a hard simple support. The paradoxical (polygon) behaviour of the simply supported Kirchhoff plate extends to the Reissner–Mindlin model with a hard support. The finite element solution of the Kirchhoff model is addressed in detail. It is shown that higher degree methods are clearly preferable and that the skewness of the elements does not influence essentially the accuracy of the method; the singularity of the solution, which strongly depends on the skewness of the plate, is the primary cause of the deterioration of the performance of the FEM.
A moving boundary circulation model for regions with large tidal flats
Authors: Gopalakrishnan T. C.
Published: November 2005

A numerical model is developed for computing two‐dimensional circulation in coastal regions dominated by large tidal flat motion. This model is based on the shallow water momentum and continuity equations being operated upon by the Galerkin finite element method. The particular advantage of the model lies in its ability to accommodate a changing domain boundary. This is accomplished by adopting finite elements that change shape so as to consistently move with the water's edge. Application of the model to the Kuwait Bay is described, and the associated results on circulation are given.
An accelerated iterative method for contact analysis
Authors: Lee Kisu
Published: November 2005

An iterative solution procedure for a frictionless contact problem is presented. Convergence to the exact solution is guaranteed by an error reduction method, and the rate of convergence is drastically improved by reduction of the ratio of extreme eigenvalues of the iteration matrix. For an ordinary linear equation, the present technique has the same theoretical value of convergence rate as the Chebyshev acceleration technique. The present acceleration technique can be directly extended for complicated frictional contact problems.
A boundary element method analysis of electrostatics in a tank during filling operations
Authors: Sidi‐Yekhlef A. , Sunderland J. E.
Published: November 2005

Electrostatic charging inside a tank is analysed numerically using the boundary integral method. The electrostatic charge is transmitted to the tank through a charged liquid. Profiles for the charge density and potential are obtained in the tank during the filling operation. The analysis is based on the equation governing the transport of charge and Poisson's equation. The results are characterized by two dimensionless parameters, the dimensionless Debye length given by the Debye length divided by the height of the tank, and the number Pe defined as a Peclet number. The results show where the maximum charge density and potential occur and give a prediction of when during the filling operation a hazardous situation may occur.
Implementation of curvilinear geometry into p‐version HT plate elements
Authors: Jirousek J. , Venkatesh A.
Published: November 2005

The formulation of the recently presented hybrid‐Trefftz (HT) p‐version elements1 has thus far been restricted to straight‐sided polygonal elements. The present paper removes this limitation. Two alternative formulations are studied. In the first one any curvilinear geometry is represented accurately but the rigid body modes are recovered only in the limit as the p‐refinement level is increased. In contrast, the second formulation represents the rigid modes exactly while the actual curvilinear geometry is approached with increasing accuracy as the p‐refinement level is increased. The practical efficiency of the two alternative approaches is studied and assessed on pertinent examples of thin plates in bending.
A consistent characteristic length for smeared cracking models
Authors: Oliver J.
Published: November 2005

A numerical scheme for crack modelling by means of continuous displacement fields is presented. In two‐dimensional problems a crack is modelled as a limiting case of two singular lines (with continuous displacements, but discontinuous displacement gradients across them) which tend to coincide with each other. An analysis of the energy dissipated inside the band bounded by both lines allows one to obtain an expression for the characteristic length as the ratio between the energy dissipated per unit surface area (fracture energy) and the energy dissipated per unit volume (specific energy) at a point. The application of these mathematical expressions to the finite element discretized medium allow one to obtain a general spatial and directional expression for the characteristic length which guarantees the objectivity of the results with respect to the size of the finite element mesh. The numerical results presented show the reliability of the proposed expressions.
Superconvergent derivatives: A Taylor series analysis
Authors: Mackinnon R. J. , Carey G. F.
Published: November 2005

An analysis, based on the use of Taylor series expansions, is developed to determine accuracy estimates for derivatives in one and two dimensions computed by differentiation of a finite‐element interpolant or approximation. The analysis clarifies some issues concerning special points at which the derivatives are believed to be exceptionally accurate with higher convergence rates (superconvergence). Moreover, it leads directly to a class of post‐processing strategies for the derivatives and offers a more direct constructive approach to the subject.
A subspace iteration method for the eigensolution of large undamped gyroscopic systems
Authors: Rodrigues José F. D. , Gmuer Thomas E. C.
Published: November 2005

This paper presents an efficient and numerically stable algorithm for computing accurately the eigenvalues of smallest moduli and the associated eigenvectors of the quadratic eigenproblem which arises in the analysis of spinning systems. Derived from the well‐known standard subspace iteration method, this solution procedure takes full advantage of the banded configuration of the structural matrices, and of the specific nature of gyroscopic systems. A numerical example is presented to show the efficiency and accuracy of the algorithm.
A unified approach to solving ill‐conditioned matrix problems
Authors: Rothwell E. , Drachman B.
Published: November 2005

A unified approach to solving ill‐conditioned matrix problems is presented, concentrating on those problems arising in engineering where measurement inaccuracy is the major source of error. By applying the singular value decomposition, it is shown that regularization with a parameter can be used without squaring the condition number of the matrix. Numerical examples demonstrate that a smaller relative error is attainable using the unified approach over the more standard technique of discarding singular values. Lastly, a simple method is presented for locating the optimal solution using a computed residual.
A Schwarz alternating procedure using spline collocation methods
Authors: Yanik Elizabeth Greenwell
Published: November 2005

A collocation method is described which obtains an approximate solution to Poisson's equation, δu = f, on an L shaped region. The L shaped region is viewed as the union of two overlapping rectangles. The Schwarz alternating procedure may be employed to reduce the problem to one in which collocation techniques are used on each rectangle. The convergence of the alternating scheme depends upon a discrete maximum principle for collocation methods. Several sample problems are presented to illustrate the order of convergence of this method and to compare it with several existing numerical methods for the L shaped region.
Time‐domain boundary element analysis of elastic wave interaction with a crack
Authors: Hirose S. , Achenbach J. D.
Published: November 2005

The mathematical formulation of the problem of transient wave interaction with a crack in a homogeneous, isotropic, linearly elastic solid has been reduced to the solution of an integral equation over the insonified crack face. The integral equation relates the unknown crack‐opening displacement, which depends on time and position, to the incident wave field. The integral equation has been solved numerically by a time‐stepping method in conjunction with a boundary element discretization of the crack surface. For normal incidence of a longitudinal step‐stress wave on a penny‐shaped crack, results as functions of time have been obtained for the crack‐opening displacement, the elastodynamic Mode‐I stress intensity factor and the scattered far‐field.
Weighted residual solutions in the time domain
Authors: Segerlind Larry J.
Published: November 2005

The Galerkin and subdomain forms of the weighted residual method are used to generate recursive equations in time for the numerical solution of a system of ordinary differential equations. The single‐step methods that result from a linear interpolation equation match currently available methods whose stability and oscillation properties are known. A three‐level scheme developed by combining two linear elements is shown to be unconditionally unstable. Two of the three schemes obtained using a quadratic interpolation equation and quadratic weighting functions are also shown to be unconditionally unstable. The third scheme is unconditionally stable, but the calculated values for a numerical solution of u̇ + u = 0, u(0) = 1 are not as accurate as the values obtained using the single‐step central difference method.
A use of linear programming for the analysis of plane strain rigid‐plastic flow
Authors: Pavier M. J.
Published: November 2005

This paper describes an application of linear programming for the analysis of plane strain rigid‐plastic flow. First, linear programming and the theory of a rigid‐plastic material are briefly revised. The implementation of linear programming for rigid‐plastic flow is then described. The method is to subdivide the material into rigid triangular blocks which may slide upon each other, dissipating energy at a rate proportional to the rate of sliding. Many different modes of deformation are possible; linear programming is used to select the mode that gives the least rate of total energy dissipation. The indentation of a strip by blunt‐nosed indenters is used as an example. Results of the linear programming method are compared with the exact slip line field solutions.
Transient finite element computations on 65536 processors: The connection machine
Authors: Farhat C. , Sobh N. , Park K. C.
Published: November 2005

This paper reports on our experience in solving large‐scale finite element transient problems on the Connection Machine. We begin with an overview of this massively parallel processor and emphasize the features which are most relevant to finite element computations. These include virtual processors, parallel disk I/O and parallel scientific visualization capabilities. We introduce a distributed data structure and discuss a strategy for mapping thousands of processors onto a discretized structure. The combination of the parallel data structure with the virtual processor mapping algorithm is shown to play a pivotal role in efficiently achieving massively parallel explicit computations on irregular and hybrid two‐ and three‐dimensional finite element meshes. The finite element kernels written in C*/Paris have run with success to solve several examples of linear and non‐linear dynamic simulations of large problem sizes. From these example runs, we have been able to assess in detail their performance on the Connection Machine. We show that mesh irregularities induce an MIMD (Multiple Instruction Multiple Data) style of programming which impacts negatively the performance of this SIMD (Single Instruction Multiple Data) machine. Finally, we address some important theoretical and implementational issues that will materially advance the application ranges of finite element computations on this highly parallel processor.
Dynamics of general flexible multibody systems
Authors: Han Ray P. S. , Zhao Zhi Cheng
Published: November 2005

A general treatment is presented for modelling the dynamics of a flexible multibody system, using a lumped mass finite element approach. The system topology considered here is defined as an arbitrary combination of both rigid and flexible bodies, connected together by joints that permit translation and compliance, in a general tree configuration. An extension to handle closed loop kinematic chains is also indicated. Kane's theory of generalized speeds, which is based on the Lagrange‐D'Alembert principle, is used to derive the equations of motion, and this results in a very efficient computer oriented methodology for solving the dynamics of such large mechanical systems. To facilitate numerical computations, these dynamical equations are transformed into a system of first‐order differential equations for an explicit formulation of the problem. The accuracy of the proposed formulation is assessed via three examples with known solutions. The results obtained indicate the method is accurate, efficient and versatile for the analysis of a general, flexible multibody system.
Power series expansions of dynamic stiffness matrices for tapered bars and shafts
Authors: Spyrakos Constantine C. , Chen Ching I
Published: November 2005

Stiffness and consistent mass matrices for tapered bars and shafts are derived with the aid of static displacement functions. Moreover, the corresponding dynamic stiffness matrices are developed in the Laplace transform domain from the exact solutions of axial/torsional governing equations. Power series expansions of the Bessel functions comprising the dynamic stiffness influence coefficients show that the stiffness and consistent mass matrices can be mathematically derived from the dynamic stiffness matrices. A discussion on the convergence of the power series expansions is also presented. The developments provide further insight into the approximations present in conventional consistent mass formulations of frameworks with tapered members.
A poisson equation formulation for pressure calculations in penalty finite element models for viscous incompressible flows
Authors: Sohn J. L. , Heinrich J. C.
Published: November 2005

The calculation of pressures when the penalty function approximation is used in finite element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from the C0 velocity approximation using a least squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.
A robust quadrilateral membrane finite element with drilling degrees of freedom
Authors: Ibrahimbegovic Adnan , Taylor Robert L. , Wilson Edward L.
Published: November 2005

A quadrilateral membrane finite element with drilling degrees of freedom is derived from variational principles employing an independent rotation field. Both displacement based and mixed approaches are investigated. The element exhibits excellent accuracy characteristics. When combined with a plate bending element, the element provides an efficient tool for linear analysis of shells.
An implementation of the hp‐version of the finite element method for Reissner‐Mindlin plate problems
Authors: Holzer Stefan , Rank Ernst , Werner Heinrich
Published: November 2005

Reissner‐Mindlin plate theory is still a topic of research in finite element analysis. One reason for the continuous development of new plate elements is that it is still difficult to construct elements which are accurate and stable against the well‐known shear locking effect. In this paper we suggest an approach which allows high order polynomial degrees of the shape functions for deflection and rotations. A balanced adaptive mesh‐refinement and increase of the polynomial degree in an hp‐version finite element program is presented and it is shown in numerical examples that the results are highly accurate and that high order elements show virtually no shear locking even for very small plate thickness.
F.E.M. in steady MHD duct flow problems
Authors: Scandiuzzi R. , Schrefler B. A.
Published: November 2005

The governing equations and the boundary conditions of steady incompressible magnetohydrodynamic (MHD) problems are adapted to the case of steady MHD flow in simply connected cross sections with arbitrary wall conductance. The problem is then solved numerically by means of the finite element method based on the weighted residual approach, and solutions for industrially relevant Hartmann numbers and non‐symmetric kinetic fields are presented.
Quasi‐Newton iterative strategies applied to the heat diffusion equation
Authors: Soria Antonio , Pegon Pierre
Published: November 2005

Several iterative procedures have been used to solve the non‐linear heat diffusion equation taking into account radiation across internal cavities. Quasi‐Newton methods are compared with Picard iteration and Newton‐Raphson methods. Among them, the rank‐one quasi‐Newton update seems to be the most effective, specially in time‐dependent cases.
Beyond first‐order upwinding: The ultra‐sharp alternative for non‐oscillatory steady‐state simulation of convection
Authors: Leonard B. P. , Mokhtari Simin
Published: November 2005

Although it is now well known that first‐order convection schemes suffer from serious inaccuracies attributable to artificial viscosity or numerical diffusion under high‐convection conditions, these methods continue to enjoy widespread popularity for numerical heat‐transfer calculations, apparently owing to a perceived lack of viable high‐accuracy alternatives. But alternatives are available. For example, non‐oscillatory methods used in gasdynamics, including currently popular ‘TVD’ schemes, can be easily adapted to multidimensional incompressible flow and convective transport. This, in itself, would be a major advance for numerical convective heat transfer, for example. But, as this paper shows, second‐order TVD schemes form only a small, overly restrictive, subclass of a much more universal, and extremely simple, non‐oscillatory flux‐limiting strategy which can be applied to convection schemes of arbitrarily high‐order accuracy, while requiring only a simple tridiagonal ADI line‐solver, as used in the majority of general‐purpose iterative codes for incompressible flow and numerical heat transfer. The new universal limiter and associated solution procedures form the so‐called ULTRA‐SHARP alternative for high‐resolution non‐oscillatory multidimensional steady‐state high‐speed convective modelling.
A layered composite shell element for elastic and thermoelastic stress and stability analysis at large deformations
Authors: Dorninger Konrad , Rammerstorfer Franz G.
Published: November 2005

A finite shell element for layered fibre reinforced composite shells has been developed. The degeneration principle is used in combination with specific kinematic assumptions. The thermo‐elastic material is either described by the behaviour of the local components, i.e. fibre and matrix material laws and geometrical configuration in each layer, or by the overall orthotropic layer material laws.

Thickness integration for obtaining the different contributions to the shell element's stiffness matrix is performed analytically and prior to the numerical in‐plane integration. This leads to a considerable saving in computer time during the incremental‐iterative analysis.

Geometrical non‐linearities in terms of large deformations and material non‐linearities in terms of layer craccking are taken into account. Accompanying eigenvalue analyses allow the determination of the—sometimes rather complicated—buckling behaviour with non‐linear prebuckling deformations.
A triangular element based on Reissner‐Mindlin plate theory
Authors: Papadopoulos Panayiotis , Taylor Robert L.
Published: November 2005

A new triangular plate bending element based on the Reissner‐Mindlin theory is developed through a mixed formulation emanating from the Hu‐Washizu variational principle. A main feature of the formulation is the use of a linear transverse shear interpolation scheme with discrete constraint conditions on the edges. The element is shown to avoid shear locking, converge to the Kirchhoff plate theory as the plate thickness approaches zero, and generally exhibit excellent behaviour on a series of standard problems and tests.
A hyperelastic‐based large strain elasto‐plastic constitutive formulation with combined isotropic‐kinematic hardening using the logarithmic stress and strain measures
Authors: Eterovic Adrian Luis , Bathe Klaus‐Jürgen
Published: November 2005

This paper addresses the formulation of a set of constitutive equations for finite deformation metal plasticity. The combined isotropic‐kinematic hardening model of the infinitesimal theory of plasticity is extended to the large strain range on the basis of three main assumptions: (i) the formulation is hyperelastic based, (ii) the stress‐strain law preserves the elastic constants of the infinitesimal theory but is written in terms of the Hencky strain tensor and its elastic work conjugate stress tensor, and (iii) the multiplicative decomposition of the deformation gradient is adopted. Since no stress rates are present, the formulation is, of course, numerically objective in the time integration. It is shown that the model gives adequate physical behaviour, and comparison is made with an equivalent constitutive model based on the additive decomposition of the strain tensor.
Three‐dimensional non‐linear fluid‐structure interaction problems: Formulation by the finite and infinite element method
Authors: Feng Y. Q. , Quevat J. P.
Published: November 2005

Using the perturbation method, the non‐linear exterior fluid‐structure interaction problem is separated into first‐ and second‐order problems. With the finite element method for the structure and the finite‐infinite element method for the fluid, we obtain a first‐order coupled matrix system and a second‐order coupled matrix system. By determining the frequencies of resonance of the structure, comparison of numerical results for a vertical cylinder and a horizontal floating cylinder shows the validity of the presented method for the resolution of three‐dimensional exterior hydroelastic problems.
Effect of the coupling between stretching and bending in the large displacement analysis of plates
Authors: Chang B. , Chen D. C. , Shabana A. A.
Published: November 2005

The effect of the rotary inertia on the non‐linear dynamics of plates that undergo a large reference displacement is examined in this paper. An assumed displacement field that accounts for the coupling between the stretching and bending of the plate as the result of considering the effect of the rotary inertia is used to identify the configuration of the plate. Furthermore, the coupling between the stretching and bending of the plate as the result of finite rotation is also considered in this investigation. Based on the assumed displacement field that accounts for the effect of the rotary inertia, a non‐linear finite element formulation is developed for the large displacement analysis of plates. The element equations of motion are expressed in terms of a set of element invariants that depend on the assumed displacement field as well as the rotary inertia. The use of the formulation presented in this paper is demonstrated using numerical examples.
Three‐dimensional finite element contact algorithm for metal forming
Authors: Marques Manuel J. M. Barata , Martins Paulo A. F.
Published: November 2005

This work presents a three‐dimensional rigid plastic finite element formulation. The workpiece is discretized with eight node hexahedral isoparametric elements. Friction is included in the formulation by means of a shear stress depending on the relative velocity between the workpiece and the tool. Special attention is given to the contact problems, and a three‐dimensional contact algorithm based on a discretization of the tool surface with triangular elements is presented.

Finally, some selected examples are solved, in order to show the capabilities of the formulation.
Bulge predictions in steady state bar rolling processes
Authors: Lee Yong‐Shin , Dawson Paul R. , Dewhurst Timothy B.
Published: November 2005

A new algorithm for free surface corrections in Eulerian finite element computations is presented and applied to a steady state bar rolling process to predict lateral spread. A variety of rolling geometries are examined, including differing height to width ratios and reductions. The bulge profiles, as well as the maximum and mean bulge amounts, are compared in detail with experiments.
An adaptive procedure for stabilizing convergence quality in frequency‐constrained design optimization of bar structures supporting non‐structural mass
Authors: Phan Khing F. , McGee Oliver G.
Published: November 2005

This paper presents an improved optimality criteria (OC) method for minimum‐weight design of bar structures supporting non‐structural mass and subjected to multiple natural frequency constraints and minimum gauge restrictions. The convergence quality of the OC method hinges on both the number of active constraints retained and the choice of a proper step size. This being the case, a criterion, which uses previous scaled designs to ‘adaptively’ tune the step size, is established with the purpose of dissolving the (sometimes violent) oscillations of scaled design weights in the iteration history. As the step size is tuned, the convergence rate is descreased. Hence, a modified Aitken's accelerator, which extrapolates from previous scaled designs to obtain an improved one, is used. Its effect is to both increase the overall rate and reduce the net cost of convergence by reducing the number of repeat finite element analyses. The method presented here is used to qualitatively survey the convergence of several OC recursive schemes compositely used to resize and to evaluate the Lagrange multipliers. Design examples are presented to demonstrat the method. The method is adaptable, as it eliminates the need for adjustments of internal parameters during the redesign stage.