bluuebunny/crossref_metadata_2025 huggingface dataset:
A block equation solver for large unsymmetric linear equation systems with dense coefficient matrices
Authors: Stabrowski M. M.
Published: August 2005

The presented solver uses the Crout L–U decomposition method. Disk memory space requirements are reduced to an absolute minimum and disk input–output is spectacularly limited. Very extensive pivoting improves numerical accuracy and stability. Experimental test runs prove the overall efficiency of the solver.
A global mapping method for improving the performance of quadratic elements
Authors: Nath B. , Potamitis S. G.
Published: August 2005

A simple method is proposed in this paper for improving the performance (accuracy and convergence) of quadratic elements. In this the physical domain of the problem, as well as the constitutive relationships, are transformed globally by implementing a suitable co‐ordinate transformation, and the problem is then solved in the mapped (transformed) domain using finite elements of the mapped space following the processes of the conventional FEM.

Results show that the method significantly improves the performance of quadratic elements in both two and three dimensions. The mathematical implications of mapping in this way indicate that the method can also be applied for improved performance to higher‐order elements if required.
An adaptive procedure for eigenvalue problems using the hierarchical finite element method
Authors: Friberg O. , Moller P. , Makovička D. , Wiberg N.‐E.
Published: August 2005

An adaptive procedure for the solution of the generalized linear eigenvalue problem within the hierarchical finite element method is described. The problem of finding for a given discretization, an upper limit eigenvalue that is accurate within a prescribed tolerance is especially studied. An error estimator is presented and a recomputational scheme for improved solutions is proposed. A numerical example is included.
Making curved interfaces straight in phase‐change problems
Authors: Storti Mario , Crivelli Luis A. , Idelsohn Sergio R.
Published: August 2005

This paper presents a method for straightening curved interfaces arising in phase‐change problems. The method works on isoparametric finite elements, performing a second transformation which maps the master element onto a new one in which the interface looks like a straight line. This allows using the current Gaussian integration technique for squares to evaluate the integrals over each phase. The method provides a better estimation of the contribution of latent heat effects to the residual vector, compared to those obtained by using the assumption that the interface is straight. Appropriate guidelines for solving the non‐linear system of equations arising in this kind of problem are also given. Several numerical examples are presented to show the performance of the method.
One‐dimensional calculations of two‐phase mixing flows
Authors: Thyagaraja A. , Fletcher D. F. , Cook I.
Published: August 2005

A new algothm for the solution of two‐phase fluid flow problems is presented. The algorithm consisently ensures that the evolved volume fractions are all positive and sum to unity, even in the presence of large spatial and temporal gradients of volume fraction. The momentum equations are then solved using an iterative pressure correction method. Example calculations for buoyancy driven flows, with and without phase changes, are presented.
Mapped infinite elements in soil consolidation
Authors: Simoni L. , Schrefler B. A.
Published: August 2005

The problems of consolidation often involve unbounded continua. The most common solution is then achieved by limiting the studied area through the introduction, at finite distance, of a boundary on which adequate conditions on the field variables are imposed. In this paper mapped infinite elements are used to model the far‐field solution. Spatial discretization is hence performed on the basis of both finite and infinite elements. In two examples, solutions involving finite and infinite elements are compared with known analytical solutions and it is shown that an excellent agreement can be achieved by the use of mapped infinite elements.
Adaptive refinement for least‐squares finite elements with element‐by‐element conjugate gradient solution
Authors: Jiang B.‐N. , Carey G. F.
Published: August 2005

An error analysis and an adaptive refinement scheme are developed for use with a class of least‐squares finite element methods. The error indicators for the refinement procedure are based on element residuals which are calculated as part of the least‐squares method. The solution scheme used in the supporting numerical studies employs an elment‐by‐element conjugate gradient algorithm. Consequently, storage and computation are not influenced by nodal numbering.
A new efficient mixed formulation for thin shell finite element models
Authors: Rhiu J. J. , Lee S. W.
Published: August 2005

A nine node shell element is developed by a new and more efficient mixed formulation. The new shell element formulation is based on the Hellinger–Reissner principle with independent strain and the concept of a degenerate solid shell. The new formulation is made more efficient in terms of computing time than the conventional mixed formulation by dividing the assumed strain fields into a lower order part and a higher order part. Numerical results demonstrate that the present nine node element is free of locking even for very thin plates and shells and is also kinematically stable. In fact the stiffness matrix associated with the higher order assumed strain plays the role of a stabilization matrix.
An improved discrete Kirchhoff quadrilateral thin‐plate bending element
Authors: Jeyachandrabose C. , Kirkhope J. , Meekisho L.
Published: August 2005

By combining discrete Kirchhoff theory with least‐squares smoothed shape functions, an improved quadrilateral thin‐plate bending element is derived. This element exhibits improved performance over an earlier DKQ element in predicting both displacements and stresses. Numerical examples are presented comparing the element with many other quadrilateral elements for standard test problems.
The front‐tracking scheme for the one‐dimensional freezing problem
Authors: Askar Hasan G.
Published: August 2005

The one‐dimensional freezing problem can be solved numerically for the temperature distribution accompanied by explicit reference to the position of the freezing front at each time interval. A new front‐tracking scheme provides accurate determination of the phase front, which is an essential requirement for the temperature distribution in the different phases of such problems. The front is made to coincide with a grid‐node throughout the analysis. The scheme uses a combination of the finite difference and the finite element methods for obtaining the solution of the freezing problems.
Substepping schemes for the numerical integration of elastoplastic stress–strain relations
Authors: Sloan S. W.
Published: August 2005

This paper describes two substepping schemes for integrating elastoplastic stress–strain relations. The schemes are designed for use in finite element plasticity calculations and solve for the stress increments assuming that the strain increments are known. Both methods are applicable to a general type of constitutive law and control the error in the integration process by adjusting the size of each substep automatically. The first method is based on the well‐known modified Euler scheme, whereas the second technique employs a high order Runge–Kutta formula. The procedures outlined do not require any form of stress correction to prevent drift from the yield surface. Their utility is illustrated by analysis of typical boundary value problems.
Triangular finite element for analysis of thick laminated plates
Authors: Chaudhuri Reaz A. , Seide Paul
Published: August 2005

The development of a general triangular C0 element, based on an assumed quadratic displacement potential energy approach, is presented for the analysis of arbitrarily laminated thick plates. The element formulation assumes transverse inextensibility and layerwise constant shear‐angle. Convergence of transverse displacement, moments and stresses, the effects of two different Gauss quadrature schemes and comparison of the present solutions with the available analytical/finite‐element results also form a part of the investigation. Furthermore, numerical results indicate close agreement between the LCST (layerwise constant shear‐angle theory) and the three‐dimensional elasticity theory with the length (or width) to thickness ratio as low as 4. Detailed comparison of the LCST‐based finite‐element solutions with those based on the CST (constant shear‐angle theory) and the CLT (classical lamination theory) clearly demonstrates the superiority of the former over the latter two, especially in the prediction of the distribution of the in‐plane displacements and stresses through the laminate thickness. This paper also introduces a new non‐dimensionalized parameter, Δθ*, which is shown to be a very useful measure for classification of the laminated plates and the suitability of different plate theories over various ranges of length‐to‐thickness ratio.
Numerical simulation of electrodeposition problems
Authors: Zamani N. G. , Chuang J. M. , Hsiung C. C.
Published: August 2005

The mathematical modelling of the electrodeposition phenomenon leads to a linear elliptic partial differential equation subject to non‐linear mixed boundary contitions. This is complicated further by the fact that the domain under consideration is evolving with time.

Owing to the nature of the mathematical model, the boundary element method is a very efficient numerical technique for the solution of such problems. The authors report their numerical simulation of the above problem which also has applications in the cathodic protection systems for corrosion prevention.
A new approach for the hybrid element method
Authors: Chen Wanji , Cheung Y. K.
Published: August 2005

A new functional which forms the basis of an improved hybrid element formulation is proposed. The variables for the functional include stresses, strains and displacements, and the displacements and stresses are further decomposed into two parts respectively. The proposed new formulation appears to be particularly suitable for improving conforming models.

Based on this formulation, a new four‐node plane hybrid element Qcs6 can be developed, and the conforming element Q4 and the non‐conforming Wilson element Q and modified Wilson element Qm6 can also be derived directly by this hybrid approach. It should be noted that more accurate stresses can be obtained from this element which utilizes the concept of two stress components.
A theorem regarding the locking of tapered four‐noded membrane elements
Authors: Macneal Richard H.
Published: August 2005

It is shown that any four‐noded membrane element with two degrees of freedom per node will either lock in inplane bending or fail to pass a C0 patch test when the element's shape is an isosceles trapezoid. This result effectively closes out further effort to extend the linear strain capability of such elements beyond what has already been achieved for rectangular and parallelogram shapes.
An ‘upwind’ finite element method for electromagnetic field problems in moving media
Authors: Hahn Song‐Yop , Bigeon Jean , Sabonnadiere Jean‐Claude
Published: August 2005

Time periodic finite element solutions for sinusoidally excited electromagnetic field problems in moving media are presented. Solutions by the Galerkin method contain spurious oscillations when the grid Peclet number is more than one. To suppress these osillations an upwind finite element method using two different time periodic test functions is introduced. One is multiplied to second and first order space derivative terms and the other to the time derivative term. Test functions are obtained from trial functions by adding or subtracting quadratic bias functions with appropriate scaling factors. Phase differences are considered between trial functions and bias functions. For simple interpretations of the phase differences complex scaling factors are used. The proposed method is developed to give nodally exact solutions for uniform grid spacing in one dimensional problems. Based on the one dimensional results a two dimensional upwinding scheme is also derived.
Composite mappings for planar mesh generation
Authors: Crawford R. H. , Waggenspack W. N. , Anderson D. C. , Bailey M. J.
Published: August 2005

A new algorithm is presented for automatically grading meshes generated over planar triangular and quadrilateral regions using parametric mappings. Rational parametric bicubic Bézier polynomials are coupled with an element density function to concentrate elements around regions of high solution gradients.
Finite element simulation of long and short circular die extrusion experiments using integral models
Authors: Luo X.‐L. , Tanner R. I.
Published: August 2005

A finite streamline element method for use with integral type constitutive equations in viscoelastic flow simulation, including thermal effects, is presented and some new results using this method in modelling the IUPAC extrusion experiments for low‐density polyethylene (LDPE), involving both long and short circular dies, are reported and discussed. It will be shown that the special streamline‐based elements provide a convenient way of particle tracking and strain tensor calculation. The extrusion calculation when using a relatively realistic KBKZ type integral model with multiple relaxation times is stable, and practically important Weissenberg numbers and swelling ratios have been reached without difficulty. The agreement with experimental swelling ratios is on the whole satisfactory. In order to make the model a good fit to the Trouton viscosity experimental data of the LDPE sample, a spectrum of elongational parameters has been introduced. The second normal stress term has also been added to the integral model to examine its effect on extrusion swelling. The non‐isothermal effects and the possibility of a wall slip near the die exit at high apparent shear rates are also discussed.
Analysis of stress and strain distributions in slab rolling using an elastic‐plastic finite‐element method
Authors: Liu C. , Hartley P. , Sturgess C. E. N. , Rowe G. W.
Published: August 2005

The cold rolling of rectangular section slabs is analysed for a range of width‐to‐height ratios (one to three) for which spread of the workpiece is appreciable. This necessitates the use of a three‐dimensional model. An elastic‐plastic finite‐element method is used to provide a complete description of the slab rolling process.

The pressure distribution at the workpiece/roll interface is found to show the typical ‘friction‐hill’ observed in near‐plane‐strain experiments, but the pressure varies across the width of the interface. The shear‐stress distribution at the roll interface provides detailed information about the ‘neutral line’ which is usually assumed to occur where the shear stress changes direction. The 3‐D analysis shows clearly that there is a flow divide in both longitudinal and transverse directions.
Approximate methods for analysing the cold drawing of polymeric fibres and films
Authors: Neale K. W. , Tuḡcu P.
Published: August 2005

Approximate methods for analysing steady‐state cold drawing processes in polymer forming are discussed. These methods are applied to both axisymmetric and plane‐strain drawing. The cold drawing process is associated with steady‐state neck propagation along the specimen. Modifications are introduced in the approximate steady‐state analysis which reflect the neck initiation and localization phases prior to steady‐state drawing. This is accomplished without resorting to an analysis of the entire load–deformation history of the process. Finite element results are also presented and compared with those of the proposed approximate analyses. These comparisons show the approximate analysis to be an extremely efficient and quite accurate computational scheme for the analysis of steady‐state cold drawing processes.
Analysis of bending effects in sheet forming operations
Authors: Wang Neng‐Ming , Tang Sing C.
Published: August 2005

The majority of work in numerical analyses of sheet metal forming operations is based on the simple membrane‐shell theory which neglects the effect of sheet bending. While useful information can be extracted from these analyses, especially for stretch‐dominated operations, the membrane theory is basically inadequate for analysing the draw‐type operations where sheet metal bends, slides and unbends over a draw radius.

This paper presents axisymmetric and plane‐strain finite element analyses of stretch/draw of sheet metal over a die corner radius. Numerical solutions obtained from a total Lagrangian formulation of a finite‐strain thin shell theory are used to indicate the relative significance of including the bending effects in various simple forming operations. Comparisons of the calculated results with available experimental data are also given.
Thermal analysis of human body‐clothing‐environment system
Authors: Imre L. , Bitai A. , Horváth C. D. , Bánhidi L. , Pammer Z.
Published: August 2005

For the solution of thermal comfort problems a coupled model is presented consisting of the thermal model of the human body and of the clothing, with boundary conditions of the third kind.

For thermal modelling the human body is divided into 16 parts according to the special character of the internal heat generation, of the blood vessel system and of the sweat secretion mechanism. Part models are connected by the flow paths of arteries and veins.

Transport phenomena in the clothing are treated by a coupled heat and mass transfer model which permits various kinds of clothing for the different parts of the body.

The equation system of the full model has been solved numerically by using time stepping schemes. As the results of the computations an approximative temperature field of the human body is produced.

Calculated results have been compared with Experimental data.
A regular indirect boundary element method for thermal analysis
Authors: Wearing J. L. , Sheikh M. A.
Published: August 2005

A Regular Indirect Boundary Element formulation is developed following a weighted residual approach. In this formulation, the fictitious source density, which appears in the integral equations of the method, is distributed on a surface which is exteriorly separated from the physical field boundary of the problem. This approach does not require the evaluation of singular integrals and produces undeteriorated solutions at geometric discontinuities. The formulation is presented here as applied to two dimensional and axisymmetric thermal problems. It includes a different subregioning scheme which treats each subregion, of a multidomain problem, separately, thereby eliminating the need for a sophisticated reduction scheme.
Solution accuracies of finite element reentry heat transfer and thermal stress analyses of space shuttle orbiter
Authors: Ko William L.
Published: August 2005

Accuracies of solutions (structural temperatures and thermal stresses) obtained from different finite element thermal and structural models set up for the space shuttle orbiter are compared and discussed. For studying the effect of element size on the solution accuracies of finite element heat transfer and thermal stress analyses of the orbiter, five structural performance and resizing (SPAR) thermal models and five NASA structural analysis (NASTRAN) structural models were set up for the orbiter wing midspan bay 3. The structural temperature distribution over the wing skin (lower and upper) surface of one bay was dome shaped and induced more severe thermal stresses in the chordwise direction than in the spanwise direction. The induced thermal stresses were extremely sensitive to slight variation in structural temperature distributions. Both internal convention and internal radiation were found to have equal effects on the orbiter structural temperatures. Minimum degrees of element fineness required for thermal and structural models for the orbiter to yield satisfactory solutions were established. In transient heat transfer analysis most of the computation time was consumed in the time‐dependent temperature calculations and not in the radiation view‐factor computations.
Failure of mechanically loaded laminated composites subjected to intense localized heating
Authors: Gularte R. C. , Nemes J. A. , Stonesifer F. R. , Chang C. I.
Published: August 2005

A numerical procedure is presented for predicting failure in laminated composites subjected to simultaneous intense localized heating and applied mechanical loads. The method consists of a non‐linear two‐dimensional, axisymmetric finite difference thermal analyser which considers the effects of surface ablation, radiation and convection losses and temperature dependent thermophysical properties. The thermal results are used in conjunction with a flat plate finite element code to predict the failure of laminated composites. Predictions based on the numerical analyses are compared with experimental results obtained from mechanically loaded graphite epoxy coupons spot‐irradiated at various intensities.
A comparative investigation on recurrence formulae in finite difference methods
Authors: Haberland Christoph , Lahrmann Andreas
Published: August 2005

To solve the transient heat‐conduction equation, the Pade‐approximation is introduced into the Finite Difference Method. But, if the time step is chosen too large relatively to the element size the Euler method (Pade (0,1) approximation) and the Crank–Nicolson solution (Pade (1,1)‐approximation) lead to significant oscillations. In contrast, the Full Implicit scheme (Pade (1,0)‐approximation) does not show this oscillatory behaviour, but is more inaccurate. Compared to these time stepping algorithms the presented Weighted Time Step method is seen to offer definite advantages.
Numerical simulation of forest fires
Authors: Richards Gwynfor D.
Published: August 2005

This paper reviews the work done to date on the numerical simulation of forest fires. A general model to predict forest fire spread under different conditions is presented and studied. The model is based on nth order reaction theory, and is sufficiently simple and flexible to conveniently deal with variations in wind velocity, forest properties, fire breaks and other phenomena of interest to the fire controller. The effects of changing various parameters in the equations are illustratd. Results for zero and constant wind velocity are given, together with the effect of abrupt wind changes and fire breaks.
Deformations and stresses in welding of shell structures
Authors: Lindgren Lars‐Erik , Karlsson Lennart
Published: August 2005

The simulation of welding of shell structures is investigated in this paper. In order to verify the implementation of the shell element adopted, two different problems were studied. In the first problem the butt‐welding of two plates was simulated. In the second problem the butt‐welding of a thin‐walled pipe was simulated. It is concluded from the analysis of the plate problem that the shell element is quite effective in the membrane state. The comparison between calculated values and experimental values for the residual stress field in the pipe shows that the shell element performs quite well in the analysis of a realistic problem.
Elasto‐plastic large deformation analysis of space‐frames: A plastic‐hinge and stress‐based explicit derivation of tangent stiffnesses
Authors: Shi G. , Atluri S. N.
Published: August 2005

This paper deals with elasto‐plastic large deformation analysis of space‐frames. It is based on a complementary energy approach. A methodology is presented wherein: (i) each member of the frame, modelled as an initially straight space‐beam, is sought to be represented by a single finite element, (ii) each member can undergo arbitrarily large rigid rotations, but only moderately large relative rotations; (iii) a plastic‐hinge method, with arbitrary locations of the hinges along the beam, is used to account for plasticity, (iv) the non‐linear bendin–stretching coupling is accounted for in each member, (v) the applied loading may be non‐conservative and (vi) an explicit expression for the tangent stiffness matrix of each element is given under conditions (i) to (v). Several examples, with both quasi‐static and dynamic loading, are given to illustrate the accuracy and efficiency of the approaches presented.
Modified shape functions for the three‐node plate bending element passing the patch test
Authors: Specht Bernhard
Published: August 2005

A polynomial displacement basis for the three‐node plate bending element (Zienkiewicz‐triangle) is developed from a relaxed C1‐continuity requirement called the interpolation test. The test provides a general convergence criterion for non‐conforming shape functions and a practical guideline to select a proper displacement basis. The resulting simple displacement type element passes the patch test. Several reduced numerical integration schemes are discussed and numerical testing provides a comparison with the standard element formulated by Zienkiewicz.
The identification and elimination of artificial stiffening errors in finite elements
Authors: Dow John O. , Byrd Doyle E.
Published: August 2005

The causes of shear locking and other discretization errors are analysed using a physically interpretable notation. This analysis provides insights that allow the errors due to shear locking to be removed either directly or indirectly. St. Venant's principle is incorporated into the stiffness matrix to directly eliminate shear locking from bending elements. Rules‐of‐thumb are suggested by the same analysis that will insure the absence of errors due to shear locking at the cost of additional degrees of freedom. It is also shown that aspect ratio stiffening in membrane elements is partially due to the same modelling error that produces shear locking. The source of parasitic shear is also identified and a direct procedure for eliminating it is given. A two node Timoshenko beam element and a four node membrane element are fully developed in symbolic form. The procedure is directly applicable to plate bending elements.
A numerical method for computing domains of attraction for dynamical systems
Authors: Guttalu R. S. , Flashner H.
Published: August 2005

The backward mapping approach for computation of global domains of attraction of asymptotically stable non‐critical equilibrium points of dynamical systems is presented. A basis for the proposed approach is an extension of Lyapunov's direct method due to LaSalle and Lefschetz. An iterative process that converges to the global domain of attraction of an asymptotically stable equilibrium point is formulated. The method applies to both continuous time and discrete time multidimensional systems. It is shown that the backward mapping approach proposed by C. S. Hsu for spiral equilibrium points of second order discrete time systems is a particular case of the algorithm presented here. The proposed method can be used for autonomous systems as well as for systems with periodic coefficients. When applied to discrete time formulation of dynamical systems, the method can be used to determine the regions of stability of periodic solutions. The paper concludes with a number of illustrative examples that demonstrate the usefulness of the proposed approach.
Development of a block Lanczos algorithm for free vibration analysis of spinning structures
Authors: Gupta K. K. , Lawson C. L.
Published: August 2005

This paper is concerned with the development of an efficient eigenproblem solution algorithm and an associated computer program for the economical solution of the free vibration problem of complex practical spinning structural systems. Thus, a detailed description of a newly developed block Lanczos procedure is presented in this paper that employs only real numbers in all relevant computations and also fully exploits sparsity of associated matrices. The procedure is capable of computing multiple roots and proves to be most efficient compared to other existing similar techniques.
On the nature of the free edge stress singularity in composite laminated plates
Authors: Bar‐Yoseph Pinhas , Avrashi Jacob
Published: August 2005

The variational‐asymptotic formulation for the edge layer problem is implemented by mixed‐hybrid finite elements. This approach is used to analyse the stress singularity at the free edge in composite laminates. Results indicate that the stress singularity (as r → 0) is very closely approximated by log r instead of r−α.
Finite element solution of a boundary integral equation for mode I embedded three‐dimensional fractures
Authors: Gu Hongren , Yew Ching H.
Published: August 2005

The singular integral equation governing the opening of a mode I embedded three‐dimensional fracture in an infinite solid was solved by applying the finite element method. The strategy is to formulate the equation into weak form, and to transfer the differentiation from the singular term, 1/r, in the equation to the test function. A numerical algorithm was thus developed. The numerical solutions for circular and elliptical fractures under the action of polynomial pressure distributions were compared with the analytical solutions by Green and Sneddon,12 Irwin,13 Shah and Kobayashi14 and Nishioka and Atluri.16 The results have demonstrated that the numerical method reported is accurate and efficient.
A new numerical formulation for parabolic differential equations under the consideration of large time steps
Authors: Lee Shong‐Leih
Published: August 2005

A new numerical formulation is proposed in this investigation for the solution of parabolic differential equations. The time step parameter λ = 2Δτ/(Δχ)2 under consideration is as large as 2000 such that only a few time steps are needed for the entire regime of transient heat conduction. Along with the formulation, a time scaling transformation is introduced to produce an accurate result for the beginning of a transient process. Although the present formulation makes reference only to the transient heat conduction problem, the idea is equally applicable to parabolic differential equations for other physical phenomena such as transformed boundary layer flow equations.
C0 finite element discretization of Kirchhoff's equations of thin plate bending
Authors: Ortiz M. , Morris G. R.
Published: August 2005

An alternative formulation of Kirchhoff's equations is given which is amenable to a standard C0 finite element discretization. In this formulation, the potential energy of the plate is formulated entirely in terms of rotations, whereas the deflections are the outcome of a subsidiary problem. The nature of the resulting equations is such that C0 interpolation can be used on both rotations and deflections. In particular, general classes of triangular and quadrilateral isoparametric elements can be used in conjunction with the method. Unlike other finite element methods which are based on three‐dimensional or Mindlin formulations, the present approach deals directly with Kirchhoff's equations of thin plate bending. Excellent accuracy is observed in standard numerical tests using both distorted and undistorted mesh patterns.
On a non‐linear formulation for curved Timoshenko beam elements considering large displacement/rotation increments
Authors: Dvorkin Eduardo N. , Onte Eugenio , Oliver Javier
Published: August 2005

An incremental Total Lagrangian Formulation for curved beam elements that includes the effect of large rotation increments is developed. A complete and symmetric tangent stiffness matrix is obtained and the numerical results show, in general, an improvement over the standard formulation where the assumption of infinitesimal rotation increments is made in the derivation of the tangent stiffness matrix.
Time‐domain transient elastodynamic analysis of 3‐D solids by BEM
Authors: Ahmad S. , Banerjee P. K.
Published: August 2005

The numerical implementation of the Direct Boundary Element formulation for time‐domain transient analysis of three‐dimensional solids is presented in a most general and complete manner. The present formulation employs the space and time dependent fundamental solution (Stokes' solution) and Graffi's dynamic reciprocal theorem to derive the boundary integral equations in the time domain. A time‐stepping scheme is then used to solve the boundary initial value problem by marching forward in time. Higher order shape functions are used to approximate the field quantities in space as well as in time, and a combination of analytical (time‐integration) and numerical (spatial‐integration) integration is carried out to form a system of linear equations. At the end of each time step, these equations are solved to obtain the unknown field quantities at that time.

Finally, the accuracy and reliability of this algorithm is demonstrated by solving a number of example problems and comparing the results against the available analytical and numerical solution.
Reliable use of determinants to solve non‐linear structural eigenvalue problems efficiently
Authors: Williams F. W. , Kennedy D.
Published: August 2005

A ‘multiple determinant parabolic interpolation method’ is described and evaluated, principally by using a plane frame test‐bed program. It is intended primarily for solving the transcendental eigenvalue problems arising when the ‘exact’ member equations obtained by solving the governing differential equations of members are used to find the eigenvalues (i.e. critical buckling loads or undamped natural frequencies) of structures. The method has five stages which together ensure successful convergence on the required eigenvalues in all circumstances. Thus, whenever checks indicate its suitability, parabolic interpolation is used to obtain eigenvalues more rapidly than would the popular bisection alternative. The checks also ensure a wise choice of the determinant used by the interpolation. The determinants available are all usually zero at eigenvalues, and comprise the determinant of the overall stiffness matrix Kn and the determinants which result, with negligible extra computation, from effectively considering all except the last m (m=1, 2,…, n−1) freedoms to which Kn corresponds as internal substructure freedoms. Tests showed time savings compared to bisection of 31 per cent when finding non‐coincident eigenvalues to relative accuracy ϵ = 10−4, increasing to 62 per cent when ϵ = 10−8. The tests also showed time savings of about 10 per cent compared with an earlier Newtonian approach. The method requires no derivatives and its use in the widely available space frame program BUNVIS‐RG has demonstrated how easily it can replace bisection, which was used in the earlier program BUNVIS.
Hierarchic plate and shell models based on p‐extension
Authors: Szabó Barna A. , Sahrmann Glenn J.
Published: August 2005

This paper is concerned with formulations of finite element models for beams, arches, plates and shells based on the principle of virtual work. The focus is on computer implementation of hierarchic sequences of finite element models suitable for numerical solution of a large variety of practical problems which may concurrently contain thin and thick plates and shells, stiffeners, and regions where three dimensional representation is required. The approximate solutions corresponding to the hierarchic sequence of models converge to the exact solution of the fully three dimensional model. The stopping criterion is based on (1) estimation of the relative error in energy norm; (2) equilibrium tests and (3) observation of the convergence of quantities of interest.
Damped second‐order Rayleigh‐Timoshenko semi‐infinite beam vibration—an exact complex dynamic member stiffness matrix
Authors: Schill Mikael
Published: August 2005

A uniform linear semi‐infinite beam in a uniform linear ambient medium is studied. The beam performs stationary harmonic damped non‐synchronous space vibration in simultaneous tension, torsion, bending and shear. Hysteretic and viscous dampings of the beam material and ambient medium are considered. Four new generalized complex Kolousek functions are derived. A 6 × 6 complex symmetric stiffness matrix is established for a semi‐infinite beam member excited at its end by prescribed harmonic translations and rotations which have the same frequency but may be out of phase. This matrix extends the range of application of the so called ‘exact analysis’ of non‐proportionally damped built‐up beam structures as described in a previous paper by Lundén and Åkesson.1 Numerical examples are given, including applications of the computer program SFVIBAT‐DAMP. Power flows are studied.
Shape optimization using the boundary element method with substructuring
Authors: Sandgren Eric , Wu Shyue‐Jian
Published: August 2005

Applications of the boundary element method for two‐ and three‐dimensional structural shape optimization are presented. The displacements and stresses are computed using the boundary element method. Sub‐structuring is used to isolate the portion of the structure undergoing geometric change. The corresponding non‐linear programming problem for the optimization is solved by the generalized reduced gradient method. B‐spline curves and surfaces are introduced to describe the shape of the design. The control points on these curves or surfaces are selected as design variables. The design objective may be either to minimize the weight or a peak stress of the component by determining the optimum shape subject to geometrical and stress constraints. The use of substructuring allows for problem solution without requiring traditional simplifications such as linearization of the constraints. The method has been successfully applied to the structural shape optimization of plane stress, plane strain and three‐dimensional elasticity problems.
Finite element Euler computations in three dimensions
Authors: Peraire Jaime , Peiro Joaquin , Formaggia Luca , Morgan Ken , Zienkiewicz Olgierd C.
Published: August 2005

An explicit finite element solution procedure for the three dimensional Euler equations is presented. The solution domain is automatically meshed using a tetrahedral mesh generator which is an extension of our previous two dimensional work. Several examples are included to illustrate the performance of the generator and solver. An adaptive mesh regeneration procedure is used for the first time in three dimensions.
A rational approach for choosing stress terms for hybrid finite element formulations
Authors: Pian Theodore H. H. , Wu Chang‐Chun
Published: August 2005

A new approach for choosing the stress terms for a hybrid stress element is based on the condition of vanishing of the virtual work along the element boundary due to the stress terms higher than constant and the additional incompatible displacement. Examples using 4‐node plane stress elements have shown that when the incompatible displacements also satisfy the constant strain patch test the resulting elements will provide the most accurate solutions. Advantages of this approach for the formulation of an axisymmetric solid are also indicated.
An approach to the vibration problem of homogeneous, non‐homogeneous and composite membranes based on the boundary element method
Authors: Katsikadelis J. T. , Sapountzakis E. J.
Published: August 2005

In this paper a boundary element approach is presented to establish the eigenfrequencies and the mode shapes of the free vibrations of flexible membranes with arbitrary shape. The membranes may be of homogeneous, non‐homogeneous or composite material, while their boundaries may be fixed or elastically supported. The implementation of the method is mainly based on the development of both a boundary element technique to compute numerically the Green function for the Laplace equation and a numerical procedure to solve domain integral equations using two‐dimensional Gauss integration on regions of arbitrary shape. The efficiency of the method presented is demonstrated by applying it to study the free vibrations of membranes consisting of homogeneous, non‐homogeneous and composite material, fixed or elastically supported on the boundary, and having various shapes, such as circular, rectangular, triangular, or elliptical, or being L‐shaped or of arbitrary shape.
Development of a method for integrating time‐dependent constitutive equations with large, small or negative strain rate sensitivity
Authors: Tanaka T. G. , Miller A. K.
Published: August 2005

A unified numerical method to integrate stiff time‐dependent constitutive equations has been developed. This method is a stable, non‐iterative and self‐correcting solution procedure which works successfully over a wide range in strain rate sensitivity. Time steps are automatically controlled during integration to achieve a user‐specified accuracy. This method is implemented in the program package NONSS whose dual purpose is examination of the behaviour of unified constitutive models by themselves (‘one‐element behaviour’) as well as providing a computationally efficient subroutine for utilizing such models with existing finite element programs for non‐linear structural and metal forming analyses.

This paper first reviews the relation between the numerical characteristic of constitutive equations and the choice of integration methods. Then the paper presents the derivation of the governing basic equations in the new method, and also derives a special algorithm which permits large integration steps within the negative strain rate sensitivity (‘serrated yielding’) regime. Examples of the program's performance are given, including plasticity at high and low temperatures, cyclic deformation and multiaxial straining.
A class of data structures for 2‐D and 3‐D adaptive mesh refinement
Authors: Carey G. F. , Sharma M. , Wang K. C.
Published: August 2005

A ‘family’ of tree data structures for adaptive mesh refinement is described and details concerning the associated logic are provided. The data structures encompass triangular elements and quadrilateral elements in two dimensions and quadrilateral bricks in three dimensions. Furthermore, both linear (bilinear) and quadratic (biquadratic) element types, respectively, are developed. Representative refinement results are given for the bilinear, trilinear and biquadratic types and associated performance studies made for the refinement procedure.
A steepest edge active set algorithm for solving sparse linear programming problems
Authors: Sloan S. W.
Published: August 2005

A steepest edge active set algorithm is described which is suitable for solving linear programming problems where the constraint matrix is sparse and has more rows than columns. The algorithm uses a steepest edge criterion for selecting the search direction at each iteration and recurrence relations are derived which enable it to execute efficiently. The canonical form for the active set method is convenient for many applications and may be exploited to devise a simple crash procedure which is employed prior to phase one. A complete two‐phase algorithm which incorporates the crash procedure is outlined. Only one artificial variable is needed to determine if the linear programming problem has a feasible solution in phase one. Some computational results are given to illustrate the effectiveness of the algorithm for a range of sparse linear programming problems. Comparisons between the steepest edge criterion and the traditional Dantzig criterion suggest that the former usually requires fewer iterations and often leads to substantial savings for large problems.
SSP algorithm for linear and non‐linear dynamic response simulation
Authors: López‐Almansa F. , Barbat A. H. , Rodellar J.
Published: August 2005

A direct integration algorithm to solve the spatially discretized equations of motion of a structure is proposed. This algorithm formulates the equations of motion in state space and uses their analytical solution to derive a recursive discrete‐time equation. The proposed structural state procedure (SSP) can be considered as a generalization for multi‐degree‐of‐freedom systems of the Duhamel's integral used for single‐degree‐of‐freedom systems. It can be noted that the proposed SSP algorithm does not need a previous modal uncoupling of the equations of motion and consequently it does not require any hypothesis about damping. SSP is shown to be stable and to give accurate results with a reasonable computation time. Stability and accuracy essentially depend on the computation of the system matrix. The SSP algorithm is combined with an iterative scheme to obtain the response of structures with non‐linear behaviour. Two examples of application of SSP are included: seismic response of a building structure with linear behaviour and free vibration of a non‐linear system with imposed initial conditions.
A partially bonded beam element model for superconducting magnet pancakes
Authors: Gori R. E. , Schrefler B. A.
Published: August 2005

The stiffness matrix of a beam made of composite superconductor elements is derived. The effects of friction between conductors through the insulation layers are taken into account. Furthermore, the effects of strand transposition of the wires, already studied by the authors, are included in the model.

Some applications of the proposed approach to superconductor layouts proposed for the NET (Next European Torus) toroidal and poloidal field coils are shown. These indicate that the effects of slip are not negligible and should be taken into account in a more reliable structural analysis of the coil system. Parametric studies with varying width and heights of the insulation layer have been also carried out and the corresponding diagrams are shown here.
Fatigue life estimation of graphite/epoxy laminates under consideration of delamination growth
Authors: Bergmann H. W. , Prinz R.
Published: August 2005

A closed form approach to the assessment of the fatigue life of graphite/epoxy laminates under cyclic tension–compression loading has been developed. The model is mechanistic and uses cyclic energy release rates for prediction of delamination growth and of critical delamination sizes which induce buckling and the final failure of the laminates. Tests performed with graphite/epoxy specimens of stacking order [0n, ϕm]s with severed central plies [ϕ], and of stacking order [02, +45, 02, −45, 0, 90]s with a central unloaded hole, indicate good correlation between estimated values and observed delamination growth, critical buckling strength of separated plies and load cycles to failure.
Composite plate analysis using a new discrete shear triangular finite element
Authors: Lardeur P. , Batoz J. L.
Published: August 2005

This paper deals with the static and dynamic (free vibrations) analysis of plates built up with a symmetric series of orthotropic layers. The formulation of a new simple triangular finite element having three nodes and three degrees of freedom per node is presented. The element called DST (Discrete Shear Triangle) is free of shear locking and has a proper rank. It coincides with DKT (Discrete Kirchhoff Triangle) when the transverse shear effects are negligible. A large number of classical problems is considered to evaluate the performance of the element for the analysis of composite plates. Very satisfactory results are obtained for displacements, stresses and frequencies.
On an SSOR matrix relationship and its consequences
Authors: Galanis S. , Hadjidimos A. , Noutsos D.
Published: August 2005

A matrix relationship connecting the Jacobi and the Symmetric Successive Overrelaxation (SSOR) matrices associated with a k‐cyclic consistently ordered matrix A is presented. Next the equivalence of the SSOR method and a certain monoparametric k‐step one for the solution of the linear algebraic system Ax = b is established. The aforementioned equivalence can be exploited to derive regions of convergence, optimum parameters involved, etc. of the two iterative methods above. This is done by studying the simplest of the two methods that is the monoparametric k‐step one. To show how the idea works the case k = 2 is very briefly discussed.