bluuebunny/crossref_metadata_2025_split huggingface dataset:
Dynamics of the bilinear Mindlin plate element
Authors: Brockman R. A. 
Published: August 2005

AbstractPlate and shell finite elements based upon Mindlin plate theory and evaluated by one‐point quadrature are attractive because of their effectiveness for both thick and thin shells, at minimal computing cost. However, these elements are rank‐deficient and must be stabilized to obtain reliable behaviour. Methods for achieving full rank of the stiffness and for stabilizing element behaviour in static analysis and in explicit dynamic calculations exist and are quite effective. This paper addresses the remaining issue of controlling spurious modes of response in vibration analysis and implicit dynamic solutions. Several alternatives for the element mass formulation are examined in detail. We show that non‐physical dynamic modes present a potential problem with most mass matrix formulations, and that spurious modes other than the familiar hourglassing motion are possible. A combination of projection methods and reduced quadrature is suggested which eliminates these deficiencies and produces accurate numerical results. The remaining techniques investigated give rise to anomalous behaviour which make them unsuitable for general use.
Second order sensitivity analysis of lumped mechanical systems in the frequency domain
Authors: Wicher Jerzy , Nalecz Andrzej G. 
Published: August 2005

AbstractThis paper presents a method for determining the second order sensitivity matrix and logarithmic sensitivity functions in the frequency domain. The procedure described is applicable to any discrete and viscously damped mechanical system.A definition of the second order logarithmic sensitivity function has been proposed. The examples shown indicate that logarithmic sensitivity functions of the second order preserve the qualitative character of first order sensitivity functions and are more sensitive to changes of system parameters. The influence of large parameter changes on second order sensitivity functions has also been investigated.
Non‐linear analysis of elastic plane frames with crooked bars
Authors: Economou A. F. , Kounadis A. N. 
Published: August 2005

AbstractIn this investigation the postbuckling response of plane frames consisting of a large number of crooked bars is achieved by means of an efficient method based on non‐linear kinematic stability analysis. The entire formulation of the non‐linear equilibrium equations presented in matrix form is implemented by the computer program NLSRF (Non‐Linear Stability of Rod Frames). Critical loads and critical displacements are obtained through a direct computation by using the additional stability condition resulting from the vanishing of the stability determinant.The efficacy of the method proposed herein is demonstrated by a three‐storey single span frame.
An incremental procedure for deformation analysis of elastic‐plastic frames
Authors: Andreaus U. , D'Asdia P. 
Published: August 2005

AbstractIn the present paper an incremental procedure is formulated for first‐order elastoplastic analysis of plane frame structures discretized into a finite number of beam elements and described by piecewise linear elastic‐perfectly plastic constitutive laws, under the assumption of both reversible and irreversible behaviour of material and using piecewise linear yield conditions at any desired degree of discretization in the space of the active stress resultants (axial force, shear force and bending moment).The proposed method, by using the independent elastic‐plastic kinematical compatibility equations, restrains the problem sizes within not more than twice the number of the redundant unknowns in the complete elastic frame, regardless of the degree of discretization of the piecewise linear yield conditions, still maintaining the advantage exhibited by the Mathematical Programming methods of requiring only one factorization of the matrix governing the problem when no local unloading occurs. Furthermore, the outlined algorithm allows the additional computational effort to be restrained in the case of local unloading, inasmuch as it requires a new factorization to be performed of a part of the matrix governing the problem, whose size is small with respect to the total size of the matrix.
On evaluation of the green functions for harmonic line loads in a viscoelastic half space
Authors: Dravinski Marijan , Mossessian Tomi K. 
Published: August 2005

AbstractComparison of different quadratures for evaluation of the improper wavenumber integrals which arise in evaluation of the Green functions for a viscoelastic half space and harmonic line loadings is investigated. The model is assumed to be of the plane strain type. Extensive testing of the numerical accuracy for various quadratures is performed. A measure of numerical efficiency of the quadratures is proposed and compared for different integration formulae. It was determined that among the procedures tested the Clenshaw‐Curtis quadrature offers the most efficient way of evaluating the wavenumber integrals numerically.
The null space and non‐conventional basis functions in the mixed finite element method
Authors: Robey T. H. , Schreyer H. L. 
Published: August 2005

AbstractThe two matrix equations obtained from the mixed finite element method are uncoupled through the use of the QR decomposition. The procedure obtains the basis for the null space which is composed of solutions to the homogeneous flux‐equilibrium equation. The result is that, even for statically indeterminate problems, stresses can be obtained without solving for the displacement field. Furthermore, the stress field can be decomposed directly into contributions from applied forces and from prescribed displacements. The appearance of kinetic modes can easily be monitored. The possibility of utilizing non‐conventional basis functions for use in conjunction with the QR decomposition is explored briefly. Simple examples are given to illustrate the theoretical results.
A variable stiffness type boundary element formulation for axisymmetric elastoplastic media
Authors: Henry D. P. , Banerjee P. K. 
Published: August 2005

AbstractA new ‘direct’ elastoplastic boundary element formulation for axisymmetric bodies is developed. The procedure exploits certain features of the constitutive relationship to express the unknwon non‐linear initial stress rate tensor as a scalar quantity which can then be eliminated from the boundary equation system though a back substitution of the (modified) stress rate equations.This formulation is implemented in a multi‐region system that utilizes quadratic isoparametric shape functions to model the geometry and field variables of the boundary and domain of a body. The kernel functions are presented in Appendix I and the singularities associated with these kernels are discussed. New techniques are described to calculate the coefficients associated with the singular nodes.
An efficient approximation technique for frequency constraints in frame optimization
Authors: Vanderplaats Garret N. , Salajegheh Eysa 
Published: August 2005

AbstractAn efficient approximation technique is presented for dealing with frequency constraints in frame optimization. The method is based on a linear approximation of the eigenvalues with respect to the member section properties. Using this, an approximate optimization problem is solved treating the physical dimensions of the beams as design variables. When the eigenvalues are required, the section properties are first calculated. Then, using the approximation, the eigenvalues are estimated and returned to the optimizer. When the approximate optimum is found, a detailed analysis is performed and the process is repeated. Examples are presented to demonstrate the method. The method is simple, yet treats the physical dimensions of the structure as design variables, and allows for large move limits during the approximate optimization.
A new hybrid transfinite element computational methodology for applicability to conduction/convection/radiation heat transfer
Authors: Tamma Kumar K. , Railkar Sudhir B. 
Published: August 2005

AbstractThis paper describes new and recent advances in the development of a hybrid transfinite element computational methodology for applicability to conduction/convection/radiation heat transfer problems. The transfinite element methodology, while retaining the modelling versatility of contemporary finite element formulations, is based on application of transform techniques in conjunction with classical Galerkin schemes and is a hybrid approach. The purpose of this paper is to provide a viable hybrid computational methodology for applicability to general transient thermal analysis. Highlights and features of the methodology are described and developed via generalized formulations and applications to several test problems. The proposed transfinite element methodology successfully provides a viable computational approach and numerical test problems validate the proposed developments for conduction/convection/radiation thermal analysis.
Formulation and solution of hierarchical finite element equations
Authors: Wiberg Nils‐Erik , Möller Peter 
Published: August 2005

AbstractThe paper presents a general hierarchical formulation applicable to both elliptic and hyperbolic problems. Static and eigenvalue linear elastic problems as well as convection–diffusion problems are studied. The hierarchical formulation is well suited for adaptive procedures.For the convection‐diffusion problem the hierarchical approximation is made in time only. Different hierarchical functions are proposed for different types of problems. Both weighted residual and least‐squares formulations are applied. A combination of these two gives a penalty method with a constraint equation corresponding to the least‐squares method. A whole class of time integration formulae is obtained. These are all suitable for adaptive procedures owing to the hierarchical approximation in the time domain. If a linear discontinuous hierarchical base function is used in the Galerkin weak formulation, the method so obtained corresponds to the discontinuous Galerkin method in time and is especially suited for convection dominated problems. The streamline‐diffusion method is found to be the aforementioned penalty method.This paper also examines the sequence of nested equation systems that results from a hierarchical finite element formulation. Properties of these systems arising from static problems are investigated. The paper presents some new possibilities for iterative solution of hierarchic element equations, and different procedures are compared in a numerical example. Finally, a simple ID convection‐diffusion problem clearly shows that the proposed hierarchical formulation in time gives a stable and accurate solution even for convection dominated flow.
A new BEM formulation for the acoustic eigenfrequency analysis
Authors: Banerjee P. K. , Ahmad S. , Wang H. C. 
Published: August 2005

AbstractA new boundary element formulation has been developed for two‐ and three‐dimensional acoustic eigenfrequency analyses. The formulation is based on the well known method of constructing a solution of a differential equation in terms of a complementary function and particular integral. An advanced isoparametric implementation with automatic error control in the integration is used. A number of realistic examples of application to automotive acoustic cavities are described.
Application of the Galerkin method to calculation of temperature in a body exposed to periodically varying boundary conditions
Authors: Jones John Dewey 
Published: August 2005

AbstractDetermination of the temperature fluctuations in the combustion‐chamber walls of an engine is one of many engineering applications requiring calculation of the temperature distribution in a body exposed to periodically varying boundary conditions. In this paper it is shown that, under suitable circumstances, the temperature distribution within such a body can be resolved into spatially varying and temporally varying terms. Repeated application of the Galerkin method allows this temperature distribution to be approximated by the solution of a complex matrix equation. The solution method is rapid, stable, and can be taken to any desired accuracy. A sample calculation is shown for the cylinder liner of an insulated diesel engine, taking into account the effects of time‐varying convective and radiative heat transfer and frictional heating.
On implementation of computational algorithms for optimal design 1: Preliminary investigation
Authors: Tseng C. H. , Arora J. S. 
Published: August 2005

AbstractIn this two part paper, the problem of implementation of computational algorithms for design optimization into a computer software is discussed. A recently developed algorithm that generates and incorporates approximate second order information about the problem is selected for detailed analyses and discussions. It is shown that numerical behaviour of the algorithm is influenced by variation of the key parameters and procedures. The concept of numerical experiments is introduced, and certain variations of the algorithm and parameters are selected and their influence on its performance is studied. It is shown that the numerical rate of convergence can be substantially improved with proper procedures and values of the parameters. The first part of the paper describes some preliminary analyses and investigations. The second part describes further numerical analyses and detailed procedures for evaluation of performance of various variations of an algorithm or different computer codes. The basic conclusion from the study is that robust and efficient implementation of algorithms requires expert knowledge and considerable numerical experimentation. A wide range of small scale and large scale problems of varying difficulty must be solved to evaluate performance of an algorithm. The study suggests development of knowledge‐based systems for practical design optimization.
On implementation of computational algorithms for optimal design 2: Extensive numerical investigation
Authors: Tseng C. H. , Arora J. S. 
Published: August 2005

AbstractIn the second part of this paper, some further refinements of a computational algorithm for optimum design are described. Results of an extensive numerical investigation are discussed. The numerical study is designed and criteria for comparing the performance of algorithms are developed. Various variations of the algorithmic parameters and procedures are evaluated. Using the procedures described in the paper, other algorithms and programs can be evaluated.
Hybrid Laplace transform/finite difference method for transient heat conduction problems
Authors: Chen Han‐Taw , Chen Cha'O‐Kuang 
Published: August 2005

AbstractThe new method involving the combined use of the Laplace transform and the finite difference method is applicable to the problem of time‐dependent heat flow systems. The present method removes the time derivatives from the governing differential equation using the Laplace transform and then solves the associated equation with the finite difference method. The transformed temperature is inverted numerically by the method of Honig and Hirdes to obtain the result in the physical quantities. The present results are compared in tables with exact solutions and those obtained from the combined use of the Laplace transform and the finite element method. It is found that the present method is reliable and efficient.
Isotherm migration method applied to fusion problems with convective boundary conditions
Authors: Gupta Radhey S. , Kumar Ambreesh 
Published: August 2005

AbstractA numerical technique based on the Isotherm Migration Method is presented for solving Moving Boundary Problems involving convective boundary conditions. The method is illustrated by solving sample problems in one dimension as well as in two dimensions. The comparison of present results with those of earlier authors shows an extremely good agreement.
Hydrodynamic analysis of the surf zone
Authors: Arcilla A. S. 
Published: August 2005

AbstractSurf zone processes are one of the most difficult and challenging topics in modern marine science and technology. Because of their scientific and practical (e.g. engineering) importance they have been extensively studied in recent years. Nevertheless, even though the basic equations are known, no complete numerical solution can even be attempted yet. Moreover, there are still many unanswered questions relating to domain definition, well‐posedness of the mathematical problem, validity of closure relationships and stability/convergence aspects of the numerical solution.This paper, starting from the basic conservation laws, derives sets of governing equations for the various flow modes present in the surf zone (currents, waves and turbulence). The emphasis will be on physical principles and simplifying hypotheses to show the application field of the different sets of equations. The paper will concentrate on the form and validity of the equations, including also some comments on discretization and numerical solution techniques.
Non‐linear stochastic response of marine vehicles
Authors: Duthoit Christophe , Armand Jean‐Louis 
Published: August 2005

AbstractThe dynamic behaviour of marine vehicles in extreme sea states is a matter of great concern following some recent and dramatic mishaps. The complex problem of its prediction can be approached from the study, yet of broader scope, of non‐linear dynamic systems subjected to stochastic excitations. However, a general non‐linear stochastic dynamic theory is not yet available.A new technique, the so‐called linearize‐and‐match method, for predicting the response statistics of non‐linear systems, is presented. Essentially, the technique involves the construction of an infinite series of linear systems aimed at the prediction of the response statistical moments of a given order.The linear systems are successively defined by linearizing the original, non‐linear system and matching the Volterra functional model response statistics to the desired order. The linear system for predicting second order statistics is shown to coincide with the one obtained using the method of equivalent linearization.Response probability distributions can be constructed from the knowledge of such statistics. Particular attention is devoted to the distribution of maximum entropy and its justification in such underdetermined moment problems.Finally, applications to the roll motion of ships serve to exemplify as well as to assess the accuracy and the versatility of the overall method. Response distributions of maxima so predicted compare very well with digital simulation estimates.
A dual adaptive procedure for the automatic determination of iteration parameters for Chebyshev acceleration
Authors: Mai Tsun‐Zee , Young David M. 
Published: August 2005

AbstractChebyshev acceleration for a symmetrizable basic iterative method u(n+1) = Gu(n) + k; requires estimates of the extreme eigenvalues m(G) and M(G) of the iteration matrix G. Adaptive procedures are often used in order to obtain good estimates for m(G) and M(G). Some existing adaptive procedures are able to give an estimate of either m(G) or M(G) but not both on any given iteration. In this paper we present an adaptive procedure which can estimate both m(G) and M(G) at the same time and which has other useful properties. Numerical results are given which show the new procedure usually requires fewer iterations than previous procedures.
Experience with the conjugate gradient method for stress analysis on a data parallel supercomputer
Authors: Johnsson S. Lennart , Mathur Kapil K. 
Published: August 2005

AbstractThe storage requirements and performance consequences of a few different data parallel implementations of the finite element method for domains discretized by three‐dimensional brick elements are reviewed. Letting a processor represent a nodal point per unassembled finite element yields a concurrency that may be one to two orders of magnitude higher for common elements than if a processor represents an unassembled finite element. The former representation also allows for higher order elements with a limited amount of storage per processor. A totally parallel stiffness matrix generation algorithm is presented. The equilibrium equations are solved by a conjugate gradient method with diagonal scaling. The results from several simulations designed to show the dependence of the number of iterations to convergence upon the Poisson ratio, the finite element discretization and the element order are reported. The domain was discretized by three‐dimensional Lagrange elements in all cases. The number of iterations to convergence increases with the Poisson ratio. Increasing the number of elements in one special dimension increases the number of iterations to convergence, linearly. Increasing the element order p in one spatial dimension increases the number of iterations to convergence as pα, where α is 1·4–1·5 for the model problems.
The D1/2‐norm of the SOR and Cyclic Chebyshev Semi‐Iterative (CCSI) methods for a class of non‐symmetric matrices
Authors: Evans D. J. , Li C. 
Published: August 2005

AbstractThe Successive Overrelaxation (SOR) and the Cyclic Chebyshev Semi‐Iterative (CCSI) methods are considered for solving the non‐symmetric linear systems Ax = b when A has the form

with D1 and D2 symmetric positive definite (SPD).The D1/2‐norms of both methods are determined and it is shown that, though the SOR method is better based on the spectral radius, the CCSI scheme is far better than SOR according to the D1/2‐norm.
Algorithms for construction of preconditioners based on incomplete block‐factorizations of the matrix
Authors: Vassilevski P. S. 
Published: August 2005

AbstractWhen applying an incomplete block‐factorization technique one needs sparse approximate inverses of the successive Schur complements computed throughout the factorization. Here we propose a method for the construction of such sparse approximate inverses. The method has an advantage over earlier versions, in that such approximate inverses of block‐tridiagonal matrices can be computed in parallel. Comparative numerical experiments for solving a number of discretized diffusion equations by this preconditioning matrix in a preconditioned conjugate gradient method and earlier versions of incomplete block‐factorization preconditioners are presented.
The application of symbolic computing to the hierarchical finite element method
Authors: Bardell N. S. 
Published: August 2005

AbstractOne difficulty associated with the hierarchical finite element method is that of accurately determining the integrals necessary to establish the stiffness and mass matrices of arbitrarily high order elements. This paper describes how such integrals can be calculated exactly using symbolic computing.Results are presented which permit the construction of high order hierarchical finite elements applicable to a variety of problems involving two‐dimensional elasticity, and plate and shell bending. Three‐dimensional solid or brick elements are not considered.
A numerical integration approach by weight factors and its accuracy
Authors: Mihailović Vojislav 
Published: August 2005

AbstractA new parabolic approach for numerical integration using weight coefficients is proposed.Several basic approaches for integration have been analysed: linear (trapezoidal), parabolic (new form), Simpson's, Newton–Cotes and Gaussian. The weight coefficients are transformed into the same form for all methods. Simpson's and Newton's formulas (for n = 3) are obtained as special cases of the general parabolic formula. A simple procedure to estimate the accuracy of the integral for final intervals is given.