bluuebunny/crossref_metadata_2025_split huggingface dataset:
A dynamic finite element preanalyser
Authors: Murti V. , Valliappan S. 
Published: August 2005

AbstractIn a mixed‐mode dynamic crack propagation problem using remeshing, certain elements in the neighbour‐hood of the propagating crack‐tips may have dimensions that do not comform to the allowable limit. Hence, they need to be refined by recursively bisecting the exclusive sides until a global conformity is achieved. ADFEP (a dynamic finite element preanalyser) has been written for this purpose. Apart from this objective, ADFEP has a wide spectrum of salient applications to various discretization related problems, such as automatic irregular generation, adaptive refinement and others. A simple energy criterion to determine the cut‐off frequency of a transient loading, and the concept of preprocessing the input loading using digital filters introduced by Valliappan and Murti1 are employed. They constitute the first module of ADFEP. The second (main) module consists of element splitting procedures where algorithms based on graph theory and element splitting templates have been extensively used. The notion of a ‘cross digraph’ introduced to carry a multiple ‘weights’ and to avoid duplication in node‐generation, is especially useful in three‐dimensional element splitting techniques. Finally, numerical inverse isoparametric mapping techniques presented by Murti and Valliappan2 are also used to interpolate the nodal quantity vectors at the newly generated nodes. These vectors are needed as initial values in subsequent iterations for a dynamic restart. This aspect, together with the node renumbering scheme, is included in the third module of ADFEP. Some illustrative examples are included to elucidate the effectiveness of ADFEP.
A finite element solution method for contact problems with friction
Authors: Chandrasekaran N. , Haisler W. E. , Goforth R. E. 
Published: August 2005

AbstractA new finite element solution method for the analysis of frictional contact problems is presented. The contact problem is solved by imposing geometric constraints on the pseudo equilibrium configuration, defined as a configuration at which the compatibility conditions are violated. The algorithm does not require any a priori knowledge of the pairs of contactor nodes or segments. The contact condition of sticking, slipping, rolling or tension release is determined from the relative magnitudes of the normal and tangential global nodal forces. Contact iterations are in general found to converge within one or two iterations. The analysis method is applied to selected problems to illustrate the applicability of the solution procedure.
Using eigenvector projections to improve convergence in non‐linear finite element equilibrium iterations
Authors: Eriksson Anders 
Published: August 2005

AbstractIn an earlier paper a method for calculation of non‐linear structural response was described. The method is based on an algorithm, proposed by Bergan, including simultaneous iterations in the load and displacement spaces. A method for selective damping of solution components parallel to critical eigenvectors was proposed reducing the risk for diverging equilibrium iterations.This method is, in the present paper, shown to be related to the ‘dynamic relaxation’ approach. The method has been further studied for practical problems, and especially adapted for the analysis of plate buckling. A method for variable damping is proposed, and compared to existing methods. The conclusions are that damping, based on eigenvector projection, is an efficient way to improve the stability in the iterations, and in this an alternative to other methods for choice of optimum corrections in N–R schemes. The extra computational effort is considered worth while in cases where restarts in the calculation are not desired.In the paper, suitable criteria for reformulation of the tangential relation during iterations in a step are also discussed.
An improved computational technique for perturbations of the generalized symmetric linear algebraic eigenvalue problem
Authors: Bickford William B. 
Published: August 2005

AbstractA technique is developed and presented which improves the accuracy of the predictions for the eigenvalues of the usual first order perturbation scheme for the generalized symmetric linear algebraic eigenvalue problem. The improved method very simply replaces the usual B‐norms appearing in the denominator of the expressions for the first order changes in the eigenvalues by BP‐norms where BP is the perturbed B matrix. With increasing sizes for the perturbations the improved technique produces results whose accuracy approaches those of the usual second order predictions. Numerical studies are presented to support the analysis.
The tanh transformation for the solution of singular integral equations
Authors: Tsamasphyros G. , Androulidakis P. 
Published: August 2005

AbstractUsing a tanh transformation a quadrature formula for the evaluation of singular integrals is obtained. The formula has the same step length h as the formula for regular integrals derived by F. Stenger. These quadrature formulae are valid for end point singularities of any order and their error exhibits an exponential decay when the number of integrations tends to infinity.Using these formulae the solution of singular integral equations does not depend on the order of the end point singularities. Furthermore the collocation points are given by a very simple equation and, in the case of constant coefficients, by a closed‐form formula.
BEM simulation of cathodic protection systems employed in infinite electrolytes
Authors: Zamani N. G. , Chuang J. M. , Porter J. F. 
Published: August 2005

AbstractThis paper describes the proper external potential formulation of a cathodic protection system employed for corrosion prevention of structures in infinite electrolytes. The boundary condition associated with the mathematical formulation is not of the standard type encountered in hydrodynamic, electrostatic or heat transfer applications. The developed mathematical model is discretized by the boundary element technique, which is then solved iteratively by the Newton–Raphson method.
A hybrid model for prismatic solids
Authors: Cannarozzi Mario 
Published: August 2005

AbstractA finite prism approach for the approximate analysis of three‐dimensional solids is proposed. The approach is based on a semi‐algebraic assumed stress hybrid model, according to Pian's scheme. Prismatic solids with various end conditions can be analysed with a traditional matrix‐displacement procedure, thus enlarging the possibilities offered by analogous compatible models.
Practical stability analysis of finite difference equations by the matrix method
Authors: Sucec James 
Published: August 2005

AbstractIt is shown how the various norms of the coefficient matrix of a set of finite difference equations can, in many cases, be employed in an easy, straightforward fashion to find sufficient conditions for stability in situations involving non‐periodic boundary conditions and variable coefficients. With the aid of the easily computed norms, particularly the infinite norm, one does not have to rely on the necessary condition provided by the spectral radius, which has been the main basis of criticism of the matrix method in the past.
The dynamic analysis of a flat plate under a moving load by the finite element method
Authors: Wu Jong‐Shyong , Lee Ming‐Ling , Lai Tser‐Shyong 
Published: August 2005

AbstractThe object of this paper is to analyse by the finite element method the dynamic responses of a flat plate subjected to various moving loads. First of all the actual continuous flat plate was replaced by a discrete system composed of isoparametric rectangular plate elements. And then the elementary and overall stiffness and mass matrices were determined and the natural frequencies and mode shapes of the flat plate were solved. Next, the Newmark direct integration method was used to find the dynamic responses of the flat plate.The effects of eccentricity, acceleration and initial velocity of the moving load, and the effect of span length were the key points of study. The dynamic behaviour of a multi‐span flat plate supported by the beam members of rigid plane frames and subjected to the action of a series of moving loads (in identical or opposite directions) were also investigated.
Least‐squares finite element method and preconditioned conjugate gradient solution
Authors: Carey G. F. , Jiang B. N. 
Published: August 2005

AbstractA least‐squares variational procedure for first‐order systems of differential equations and an approximate formulation based on finite elements are developed. Error estimates, a condition number bound and analysis of weighting factors are given. Steepest descent and conjugate gradient solution procedures are examined, and an appropriate preconditioner constructed which is demonstrated to yield rapid convergence and to be insensitive to problem size. Numerical studies of rates of convergence for a test problem are given.
Numerical experiments on turbulent flow using the random vortex method
Authors: Laitone Jonathan 
Published: August 2005

AbstractChorin's random vortex method is used to predict the growth of a large‐scale coherent vortex structure in the early stages of the development of turbulence in a two‐dimensional co‐flowing shear layer. The numerical algorithm has been simplified to such an extent that the numerical analysis can be performed on a microcomputer. The numerical solution exhibits the same early turbulent instabilities and vorticity pairings as found in recent flow‐visualization experiments. In addition the results are in reasonable agreement with experimental measurements of mean velocity, root mean square fluctuations and Reynolds stresses. One could thus test the shear layer sensitivity to initial conditions and the upsteam boundary conditions.
Singular element construction using a mapping technique
Authors: Tsamasphyros George 
Published: August 2005

AbstractConformal mapping regularizes (in the new plane) the singular stress field around the crack tip. So, conventional finite elements can be used in the transformed plane. The inverse mapping of the above elements gives another class of ‘mapped elements’. The crack‐tip mapped element is a singular element. Thus, using various elements (the ‘parent elements’) in the mapped plane we obtain an infinity of singular elements, the ‘product elements’. These singular elements are introduced naturally and have no defect, as many other singular elements have.
A grid generator based on 4‐triangles conforming mesh‐refinement algorithms
Authors: Rivara Maria‐Cecilia 
Published: August 2005

AbstractA procedure to generate 2D meshes of triangles in a quite general fashion allowing for local and selective mesh‐refinement is presented and discussed. The grid generator is based on the iterative application of 4‐triangles conforming mesh‐refinement algorithms for triangulations, which are also introduced in this paper. These algorithms are modified versions of those proposed in Int. j. numer. methods eng., 20, 745–756 (1984), and they can be used for global refinement of a grid, as well as for local refinement. The grid generator works in the following way: given any initial coarse triangulation which properly defines the geometry of the problem, a set of user‐defined refinement subregions Ri, i = 1,2,…, N, and an associated set of tolerance parameters hi, an irregular and conforming final triangulation is automatically constructed in such a way that the diameter of all the triangles contained in Ri is smaller than hi, i= 1,2,…, N. Moreover, all angles in the final triangulation are greater than or equal to half the smallest angle in the initial, coarse one. The refinement is propagated only to assure the conformity and smoothness of the grid, and consequently, the number of involved nodes will be minimized. The refinement of the final mesh will be determined by the subregions Ri and the parameters Ni and will be essentially independent of the initial coarse grid. The 4‐triangles conforming mesh‐refinement algorithms are presented and their properties discussed. The implementation of these techniques is discussed and examples of the application of the grid generator are given.
On the numerical integration of a class of pressure‐dependent plasticity models
Authors: Aravas N. 
Published: August 2005

AbstractAn unconditionally stable algorithm for the numerical integration of elastoplastic pressure‐dependent constitutive relations is analysed in detail in this paper. The application of the method to plane stress problems, in which the out‐of‐plane strain component is not defined kinematically, is discussed. The tangent moduli resulting from this integration algorithm are obtained by consistent linearization of the elastoplastic constitutive equations. The algorithm is applied to Gurson's constitutive model, some one‐dimensional problems are solved, and comparisons with exact solutions are made. The paper closes with a numerical study of the necking of an axi‐symmetric specimen using Gurson's plasticity model to describe the constitutive behaviour of the material.
Dynamic response optimization using an active set RQP algorithm
Authors: Lim O. K. , Arora J. S. 
Published: August 2005

AbstractA recently developed recursive quadratic programming (RQP) algorithm is applied to dynamic response design problems. The algorithm incorporates updated Hessians of the Lagrange function and uses an active set strategy in which only a subset of the constraints is included in the direction finding QP subproblem. Hessian updating with dynamic response constraints presents some difficulties. The primary difficulty is that the total number of constraints and the location of time points where they have to be imposed can change from iteration to iteration. This can cause inconsistencies in Hessian updating if proper numerical procedures are not used. A numerical procedure to handle the situation is developed, implemented and evaluated. Automatic restarting procedures are necessary for proper convergence of the algorithm. The new algorithm is robust as well as more efficient than the purely linear algorithm. The active set strategy plays an important role for application to dynamic response problems. The RQP algorithms that do not use such a strategy are not applicable to this class of problems.
Interactive solution to multiobjective optimization problems
Authors: Diaz Alejandro 
Published: August 2005

AbstractSensitivity analysis is presented as a natural addition to interactive multiobjective optimization methods based on compromise programming. It is shown that useful information regarding trade‐offs in the objectives can be generated effectively by means of an analysis of the sensitivity of solutions to variations in preference structures. An implementation based on sequential quadrative programming is provided and examples are given for illustration.
A posteriori estimates of the solution error caused by discretization in the finite element, finite difference and boundary element methods
Authors: Kelly D. W. , Mills R. J. , Reizes J. A. , Miller A. D. 
Published: August 2005

AbstractA theory is described which guarantees an upper and lower bound estimate of the discretization error in numerical solutions of elliptic boundary value problems. This method gives bounded global estimates of the error in the energy norm. Pointwise estimates of the error in the solution variable or its derivatives can then be obtained if the numerical solution is exhibiting pointwise monotonic convergence.The versatility of this method is illustrated by its application to numerical solutions from finite element, finite difference and boundary element methods.
Convected systems for curved structural elements
Authors: Gattass Marcelo , Abel John F. 
Published: August 2005

AbstractThis paper presents a new approach to the use of the updated Lagrangian formulation with convected systems. The development of this new method is similar to the updated Lagrangian formulation presented by Bathe et al.4 The main difference is that here the tensors are written in their components in the curvilinear convected system, while Bathe, Ramm, and Wilson employ Cartesian components. A special form of the natural approach5 is also introduced in this formulation to simplify the element computations. The matrices of a two‐dimensional curved beam‐column element are derived as an example of this new formulation. Finally, a numerical evaluation is performed to evaluate critically the new curved element and the method proposed here.
On artificial strain of thin curved elements
Authors: Gattass Marcelo , Abel John F. 
Published: August 2005

AbstractThis paper presents an attempt to clarify further the nature of the overstiffness of thin curved structural elements. It follows the approach presented by Ashwell and co‐workers1,2 who based their study on shape functions of arch elements. Such elements display the same stiff behaviour as complex shell elements but are simpler to study and understand. An examination of several discretizations for a two‐dimensional curved beam‐column element for linear elastic analysis of arches is performed. This examination and the numerical results obtained from these approximations provide a new interpretation of the artificial strains based on the mapping variables of shape functions. Two new methods to reduce the artificial stiffness of the element are proposed.
Selective refinement: A new strategy for automatic node placement in graded triangular meshes
Authors: Frey William H. 
Published: August 2005

AbstractAutomating triangular finite element mesh generation involves two interrelated tasks: generatine a distribution of well‐placed nodes on the boundary and in the interior of a domain, and constructing a triangulation of these nodes. For a given distribution of nodes, the Delaunay triangulation generally provides a suitable mesh, and Watson's algorithm26 provides a flexible means of constructing it. In this paper, a new method is described for automating node placement in a Delaunay triangulation by seieclive refinement of an initial triangulation. Grading of the mesh is controlled by an explicit or implicit node spacing function. Although this paper describes the technique only in the planar context, the method generalizes to three dimensions as well.
Petrov—Galerkin method for multidimensional, time‐dependent, convective‐diffusion equations
Authors: Yu C.‐C. , Heinrich J. C. 
Published: August 2005

AbstractA Petrov—Galerkin finite element method for two and three‐dimensional time dependent convection‐diffusion equations is presented in the context of two space dimensions. The method involves perturbed weighting functions in the weighted residuals formulation, that are bilinear in space and quadratic in time and depend on two parameters which are calculated according to a local analysis for the one dimensional case. The perturbations to the weighting functions can be interpreted as an added local anisotropic balancing diffusion and an added dispersion in the direction of the convective motion. The effectiveness of the method is shown through several examples involving the convective and diffusive transport of scalar distributions in known velocity fields.
A new partially bonded beam element for analysis of shear walls
Authors: Chakrabarti S. C. , Nayak G. C. , Paul D. K. 
Published: August 2005

AbstractA finite element formulation for multi‐panel shear walls based on a partially bonded beam system has been proposed. Idealization of a shear wall by a partially bonded multi‐layered beam element reduces the storage and computer time considerably. The finite element model has been employed extensively for parametric study of prefabricated shear walls of different widths and heights. Different numbers of in‐situ joints in the prefabricated shear wall assembly with varying shear stiffness of joints have also been considered. The parametric study gave an insight to the structural response of the wall system. Based on the non‐linear shear stiffness characteristic of in‐situ joints determined experimentally, the nonliner behaviour of a prefabricated shear wall has been determined and the failure load has been predicted.
A new approach to the finite element modelling of beams with warping effect
Authors: Lee S. W. , Kim Y. H. 
Published: August 2005

AbstractAs a first step toward developing a finite element formulation that can model coupling among extensional, bending and torsional behaviour of beams, a new method is proposed to properly represent the warping of arbitrary cross‐sections. The basic approach is to introduce a small warping displacement superimposed over flat cross‐sections of a shear‐flexible beam in a deformed configuration. Numerical tests involving simple isotropic beams undergoing a small elastic displacement demonstrate the validity of the new approach. The present approach can be extended to composite beams as well as isotropic beams experiencing a large deflection or finite rotation.
An assumed covariant strain based 9‐node shell element
Authors: Jang Junho , Pinsky Peter M. 
Published: August 2005

AbstractA new shell element, which is free from serious locking problems and which does not possess hourglass modes, is proposed. Solutions obtained with this element exhibit good convergence and are satisfactorily insensitive to mesh distortion. The element also exhibits good convergence for plates with variable thickness. This element is based on the use of assumed covariant strains which are obtained from the covariant strain field defined with respect to the element natural co‐ordinate system. Only the linear version for thin shell cases is considered. The element performance is tested by application to several standard plate and shell problems. A problem involving variable thickness is also presented.
A parallel householder tridiagonalization stratagem using scattered row decomposition
Authors: Chang H. Y. , Utku S. , Salama M. , Rapp D. 
Published: August 2005

AbstractHouseholder's method for tridiagonalizing a real symmetric matrix, a major step in evaluating eigenvalues of the matrix, is modified into a parallel algorithm for a concurrent machine of message passing type. Each processor of the concurrent machine has its own CPU, communications control and local memory. Messages are passed through connections between processors. Although the basic algorithm is inherently serial, the computations can be spread over all processors by scattering different rows of the matrix into processors, hence the term “Scattered Row Decomposition”. The steps in the serial and the parallel algorithms are identified. Expressions for efficiency and speedup are given in terms of problem and machine parameters. For a concurrent machine of ring type interconnection, a selected representative problem of large order exhibits efficiency approaching 66 per cent.
Quadratic‐spline collocation methods for two‐point boundary value problems
Authors: Houstis E. N. , Christara C. C. , Rice J. R. 
Published: August 2005

AbstractA new collocation method based on quadratic splines is presented for second order two‐point boundary value problems. First, O(h4) approximations to the first and second derivative of a function are derived using a quadratic‐spline interpolant of u. Then these approximations are used to define an O(h4) perturbation of the given boundary value problem. Second, the perturbed problem is used to define a collocation approximation at interval midpoints for which an optimal O(h3‐J) global estimate for the jth derivative of the error is derived. Further, O(h4‐J) error bounds for the jth derivative are obtained for certain superconvergence points. It should be observed that standard collocation at midpoints gives O(h2‐J) bounds. Results from numerical experiments are reported that verify the theoretical behaviour of the method.