bluuebunny/crossref_metadata_2025 huggingface dataset:
Analysis of parameter estimation heat conduction problems with phase change using the finite element method
Authors: Ouyang Tianhong
Published: August 2005

A solution to a parameter estimation problem in heat conduction with phase change is presented. Specifically, the thermophysical properties of the material are estimated by using the temperature measurements of several sensors located inside the fixed domain.

In the parameter estimation problem the error is minimized between given and modelled temperatures at sensor locations over the time interval where the experiment involved variation of the material parameters. The methods are illustrated with several examples. The effects on the solution of the locations of the sensors, the number of the sensors, the time step and the number of time steps are examined.
Stress oscillations and spurious load mechanisms in variationally inconsistent assumed strain formulations
Authors: Prathap G. , Naganarayana B. P.
Published: August 2005

Assumed field‐consistent strain formulations of the displacement finite element procedure can lead to poor convergence and spurious stress oscillations if the assumed strain fields are not variationally correct, i.e. they do not satisfy an important orthogonality condition emerging from the equivalence sought between assumed strain displacement procedures and mixed procedures based on the Hellinger–Reissner theorem. Failure to ensure variational correctness introduces errors which can be equated to the presence of spurious loading mechanisms that cause stress oscillations. In this paper, we use the Timoshenko beam element to demonstrate that field‐consistency and variational' consistency are two complementary but mutually exclusive principles—one does not imply the other and that both are necessary to successfully implement a displacement type finite element for constrained media.
A Laplace‐transform‐based three‐dimensional BEM for poroelasticity
Authors: Badmus T. , Cheng A. H‐D. , Grilli S.
Published: August 2005

This paper presents the formulation and the numerical implementation of a three‐dimensional direct boundary element method for the Biot theory of poroelasticity. To avoid the need of time‐stepping and volume integration, the solution is performed in the Laplace transform space. Solution in time is obtained via numerical inversion. Several examples, including the settlement of a rectangular footing and a modified Mandel problem, are examined.
Triangular C0 bending elements based on the Hu‐Washizu principle and orthogonality conditions
Authors: Karakostas C. , Talaslidis D. , Wempner G.
Published: August 2005

This paper deals with simple and effective C0 linear triangular bending elements based on the Hu‐Washizu variational principle. The following key features are inherent in the proposed formulation: extensional, flexural and transverse shear strains and the corresponding stresses are referred to the directions of the triangle sides. The independent variation of displacements, strains and stresses yields discrete approximations consistent with the continuum theory. Furthermore, a proper identification of the deformational modes and the orthogonality requirements between the assumed transverse shear forces and the undesirable strain fields lead to element formulations with important attributes: minimization of superfluous energy, properly justified assumptions, simplicity of formulation and straightforward extension to non‐linear problems. Alternative approximations of strains and stresses, also presented, enhance the element performance in the case of both thick and thin plates and shells. Test examples demonstrate the characteristic properties of the proposed element formulations.
On improved predictions for structural equilibrium path evaluations
Authors: Eriksson Anders
Published: August 2005

The paper describes how several procedures for higher‐order predictions have been introduced in order to improve the convergence speed in a general finite element program for non‐linear structural analysis. In addition to higher‐order Taylor expansions earlier discussed, Lagrangian extrapolations and some methods commonly used for the integration of initial value problems have been introduced. The methods are used for improved predictions in the stepwise solution of equilibrium states and for accurate descriptions of the initial post‐bifurcation behaviour. They are used in a general solution algorithm, based on a parameter formulation. The methods are discussed in the light of the strategies for re‐creation of the tangential stiffness matrix, used for equilibrium iterations.

Numerical examples, exhibiting different limit and bifurcation behaviours for trusses, frames and shells, are used to evaluate the numerical properties and efficiencies of the methods.

The paper concludes that the overall efficiency in the algorithm can be improved by introduction of more accurate predictions than the standard Euler prediction. In terms of reliability combined with efficiency, an implicit generalized Simpson method is the preferred method.
Generalized midpoint finite element dynamic analysis of elastoplastic systems
Authors: Corigliano A. , Perego U.
Published: August 2005

The application of a four‐parameter generalized midpoint integration method to small‐displacement elastoplastic dynamic problems is considered. The integration of the governing relations over a time step is formulated as a non‐linear algebraic problem (finite‐step problem) by making use of generalized variables finite element modelling. Uniqueness and an extremum characterization of the solution of the finite‐step problem are discussed. Sufficient conditions for convergence of various iterative algorithms, including Newton‐Raphson, are given. The B‐stability of the proposed procedure is assessed.
Numerical methods for second‐order shape sensitivity analysis with applications to heat conduction problems
Authors: Hou Gene J. ‐W. , Sheen Jeenson
Published: August 2005

In this paper, two finite‐element‐based schemes for second‐order shape sensitivity analysis are presented. In the first formulation, the AV‐DD method, the first‐order shape sensitivity equation is derived and expressed in terms of state and adjoint variables. The resultant equation is then directly differentiated to obtain the second‐order shape sensitivity equation. In the second formulation, the DD‐AV method, the functional of concern is differentiated twice to yield the second‐order sensitivity equation in which the second‐order shape derivatives can be eliminated by introducing a proper adjoint equation. A thermal fin problem and a thermal insulation layer problem have been studied to validate the proposed schemes. It is shown that both methods yield identical results, though the DD‐AV method is computationally more efficient.
Computation of heat conduction in materials with random variable thermophysical properties
Authors: Nicolaï Bart M. , De Baerdemaeker Josse
Published: August 2005

A method for the direct computation of mean values and variances of the temperature in conduction‐heated objects with random variable thermophysical properties is presented. This method is based on a Taylor expansion of the finite element formulation of the heat conduction equation and offers a powerful alternative to the computationally expensive Monte Carlo method. Both steady‐state and transient problems are considered. Some example problems are solved and the results discussed. The simulations indicate that the variability of the thermophysical properties may cause a considerable variability of the temperature within the heated object. This may have important consequences on the design of heating operations in food process engineering.
Moving‐grid finite element modelling of thermal ablation and consolidation in porous media
Authors: Mackinnon R. J. , Carey G. F.
Published: August 2005

A moving‐grid finite element model for the analysis of thermal ablation, fluid flow and deformation in elastic porous media is presented. The model is formulated in terms of temperatures, fluid pressures and solid displacements, and takes into account a moving phase boundary. Supporting algorithms for treating the moving phase boundary and solving the coupled equations are described. The model has application to several important moving‐boundary geotechnical problems. Numerical test cases are provided for model verification and example applications corresponding to thermal ablation, consolidation and underground coal gasification are given.
Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics
Authors: Farhat Charbel , Lesoinne Michel
Published: August 2005

Most of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost‐effective algorithms for the automatic partitioning of arbitrary two‐ and three‐dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.
Trefftz method for Kirchhoff plate bending problems
Authors: Jin W. G. , Cheung Y. K. , Zienkiewicz O. C.
Published: August 2005

Kirchhoff plate bending problems were studied by both the Trefftz direct and indirect approximations in which non‐singular, complete Trefftz functions are used as the weighting and/or trial functions. The Trefftz direct method involved only the quantities of engineering interest. Numerical results are given to show the efficiency and the excellent accuracy of the present method.
A new 3‐D finite element model to evaluate added mass for analysis of fluid‐structure interaction problems
Authors: Rajasankar J. , Iyer Nagesh R. , Rao T. V. S. R. Appa
Published: August 2005

The paper presents the results of investigations conducted to evaluate the added mass to represent fluid‐structure interaction effects in vibration/dynamic analysis of floating bodies such as ship hulls. While the structural plating is idealized by 9‐noded plate/shell finite elements, the fluid domain is modelled by 20‐noded/21‐noded 3‐D finite elements in the investigations conducted. A new 8‐noded element has been developed to model the interface between the structure and the fluid. An efficient computational methodology has been used for computation of added mass. The finite element models are validated by comparing the results with those given by analytical solution for a submerged sphere. The efficacy of the finite element model is demonstrated through convergence of the results obtained for a floating barge problem. A better convergence rate and distribution of added mass in three orthogonal directions have been obtained.
General behaviour of collapsed 8‐node 2‐D and 20‐node 3‐D isoparametric elements
Authors: Dhondt Guido
Published: August 2005

This paper presents a simple and thorough technique to examine the general behaviour of two‐dimensional (2‐D) 8‐node and 3‐D 20‐node isoparametric elements, collapsed at one side. With this method the conditions for the well‐known quarter‐point and half‐point elements, frequently used in fracture mechanics applications to model the crack tip behaviour, are arrived at in a natural way. It also allows for an in‐depth analysis of the Jacobian determinant, and can easily be applied to other types of elements.
Three‐dimensional solid‐to‐beam transition elements for structural dynamics analysis
Authors: Gmür Thomas C. , Kauten Randy H.
Published: August 2005

Complex structural components such as those encountered in many industrial applications may generally be considered as being composed of shell‐ or beam‐like portions linked to three‐dimensional solid continua. When discretized into finite elements, these structures present geometrical and mathematical difficulties at the connections between the different element types since the nodal degrees of freedom allocated to the solid, shell and beam elements are incompatible with each other. The development of specific and reliable transition finite elements is, thus, of outstanding practical importance. This paper presents efficient C0 compatible transition elements with a variable number of nodes for modelling solid to beam junctions. Based upon the standard isoparametric solid and beam formulations, the current approach includes the properties of both solids and beams, verifies the basic continuity, smoothness and completeness criteria inherent in the finite element convergence requirements, and avoids the shear locking phenomenon typical of C0 elements by using a strain‐projection method. Several numerical examples which compare this formulation to analytical and experimental solutions are provided in order to show the applicability and efficiency of this approach.
Regularization of hypersingular and nearly singular integrals in the potential theory and elasticity
Authors: Sladek V. , Sladek J. , Tanaka M.
Published: August 2005

Both the hypersingular and nearly singular integrals, which appear in the hypersingular boundary integralequations and integral representations of the secondary fields, respectively, are regularized by the application of the superposition principle. Two kinds of the non‐singular formulations, namely, those with the strongly singular and weakly singular kernels, are presented in this paper. The formulations are given in terms of the relevant boundary quantities and the collocation at element junctions is possible. Two‐ and three‐dimensional problems are analysed simultaneously in a unique way for either internal or external problems of the potential theory and elasticity.
Generation of unstructured tetrahedral meshes by advancing front technique
Authors: Jin H. , Tanner R. I.
Published: August 2005

An algorithm for generating unstructured tetrahedral meshes by the advancing front technique is presented. Emphasis is placed on the construction of tetrahedral elements. Several measures are employed to prevent difficult situations. A control line/surface scheme is used to specify element size. Numerical examples are provided to show the performance of the algorithm.
Thin shells with finite rotations formulated in biot stresses: Theory and finite element formulation
Authors: Wriggers P. , Gruttmann F.
Published: August 2005

A bending theory for thin shells undergoing finite rotations is presented, and its associated finite element model is described. The kinematic assumption is based on a shear elastic Reissner‐Mindlin theory. The starting point for the derivation of the strain measures are the resultant equilibrium equations and the associated principle of virtual work. Within this formulation the polar decomposition of the shell material deformation gradient leads to symmetric strain measures. The associated work‐conjugate stress resultants and stress couples are integrals of the Biot stress tensor. This tensor is invariant with respect to rigid body motions and, therefore, appropriate for the formulation of constitutive equations. Finite rotations are introduced via Eulerian angles. The finite element discretization of arbitrary shells is based on the isoparametric concept formulated with respect to a plane reference configuration. The numerical model is applied to different non‐linear plate and shell problems and compared with existing formulations. Due to a consistent linearization, the step size of a load increment is only limited by the local convergence behaviour of Newton's method.
Symmetric Galerkin boundary formulations employing curved elements
Authors: Kane J. H. , Balakrishna C.
Published: August 2005

Accounts of the symmetric Galerkin approach to boundary element analysis (BEA) have recently been published. This paper attempts to add to the understanding of this method by addressing a series of fundamental issues associated with its potential computational efficiency. A new symmetric Galerkin theoretical formulation for both the (harmonic) heat conduction and the (biharmonic) elasticity problem that employs regularized singular and hypersingular boundary integral equations (BIEs) is presented. The novel use of regularized BIEs in the Galerkin context is shown to allow straightforward incorporation of curved, isoparametric elements. A symmetric reusable intrinsic sample point (RISP) numerical integration algorithm is shown to produce a Galerkin (i.e. double) integration strategy that is competitive with its counterpart (i.e. singular) integration procedure in the collocation BEA approach when the time saved in the symmetric equation solution phase is also taken into account. This new formulation is shown to be capable of employing hypersingular BIEs while obviating the requirement of C1 continuity, a fact that allows the employment of the popular continuous element technology. The behaviour of the symmetric Galerkin BEA method with regard to both direct and iterative equation solution operations is also addressed. A series of example problems are presented to quantify the performance of this symmetric approach, relative to the more conventional unsymmetric BEA, in terms of both accuracy and efficiency. It is concluded that appropriate implementations of the symmetric Galerkin approach to BEA indeed have the potential to be competitive with, if not superior to, collocation‐based BEA, for large‐scale problems.
Performance of the h–p version of the finite element method with various elements
Authors: Babuška I. , Elman H. C.
Published: August 2005

The paper addresses the performance of square elements of type Q(p) and Q′(p). (Q(p) and Q′(p) are elements of degree p, analogous to the well‐known 9‐ and 8‐noded elements for p = 2.) The performance is analysed theoretically for the class of analytic functions. Numerical experiments confirm the conclusions drawn from the theory. The computational complexity of a solution algorithm is studied using timings of the computation on an Alliant FX/8 computer. The data show that high‐order elements are very effective for the considered class of solutions.
A new boundary element approach for contact problems with friction
Authors: Olukoko O. A. , Becker A. A. , Fenner R. T.
Published: August 2005

A new boundary element solution algorithm for two‐dimensional and axisymmetric contact problems with friction, based on an independent discretization of the contacting surfaces and under static and proportional loading conditions, is presented. The solution procedure uses the element shape functions to distribute the geometry, tractions and displacements on each contact element. The contact constraints are then applied between each contacting node and the opposite contact segment. The overall boundary element matrix equations for the contacting bodies are coupled using the contact conditions at the interface without introducing any additional variables into the solution matrix. The algorithm is applied to several two‐dimensional and axisymmetric frictional contact examples and the results obtained are in very good agreement with finite element and analytical solutions.
Calculation of the move limits for the sequential linear programming method
Authors: Chen Ting‐Yu
Published: August 2005

The sequential linear programming (SLP) method is one of the easiest optimization techniques used to treat non‐linear optimization problems. The successful application of the method is based on the proper choice of the move limits, which are unfortunately uncertain in the SLP algorithm. To enhance the efficiency and reliability of the SLP algorithm, six methods are proposed to calculate the move limits. The first three methods use the constraint equations to compute the minimum variations needed from the current design point to reach the constraint boundaries. The fourth method incorporates the cost function information as well as the constraints to figure out the move limits. The last two methods form a quadratic programming (QP) subproblem and solve for the change of the quadratic cost function. The move limits used in SLP are then computed from the estimated change of the linear cost function from the QP solution. Four numerical examples are employed to demonstrate the solution process by the methods proposed. The advantages and disadvantages of these methods are discussed.
A non‐recursive Lagrangian solution of the non‐causal inverse dynamics of flexible multibody systems: The planar case
Authors: Ledesma Ragnar , Bayo Eduardo
Published: August 2005

A technique is presented for solving the inverse dynamics of flexible planar multibody systems. This technique yields the non‐causal joint efforts (inverse dynamics) as well as the internal states (inverse kinematics) that produce a prescribed nominal trajectory of the end effector. A non‐recursive Lagrangian approach is used in formulating the equations of motion as well as in solving the inverse dynamics equations. Contrary to the recursive method previously presented, the proposed method solves the inverse problem in a systematic and direct manner for both open‐chain as well as closed‐chain configurations. Numerical simulation shows that the proposed procedure provides an excellent tracking of the desired end effector trajectory.
Adaptive and hierarchical modelling of fatigue crack propagation
Authors: Fish Jacob , Nath Aditya
Published: August 2005

A methodology is developed to simulate adaptively and hierarchically fatigue crack growth in structural components. Cracks are modelled, by overlaying portions of the finite element mesh free of cracks with a discontinuous finite element field containing unconstrained double nodes along the discontinuity. Crack propagation is simulated by advancing the crack front in the superimposed mesh only keeping the underlying mesh fixed. Adaptivity in time and space domain together with the hierarchical nature of the method ensure both economical and reliable simulation of crack propagation. Numerical results of fatigue crack growth in the attachment lug were found to be, in good agreement with the experimental data.
A parallel row‐oriented sparse solution method for finite element structural analysis
Authors: Law Kincho H. , Mackay David R.
Published: August 2005

This paper describes a parallel implementation of LDLT factorization on a distributed‐memory parallel computer. Specifically, the parallel LDLT factorization procedure is based on a row‐oriented sparse storage scheme. In addition, a strategy is proposed for the parallel solution of a triangular system of equations. The strategy is to compute the inverses of the dense principal diagonal block submatrices of the factor L, stored in a row‐oriented structure. Experimental results for a number of finite element models are presented to illustrate the effectiveness of the parallel solution schemes.
Non‐linear co‐ordinate transformation of finite part integrals in two‐dimensional boundary element analysis
Authors: Hildenbrand J. , Kuhn G.
Published: August 2005

This paper describes a method for the numerical computation of hypersingular integrals as they appear in the boundary element analysis. The proposed method is based on the finite part concept and allows for arbitrary curved boundary elements. Owing to the unknown transformation properties of finite part integrals undergoing a non‐linear co‐ordinate transformation, the definition formula of finite part integrals is applied prior to the transformation into the usual element co‐ordinate system. The resulting integrals are regular and may be evaluated by standard Gaussian quadrature rules. The method is described in detail for the boundary integrals of two‐dimensional linear elastostatics. Numerical examples are inclcded for this type of problem, but the method may easily be adapted to other two‐dimensional problems.
Crack length measurements with a potential drop method: A finite element simulation
Authors: Ke Y. , Ståhle P.
Published: August 2005

A potential drop method, as used for estimations of crack lengths during three‐point‐beind experiments, is studied. The mechanical state is calculated using a finite element method. The deformed body obtained is used for a subsequent calculation of the electrostatic state. Calculations are performed for both two‐ and three‐dimensional models. The material is assumed to be elastic, linearly hardening plastic and electrostatically linear. Large deformations are considered. Further, the non‐linearity caused by the load, depending on the contact area between the cylinder on which the load is applied and the specimen, is considered. The increased contact area did not influence the mechanical state very much but had a direct impact on the electrostatic state. The changes in the potential drop recordings due to deformation and electrical current passing through the load cylinder were shown to be considerable. The study explains, at least partly, the experimental observations. A more reliable registration of crack growth initiation is the main outcome of the analysis.
Some useful renumbering strategies for unstructured grids
Authors: Löhner Rainald
Published: August 2005

Several renumbering strategies for unstructured grids are discussed. They lead to a minimization of eache‐misses and an optimal grouping of elements for different computer platforms, from superscalar workstations to multiprocessor register‐to‐register vector machines. Timings for a typical computational fluid dynamics (CFD) code that employs these renumbering strategies indicate that CPU requirements may be halved by applying them. The renumbering strategies discussed are all of linear time complexity, making them ideally suited for applications requiring frequent mesh changes. Furthermore, these renumbering strategies are not only valid for element‐based codes but carry over to edge‐based or face‐based field solvers.
Numerical design of thin‐walled structural members on account of their strength
Authors: Kalamkarov Alexander L. , Kolpakov Alexander G.
Published: August 2005

The numerical design and optimization problems for the reinforced thin‐walled structural members on account of a local strength criterion are considered. Two types of the elements of construction are analysed in detail: wafer plates and honeycomb‐like shells. The optimal design concerns the following factors: the values of the effective stiffness moduli; the minimization of the weight; the ability to sustain the required ultimate strains. The computations are based on the application of the general homogenized shell model. The effective computational algorithm for a global minimum search for the function of several variables under the restrictions and the computer software are developed and applied. The asymptotically correct results for the effective stiffness moduli and the local stress distributions, which are available in the framework of the general homogenized shell model, ensure that the gain of optimization will not be overlapped by modelling errors. The effectiveness and advantages of the developed approach is illustrated by several numerical examples. The optimal design computational algorithm is extended to the case of fatigue failure analysis.
Pathologies associated with the numerical analysis of hyper‐anisotropic materials
Authors: šimáček Pavel , Kaliakin Victor N. , Pipes R. Byron
Published: August 2005

The rise in popularity of composite materials has brought to light the necessity of analysing materials exhibiting the kinematic constraint of directional inextensibility. Numerical phenomena associated with the analysis of such hyperanisotropic materials are described herein. The phenomena include: element locking dependent on fibre orientation, spurious tension modes and difficulties associated with elements possessing large material parameter ratios. To facilitate the present description, these phenomena are compared to, and contrasted with the well‐documented problems associated with the analysis of incompressible or nearly incompressible media. Based on the results of eigenvalue analyses, elements satisfying the Babuška‐Brezzi condition for incompressible media are found to perform rather poorly when analysing hyperanisotropic materials. These findings are supported by the results of a simple example.
Effects of element distortions on the performance of isoparametric elements
Authors: Lee Nam‐Sua , Bathe Klaus‐Jurgen
Published: August 2005

We discuss the effects of element distortions on the performance of displacement‐based isoparametric quadrilateral finite elements. Suitable example problems for both the Lagrangian and the serendipity types of elements are used to show numerically the effects of element distortions. The effects of angular and curved‐edge distortions are evaluated analytically in terms of the abilities of the elements to represent exactly various polynomial displacement fields. We then solve a plane stress problem adaptively to demonstrate the effect of element distortions on the accuracy of the stress distribution. The conclusion is that the Lagrangian elements are not affected by angular distortions and are therefore the more reliable elements for general use.
An efficient numerical method for modelling initiation and propagation of cracks along material interfaces
Authors: Beer G.
Published: August 2005

A numerical method, based on the multiregion concept in the boundary element method, is presented for modelling crack propagation. The advantage of the method is that the non‐linear iterations only involve interface degrees of freedom and that the propagation of cracks is modelled by disconnecting degrees of freedom and no remeshing is necessary.
p‐version least‐squares finite element formulation of Burgers' equation
Authors: Winterscheidt Daniel , Surana Karan S.
Published: August 2005

A p‐version least‐squares finite element formulation for non‐linear problems is presented and applied to the steady‐state, one‐dimensional Burgers' equation. The second‐order equation is recast as a set of first‐order equations which permit the use of C0 elements. The primary and auxiliary variables are approximated using equal‐order p‐version hierarchical approximation functions. The system of non‐linear simultaneous algebraic equations resulting from the least‐squares process is solved using Newton's method with a line search. The use of ‘exact’ and ‘reduced’ quadrature rules is investigated and the results are compared. The formulation is found to produce excellent results when the ‘exact’ integration rule is used. The combination of least‐squares finite element formulation and p‐version works extremely well for Burgers' equation and appears to have great potential in fluid dynamics problems.
Higher‐order MITC general shell elements
Authors: Bucalem Miguel Luiz , Bathe Klaus‐Jüen
Published: August 2005

Two mixed‐interpolated general shell finite elements for non‐linear analysis‐a 9‐node element and a 16‐node element‐are presented. The elements are based on the Mixed Interpolation of Tensorial Components (MITC) approach in which the covariant strain component fields for the in‐plane and shear actions are interpolated and tied to the also interpolated displacement field. Both the 9‐node element, referred to as the MITC9 element, and the 16‐node element, referred to as the MITC16 element, are tested numerically and found to have high predictive capabilities.
Flow past a cylinder with and without an appurtenance
Authors: Tamaddon‐Jahromi H. R. , Townsend P. , Webster M. F.
Published: August 2005

This paper constitutes a numerical study of flow around a cylinder for cases with and without an appurtenance, and throughout a range of Reynolds numbers. This is achieved by solving the two‐dimensional evolutionary Navier‐Stokes equations using a pressure‐velocity finite element method. The particular form of scheme employed is a combination of Taylor‐Galerkin and pressure‐correction methods. This scheme delivers second‐order accuracy in time and introduces three fractional stages within each time‐step. One of the practical applications of this work is the prediction of flows around gas and oil platforms at sea, and of concern to off‐shore engineers are the effects of adding a sacrificial anode to the cylindrical legs of a platform. Such an appurtenance added to the basic cylindrical shape induces different drag forces on the legs depending on the angle of attack of the motion of the sea relative to the appurtenance location. Unidirectional and oscillatory flow solutions are reported, concentrating on flow patterns and forces experienced on the body surface, and the vortex shedding process.
Modelling edge effects with the C0 plate bending elements: Part 2. The performance of the reformulated four‐node element
Authors: Briassoulis D.
Published: August 2005

The reformulated four‐node element has exhibited an excellent behaviour in static finite element analyses being free of shear and machine locking problems and of zero energy modes and modelling accurately relatively thick plates. In the present paper, the element under consideration is shown to exhibit an analogous excellent performance in modelling highly demanding boundary layer plate bending problems.
Application of the hybrid zone/Monte Carlo method to 3‐D curvilinear grids in radiative heat transfer
Authors: Haidekker A. , Charette A. , Kocaefe Y. S.
Published: August 2005

The zone method is applied to non‐orthogonal curvilinear grids for the computation of radiative heat transfer. The interchange areas are calculated by the Monte Carlo technique which has been fitted with a generalized ray tracing procedure. The method is applied to two complex three‐dimensional (3‐D) cases where in homogeneities are present in the radiation space (non‐uniform gas properties and/or shadowing effects), and the gas is taken as gray. For comparison purposes, the same examples are worked out with the discrete transfer method. Very small discrepancies are found between the two methods for the surface heat fluxes, but the gas volumetric radiative sources are much more sensitive to inhomogeneities in the gas phase, resulting in higher discrepancies for these terms. The method can be readily extended to incorporate real gases and scattering effects.
Generalized mixed finite element model for pre‐ and post‐quasistatic buckling response of thin‐walled framed structures
Authors: Gendy A. S. , Saleeb A. F.
Published: August 2005

Adopting an updated Lagrangian approach, the general framework for the fully non‐linear analysis of thin‐walled framed structures is developed using a simple, two‐node, C0‐model (HMB2). The governing equations are derived based on a consistent linearization of an incremental mixed variational principle of modified Hellinger/Reissner type with independent assumptions for displacement and strain fields. All coupled significant modes of deformations, i.e. stretching, bending, shear, torsion and warping, are accounted for in the generalized‐beam theory employed. Emphasis is placed on devising effective solution procedures to deal with finite rotations in space, particularly with regard to their effect on the derivations of load‐correction matrices corresponding to configuration‐dependent externally applied forces/moments. The effectiveness and practical usefulness of present model are demonstrated through a number of test problems involving beam assemblages undergoing large displacements and rotations in space.
Dynamic analysis of structures with unilateral constraints: Numerical integration and reduction of structural equations
Authors: Barauskas Rimantas
Published: August 2005

Structural dynamic equations with unilateral constraints upon the displacements, velocities and accelerations are employed in order to represent vibrating elastic structures with normal, oblique impact and friction interaction points.

For obtaining a numerical integration scheme the Lagrange multipliers and a minimum work approach are employed at each time step. The algorithm is presented as an extension of the generalized Newmark scheme. It seems to retain the asymptotic features of the original one.

The reduction of the number of dynamic degrees of freedom of the unilaterally constrained structures is carried out by representing the equations of motion in modal co‐ordinates of the unconstrained structure and truncating the dynamic contributions of higher modes.

The presented techniques have been verified by investigating free longitudinal vibroimpact motion laws of an elastic vibroconverter and free longitudinal and bending vibration of a vibroconverter interacting with a moving rigid body by oblique impact and friction forces.
Numerical flow modelling in a locally refined grid
Authors: De Lange H. C. , De Goey L. P. H.
Published: August 2005

An algorithm is presented to model two‐dimensional, non‐isothermal, low Mach number flows with a local steep density gradient. The algorithm uses an adaptive, locally refined, non‐staggered grid and has been developed, especially for modelling laminar flames. The governing equations, based on a stream‐function–vorticity formulation, are presented and discretized using hybrid finite differences. A (isothermal) test problem is presented to compare the accuracy of the results of the solver presented in this paper, with the results of algorithms found in the literature. However, this test problem proves to be not well suited for the application of a locally refined grid, since it does not contain a local steep gradient. For this reason an additional test problem is constructed that clearly shows the advantages of the locally refined grid as compared to a uniform grid with respect to both the calculation time as well as the number of grid nodes needed. Furthermore, a laminar premixed flame is modelled with simple chemistry to show that the algorithm, presented in this paper, converges to a stabilized flame when an adaptive grid technique is used.
Analysis of sheet metal forming operations by a stress resultant constitutive law
Authors: Chou C. H. , Pan J. , Tang S. C.
Published: August 2005

Sheet metal forming is simulated by finite element methods using a stress resultant constitutive law in this paper. A Lagrangian description of axisymmetric and plane‐strain shell deformation is first reviewed. Then a stress resultant constitutive law in rate form is presented, where the effect of thickness reduction due to large plastic deformation is considered. A finite element formulation in terms of stress resultants and their work‐conjugate generalized strain rates is derived based on the virtual work principle. A hemispherical punch stretching operation and a plane‐strain draw operation are simulated by a finite element program based on the finite element formulation. The results of these finite element simulations are in good‐agreement with those using the through‐the‐thickness integration method. The results of the hemispherical punch stretching simulation suggest that the coupling term of moments and membrane forces of the modified Ilyushin yield function should be eliminated to avoid numerical instability under stretching‐dominated conditions for this rate‐independent plasticity formulation. Further, the results suggest that the hardening rule in a power‐law form based on the small‐strain approach must be modified to take account for finite deformation effects of combined stretching and bending. Under the plane‐strain draw operation, the sheet experiences a large amount of bending before the final stretching. The simulation based on the stress resultant constitutive law can produce this essential aspect of deformation pattern as that of the through‐the‐thickness integration method, whereas a simulation based on a membrane theory cannot. In conclusion, the results of these simulations indicate that a finite element program based on the stress resultant constitutive law can simulate sheet‐forming processes with much shorter computational time than that based on the through‐the‐thickness integration method.
Exterior stable domain segmentation integral equation method for scattering problems
Authors: Zeng Xiaogang , Bielak Jacobo
Published: August 2005

This paper is concerned with the development of an exterior domain segmentation method for the solution of two‐ or three‐dimensional time‐harmonic scattering problems in acoustic media. This method, based on a variational localized, symmetric, boundary integral equation formulation leads, upon discretization, to a sparse system of algebraic equations whose solution requires only O(N) multiplications, where N is the number of unknown nodal pressures on the scatterer surface. The new procedure is analogous to the one developed recently1 except that in the present formulation we avoid completely the use of the hypersingular operator, thereby reducing the computational complexity. Numerical experiments for a rigid circular cylindrical scatterer subjected to a plane incident wave serve to assess its accuracy for normalized wave numbers, ka, ranging from 0 to 30, both directly on the scatterer and in the far field, and to confirm that, contrary to standard boundary integral equation formulations, the present procedure is valid for critical frequencies.
On the membrane locking of h–p finite elements in a cylindrical shell problem
Authors: Leino Yrjö , Pitkäranta Juhani
Published: August 2005

We study the performance of high‐order h–p finite clement schemes in approximating the nearly inexlensional deformation state of a thin cylindrical shell roof with both ends free. Severe locking is demonstrated for both quadratic and cubic elements, and even for higher order if the grid is not aligned with the axis of the cylinder.

Carefully designed selective reduced integration is shown to improve the accuracy of the finite element approximation at low and moderately high orders. However, so far this technique seems to work well only on aligned grids.
Contact forces in the non‐linear dynamic analysis of tracked vehicles
Authors: Nakanishi Toshikazu , Shabana A. A.
Published: August 2005

It is known that when two springs are connected in series, the stiffness coefficient of an equivalent system that consists of one spring is less than the stiffness coefficients of the original springs. Experimental observations indicate that this fact can be very useful in determining the overall vibration characteristics of tracked vehicles. This simple fact is used in this investigation to develop a computer aided analysis procedure for the dynamic simulation of large‐scale tracked vehicles. The track is considered as a closed kinematic chain that consists of rigid bodies connected by revolute joints. The contacts between the track links and the rollers, the sprocket, and the idler are represented by non‐linear continuous force models. The stiffness and damping coefficients in these contact force models are determined by studying the viberation characteristics of the tracked vehicle. The tooth of the sprocket is defined using three surfaces. These are the left, the bottom, and the fight surfaces. Three successive transformations are used to define the contact kinematic relationships between the sprocket teeth and the pins of the track links. The equations of motions of the vehicle are formulated using the Lagrangian approach. Non‐linear constraint equations that describe mechanical joints and specified motion trajectories in the system are adjoined to the differential equations of motion using the technique of Lagrange multipliers. The resulting mixed system of differential and algebraic equations is solved numerically using a direct numerical integration method. A Newton–Raphson algorithm is used to check on the violations in the kinematic constraints. The results presented in this paper are obtained using a 54 body planer tracked vehicle in which the track consists of 42 rigid links connected by revolute joints.
An iterative solution scheme for systems of boundary element equations
Authors: Davey K. , Rosindale I.
Published: August 2005

In this paper an iterative scheme of first order is developed for the purpose of solving linear systems of equations. In particular, systems that are derived from boundary integral equations are investigated. The iterative schemes to be considered are of the form Ex(k+1) = Dx(k) + d, where E and D are square matrices. It will be assumed that E is a lower matrix, i.e. the coefficients above the central diagonal are zero. It will be shown that by considering matrix D embedded in a vector space and reducing its size with respect to a chosen metric, that convergence rates can be substantially improved. Equation ordering and parameter matrices are used to reduce the magnitude of D. A number of examples are tested to illustrate the importance of the choice of metric, equation ordering and the parameter matrix. Computation times are determined for both the iterative procedure and Gauss elimination indicating the usefulness of iteration which can be orders of magnitude faster.
The monomial method: Extensions, variations, and performance issues
Authors: Burns Scott A.
Published: August 2005

The monomial method solves systems of non‐linear algebraic equations by constructing a sequence of approximating monomial (single‐term polynomial) systems, much as Newton's method generates a sequence of linear systems to do this. Since the monomial system becomes linear through a logarithmic transformation of variables, the monomial method can be considered to be an alternative linearization scheme. Although the monomial method is closely related to Newton's method, it exhibits many special invariance properties not shared by Newton's method that enhance performance. This paper first briefly reviews the monomial method and its special properties. Two new versions of the algorithm are presented, both of which, are simplified and computationally more efficient to implement in comparison to the original algorithm. The monomial method is also extended to apply to certain non‐algebraic systems. Since the monomial method can be interpreted as Newton's method applied to a three‐part reformulation of the algebraic system, graphical experiments are presented which investigate the role that each part of the reformulation plays in contributing to the enchanced performance. Finally, instances in which difficulties have arisen using the monomial method are discussed.
An intrinsic beam model based on a helicoidal approximation—Part II: Linearization and finite element implementation
Authors: Borri Marco , Bottasso Carlo
Published: August 2005

The helicoidal beam model developed in the first part of this work is applied here to the development of a mixed finite element for space‐curved and twisted beams undergoing large displacements and finite rotations. Starting from the governing weak form expressed by the principle of virtual work, a consistent linearization is obtained in the following and a novel updated Lagrangian finite element implementation is thoroughly discussed.

The unique features and the distinguishing properties previously claimed for the helicoidal model are shown here to imply remarkable numerical consequences. For this purpose, meaningful example problems regarding the non‐linear static response of beams are addressed in the following and the results are compared with those available from the literature.

Furthermore, a finite element in time for the rigid body dynamic problem is developed within the framework of the helicoidal geometry. The underlying philosophy of this novel finite element for dynamics is the realization of the helicoidal decomposition of the rigid body motion within a time step.