bluuebunny/crossref_metadata_2025_split huggingface dataset:
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

AbstractThe 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

AbstractA 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

AbstractThe 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

AbstractAnalytical 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

AbstractThe 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

AbstractFully 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

AbstractThe 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

AbstractA 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

AbstractA 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

AbstractThe 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

AbstractAdopting 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

AbstractA 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

AbstractThis 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

AbstractThree 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

AbstractA 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

AbstractThis 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

AbstractThe 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

AbstractThe 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.
Consistent force resultant distributions in displacement elements with varying sectional properties
Authors: Prathap G. , Naganarayana B. P. 
Published: August 2005

AbstractForce fields computed directly from strains calculated in a displacement type finite element description of a structural element of varying sectional rigidities show extraneous oscillations. The origin of these oscillations is traced to the fact that the displacement type finite element procedure determines strains derived from the displacement field in a least squares correct sense and that force resultants computed using these strain fields and the actual sectional rigidities result in unwanted oscillations. It is necessary to introduce the concept of redistributed assumed force resultant fields that maintain a ‘consistent’ relationship to the strain fields and also are orthogonal to these strain functions. In this paper, the Hu–Washizu theorem is invoked to justify the introduction of an orthogonally correct reconstituted assumed force resultant field which will then be free of extraneous oscillations. The quadratic isoparametric tapered bar element serves to illustrate the underlying principles.It follows that the extremely general Hu–Washizu principle is the most practical procedure of implementing an assumed force resultant, assumed strain displacement type formulation to introduce consistency and thereby remove problems associated with field‐inconsistency (such as cause locking in constrained media elasticity) and force resultant oscillations due to varying sectional properties.
Some observations on time domain and frequency domain boundary elements
Authors: Von Estorff O. , Pais A. L. , Kausel E. 
Published: August 2005

AbstractThe numerical solution of problems in elastodynamics involving infinite media calls for the use of discrete techniques such as the boundary element method and the finite element method. These techniques can, in turn, be formulated in the time or frequency domains, and have each relative merits and drawbacks. This paper presents a comparative study of the accuracy and limitations of three different implementations of these methods.The problem studied is that of transient loads on the surface of homogeneous elastic halfspaces, and of finite depth strata. In each case, the response is computed first for an uninterrupted (continuous) medium, and then for a medium that includes a trench (or cavity).Three independent computer programs were used that incorporated the following methods: (i) frequency domain boundary element method (FD‐BEM), using a discrete fundamental solution; (ii) time domain boundary element method (TD‐BEM) using an analytical fundamental solution; and (iii) a coupled time domain boundary element‐finite element model (BEM/FEM).It is found that for convex domains (halfspace or stratum without a trench) the three independent implementations are in excellent agreement, while for non‐convex domains (trench in the path of the waves), numerical errors associated with non‐causal behaviour become evident in some cases.