bluuebunny/crossref_metadata_2025_split huggingface dataset:
On an SSOR matrix relationship and its consequences
Authors: Galanis S. , Hadjidimos A. , Noutsos D. 
Published: August 2005

AbstractA matrix relationship connecting the Jacobi and the Symmetric Successive Overrelaxation (SSOR) matrices associated with a k‐cyclic consistently ordered matrix A is presented. Next the equivalence of the SSOR method and a certain monoparametric k‐step one for the solution of the linear algebraic system Ax = b is established. The aforementioned equivalence can be exploited to derive regions of convergence, optimum parameters involved, etc. of the two iterative methods above. This is done by studying the simplest of the two methods that is the monoparametric k‐step one. To show how the idea works the case k = 2 is very briefly discussed.
First‐order design sensitivities for transient conduction problems by an adjoint method
Authors: Tortorelli Daniel A. , Haber Robert B. 
Published: August 2005

AbstractAn adjoint approach is presented for the design sensitivity analysis of transient conduction problems. Variations of a general design functional are expressed in explicit form with respect to all design quantities, i.e. material properties, shape, applied thermal loads including convection, and initial conditions. The methodology incorporates the mutual energy between the real and adjoint thermal problems and a geometric mapping to describe shape variations. Finite element implementation of the method is discussed and an example is provided. Some potential difficulties that might be encountered when using the adjoint method with the finite element method are addressed. These involve the application of impulse loadings and Dirac temperature fields in the adjoint loadings.
Upwind techniques via variational principles
Authors: Idelsohn Sergio R. 
Published: August 2005

AbstractThe amount of upwind or magnitude of off‐centering needed in the numerical solution of second order differential equations with significant first derivatives is justified more rigorously in this paper by requiring the satisfaction of a variational principle. It will be shown that, for a discrete solution, a set of variational principles can be found which allow the problem to be solved as a self‐adjoint system. The technique presented here will give a clear indication of those regions where (i) upwind techniques are not required, (ii) upwind techniques are necessary and sufficient and (iii) upwind techniques are insufficient and artificial viscosity is required.
A three‐dimensional hydraulic fracturing simulator
Authors: Vandamme L. , Curran J. H. 
Published: August 2005

AbstractThe propagation of non‐planar hydraulic fractures is modelled using a three‐dimensional numerical simulator. This paper describes the different components of the model (stress/displacement analysis, fluid‐flow analysis, propagation criterion) with an emphasis on the numerical techniques used. A few examples of out‐of‐plane fracture geometries are provided.
Simplifications using isoparametric elements in flexible linkage analysis
Authors: Giovagnoni Marco 
Published: August 2005

AbstractThis paper concerns finite element techniques applied to the analysis of mechanisms where a rigidity hypothesis for the links is unacceptable. Isoparametric elements may simplify the resulting equations because a good many of the terms arising from derivatives of rotation matrices disappear. Furthermore, the isoparametric approach leads to element matrices where integrations over element volumes do not depend on the gross motion of the linkage.
Accuracy in finite element computation for eigenfrequencies
Authors: Ladeveze P. , Pelle J. P. 
Published: August 2005

AbstractIn this paper we propose an original numerical method to get upper and lower bounds for the eigenfrequencies of an elastic structure.This method is based on a ‘static’ formulation for eigenvalue problems built up from a new quotient Rs which is defined on a load space. From Rs properties, upper and lower bounds for the exact eigenfrequencies are proved. The application of the method requires the solution of an eigenvalue problem of finite dimension and the computation of a constant which is characteristic of the discretization subspace. Results of numerical tests are given for the vibration problem of an elastic clamped membrane.
Advanced development of the boundary element method for steady‐state heat conduction
Authors: Dargush G. F. , Banerjee P. K. 
Published: August 2005

AbstractConsiderable progress has been made in recent years toward advancing the state‐of‐the‐art in solid mechanics boundary element technology. In the present work, much of this new technology is applied in the development of a general‐purpose boundary element method (BEM) for steady‐state heat conduction. In particular, the BEM implementation involves the use of higher‐order conforming elements, self‐adaptive integration and multi‐region capability. Two‐ and three‐dimensional, as well as axisymmetric analyses, are incorporated within a unified framework. In addition, techniques are introduced for the calculation of boundary flux, and for the inclusion of thermal resistance across interfaces. As a final extension, an efficient formulation is developed for the analysis of solid three‐dimensional bodies with embedded holes. For this last class of problems, the new BEM formulation is particularly attractive, since use of the alternatives (i.e. finite element or finite difference methods) is not practical. A number of detailed examples illustrate the suitability and robustness of the present approach for steady‐state heat conduction.
Stress computations for nearly incompressible materials by the p‐version of the finite element method
Authors: Szabó Barna A. , Babuška Ivo , Chayapathy Bidar K. 
Published: August 2005

AbstractIn the case of nearly incompressible elastic materials the strain energy, the shear stress and the difference of normal stresses can be computed accurately by direct methods when the p‐version of the finite element method is used. Computation of the sum of the normal stresses requires special procedures. In this paper such procedures are described and examples are presented.
The dynamic analysis of a suspended cable due to a moving load
Authors: Wu Jong‐Shyong , Chen Chi‐Ching 
Published: August 2005

AbstractThe dynamic behaviour of a saggy suspension cable under a moving load was investigated. First of all, the updated Lagrangian formulation and the finite element method were used to derive the property matrices of a saggy suspension cable in order to define the discretized equations of motion. Then, the Jacobi method was applied to the determination of the natural frequencies and the mode shapes of the suspended cable. The moving‐load‐induced dynamic responses of the saggy suspended cable were obtained by using the Newmark direct integration method incorporated with the Newton–Raphson iteration technique. The influence of some pertinent factors, such as speed of moving load, ratio of axial rigidity to total cable weight (AE/0m̄g0L) and ratio of moving load mass to total cable mass, is the key point of the dynamic analysis.
An inverse finite element method for directly formulated free boundary problems
Authors: Alexandrou Andreas N. 
Published: August 2005

AbstractIn free boundary problems, in addition to the primary field variables, velocity, pressure and temperature, unknown geometric parameters need to be evaluated. A characteristic feature of the problems is a demarcation line which separates two domains with different material properties. The problems are highly non‐linear and difficult to handle computationally. Here an accurate and efficient method is presented which can appropriately handle the complexities associated with these problems. The method is based on a tesselation that is constructed by isolines as characteristic co‐ordinate lines. Thus opposite sides of finite elements lie on isolines. The method allows the simultaneous determination of the location of the isolines with the primary unknowns. Its accuracy and efficiency is demonstrated in a number of one and two dimensional steady and unsteady model problems.
An efficient through‐thickness integration scheme in an unlimited layer doubly curved isoparametric composite shell element
Authors: Yunus Shah M. , Kohnke Peter C. , Saigal Sunil 
Published: August 2005

AbstractThis paper presents an efficient numerical integration scheme for evaluating the matrices (stiffness, mass, stress‐stiffness and thermal load) for a doubly curved, multilayered, composite, quadrilateral shell finite element. The element formulation is based on three‐dimensional continuum mechanics theory and it is applicable to the analysis of thin and moderately thick composite shells.The conventional formulation requires a 2 × 2 × 2 or 2 × 2 × 1 Gauss integration per layer for the calculation of element matrices. This method becomes uneconomical when a large number of layers is used owing to an excessive amount of computations. The present formulation is based on explicit separation of the thickness variable from the shell surface parallel variables. With the through‐thickness variables separated, they are combined with the thickness dependent material properties and integrated separately. The element matrices are computed using the integrated material matrices and only a 2 × 2 spatial Gauss integration scheme. The response results using the present formulation are identical to those obtained using the conventional formulation. For a small number of layers, the present method requires slightly more CPU time. However, for a larger number of layers, numerical data are presented to demonstrate that the present formulation is an order‐of‐magnitude economical compared to the conventional scheme.
On the rotation of conductors of finite torsional stiffness by eccentric snow loading and control of rotation using counterweights
Authors: Skelton P. L. I. , Poots G. 
Published: August 2005

AbstractThis paper is concerned with the prevention of snow loading on an overhead conductor caused by the mechanism of cylindrical‐sleeve growth. The eccentric snow loading on the windward side of the conductor, having finite torsional stiffness, causes the conductor to rotate and a theoretical study of how this rotation can be controlled on attaching counterweights along the span of the conductor is presented. In the absence of counterweights, the non‐linear rotation equation is solved analytically in terms of elliptic functions, simulating ice loading by a uniform torque density; for large torque density an asymptotic solution is obtained using matched asymptotic expansions. In the rotation equation the counterweights producing torque at discrete points are incorporated as delta functions which enable the discontinuity in the twisting couple at such locations to be accounted for by means of an integral moment balance. A simple algorithm is then presented for integrating the equation of rotation as an initial value problem which can deal with any distribution of counterweights along the span of the conductor. Illustrative numerical results are presented for zero, one, two, three and four counterweights per span; in the absence of counterweights analytical and numerical solutions are in exact agreement.
An embedding method for the numerical solution of the cathode design problem in electrochemical machining
Authors: Hunt Roland 
Published: August 2005

AbstractAn embedding method is considered for the numerical determination of the cathode shape for a given anode shape in a two‐dimensional electrolytic cell. Reference is made to an analytic solution to illustrate the difficulties which have to be overcome by any numerical method applied to this ill‐posed problem. The embedding method searches amongst the direct solutions (i.e. anodes for given cathodes) since these, resulting from a well‐posed problem, are less troublesome to compute. For anodes of the form βG(x), x the transverse direction, the embedding method gives good results for β less than 30–60 percent of the β for which the cathode first contains cusps or becomes triple‐valued. It is shown that the embedding method performs better than some other numerical methods in overcoming the error growth difficulties associated with the illposedness of the problem.
A hybrid differential‐algebraic method for three‐dimensional grid generation
Authors: Zhu J. 
Published: August 2005

AbstractAn effective method is presented for generating three‐dimensional boundary‐fitted grids. The technique is based on a two‐step procedure involving the solution of differential equations and algebraic interpolations. A coarse grid with an arbitrarily given point distribution at all the boundaries is first generated by solving the Poisson equations, with the forcing functions being automatically adjusted during the grid generation to achieve orthogonality at the boundaries. A fine grid with a desired concentration of grid lines is then obtained by fitting tricubic spline functions on the coarse grid. A primary feature of the method is that the mesh spacing can be quickly and explicitly changed while retaining the smoothness over the entire field and the boundary orthogonality. Applications to a variety of geometries demonstrate the performance of the method.
Prediction of thermal stress and deformations due to phase change in solidifying objects via flux/stress based finite element representations
Authors: Tamma Kumar K. , Namburu Raju R. 
Published: August 2005

AbstractThe paper presents numerical simulations for the prediction of thermal‐stress and deformation fields resulting from phase change in solidifying bodies employing new finite element representations. The formulations developed in this paper provide different perspectives and physical interpretation for the modelling/analysis of thermo‐mechanical problems and possess several inherent advantages. In comparison to traditional approaches for solving similar problems, the paper employs new computational architectures in conjunction with flux/stress based representations to enhance the overall effectiveness. Comparative numerical applications validate applicability of the formulations for predicting the temperature induced deformations and stresses resulting from effects due to phase change.
Two‐dimensional mesh generation, adaptive remeshing and refinement
Authors: Jin H. , Wiberg N.‐E. 
Published: August 2005

AbstractThis paper discusses the generation of unstructured triangular meshes by the advancing front technique. We also employ the technique to discretize surfaces. A simple and effective algorithm for the specification of element sizes is described. A similar idea is then applied to adaptive remeshing where a completely new mesh is created on the basis of the isolines of a certain important variable. The isolines are obtained from the FE‐calculation based on the previous mesh. In this paper, attention is focused on the Poisson's equation. The optimal a priori error estimate for the problem is used to estimate the number of isolines needed for the remeshing. When the estimated error exceeds the tolerance in only a small part of the domain, the adaptive procedure is switched automatically to an adaptive refinement.
Inverse finite element techniques for the analysis of solidification processes
Authors: Zabaras Nicholas 
Published: August 2005

AbstractThis paper provides a finite element methodology (FEM) for the solution of several one‐dimensional inverse solidification problems. In particular two design related problems will be addressed. The first one uses an inverse technique to calculate the boundary heat flux history that will achieve a specified velocity and flux at the freezing front. This front velocity and flux history can be appropriately selected so that the cast structure is controlled. The second problem is the calculation of the boundary heat flux and freezing front position, given appropriate estimates of the temperature field in a specified number of sensor locations (thermocouples) inside a solidifying body.Front fixing and front tracking FEM techniques are used for the solution of the first problem, while a fixed domain finite element formulation (enthalpy method) is used for the solution of the second one. The ‘future information technique’ is employed in both problems. A detailed analysis of the effect on the solution of the error in the data, amount of future information used, time step, number of sensors and their location and of other parameters in the solution will be examined via several numerical tests. Finally, further applications of such inverse methodologies on the control of casting processes will be mentioned.
Effect of integration methods on the solution of an adiabatic shear banding problem
Authors: Batra R. C. , Kim C. H. 
Published: August 2005

AbstractEquations governing the thermomechanical deformations of a block made of a viscoplastic material, and undergoing overall simple shearing deformations, are stiff in the sense that time scales associated with the heat conduction, viscous effects, strain hardening and strain‐rate hardening may differ by several orders of magnitude as localization of the deformation initiates and proceeds. Because of the presence of high spatial gradients within the region of localization of the deformation, we also consider a viscoplasticity theory in which the strain gradient is taken as a kinematic variable. The Galerkin approximation of the pertinent initial‐boundary‐value problem yields an initial‐value problem involving a set of coupled non‐linear ordinary differential equations. The solution of these equations by the Crank–Nicolson, Adams–Moulton and the Gear methods reveals that the three methods give qualitatively similar results. However, quantitatively the results by the three methods differ somewhat, the difference being more for the dipolar theory.
Solution of radiative problems using variational based finite element method
Authors: Breitbach G. , Altes J. , Sczimarowsky M. 
Published: August 2005

AbstractThe calculation of temperature distributions for systems exchanging radiation heat requires as a first step the determination of the heat fluxes caused by radiation at its surfaces. The functional of the variational principle is the starting point of a numerical solution method.By using finite element procedures a system of linear equations is derived, which supplies an approximation of the radiosity. Having the radiosity, the heat flux at the surfaces, which governs the boundary condition for the temperature distribution in the structure, can be calculated. A method of determining the view‐factors using the concept of the finite element method is also given.
On the strain Assumption in a finite element model for plates and shells
Authors: Yeom C. H. , Lee S. W. 
Published: August 2005

AbstractTwo different methods of assuming independent strain fields are examined for the nine node degenerate solid shell element. In the first case, the assumed strain field is chosen for the local orthogonal co‐ordinate systems defined at the Gaussian integration points. In the second case, the independent strain is assumed for a local orthogonal co‐ordinate system defined at the origin of the parent co‐ordinates. The results of numerical tests involving simple example problems demonstrate that the second method is capable of exactly representing constant stress or moment states even when element geometries are distorted. In addition, both methods lead to a finite element model which is free of locking.
Elastic stress analysis of three‐dimensional solids with small holes by BEM
Authors: Henry D. P. , Banerjee P. K. 
Published: August 2005

AbstractAn advanced level development of the boundary element method is presented for the elastic stress analysis of a three‐dimensional solid containing a large number of small diameter, tubular shaped holes. The formulation has been developed such that these holes can be modelled by a system of curvilinear line elements, resulting in substantial savings in both data preparation and computing costs. This is accomplished by assuming a variation in the displacement field along the circumference defined in terms of trigonometric functions together with a linear or quadratic variation of displacements along the longitudinal direction.
Contact‐impact by the pinball algorithm with penalty and Lagrangian methods
Authors: Belytschko Ted , Neal Mark O. 
Published: August 2005

AbstractContact‐impact algorithms, which are sometimes called slideline algorithms, are a computationally time‐consuming part of many explicit simulations of non‐linear problems because they involve many branches, so they are not amenable to vectorization, which is essential for speed on supercomputers. The pinball algorithm is a simplified slideline algorithm which is readily vectorized. Its major idea is to embed pinballs in surface elements and to enforce the impenetrability condition only to pinballs. It can be implemented in either a Lagrange multiplier or penalty method. It is shown that, in any Lagrange multiplier method, no iterations are needed to define the contact surface. Examples of solutions and running times are given.
Solid elements with rotational degrees of freedom: Part II—tetrahedron elements
Authors: Pawlak Timothy P. , Yunus Shah M. , Cook Robert D. 
Published: August 2005

AbstractThis is the second part of a two part paper on three‐dimensional finite elements with rotational degrees of freedom (DOF). Part II introduces a solid tetrahedron element having 3 translational and 3 rotational DOF per node. The corner rotations are introduced by transformation of the midside translational DOF of a 10‐node tetrahedron element. To further enhance the element performance a least squares strain extraction technique is also implemented to develop the stiffness matrix with a desired field. The strain smoothing improves performance without causing a loss in generality.As with the hexahedron in Part I, the element stiffness is augmented with a small penalty stiffness to eliminate any possible spurious zero energy modes. The new tetrahedron element passes the patch test and demonstrates much improved performance over the 4‐node translational DOF only (constant strain) tetrahedron element.
Application of discrete Fourier series to the finite element stress analysis of axi‐symmetric solids
Authors: Lai J. Y. , Booker J. R. 
Published: August 2005

AbstractThis paper describes an efficient formulation, based on a discrete Fourier series expansion, for the analysis of axi‐symmetric solids subjected to non‐symmetric loading. In contrast to the commonly adopted continuous Fourier series approach, the discrete Fourier series representation has largely overcome problems such as the presence of Gibb's phenomenon and the lack of conformity of elements. The computational advantage over a fully three‐dimensional formulation is illustrated. Finally, the method is demonstrated through a finite element study of rigid caissons founded in both elastic and elasto‐plastic soils.