bluuebunny/crossref_metadata_2025 huggingface dataset:
Application of differential quadrature to static analysis of structural components
Authors: Jang Sung K. , Bert Charles W. , Striz Alfred G.
Published: November 2005

The numerical technique of differential quadrature for the solution of linear and non‐linear partial differential equations, first introduced by Bellman and his associates, is applied to the equations governing the deflection and buckling behaviour of one‐ and two‐dimensional structural components. Separate transformations are used for higher‐order derivatives, as suggested by Mingle, thus extending the method to treat fourth‐order equations and to include multiple, boundary conditions in the respective co‐ordinate directions. Results are obtained for various boundary and loading conditions and are compared with existing exact and numerical solutions by other methods. The application of differential quadrature to this class of problems is seen to lead to accurate results with relatively small computational effort.
An optimality criterion method for dynamic optimization of structures
Authors: Sadek Edward A.
Published: November 2005

This paper presents an optimality criterion method for the determination of the least weight design of a structural system which satisfies a specific frequency requirement plus upper and lower bounds on the design variables. The design algorithm is an iterative solution of the Kuhn–Tucker optimality criterion based on choosing a single value of the Lagrange multiplier which minimizes the sum of the squares of residuals.

The method has been applied to a variety of structures. Results assert that the method is capable of locating the optimal design in a small number of redesign cycles. The method avoids the scaling of design variables. It can treat non‐structural masses and is applicable to. structural elements with a wide variety of size‐stiffness. The procedure has been completely automated in a computer program on an IBM‐PC microcomputer.
Efficient optimization of integrated aerodynamic–structural design
Authors: Haftka R. T. , Grossman B. , Eppard W. M. , Kao P. J. , Polen D. M.
Published: November 2005

The introduction of composite materials is having a profound effect on the design process. Because these materials permit the designer to tailor material properties to improve structural, aerodynamic and acoustic performance, they require a more integrated multidisciplinary design process. Because of the complexity of the design process numerical optimization methods are required.

The present paper is focused on a major difficulty associated with the multidisciplinary design optimization process—its enormous computational cost. We consider two approaches for reducing this computational burden: (i)development of efficient methods for cross‐sensitivity calculation using perturbation methods; and (ii) the use of approximate numerical optimization procedures. Our efforts are concentrated upon combined aerodynamic‐structural optimization. Results are presented for the integrated design of a sailplane wing. The impact of our computational procedures on the computational costs of integrated designs is discussed.
A new C1 finite element: Full heptic
Authors: Boisserie J. M.
Published: November 2005

A new C1 finite element complete in 7th degree polynomial basis is described and compared with other C1 elements in an eigen‐elements analysis.
A stream tube based upper bound approach to plane strain metal forming analysis
Authors: Walker Norman D.
Published: November 2005

In an attempt to establish a practicable computer based metal forming analysis capability, the classical upper bound theorem has been revisited. The result is an enhanced methodology which holds promise of providing some of the capabilities associated with more sophisticated finite element formulations without the attendant costs. The procedures developed here culminate with two sample applications.
Iterated θ‐method for hyperbolic equations
Authors: van der Houwen P. J. , Sommeijer B. P.
Published: November 2005

The iterated θ‐methods employing residue smoothing for finding both steady state and time‐accurate solutions of semidiscrete hyperbolic differential equations are analysed. By the technique of residue smoothing the stability condition is considerably relaxed, so that larger time steps are allowed which improves the efficiency of the method. The additional computational effort involved by the explicit smoothing technique used here is rather low when compared with its stabilizing effect. However, in the case where time‐accurate solutions are desired, the overall accuracy may be decreased. This paper investigates the effect of residue smoothing on both the stability and accuracy, and presents a number of explicitly given methods based on the iterated implicit midpoint rule (θ = 1/2). Numerical examples confirm the theoretical results.
A finite element spectral method with application to the thermoelastic analysis of space structures
Authors: Rand Omri , Givoli Dan
Published: November 2005

A combined spectral finite element method is devised for use in finding the thermal and thermoelastic dynamic response of truss structures to time‐periodic loading. The thermal problem is strongly non‐linear due to the presence of heat radiation. The problems considered are typical in the analysis of space structures. In the method proposed, the spatial domain is first discretized using a consistent finite element formulation. Then the resulting semi‐discrete equations in time are solved analytically by using a spectral method that is symbolically coded. Some numerical examples are presented which demonstrate the performance of the method and its ability to identify some key characteristics in space structure problems.
A Petrov–Galerkin/modified operator formulation for convection–diffusion problems
Authors: de Sampaio P. A. B.
Published: November 2005

A new Petrov–Galerkin method to deal with convection–diffusion problems is presented. The formulation is derived from the concept of using a modifying function to make the differential operator self‐adjoint. The so‐called ‘optimal upwind’ parameter (α) arises naturally from the process of approximating the modifying function. Transient and steady‐state examples on uniform and non‐uniform meshes are shown.
Thermo‐mechanical finite element model of casting systems
Authors: Song R. , Dhatt G. , Cheikh A. Ben
Published: November 2005

A coupled finite element model is developed to simulate the metal casting process. We present a new method for capturing the solidification zone and obtaining the corresponding rate of phase change. The latent energy release is predicted by the heat conduction rate and introduced by following the enthalpy‐temperature curve. The influence of mould‐metal contact is considered in calculating the heat flux through the mould‐metal interface. A viscoplastic model is employed to predict the gap opening and evolution of plastification.

Four examples are presented to demonstrate certain numerical aspects and the capability of the model for industrial applications.
The numerical simulation of heat conduction in irregularly‐shaped materials of thermally‐dependent properties
Authors: Schreiber W. C.
Published: November 2005

The numerical simulation of conduction heat transfer in arbitrarily‐shaped regions is relevant to many engineering applications including the casting of plastics and metals, cold region problems and latent heat storage. This class of problem offers its particular challenges. The accurate computational simulation of conduction with thermally‐dependent properties requires a solution technique with good conservation properties. The boundary‐fitted co‐ordinates of an arbitrary solution domain typically yield grids which are non‐orthogonal and which, consequently, make energy conservation difficult to model.

In the current article, a technique is described to simulate accurately the conduction heat transfer in materials of thermally‐dependent properties in irregular domains. The method combines boundary‐fitted co‐ordinates with the finite volume method, FVM, to produce a numerical technique which will accurately solve this non‐linear conduction problem using a grid which may be highly skewed. This capability is achieved through a unique treatment of the cross‐derivative terms that arise when the heat conduction equation is transformed to a non‐orthogonal grid. The cross‐derivative terms represent the non‐normal components of the heat fluxes into the skewed control volume. The tangent components of the heat fluxes are interpreted in a special way to produce finite difference expressions which accurately model the cross‐derivative partial.

The numerical procedure is validated by comparing it against a purely analytical mathematical method. Although the numerical results have been obtained using a highly skewed grid, they exhibit close agreement with the analytically‐derived solution.
A conservative algorithm for multidimensional conduction phase change
Authors: Comini G. , Giudice S. Del , Saro O.
Published: November 2005

In this paper, a generally applicable version of an algorithm, for multidimensional phase change conduction, is presented which bridges the gap between ‘full enthalpy’ and ‘equivalent heat capacity’ methods. In the text the problem is formulated first with reference to the three‐time‐level method for the FE analysis of non‐linear heat conduction. Then the suggested algorithm is utilized as a ‘corrector’ which can be activated for the analysis of isothermal phase change problems. In the corrector step the enthalpy balance is recovered from the standard formulation, and temperatures are post‐calculated by means of the inverse temperature vs. enthalpy function. The algorithm is verified in one‐dimensional situations by comparing the results obtained with available analytical and numerical solutions for boundary conditions of the first kind (temperature) and of the third kind (convection). Finally, as a 2‐D test problem, a solution is presented for inward solidification in a cylinder, using Cartesian co‐ordinates to demonstrate robustness with respect to space deformation of the mesh.
Computer simulation of salami drying
Authors: Imre L. , Környey T.
Published: November 2005

Salami sorts are made of special meat pastes filled in hygroscopic casing and preserved by drying.

The characteristic features and the time of drying are greatly affected by the operational conditions. Factories are interested in reducing the time of the drying treatment. To determine a reliable and economic drying schedule a physical‐mathematical model has been elaborated and used. The system of equations has been solved numerically by using the FDM technique for the determination of the temperature, concentration and stress fields as a function of the time. Computed results have been verified by experiments.

By the numerical analysis it has been proved that the maximum rate of drying to be permitted is limited by the danger of possible deformations and inner fissures caused by tensile stresses occurring if shrinkage is prevented.

On the basis of the proper drying schedule an algorithm and a strategy of the microprocessing operational control has been elaborated.
Recent advances, trends and new perspectives via enthalpy‐based finite element formulations for applications to solidification problems
Authors: Tamma Kumar K. , Namburu Raju R.
Published: November 2005

The present paper describes recent advances and trends in finite element developments and applications for solidification problems. In particular, in comparison to traditional methods of approach, new enthalpy‐based architectures based on a generalized trapezoidal family of representations are presented which provide different perspectives, physical interpretation and solution architectures for effective numerical simulation of phase change processes encountered in solidification problems. Various numerical test models are presented and the results support the proposition for employing such formulations for general phase change applications.
Approximate predictions of ice accretion along conductors of finite torsional stiffness and control of rotation using counterweights
Authors: Skelton P. L. I. , Poots G.
Published: November 2005

A mathematical/computational model for the approximate prediction of ice accretion on a conductor of finite torsional stiffness is constructed. The model, which is adapted to allow for the attachment of counterweights along the span, is three‐dimensional and time‐dependent. In the absence of counterweights, axial growth is predicted near the anchors, and cylindrical‐sleeve growth at the centre of the conductor span. The latter is caused by eccentric ice loading on the windward side of the conductor which then induces the conductor to rotate.

The ‘icing‐clock’ model, based on the use of the large relaxation time approximation for particle impaction, yields an upper bound to the mass of ice accreted. At the end of each deposit time the torque density along the conductor span due to ice loading is calculated. On solving the non‐linear torsion equation for the conductor the rotation of the conductor and location of the evolving ice surface as a function of the distance from the tower and the accretion time are then deduced.

Numerical results are given for conductor with varying mechanical properties, which are represented in terms of a single dimensionless torque parameter, with and without the attachment of counterweights. For a specific case illustrative results are given for the mass of ice accreted and conductor rotation when one, two, three and four counterweights are attached per span.
Computational enhancement of an unsymmetric block Lanczos algorithm
Authors: Kim Hyoung M. , Craig Roy R.
Published: November 2005

An unsymmetric block Lanczos algorithm has been employed for the dynamic analysis of a large system which has arbitrary damping and/or repeated (or closely spaced) eigenvalues. In the algorithm development, the right and left Lanczos vectors are all theoretically biorthogonal to each other. However, these vectors may lose the biorthogonality owing to cancellation and roundoff errors. For the unsymmetric case there can be a breakdown, even without numerical errors. This paper describes computational techniques which have led to a robust unsymmetric block Lanczos algorithm.
New hybrid Laplace transform/finite element method for three‐dimensional transient heat conduction problem
Authors: Chen Cha'o‐Kuang , Chen Tzer‐Ming
Published: November 2005

The paper presents results obtained by the implementation of a new hybrid Laplace transform/finite element method developed by the authors. The present method removes the time derivatives from the governing differential equation using the Laplace transform and then solves the associated equation with the finite element method. Previously reported hybrid Laplace transform/finite element methods1 have been confined to one nodal solution at a time. When applied to many nodes it takes an excessive amount of computer time. By using a similarity transform method on the matrix of the complex number coefficients this restriction is removed and the reported new method provides a more useful tool for the solution of linear transient problems. Test examples are used to show that the basic accuracy is comparable to that obtainable by analytical, finite difference and finite element methods.
Lagrange constraints for transient finite element surface contact
Authors: Carpenter Nicholas J. , Taylor Robert L. , Katona Michael G.
Published: November 2005

A new approach to enforce surface contact conditions in transient non‐linear finite element problems is developed in this paper. The method is based on the Lagrange multiplier concept and is compatible with explicit time integration operators. Compatibility with explicit operators is established by referencing Lagrange multipliers one time increment ahead of associated surface contact displacement constraints. However, the method is not purely explicit because a coupled system of equations must be solved to obtain the Lagrange multipliers. An important development herein is the formulation of a highly efficient method to solve the Lagrange multiplier equations. The equation solving strategy is a modified Gauss‐Seidel method in which non‐linear surface contact force conditions are enforced during iteration. The new surface contact method presented has two significant advantages over the widely accepted penalty function method: surface contact conditions are satisfied more precisely, and the method does not adversely affect the numerical stability of explicit integration. Transient finite element analysis results are presented for problems involving impact and sliding with friction. A brief review of the classical Lagrange multiplier method with implicit integration is also included.
An efficient hybrid quadrilateral Kirchhoff plate bending element
Authors: Sze K. Y. , Chow C. L.
Published: November 2005

This paper discusses the formulation of a hybrid stress quadrilateral Kirchhoff plate bending element based on an extended complementary energy functional first proposed by Tong. With the inclusion of a Lagrange multiplier in the functional to enforce a constraint on the assumed moment space, the construction of the C1 deflection profile inside the element is no longer necessary. The continuity requirement on the deflection across the element interfaces is fulfilled by interpolating the generalized nodal displacements over the element boundary in the usual way. Special attention is paid to the selection of assumed moment space such that the element stability, convergency, invariance and nodal point numbering insensitivity are secured while the implementational cost of the element is kept low. Quadratic serendipity interpolation of the transverse deflection is adopted to discretize the distributed transverse loading. Numerical examples are presented and the accuracy achieved is found to be satisfactory.
Efficient boundary element analysis of sharp notched plates
Authors: Portela A. , Aliabadi M. H. , Rooke D. P.
Published: November 2005

The present paper further develops the boundary element singularity subtraction technique, to provide an efficient and accurate method of analysing the general mixed‐mode deformation of two‐dimensional linear elastic structures containing sharp notches. The elastic field around sharp notches is singular. Because of the convergence difficulties that arise in numerical modelling of elastostatic problems with singular fields, these singularities are subtracted out of the original elastic field, using the first term of the Williams series expansion. This regularization procedure introduces the stress intensity factors as additional unknowns in the problem; hence extra conditions are required to obtain a solution. Extra conditions are defined such that the local solution in the neighbourhood of the notch tip is identical to the Williams solution; the procedure can take into account any number of terms of the series expansion. The standard boundary element method is modified to handle additional unknowns and extra boundary conditions. Analysis of plates with symmetry boundary conditions is shown to be straightforward, with the modified boundary element method. In the case of non‐symmetrical plates, the singular tip‐tractions are not primary boundary element unknowns. The boundary element method must be further modified to introduce the boundary integral stress equations of an internal point, approaching the notch‐tip, as primary unknowns in the formulation. The accuracy and efficiency of the method is demonstrated with some benchmark tests of mixed‐mode problems. New results are presented for the mixed‐mode analysis of a non‐symmetrical configuration of a single edge notched plate.
Optimal use of a numerical method for solving differential equations based on Taylor series expansions
Authors: Sonnemans P. J. M. , de Goey L. P. H. , Nieuwenhuizen J. K.
Published: November 2005

Efficiency in solving differential equations is improved by increasing the order of a Taylor series approximation. Computing time can be reduced up to a factor of 40 and an amount of memory storage can be saved, up to a factor of 70.

The truncation error can be estimated not only by order but also by magnitude.
The moment redistribution effect of the C0 structural elements formulation
Authors: Briassoulis D.
Published: November 2005

A new formulation was proposed recently for the removal of the shear and membrane locking mechanisms from the C0 structural elements. The performance of the new formulation was shown to be excellent in many cases of beam, plate and shell element applications, completely eliminating all locking problems. However, this formulation has its own problems. The potential introduction of softening effects (yielding softer models) and a rotational zero energy mode describe the problematic behaviour of the new formulation in cases of C0 plate and shell element applications. Analysis of this behaviour reveals some interesting aspects of the classical finite element formulation and allows for a better insight into the overall behaviour of the C0 structural elements. As a result of the present analysis, a modification of new formulation, remedying its problematic behaviour, will appear soon.
Static and dynamic contact/impact problems using fictitious forces
Authors: Ayari Mohamed L. , Saouma Victor E.
Published: November 2005

A new finite element model for the contact/impact problem is presented, and both its static and dynamic implementations are described. In this geometrical non‐linear formulation, contact (from node to surface) is simulated through fictitious equivalent pressure along the boundary. Contrary to most existing models, this formulation entails relatively few matrix decompositions and thus is computationally inexpensive. The model is first assessed through some classical contact problems, and is subsequently applied to the fracture mechanics based analysis of a cracked dam under seismic excitation.
Automatic three‐dimensional mesh generation by the finite octree technique
Authors: Shephard Mark S. , Georges Marcel K.
Published: November 2005

An octree‐based fully automatic three‐dimensional mesh generator is presented. The mesh generator is capable of meshing non‐manifold models of arbitrary geometric complexity through the explicit tracking and enforcement of geometric compatibility and geometric similarity at each step of the meshing process. The resulting procedure demonstrates a linear growth rate with respect to the number of elements and can be easily integrated with any geometric modeller through a set of geometric operators.
Adaptivity and mesh generation
Authors: Zienkiewicz O. C. , Zhu J. Z.
Published: November 2005

The objective of achieving economically finite element solutions of specified accuracy is now within reach. The importance of this objective is finally recognized by commercial code originators and efforts directed at automating the process are meeting with success.

Three essential ingredients are here necessary. These are: (i) economical and efficient a posteriori error estimating processes; (ii) close prediction of the refinement necessary for a specific accuracy to be achieved so that numerous trial and error solutions can be avoided; (iii) implementation of the predicted refinement.

With h and h‐p adaptive processes Step (iii) requires powerful mesh generator facilities capable of achieving meshes of specified density.

The paper considers all three aspects, introducing some novel concepts in error estimation and discussing in some detail the problem of mesh generation. As such, it introduces the other papers of this special issue, which discuss various aspects in more detail.
A modified Euler method for dynamic analyses
Authors: Hahn G. D.
Published: November 2005

A modified version of the well known Euler method for numerical integration is presented, and its application in analyses of the dynamic response of structures is discussed. This modified method was first introduced in 1981, and it has been reported that it was discovered by accident. When first introduced, however, valuable information related to the accuracy, stability and merits of the method were not provided. It is shown that the modified Euler method has features that make it an attractive approach for applications in dynamic analyses of structures. Accuracy and stability analyses are made for the method by considering free‐vibrational responses of linear, undamped, single‐degree‐of‐freedom systems. The method is explicit and extremely easy to use. However, it is conditionally stable. Applications of the method are also made which illustrate its usefulness and inherent simplicity. Furthermore, comparisons of the modified Euler method and the Newmark beta method are reported which elucidate the relative merits of these methods.
A two‐node beam element including transverse shear and transverse normal deformations
Authors: Tessler Alexander
Published: November 2005

A variational higher‐order theory for bending and stretching of linearly elastic orthotropic beams including the deformations due to transverse shearing and stretching of the transverse normal fibre is presented. The theory assumes a linear distribution for the longitudinal displacement and a parabolic variation of the transverse displacement across the thickness. Additionally, independent expansions are introduced for the through‐thickness displacement gradients with the requirement of a least‐square compatibility for the transverse strains and the satisfaction of exact stress boundary conditions at the top/bottom beam surfaces. The theory is shown to be well suited for finite element development requiring simple C0‐ and C−1‐ continuous displacement interpolation fields. To demonstrate the computational utility of the theory, a simple two‐node stretching‐bending finite element is formulated. The analytic and finite element results are obtained for a simple bending problem for which an exact elasticity solution is available. It is shown that the inclusion of the transverse normal deformation in the present theory enables improved displacement, strain and stress predictions, particularly, in the analysis of deep beams.
Modelling of superelements in mechanism analysis
Authors: Cardona Alberto , Geradin Michel
Published: November 2005

The paper deals with substructuring for dynamic analysis of flexible multibody systems. Three different techniques based on component synthesis are discussed, corresponding respectively to fully consistent mass discretization, lumped mass discretization and corotational approximation of inertia forces. To simplify the computer implementation, only the lumped mass and corotational approximations have been considered in detail and programmed. Both approaches are validated on simple examples of rotating beams for which a full elastic model is available using a fully non‐linear beam element. The computational efficiency of the corotational inertia approach is also demonstrated on the deployment of a large flexible satellite antenna.
Contribution to symbolic analysis of deformable multi‐body systems
Authors: Fisette P. , Samin J. Cl. , Willems P. Y.
Published: November 2005

The aim of this paper is to present the equations of motion of deformable multi‐body systems in a compact form which is suitable for symbolic generation. Particular attention is paid to obtaining the various equations corresponding to joint displacements and body deformations in a unified manner. A large number of common intermediate terms are identified and appropriately assembled in the final form of the equations; for the various applications, this simple consideration permits one to drastically save on the computational effort. This paper also presents the data which are necessary to completely formulate the problem when the body deformations are described by a linear elasticity model (obtained from a modal or finite element description).
A method for selecting deformation modes in flexible multibody dynamics
Authors: Friberg Olof
Published: November 2005

In multibody dynamics one may use a number of mode shapes for each body to capture flexibility effects. If a co‐rotational and co‐translational formulation is applied, rigid body motions are described using special generalized co‐ordinates for reference frames and such motions cannot therefore be spanned by the chosen set of mode shapes.

Constraint modes are attractive to use following the FEM direct stiffness appraoch and can give accurate solutions with a minimum number of mode shapes in static and low frequency excitation problems. A set of constraint modes often span rigid body motions.

The objective of this paper is to show the usefulness of combining constraint modes with an orthogonalization and subsequent rigid body mode shape rejections. In this way the remaining deformation modes together with the reference frame generalized co‐ordinates span the solution space of the original set of constraint modes.

Two numerical examples are included. A simulation of a truck frame vehicle passing a bump was carried out. A rotating structure with positioning PID‐control was studied.
An exact finite rotation shell theory, its mixed variational formulation and its finite element implementation
Authors: Sansour Carlo , Bufler Hans
Published: November 2005

A non‐linear shell theory, including transverse shear strains, with exact description of the kinematical fields is developed. The strain measures are derived via the polar decomposition theorem allowing for an explicit use of a three parametric rotation tensor. Thus in‐plane rotations, also called drilling degrees of freedom, are included in a natural way. Various alternatives of the theory are derived. For a special version of the theory, with altogether six kinematical fields, different mixed variational principles are given. A hybrid finite element formulation, which does not exhibit locking phenomena, is developed. Numerical examples of shell deformation at finite rotations, with excellent element performance, are presented. Comparison with results reported in the literature demonstrates the features of the theory as well as the proposed finite element formulation.
Adaptive finite difference methods for liquid membranes
Authors: Ramos J. I.
Published: November 2005

A domain‐adaptive technique and an iterative, block bidiagonal method are used to analyse the unsteady dynamics of annular liquid membranes subject to fluctuations in the mass injected into the volume enclosed by the membranes. The domain‐adaptive technique maps the unknown, time‐dependent, curvilinear geometry of the liquid membrane into a unit interval. The condition that the membrane's radius is zero at the convergence point is used to determine the convergence length, which is governed by an ordinary differential equation. This equation is solved iteratively together with those which govern the fluid dynamics equations. A block bidiagonal technique is used to determine the mass per unit length, radius, and axial and radial velocity components of the membrane. It is shown that the pressure of the gases enclosed by the liquid membrane responds instantaneously to changes in and exhibits the same periodic behaviour as the mass injection rate. The convergence length takes a delay time to respond to the mass injection rate fluctuations. The magnitude of this delay time increases as the Froude and Weber numbers and the nozzle exit angle are increased. The amplitude of the oscillations of both the convergence length and the pressure coefficient increases as the pressure difference across the membrane and the amplitude of the mass injection rate fluctuations are increased.
Shape functions and integration formulas for three‐dimensional finite element analysis
Authors: Bedrosian G.
Published: November 2005

Shape functions and numerical integration formulas for three‐dimensional finite element analysis as found in most finite element reference books are incomplete. For example, shape functions and integration formulas for a pyramid with a quadrilateral base are missing. It is also difficult to find symmetric higher‐order integration formulas for triangular and tetrahedral elements. In general, these shape functions and integration formulas cannot be satisfactorily derived as degenerate cases of shape functions and integration formulas for hexahedral (brick) elements. In this paper we present C°‐continuous quadrilateral pyramid elements and integration formulas for two‐ and three‐dimensional elements.
An adaptive h‐refinement using transition element for plate bending problems
Authors: Choi Chang‐Koon , Park Yong‐Myung
Published: November 2005

An adaptive h‐refinement procedure utilizing compatible 5‐ to 7‐node quadrilateral transition elements together with 4‐node elements is presented for Reissner–Mindlin plate bending problems. By introducing the transition elements which have physical midside nodes, some difficulties associated with imposing displacement constraints on irregular nodes to enforce interelement compatibility in common adaptive h‐refinement on quadrilateral mesh are easily overcome. Numerical examples are presented to show the effectiveness of using the transition elements for the adaptive h‐refinement.
The iterative solution of Taylor—Galerkin augmented mass matrix equations
Authors: Ding D. , Townsend P. , Webster M. F.
Published: November 2005

This paper investigates the convergence properties of iterative schemes for the solution of finite element mass matrix equations that arise through the application of a Taylor‐Galerkin algorithm to solve instationary Navier‐Stokes equations. This is a time‐stepping algorithm that involves Galerkin mass matrix equations at fractional stages within each time‐step. Plane Poiseuille flow and shear‐driven cavity flow are selected as benchmark problems on which to investigate the effects of various choice of scheme and time‐step dependency. The iterative convergence of each mass matrix equation for a single fractional stage is studied, both at the element and the system matrix level. The underlying theory is confirmed and it is shown how optimal iterative convergence rates may be achieved for a Jacobi scheme by employing an appropriate acceleration factor. Moreover, this factor is trivial to compute. The consequential effects on the convergence of the time‐stepping procedure to reach steady‐state are also considered where non‐linear effects are present.
New variational formulations for minimal surfaces
Authors: Tabarrok B. , Tong Liyong
Published: November 2005

Using curvilinear co‐ordinates of the surface, a functional is developed for the classical formulation for minimum surfaces and is then utilized to obtain a complementary formulation. Unlike the classical formulation in Cartesian co‐ordinates, these two formulations are applicable to multi‐valued surfaces and give upper and lower bounds to the exact solution when used in an approximate analysis, e.g. finite elements. By means of Lagrange multipliers, a constraint on enclosed volume is incorporated into the basic functional.
Gradient‐dependent plasticity: Formulation and algorithmic aspects
Authors: De Borst René , Mühlhaus Hans‐Bernd
Published: November 2005

A plasticity theory is proposed in which the yield strength not only depends on an equivalent plastic strain measure (hardening parameter), but also on the Laplacian thereof. The consistency condition now results in a differential equation instead of an algebraic equation as in conventional plasticity. To properly solve the set of non‐linear differential equations the plastic multiplier is discretized in addition to the usual discretization of the displacements. For appropriate boundary conditions this formulation can also be derived from a variational principle. Accordingly, the theory is complete.

The addition of gradient terms becomes significant when modelling strain‐softening solids. Classical models then result in loss of ellipticity of the governing set of partial differential equations. The addition of the gradient terms preserves ellipticity after the strain‐softening regime has been entered. As a result, pathological mesh dependence as obtained in finite element computations with conventional continuum models is no longer encountered. This is demonstrated by some numerical simulations.
Error estimators using global–local methods
Authors: Mao K. M. , Sun C. T.
Published: November 2005

Error estimators were derived using global‐local and refined global‐local finite element methods and an extrapolation technique. The proposed error estimators are to be used in estimating the global error energy norm, local error energy norm and nodal displacement error. These error estimators were applied to three numerical examples. The results clearly demonstrated that these error estimators are of high quality.
Spacecraft thermal modelling
Authors: Chin J. H. , Panczak T. D. , Fried L.
Published: November 2005

Thermal modelling of spacecraft requires approaches which can handle dominant radiative heat transfers and many special thermal control components. Present network‐type thermal analysers allow simulation, especially for components with rectangular geometries, but at the expense of considerable awkwardness and much error‐prone manual input. The user interfaces for pre‐ and postprocessing for these analysers are also very deficient. Finite element thermal analysers solve some of the analytical difficulties, but are not widely used because they lack the flexibility to simulate special operations. The Galerkin finite element method (GFEM) distributes the contributions within an element to the element nodal points. The assembly of the contributions from all elements yields a systems of energy balance equations for the nodal points of the system. Monte Carlo raytracing, in conjunction with a GFEM energy distribution to element nodal points, yields a procedure of consistent non‐isothermal surface radiation exchange. This procedure reduces a source of simulation error caused by non‐uniform element illumination and shading. Orbital heating, fluid flow and special analysis features are discussed. The main analysis program is interfaced to the preprocessing and postprocessing modules. Example results are given.
Adaptive explicit and implicit finite element methods for transient thermal analysis
Authors: Probert E. J. , Hassan O. , Morgan K. , Peraire J.
Published: November 2005

The application of adaptive finite element methods to the solution of transient heat conduction problems in two dimensions is investigated. The computational domain is represented by an unstructured assembly of linear triangular elements and the mesh adaptation is achieved by local regeneration of the grid, using an error estimation procedure coupled to an automatic triangular mesh generator. Two alternative solution procedures are considered. In the first procedure, the solution is advanced by explicit timestepping, with domain decomposition being used to improve the computational efficiency of the method. In the second procedure, an algorithm for constructing continuous lines which pass only once through each node of the mesh is employed. The lines are used as the basis of a fully implicit method, in which the equation system is solved by line relaxation using a block tridiagonal equation solver. The numerical performance of the two procedures is compared for the analysis of a problem involving a moving heat source applied to a convectively cooled cylindrical leading edge.
A physical interpretation of conservative and non‐conservative finite element formulations of convection‐type problems
Authors: Giudice S. Del , Comini G. , Nonino C.
Published: November 2005

In this paper, finite element formulations of convection‐type problems are derived by means of an essentially physical approach. No new expressions are obtained for global matrices and vectors, but clear physical interpretations are provided for all the essential steps of conventional procedures based on the Galerkin method. The final systems of discretized equations are obtained from energy balances which yield conservative numerical models if reference is made to the conservative forms of the differential equations, or non‐conservative numerical models if, instead, the non‐conservative forms of the differential equations are considered.
Modelling and computation of slow‐burning pyrotechnical compositions using a fixed mesh finite element formulation
Authors: Loyd Dan , Andersson Gunnar , Karlsson Matts
Published: November 2005

The ignition of explosives and illuminants can be controlled and delayed by using a combination of different pyrotechnical compositions. For quick‐burning compositions the burning velocity is mostly determined by the properties of the compositions and by the geometry of the case: For low burning velocity, however, both the initial temperature and the heat transfer from the compositions are important factors. The influence of a phase transition process in the composition is here a factor important for the burning velocity.

By a suitable design of the case containing the pyrotechnical compositions and a suitable choice of these compositions, performance, as well as safety, can be improved. The design work is complex and comprises numerical simulations, laboratory tests and full scale tests. Generally it is preferable to start with a numerical analysis of the problem. The number of laboratory and full scale tests must always be minimized as they are time‐consuming and expensive, and thus numerical models are essential as a cheap and reliable tool in the design work.

Statistical design of experiments has been used to reduce the number of numerical calculations required for evaluating the influence of different parameters essential for the burning velocity. From these calculations a limited number of laboratory and full scale experiments are planned. The number of tests as well as the cost will be reduced.

Special procedures based on the finite element method are used both for the phase transition process and for the combustion process. The latent heat of a region with phase change material is concentrated at the nodes of the elements in that region. A fixed finite element mesh is used. The temperature of a node with latent heat is kept at the melting temperature during the transition process.

The heat of combustion is associated with the finite elements. The combustion starts when the mean temperature of such an element exceeds the ignition temperature of the composition and ceases when all the heat of combustion in the element is released or if the temperature of the element falls below the ignition temperature. The elements with ongoing combustion form a reaction zone, which propagates into the pyrotechnical composition.

In the present study the method is applied to a test case in order to investigate the applicability of the method.
Development of a monte carlo method for numerical analysis on radiative energy transfer through non‐grey‐gas layer
Authors: Taniguchi Hiroshi , Kudo Kazuhiko , Otaka Maromu , Sumarsono Markus , Obata Masakazu
Published: November 2005

An analytical method is developed to study the radiative energy transfer in a non‐grey‐gas layer by using a Monte Carlo method. The gas is composed of water vapour, carbon dioxide and nitrogen. The profiles of the monochromatic absorption coefficient of each component gas are calculated by using the Elsasser model and wide band model parameters derived by Edwards. The validity of this method is confirmed by comparing the results of the gas emissivity with the ones obtained from Hottel's chart. By using this method, radiative energy transfer is analysed through a one dimensional gas layer between two parallel solid walls with different temperatures. From the analyses, it is shown that the temperature profile in the gas layer is not properly estimated by using Hottel's gas‐emissivity charts, though the net heat flux between the bounding walls is estimated properly.
A simple class of finite elements for plate and shell problems. I: Elements for beams and thin flat plates
Authors: Phaal R. , Calladine C. R.
Published: November 2005

This is the first paper of a pair which together discuss the development of a class of overlapping hinged bending finite elements which are suitable for the analysis of thin‐shell, plate and beam structures. These elements rely on a simple physical analogy, involving overlapping hinged facets. They are based on quadratic overlapping assumed displacement functions. Only translational nodal degrees of freedom are necessary, which is a significant simplification over most other currently available beam, plate and shell finite elements which employ translational, rotational and higher‐order nodal variables. In this paper the hinged bending element concept is introduced, and the hinged beam bending (HBB) and hinged plate bending (HPB) elements are formulated. In paper II these concepts are extended to develop a hinged shell bending (HSB) element. The HSB element can be readily combined with the constant strain triangular (CST) plane stress finite element for the modelling of thin‐shell structures.
A simple class of finite elements for plate and shell problems. II: An element for thin shells, with only translational degrees of freedom
Authors: Phaal R. , Calladine C. R.
Published: November 2005

This paper is the second of a pair which discuss the development of a class of overlapping hinged bending finite elements, which are suitable for the analysis of thin‐shell, plate and beam structures. These elements rely on a simple physically appealing analogy, in which overlapping hinged facets are used to represent bending effects. They are based on quadratic overlapping assumed displacement functions, which results in constant stress/strain representation. Only translational nodal degrees of freedom are necessary, which is a significant advantage over most other currently available beam, plate and shell finite elements which employ translational, rotational and higher‐order nodal variables. In paper I the hinged bending element concept has been introduced, and the hinged beam bending (HBB) and hinged plate bending (HPB) elements formulated. In the present paper these concepts are extended to develop a hinged shell bending (HSB) element. The HSB element can be readily combined with the constant strain triangular (CST) plane stress finite element for the modelling of thin‐shell structures; and the combined HSB‐CST element is tested against a number of 'standard' thin‐shell problems. The present paper, like paper I, is conducted entirely in the context of small‐displacement elastic behaviour.
Tabu search method with random moves for globally optimal design
Authors: Hu Nanfang
Published: November 2005

Optimum engineering design problems are usually formulated as non‐convex optimization problems of continuous variables. Because of the absence of convexity structure, they can have multiple minima, and global optimization becomes difficult. Traditional methods of optimization, such as penalty methods, can often be trapped at a local optimum. The tabu search method with random moves to solve approximately these problems is introduced. Its reliability and efficiency are examined with the help of standard test functions. By the analysis of the implementations, it is seen that this method is easy to use, and no derivative information is necessary. It outperforms the random search method and composite genetic algorithm. In particular, it is applied to minimum weight design examples of a three‐bar truss, coil springs, a Z‐section and a channel section. For the channel section, the optimal design using the tabu search method with random moves saved 26.14 per cent over the weight of the SUMT method.