bluuebunny/crossref_metadata_2025 huggingface dataset:
Modelling coastal/shelf systems with emphasis on long term trends
Authors: Nihoul Jacques C. J. , Djenidi S. , Hecq J. H.
Published: August 2005

Hydrodynamic studies of continental seas have been primarily concerned with tides and storm surges and the associated currents which can have velocities as high as several metres per second.

However, the period of the dominant tide is only about half a day and the characteristic life time of a synoptic weather pattern is of the order of a few days. The very strong currents which are produced by the tides and the atmospheric forcing are thus relatively transitory and, over time scales of biological interest, they change and reverse so many times that they more or less cancel out, leaving only a small residual contribution to the net water circulation.

Mathematical modelling appears at present as the most reliable approach to the determination of the residual circulation and of the long term transport of nutrients and pollutants in the sea.

The residual circulation model developed at the GeoHydrodynamics and Environment Research Laboratory of Liège University (GHER) is described and illustrated by its application to the West‐European Continetal Shelf.

Residual flow patterns on the shelf, and in particular in the Irish Sea and the North Sea, are presented and shown to be in excellent agreement with the observations.

The results are exploited to estimate the typical routes and times of residence of nutrients and pollutants and the subsequent long term changes in shelf ecosystems and in the Belgian coastal zone.
A three dimensional global weather prediction model using a finite element scheme for vertical discretization
Authors: Steppeler J.
Published: August 2005

A global three dimensional model for numerical weather prediction is described. It uses spheric harmonic basis functions with triangular truncation in the horizontal and a finite element discretization for the vertical. Model experiments are used to compare this model with another version, which uses a finite difference scheme for vertical discretization.
Calculation of the force coefficients of a tubular jacket structural member with an appurtenance by the discrete vortex method
Authors: Downie M. J. , Murray B. A. , Bettess P.
Published: August 2005

Jacket structures have many sub‐sea appurtenances attached to them. For example, a typical jacket structure has hundreds of sacrificial anodes attached to its members. The fluid loading of these structures is calculated using Morison's formula. The force coefficients used in the equation are based on experiments carried out, for the most part, on single cylinders in laboratories in ideal flow. There are very few experimental data available for the fluid loading of cylinders with appurtenances. Moreover, it is not possible to calculate theoretically the loading on such configurations in flows of practical interest using approaches such as the finite element method. However, appurtenances can contribute significantly to the overall loading on a structure. This paper presents the preliminary theoretical work that has been carried out as part of a programme to establish a rational method for estimating the fluid loading on tubular members with appurtenances.
Application of soil–structure interaction to off‐shore foundations with specific reference to consolidation analysis
Authors: Lewis R. W. , Tran D. V.
Published: August 2005

Consolidation problems associated with foundations for off‐shore structures are described and analysed using the finite element method. The structure itself and the soft underlying soil are modelled by finite elements with different constitutive relationships for each. Interfacial behaviour between the two is simulated by six‐noded elements, with a hyperbolic stress–strain relationship.

Having modelled the soil–structure system behaviour during the consolidation stage, a soil–structure interaction analysis is then carried out for both shallow and deep foundations. Other important factors, such as the redistribution of stresses in the structure itself which have resulted from differential settlements, will also be investigated.
F.E. solution of a vertically averaged model for regional land subsidence
Authors: Simoni L. , Schrefler B. A.
Published: August 2005

In this paper a mathematical model is presented, based on the application of an averaging technique, in which the equations governing the behaviour of saturated porous media are integrated (averaged) over the smallest dimension of the domain of the problem (thickness). This results in a two dimensional model, in which the three dimensional nature of the problem is accounted for. In fact, the solution is sought in terms of the mean values over the thickness of the field variables and of the transverse displacement components. For the solution of the resulting governing equations a partitioned procedure is employed, which improves the efficiency of the method. The proposed model is very useful in solving problems in which the spatial nature prevents the applications of two dimensional models.

Examples are presented, which illustrate the validity of this approach.
New techniques for fast hybrid solutions of systems of equations
Authors: Mandel J. , Miranker W. L.
Published: August 2005

A fast analogue solver with limited precision is used as a preconditioner in an iterative process which develops full digital precision. This hybrid process is highly parallel, and, in principle, it can be faster than digital computations alone. A problematic feature of this process is that the low analogue precision can adversely affect convergence speed. New techniques are introduced to address this limitation. A partial separation of analogue imprecision and poor problem condition is made. Fully parallel digital (smoothing) iterations are introduced to eliminate the effect of random errors which accompany analogue–digital conversion. Application is made to the problem of repeated summation.
A unified treatment of superconvergent recovered gradient functions for piecewise linear finite element approximations
Authors: Goodsell G. , Whiteman J. R.
Published: August 2005

Piecewise linear finite element approximations to two‐dimensional Poisson problems are treated. For simplicity, consideration is restricted to problems having Dirichlet boundary conditions and defined on rectangular domains Ω which are partitioned by a uniform triangular mesh. It is also required that the solutions u ∈ H3 (Ω). A method is proposed for recovering the gradients of the finite element approximations to a root mean square accuracy of O(h2), both at element edge mid‐points and element vertices, using simple averaging schemes over adjacent elements. Piecewise linear interpolants (respectively discontinuous and continuous) are then fitted to these recovered gradients, and are shown to be O(h2) estimates for ∇u in the L2‐norm, and thus superconvergent. A discussion is given of the extension of the results to problems with more general region and mesh geometries, boundary conditions and with solutions of lower regularity, and also to other second‐order elliptic boundary value problems, e.g. the problem of planar linear elasticity.
Fully vectorizable block preconditionings with approximate inverses for non‐symmetric systems of equations
Authors: Diaz J. C. , Macedo C. G.
Published: August 2005

We used a conjugate gradient type method, with preconditioning, to solve the sparse linear systems arising from the discretization of PDEs. With such methods, the main obstacles for complete vectorization have been the preconditioning calculation and its application step within the iteration: for the matrices obtained using 5‐ or 9‐point discretization operators, some well known existing preconditionings (like ILU) require a block‐recursive procedure which prevents vectorization. Preconditioners based on nested incomplete factorization, which require the calculation of approximate inverses of tridiagonal matrices, allow complete vectorization of the application step. We present a formulation of such a preconditioning, using a Frobenius norm minimization to calculate the inverses, which also allows complete vectorization of the inverses' calculation, thus making the iterative solver completely vectorizable. Numerical experiments show that the method is robust over a range of symmetric and non‐symmetric problems, and up to 4 times faster than other existing methods, such as ILU, depending on the computer and compiler being used. We also show the importance of diagonal scaling used in conjunction with other preconditionings and present some theoretical results concerning the approximate inverses of tridiagonal matrices, calculated using the Frobenius norm minimization.
The vectorization of ITPACK 2C
Authors: Oppe Thomas C.
Published: August 2005

ITPACK 2C14 is a package of seven iterative algorithms for solving sparse linear systems represented by Au = b, where A is symmetric and positive definite or mildly non‐symmetric. This paper describes the techniques used to vectorize the iterative algorithms in the ITPACK 2C package for the Cyber 205 and Cray X‐MP vector computers. The resulting package was named ITPACKV 2C.15 The basic iterative methods in ITPACK 2C are described in terms of matrix–vector multiplications and forward and backward solutions, and the techniques used in the vectorization of these and other computational kernels are given. Results of experiments using ITPACK 2C and ITPACKV 2C are given, including a comparison of megaflop rates and timings for two model problems.
Multigrid solution and grid redistribution for convection–diffusion
Authors: Carey G. F. , Pardhanani A.
Published: August 2005

We examine multigrid solution for convection–diffusion problems in which convective effects are significant. In particular, we consider the case where the fine grid satisfies the associated cell or diagonal dominance condition but coarse grid levels violate this condition. Related numerical experiments are conducted. We also introduce an alternative local elliptic projection technique and compare this with interpolating the error corrections from coarse to fine grids. In addition, we demonstrate the use of grid redistribution and optimization techniques in the multilevel context.
A bi‐cubic transformation for the numerical evaluation of the Cauchy principal value integrals in boundary methods
Authors: Cerrolaza M. , Alarcon E.
Published: August 2005

The numerical strategies employed in the evaluation of singular integrals existing in the Cauchy principal value (CPV) sense are, undoubtedly, one of the key aspects which remarkably affect the performance and accuracy of the boundary element method (BEM).

Thus, a new procedure, based upon a bi‐cubic co‐ordinate transformation and oriented towards the numerical evaluation of both the CPV integrals and some others which contain different types of singularity is developed.

Both the ideas and some details involved in the proposed formulae are presented, obtaining rather simple and‐attractive expressions for the numerical quadrature which are also easily embodied into existing BEM codes.

Some illustrative examples which assess the stability and accuracy of the new formulae are included.
A move coordination method for alternative loads in structural optimization
Authors: Chibani Lahbib , Burns Scott A. , Khachaturian Narbey
Published: August 2005

A decomposition technique for alternative loading conditions in the integrated optimal structural design is developed. The method, called the move coordination, consists of partitioning the large structural optimization problem into a set of smaller coupled subproblems. In each subproblem only one loading condition is considered and the subproblems are solved in a parallel cyclic way. The coupling among the subproblems is accomplished through the introduction of coordinating constraints between each subproblem. These constraints ensure that the final design is the same and feasible for all subproblems. The method developed is illustrated by two examples of member sizing of truss structures using the integrated optimal design formulation and geometric programming. The method presents the advantage of reducing the size of the optimization problem as well as the computer processing time. The method is also suitable for implementation on computers using parallel processing.
Consistent higher degree Petrov–Galerkin methods for the solution of the transient convection–diffusion equation
Authors: Westerink J. J. , Shea D.
Published: August 2005

The solution of the convection–diffusion equation for convection dominated problems is examined using both N + 1 and N + 2 degree Petrov–Galerkin finite element methods in space and a Crank–Nicolson finite difference scheme in time. While traditional N + 1 degree Petrov–Galerkin methods, which use test functions one polynomial degree higher than the trial functions, work well for steady‐state problems, they fail to adequately improve the solution for the transient problem. However, using novel N + 2 degree Petrov–Galerkin methods, which use test functions two polynomial degrees higher than the trial functions, yields dramatically improved solutions which in fact get better as the Courani number increases to 1·0. Specifically, cubic test functions with linear trial functions and quartic test functions in conjunction with quadratic trial functions are examined.

Analysis and examples indicate that N + 2 degree Petrov–Galerkin methods very effectively eliminate space and especially time truncation errors. This results in substantially improved phase behaviour while not adversely affecting the ratio of numerical to analytical damping.
A numerical model for the thermo‐elasto‐plastic behaviour of a material
Authors: Ray Sujit K. , Utku Senol
Published: August 2005

This paper presents a numerical model for the thermo‐elasto‐plastic behaviour of an isotropic material. The model is based on the assumption that the yielding of the material obeys von Mises distortion energy theory and the material exhibits isotropic strain hardening. This unique model can be used both for isothermal and non‐isothermal cases. The original formulation for the non‐isothermal three‐dimensional case has been specialized for plane stress conditions and the equations for the computation of warping and thickness change are provided. The finite element implementation of this model is also outlined.
An effective quadrilateral plate bending element
Authors: He‐Xiang Lü , Shu‐Ning Xu
Published: August 2005

An effective arbitrary quadrilateral thin plate bending element with a quasi‐conforming, QCQ element, is presented in this paper. The elements pass the patch test with constant strain and the patch test with linear strains approximately. When the element degenerates to a rectangle the patch test with linear strains is passed. The calculation of the element stiffness matrix is simple without numerical integration. The numerical examples show that the QCQ element has a higher accuracy and a faster convergence rate.
A dynamic programming method for analysis of bridges under multiple moving loads
Authors: Adeli Hojjat , Ge Yaojun
Published: August 2005

A dynamic programming (DP) method is presented for analysis of statically determinate and indeterminate bridges subjected to moving loads such as those specified by the American Association of State Highway and Transportation Officials (AASHTO) specifications. These loads consist of uniform lane loading, two‐axle truck loading and two‐axle truck plus one‐axle semitrailer loading. The solution of the DP problem is based on the use of influence line diagrams and extremum functions. Recurrence formulae have been developed for various types of AASHTO live loads. The procedure presented in this article is quite general and can be applied to any type of structures with linear behaviour and any type of moving loads. Six examples are presented: a simply‐supported beam, a simply‐supported Pratt truss, an arch bridge, a continuous Pratt truss, a continuous frame and a cable‐stayed bridge.
Coupled bending–torsional dynamic stiffness matrix for beam elements
Authors: Banerjee J. R.
Published: August 2005

Explicit expressions for the coupled bending–torsional dynamic stiffness matrix of a uniform beam element are derived in an exact sense by solving the governing differential equation of the beam. Implementation of the derived dynamic stiffness matrix in a space frame computer program is discussed with particular reference to an established algorithm to enable vibration analysis of coupled systems to be made. The application of the theory is demonstrated by an illustrative example wherein the results for a cantilever beam with a substantial amount of coupling between bending and torsion are highlighted. The correctness of the theory is confirmed to a high degree of accuracy by computed results and numerical checks.
PCG methods in transient FE analysis. Part I: First order problems
Authors: Smith I. M. , Wong S. W. , Gladwell I. , Gilvary B.
Published: August 2005

The performances of some PCG (preconditioned conjugate gradient) algorithms are evaluated in the solution of first order time dependent parabolic partial differential equations, such as the heat conduction equation, which have been spatially discretized using finite elements. ‘Consistent mass’ discretizations are preferred by the authors to ‘lumped mass’ ones and various preconditioners are then compared—diagonal, incomplete Choleski and EBE (‘element‐by‐element’). Recommendations are made and implications for parallel computation outlined.
An assumed strain finite element model for large deflection composite shells
Authors: Yeom C. H. , Lee S. W.
Published: August 2005

A nine node finite element model has been developed for analysis of geometrically non‐linear laminated composite shells. The formulation is based on the degenerate solid shell concept and utilizes a set of assumed strain fields as well as assumed displacement Two different local orthogonal co‐ordinate systems were used to maintain invariance of the element stiffness matrix. The formulation assumes strain and the determinant of the Jacobian matrix to be linear in the thickness direction. This allows analytical integration in the thickness direction regardless of ply layups. The formulation also allows the reference plane to be different from the shell midsurface. The results of numerical tests demonstrate the validity and the effectiveness of the present approach.
Symmetry‐preserving return mapping algorithms and incrementally extremal paths: A unification of concepts
Authors: Ortiz Michael , Martin John B.
Published: August 2005

In this work we seek to characterize the conditions under which an elastic–plastic stress update algorithm preserves the symmetries inherent to the material response. From a numerical standpoint, the aim is to determine under what conditions a stress update algorithm produces symmetric consistent tangents when applied to materials obeying normality. For the ideally plastic solid we show that only the fully implicit or closest point return mapping algorithm is symmetry preserving. For hardening plasticity, symmetry cannot be preserved in general unless suitable restrictions are imposed on the constitutive equations. We show that these restrictions amount to the existence of a pseudo‐internal energy function acting as a joint potential for both the direction of plastic flow and the hardening moduli. In view of the fact that holonomic methods based on incrementally extremal paths also result in update rules possessing a potential structure and, hence, in symmetric tangents, we address the question of whether any connections exist between the two approaches. We show that holonomic methods and the fully implicit algorithm may indeed be brought into correspondence.
Free vibration of symmetrically laminated plates using a higher‐order theory with finite element technique
Authors: Mallikarjuna  , Kant T.
Published: August 2005

A C0 finite element formulation of the higher‐order theory is used to determine the natural frequencies of isotropic, orthotropic and layered anisotropic composite and sandwich plates. The material properties that are typical of high modulus fibre reinforced composites are used to show the parametric effects of plate aspect ratio, length‐to‐thickness ratio, degree of orthotropy, number of layers and lamination angle/scheme. The present theory is based on a higher‐order displacement model and the three‐dimensional Hooke's laws for plate material. The theory represents a more realistic quadratic variation of the transverse shearing strains and linear variation of the transverse normal strains through the plate thickness. A special mass matrix diagonalization scheme is adopted which conserves the total mass of the element and includes the effects due to rotary inertia terms. The results presented should be useful in obtaining better correlation between theory and experiment, and to numerical analysts in verifying their results.
Free and forced vibrations of plates by boundary and interior elements
Authors: Providakis C. P. , Beskos D. E.
Published: August 2005

A direct boundary element method is developed for the dynamic analysis of thin elastic flexural plates of arbitrary planform and boundary conditions. The formulation employs the static fundamental solution of the problem and this creates not only boundary integrals but surface integrals as well owing to the presence of the inertia force. Thus the discretization consists of boundary as well as interior elements. Quadratic isoparametric elements and quadratic isoparametric or constant elements are employed for the boundary and interior discretization, respectively. Both free and forced vibrations are considered. The free vibration problem is reduced to a matrix eigenvalue problem with matrix coefficients independent of frequency. The forced vibration problem is solved with the aid of the Laplace transform with respect to time and this requires a numerical inversion of the transformed solution to obtain the plate dynamic response to arbitrary transient loading. The effect of external viscous or internal viscoelastic damping on the response is also studied. The proposed method is compared against the direct boundary element method in conjunction with the dynamic fundamental solution as well as the finite element method primarily by means of a number of numerical examples. These examples also serve to illustrate the use of the proposed method.
An upwind method for solving transport–diffusion–reaction systems
Authors: Bermudez A. , Durany J. , Posse M. , Vázquez C.
Published: August 2005

A combination of the characteristics method and finite elements techniques is applied to solve a coupled heat transfer–chemical reaction system in the stationary case. The solution of the non‐linear discretized system is obtained by using Newton's algorithm. Finally, numerical results for several problems are presented to test the accuracy and stability of the method.
Efficient approximation concepts using second order information
Authors: Fleury Claude
Published: August 2005

The primary goal of this paper is to show how second derivative information can be used in an effective way in structural optimization problems. The basic idea is to generate such an information at the expense of only one more ‘virtual load case’ in the sensitivity analysis part of the finite element code. To achieve this goal a primal–dual approach is employed, that can also be interpreted as a sequential quadratic programming method.

Another objective is to relate the proposed method to the well known family of approximation concepts techniques, where the primary optimization problem is transformed into a sequence of non‐linear explicit subproblems. When restricted to diagonal second derivatives, the new approach can be viewed as a recursive convex programming method, similar to the ‘Convex Linearization’ method (CONLIN), and to its recent generalization, the ‘Method of Moving Asymptotes’ (MMA).

This new method has been successfully tested on simple problems that can be solved in closed form, as well as on sizing optimization of trusses. In all cases the method converges faster than CONLIN, MMA or other approximation techniques based on reciprocal variables.
A study of stabilization and projection in the 4‐node Mindlin plate element
Authors: Wang Xiao‐Jun , Belytschko Ted
Published: August 2005

In this paper, a Mindlin plate element is formulated based on the Hellinger–Reissner principle and the γ‐technique. The stiffness consists of a constant stress (one‐point quadrature) matrix and a stabilization matrix. The stabilization matrix is compared with those previously proposed. In addition, the element uses a projection to modify the nodal displacements so that the patch test is satisfied. The projection matrix is based on a mode decomposition. Several numerical cases are presented, and it is shown that the mode decomposition projection is necessary both for satisfaction of the patch test and convergence.
An improved procedure for solving transient heat conduction problems using the boundary element method
Authors: Davey K. , Hinduja S.
Published: August 2005

In employing the boundary element method to solve transient heat conduction problems, domain integrals need to be calculated. These integrals can be calculated either by directly discretizing the domain, or indirectly by utilizing a time‐marching scheme which requires the time integrations to be evaluated from the initial time. Although the second approach overcomes the need for domain discretization, it has the disadvantage of requiring large storage and CPU time for increasing number of time steps.

This paper is concerned with a procedure which approximates the domain integrals without the need for domain discretization. The time‐marching scheme is employed so that the domain integrals can be calculated at a particular time with a known weighting and temperature distribution. These integrals can then be utilized to approximate similar domain integrals with a different weighting. It is shown that the method proposed dramatically reduces the storage requirements and CPU time, even for a small number of time divisions.
Modal parameter identification using Z‐transforms
Authors: Mickleborough N. C. , Pi Y. L.
Published: August 2005

A method for the time domain identification of modal parameters of a vibrating structure using Z‐transformation sequences is presented in this paper.

This identification proceeds using the Z‐transfer function of a vibrating structure from which an auto‐regressive and moving‐average (ARMA) model of the vibrating structure is derived. From this ARMA model and time domain data, the modal parameters can be identified. The time domain data can be obtained from single point or multiple shaker excitation modal testing. To demonstrate the application and efficiency of the method, a test on a simulated cantilever beam is presented.
Numerical analysis of crack‐tip fields using the hodograph transformation
Authors: Silling S. A.
Published: August 2005

A numerical method is discussed for analysis of anti‐plane shear crack‐tip fields in linear and non‐linear materials, including possible anisotropy. The method is based on the hodograph transformation. It allows efficient computation of singular stress fields because the transformed partial differential equation to be solved numerically is linear. The inversion of the transformation is also done numerically. The method is promising for the study of localizations, since regions with the largest stress gradients are automatically discretized with the finest mesh owing to the nature of the transformation.
The use of profile reduction algorithms with a frontal code
Authors: Duff I. S. , Reid J. K. , Scott J. A.
Published: August 2005

We study profile reduction algorithms when used to order the elements for the frontal solution of a system of linear equations with a symmetric sparsity pattern. We consider two distinct procedures for producing an efficient element ordering; one based on assembling the pattern of the finite‐element matrix, reordering the variables and using the new variable order to resequence the elements, and the other based on generating adjacency lists for the elements themselves and reordering the elements directly.

We compare the results of using several variants of these algorithms in conjunction with the Harwell frontal code, MA32, on the CRAY‐2 for a range of practical problems. We find that, given suitable enhancements, both approaches are practical and neither is consistently superior to the other.
A mixed‐variable continuously deforming finite element method for parabolic evolution problems. Part II: The coupled problem of phase‐change in porous media
Authors: Kececioglu Ifiyenia , Rubinsky Boris
Published: August 2005

The conceptual framework of a least squares rate variational approach to the formulation of continuously deforming mixed‐variable finite element computational scheme for a single evolution equation was presented in Part I.1 In this paper (Part II), we extend these concepts and present an adaptively deforming mixed variable finite element method for solving general two‐dimensional transport problems governed by a system of coupled non‐linear partial differential evolution equations. In particular, we consider porous media problems that involve coupled heat and mass transport processes that yield steep continuous moving fronts, and abrupt, discontinuous, moving phase‐change interfaces. In this method, the potentials, such as the temperature, pressure and species concentration, and the corresponding fluxes, are permitted to jump in value across the phase‐change interfaces. The equations, and the jump conditions, governing the physical phenomena, which were specialized from a general multiphase, multiconstituent mixture theory, provided the basis for the development and implementation of a two‐dimensional numerical simulator. This simulator can effectively resolve steep continuous fronts (i.e. shock capturing) without oscillations or numerical dispersion, and can accurately represent and track discontinuous fronts (i.e. shock fitting) through adaptive grid deformation and redistribution. The numerical implementation of this simulator and numerical examples that demonstrate the performance of the computational method are presented in Part III2 of this paper.
A FORTRAN program for profile and wavefront reduction
Authors: Sloan S. W.
Published: August 2005

A FORTRAN 77 program for reducing the profile and wavefront of a sparse matrix with a symmetric structure is described. The implementation is based on an algorithm published previously by the Author and appears in response to a large number of enquiries for the source code. Extensive testing of the scheme suggests that its performance is consistently superior to that of the widely used reverse Cuthill–McKee and Gibbs–King methods. In addition to presenting a complete listing of the program, we also describe how to interface it with a typical finite element code. The scheme is especially useful in finite element analysis where it can be employed to derive efficient orderings for both profile and frontal solution schemes.
Status of the finite element method in the thermoforming process
Authors: Zamani N. G. , Watt D. F. , Esteghamatian M.
Published: August 2005

The purpose of this article is to review the publications dealing with the application of finite elements in the thermoforming process. Although no attempt has been made to discuss the theoretical aspects of these publications, their general methodologies have been presented. The paper is particularly aimed at readers who are seeking an overall view of the subject and possibly interested in acquiring a CAD system for thermoforming technology.
An accurate determination of stresses in thick laminates using a generalized plate theory
Authors: Barbero E. J. , Reddy J. N. , Teply Jan
Published: August 2005

Analytical solutions for displacements and stresses in composite laminates are developed using the laminate plate theory of Reddy. The theory accounts for a desired degree of approximation of the displacements through the laminate thickness, allowing for piecewise approximation of the inplane deformation through individual laminae. The solutions are compared with the 3‐D elasticity solutions for the simply supported case and excellent agreement is found. Analytical solutions are also presented for other boundary conditions. The results indicate that the generalized shear deformation plate theory predicts accurate stress distributions in thick composite laminates.
A full tangent stiffness field‐boundary‐element formulation for geometric and material non‐linear problems of solid mechanics
Authors: Okada H. , Rajiyah H. , Atluri S. N.
Published: August 2005

The field‐boundary‐element method naturally admits the solution algorithm in the incompressible regimes of fully developed plastic flow. This is not the case with the generally popular finite‐element method, without further modifications to the method such as reduced integration or a mixed method for treating the dilatational deformation. The analyses by the field‐boundary‐element method for geometric and material non‐linear problems are generally carried out by an incremental algorithm, where the velocities (or displacement increments) on the boundary are treated as the primary variables and an initial strain iteration method is commonly used to obtain the state of equilibrium. For problems such as buckling and diffused tensile necking, involving very large strains, such a solution scheme may not be able to capture the bifurcation phenomena, or the convergence will be unacceptably slow when the post‐bifurcation behaviour needs to be analysed. To avoid this predicament, a full tangent stiffness field‐boundary‐element formulation which takes the initial stress–velocity gradient (displacement gradient) coupling terms accurately into account is presented in this paper. Here, the velocity field both inside and on the boundary are treated as primary variables. The large strain plasticity constitutive equation employed is based on an endochronic model of combined isotropic/kinematic hardening plasticity using the concepts of material director triad and the associated plastic spin. A generalized mid‐point radial return algorithm is presented for determining the objective increments of stress from the computed velocity gradients. Numerical results are presented for problems of diffuse necking, involving very large strains and plastic instability, in initially perfect elastic–plastic plates under tension. These results demonstrate the clear superiority of the full tangent stiffness algorithm over the initial strain algorithm, in the context of the integral equation formulations for large strain plasticity.
A combined octree/delaunay method for fully automatic 3‐D mesh generation
Authors: Schroeder W. J. , Shephard M. S.
Published: August 2005

Fully automatic three‐dimensional mesh generation is a fundamental requirement for automating the numerical solution of partial differential equations. Two techniques in particular—the octree and Delaunay approaches—have been used towards this end. A method that combines both approaches to fully automatic mesh generation is presented here. The resulting algorithm provides the linear growth rate and divide‐and‐conquer approach of the octree method with the simplicity and optimal properties of the Delaunay triangulation.
Numerical integration strategy for plates and shells
Authors: Burgoyne C. J. , Crisfield M. A.
Published: August 2005

The paper compares the overall performance of a wide range of numerical procedures that can be used to integrate through the thickness of plates and shells. Results are presented for the accuracy of the calculations when there are discontinuities in the stress through the depth of the plate, and the available methods are ranked according to their accuracy.
Element by element a posteriori error estimation and improvement of stress solutions for two‐dimensional elastic problems
Authors: Ohtsubo Hideomi , Kitamura Mitsuru
Published: August 2005

A quantitative method of a posteriori error estimation based on finite element solutions is developed. The proposed method can estimate the error of solutions obtained by the finite element method for two‐dimensional elastic problems with 4‐node elements. Since the error is estimated element by element, the proposed method does not require a large memory or long computing time. Not only rectangular elements but also arbitrarily shaped 4‐node elements can be used in this method for estimating the error in the finite element computation with high accuracy. The finite element solutions are improved by adding the estimated errors onto the original solutions. The proposed method can be utilized for any type of linear problem if an isoparametric finite element method is used.
Higher derivative explicit one step methods for non‐linear dynamic problems. Part I: Design and theory
Authors: Hoff C. , Taylor R. L.
Published: August 2005

A new higher order explicit one step scheme is presented for use in the solution of a certain class of non‐linear problems in structural dynamics. The generalized scheme covers some recently developed multistep algorithms as well as some new one step methods with improved numerical properties. A weighted residual approach is used which contains new aspects for design of single step algorithms. Accuracy and stability are investigated for linear and non‐linear systems. Algorithms with higher accurary than the central difference method are developed and optimized to minimize the reduction in the stability limit.
Non‐linear vibration of frames by the incremental dynamic stiffness method
Authors: Leung A. Y. T. , Fung T. C.
Published: August 2005

The dynamic stiffness method is extended to large amplitude free and forced vibrations of frames. When the steady state vibration is concerned, the time variable is replaced by the frequency parameter in the Fourier series sense and the governing partial differential equations are replaced by a set of ordinary differential equations in the spatial variables alone. The frequency‐dependent shape functons are generated approximately for the spatial discretization. These shape functions are the exact solutions of a beam element subjected to mono‐frequency excitation and constant axial force to minimize the spatial discretization errors. The system of ordinary differential equations is replaced by a system of non‐linear algebraic equations with the Fourier coefficients of the nodal displacements as unknowns. The Fourier nodal coefficients are solved by the Newtonian algorithm in an incremental manner. When an approximate solution is available, an improved solution is obtained by solving a system of linear equations with the Fourier nodal increments as unknowns. The method is very suitable for parametric studies. When the excitation frequency is taken as a parameter, the free vibration response of various resonances can be obtained without actually computing the linear natural modes. For regular points along the response curves, the accuracy of the gradient matrix (Jacobian or tangential stiffness matrix) is secondary (cf. the modified Newtonian method). However, at the critical positions such as the turning points at resonances and the branching points at bifurcations, the gradient matrix becomes important. The minimum number of harmonic terms required is governed by the conditions of completeness and balanceability for predicting physically realistic response curves. The evaluations of the newly introduced mixed geometric matrices and their derivatives are given explicitly for the computation of the gradient matrix.
A hybrid/mixed model for non‐linear shell analysis and its applications to large‐rotation problems
Authors: Saleeb A. F. , Chang T. Y. , Graf W. , Yingyeunyong S.
Published: August 2005

Adopting an updated Lagrange approach, the general framework for the fully non‐linear analysis of curved shells is developed using a simple quadrilateral C0 model (HMSH5). The governing equations are derived based on a consistent linearization of an incremental mixed variational principle of the modified Hellinger/Reissner type with independent assumptions for displacement and strain fields. Emphasis is placed on devising effective solution procedures to deal with large rotations in space, finite stretches and generalized rate‐type material models. In particular, a geometrically exact scheme for configuration update is developed by making use of the so‐called exponential mapping algorithm, and the resulting element was shown to exhibit a quadratic rate of (asymptotic) convergence in solving practical shell problems with Newton–Raphson type iterative schemes. For the purpose of updating the spatial stress field of the element, an ‘objective’ generalized midpoint integration rule is utilized, which relies crucially on the concept of polar decomposition for the deformation gradient, and is in keeping with the underlying mixed method. Finally, the effectiveness and practical usefulness of the HMSH5 element are demonstrated through a number of test cases involving beams, plates and shells undergoing very large displacements and rotations.
A panel method computation for oscillating aerofoil in compressible flow
Authors: Leong Swee Hung
Published: August 2005

A panel method using source and doublet singularity has been proposed to solve for subcritical aerodynamics of a two dimensional steady and unsteady aerofoil. The source singularities are placed on the aerofoil surface. The doublet singularity is distributed by a function along the chordline of the aerofoil; this distribution is further projected downstream into infinity.

The aerodynamics of an oscillating aerofoil is investigated. The governing unsteady linearized potential equation has a Hankel function as its fundamental solution, which is a source type function. A combination of source and doublet singularity is therefore used for solving the unsteady compressible problem by means of the panel method, this methodology being an extension of a steady aerofoil formulation. Incremental effects of profile change in aerofoil and wake geometry are accounted for. A surface boundary condition is applied on the stationary mean aerofoil surface with time dependent geometrical changes accounted for. An unsteady Kutta condition of equal pressure across the trailing edge is assumed. Results are presented on the aerodynamic influence of Mach number, oscillating frequency parameter, angle of incidence and change of pivoting point. Results are also compared with linear theory, a subsonic experimental result and a subcritical solution of a transonic model.
Model reduction for thermal diffusion: Application of the Eitelberg, Marshall and aggregation methods to a heat transmission tube model
Authors: Ben Jaǎfar M. T. , Pasquetti R. , Petit D.
Published: August 2005

This study, dealing with model reduction for thermal diffusion, describes the numerical techniques used: the Eitelberg, Marshall and aggregation methods. The non‐linear model of a heat transmission tube, to which these methods are applied, is then described, pointing out the necessary initial algebraic treatment for reduction. Finally the outputs of the complete model and of several reduced ones are compared for some characteristic variations of the inputs. For this problem, the Eitelberg and Marshall methods, which can be used with a high coefficient of reduction, are well adapted.
Parallel multisplitting, block Jacobi type solutions of linear systems of equations
Authors: Roditis Yanis S. , Kiousis Panos D.
Published: August 2005

Three parallel iterative schemes to solve banded systems of equations are presented in this study. The techniques are special implementations of the theory of matrix multisplitting. The resulting algorithms are implemented on a Multiple Instruction Multiple Data (MIMD) grid architecture using 16 Transputer processors. Parametric analyses are performed to develop convergence criteria and examine the speed‐up of solution. It is concluded that the algorithms make very efficient use of the parallel computer architecture, especially if this consists of a large number of nodes.
A surface fitting method for three dimensional scattered data
Authors: Balaras Constantinos A. , Jeter Sheldon M.
Published: August 2005

A method is presented that may be used to empirically establish the type of relationship that is present between a response variable and its influencing factors, by fitting a mathematical model to three dimensional scattered data. The generated response surface is composed of continuous triangular planes that are fitted to the corresponding data in the least squares sense. The method may be easily implemented. It requires some fairly large number of scattered data, two initial boundary conditions and a desired accuracy for the band‐wise partitioning of the data. The proposed surface fitting technique has been successfully applied to solar radiation modelling for a number of different data combinations.
Vibration analysis of fluid–solid systems using a finite element displacement formulation
Authors: Chen Harn C. , Taylor Robert L.
Published: August 2005

This report presents a finite element solution for the vibration interaction between an inviscid fluid and a solid. The equation of motion governing the inviscid fluid is expressed in terms of the displacements. This ensures that compatibility and equilibrium will be satisfied automatically along the interface of the coupled systems. To suppress circulation modes with non‐zero energy, reduced integration is used when computing the element stiffness matrix contributed by the fluid. In addition, a projection is used on the element mass matrix in order to remove the spurious modes which result from the use of reduced integration. Numerical examples for both fluid and coupled fluid–solid systems are performed and the results are shown.
Singular behaviour near an interface crack tip of power law hardening materials using The Finite Element Iterative Method
Authors: Barsoum Roshdy S.
Published: August 2005

The Finite Element Iterative Method (FEIM) is extended to the analysis of asymptotic fields of materials with non‐linear behaviour. It is used in the investigation of the asymptotic field of an interfacial crack of power law hardening materials. The material is assumed to deform according to the total deformation theory of plasticity. The results of the analysis provide evidence to support the hypothesis that the asymptotic field can be cast in the form of the HRR‐singularity multiplied by a function of the product form. This function can be written as a series of oscillatory functions, similar to those encountered in an elastic field, each of which is valid over a substantial range of the process zone. The real part of these terms depends on the loading mode, process zone size as well as material properties; it is, however, very small compared to the HRR‐singularity. The imaginary part which gives the phase shift is much smaller than the elastic value and is a weak function of the hardening power and the size of the process zone of interest; it eventually vanished at extremely small distances.
The multigrid method in solid mechanics: Part II—Practical applications
Authors: Parsons I. D. , Hall J. F.
Published: August 2005

The performance of the multigrid algorithm is investigated by solving some large, practical, three dimensional solid mechanics problems. The convergence of the method is sensitive to factors such as the amount of bending present and the degree of mesh non‐uniformity, as was also observed in Part I for two dimensional problems. However, in contrast to Part I, no proportionality is observed between the total number of operations to convergence and the problem size. Despite such behaviour, the multigrid algorithm proves to be an effective matrix equation solver for solid mechanics poblems. It is orders of magnitude faster than a direct factorization method, and yields converged solutions several times faster than the Jacobi preconditioned conjugate gradient method.