bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the use of quarter‐point boundary elements for stress intensity factor computations
Authors: Martínez José , Domínguez José 
Published: August 2005

AbstractThis communication studies a procedure for stress intensity factor computations using traction singular quarter‐point boundary elements. Opening mode stress intensity factors are computed from the tractions' nodal values at the crack tip. A comparison is made between the factors calculated using this procedure and those obtained by previously recommended methods which made use of the nodal values of the displacements. The proposed procedure was seen to be less discretization sensitive than any other of the considered methods. Accurate results were obtained even in the case of coarse meshes.
A unified set of single step algorithms. Part 2: Theory
Authors: Wood W. L. 
Published: August 2005

AbstractPart 1 of this paper1 presents a very general single step algorithm SSpj for the numerical integration of first and second order time dependent differential equations. In Part 2 we present and discuss results of the accuracy and stability analysis for SS11, SS21, SS31, SS22 and SS32. There is also a detailed comparison of SS22 and the Newmark algorithm.
Accelerated ‘relaxation’ or direct solution? Future prospects for fem
Authors: Zienkiewicz O. C. , Löhner R. 
Published: August 2005

Abstract‘Dynamic’ or ‘viscous’ relaxation procedures have not gained much popularity in finite element analysis in which the direct (Gaussian elimination) solution dominates. Reasons for this are various—the most important being the rather slow convergence generally achieved for such procedures. However, it is possible to accelerate this quite dramatically and a method of doing so is shown in this paper. With the use of such acceleration and the inherent advantages of greatly reduced storage requirements and simplicity of programming, relaxation procedures promise an exciting possibility for the solution of large two‐ and three‐dimensional problems in both linear and nonlinear ranges.
Sparse matrix factor modification in structural reanalysis
Authors: Law Kincho H. 
Published: August 2005

AbstractStructural reanalysis problems, such as in nonlinear finite element analysis or optimum design, involve progressive changes in the global stiffness matrix and its matrix factors. Although many studies have been devoted to the subject of matrix factor modification, most investigations have dealt with the problem separately from sparse matrix methods. This paper introduces a graph‐theoretic model for the forward solution procedure which is applicable for identifying the modified entries of the matrix factors due to changes in the original matrix. Applications of this graph‐theoretic model to existing refactorization methods are presented. The relation between substructuring and sparse matrix ordering strategies, and their effects on reanalysis are discussed. Modification of a sparse matrix associated with an n × n finite element grid ordered by the nested dissection scheme is analysed.
A boundary integral equation method for radiation and scattering of elastic waves in three dimensions
Authors: Rizzo F. J. , Shippy D. J. , Rezayat M. 
Published: August 2005

AbstractA vector boundary integral equation (BIE) formulation and numerical solution procedure is presented for problems of three‐dimensional elastic wave radiation and scattering from arbitrarily shaped obstacles. The formulation is explicitly in terms of surface traction and displacement, rather than wave potentials, and the BIE on which numerical work is based is written in a form entirely free of Cauchy principal value integrals. Indeed, the subsequent computational process, based on quadratic isoparametric boundary elements, renders all integrals free of singularities, so that ordinary Gaussian quadrature may be used. Numerical examples include scattering from spherical surfaces and radiation from a cube.
A six‐node finite element for plate bending
Authors: Lee S. W. , Zhang J. C. 
Published: August 2005

AbstractA six‐node plate bending element has been developed by employing mixed formulation based on a modified Hellinger–Reissner principle and the Reissner–Mindlin plate bending theory. The numerical result indicates that, among the types of assumed independent transverse shear strains considered, a combination of 2α version with either 5α version or 6α version is free of spurious kinematic modes and leads to accurate and reliable solutions even for very thin plates.
A simple approach to bifurcation and limit point calculations
Authors: Fujikake Masahisa 
Published: August 2005

AbstractA simple approach is proposed to calculate the bifurcation and limit points of structures, talcing into account the pre‐unstable behaviour, by the finite element method. The approach is as follows: at each load step, the triangular factorization of the tangent stiffness matrix is checked to determine if the matrix is positive definite or not. When the tangent stiffness matrix is positive definite at a certain load step and non‐positive definite at the next load step, the structure is considered to become unstable between the two load steps and an eigenproblem is constructed based on the difference of the tangent stiffness matrices at the two load steps. The critical load and corresponding mode of the structure are then derived from solving the eigenproblem. The proposed procedure is simple and economical, and it can be easily incorporated into a conventional geometric nonlinear analysis computer program. It is implemented in the ADINA program and some sample calculations are shown.
Finite element analysis of nonlinear oscillators
Authors: Krishnamurthy K. , Burton Thomas D. , Zeller Lavern D. 
Published: August 2005

AbstractPresented in this paper is a finite element method for the analysis of nonlinear oscillations which exhibit periodic response. The basic idea of the method is to recast the initial value problem as a boundary value problem in which the domain (that is, period) may be unknown. We apply the method to study the free response of the conservative oscillator ü + mu + ϵf(u)=0, where m is either − 1, 0 or 1, f(u) is an odd nonlinear function, and ϵ need not be small. The harmonically forced case, ü + mu + ϵf(u) = Psin Ωt, is also considered, and it is shown that the superharmonic response can be efficiently calculated using this technique.
Multiple coplanar embedded elliptical cracks in an infinite solid subject to arbitrary crack face tractions
Authors: O'Donoghue P. E. , Nishioka T. , Atluri S. N. 
Published: August 2005

AbstractThis paper extends the earlier work by the present authors for a single embedded crack in an infinite solid and presents a solution to the problem of multiple coplanar cracks in an infinite medium. An alternating method in conjunction with an analytical solution for a single crack is used to determine the stress intensity factors for interacting multiple coplanar embedded cracks in an infinite body. The alternating method, as implemented here, leads to a highly accurate evaluation of the appropriate stress intensity factors.
An isoparametric joint/interface element for finite element analysis
Authors: Bfer G. 
Published: August 2005

AbstractA generally applicable and simple joint/interface element for three‐ and two‐dimensional finite element analysis is presented. The proposed element can model joints/interfaces between solid finite elements and shell finite elements. The derivation of the joint element stiffness is presented and algorithms for the treatment of nonlinear joint behaviour discussed. The performance of the element is tested on typical problems involving shell‐to‐shell and shell‐to‐solid interfaces.
Variational approach to first‐ and second‐order sensitivity analysis of elastic structures
Authors: Dems K. , Mróz Z. 
Published: August 2005

AbstractFor a linear elastic structure, the first variations of arbitrary stress, strain and displacement functionals were explicitly expressed in terms of variations of material stiffness parameters within specified domain, in References 1 and 2, by using the solutions for primary and adjoint systems. In this paper, explicit expressions for second variations are derived for the case when the material stiffness or compliance variations depend on a set of parameters. These expressions arc obtained in terms of variations of stiffness or compliance parameters by using the solutions of two additional sets of adjoint systems. Furthermore, the variation of local stress, strain or displacement is considered. Several illustrative examples are provided for the first‐ and second‐order sensitivity analysis of beams.
The gradient of the finite element variational indicator with respect to nodal and applications in fracture mechanics and mesh optimization
Authors: Sussman Theodore , Bathe Klaus‐Jurgen 
Published: August 2005

AbstractWe derive a closed‐form expression for the change in the variational indicator of a finite element mesh with respect to perturbations in nodal point co‐ordinates. The expression is evaluated very effectively from standard finite element data obtained in one solution, and may be easily programmed as part of a general finite element code. We present the derivation for two‐ and three‐dimensional isoparametric elements used in linear and nonlincar elasticity. The expression has practical applications in the computation of stress intensity factors in fracture mechanics and in the determination of the ‘optimal’ mesh with a given element‐node connectivity. We demonstrate both applications by accurately determining the stress intensity factor of a Mode I crack using a finite element mesh which was improved using mesh optimization.
On body‐fitted co‐ordinates for separated laminar flows past wall‐mounted obstacles
Authors: Yeung P. K. , Kot S. C. 
Published: August 2005

AbstractA body‐fitted curvilinear co‐ordinate system is used to solve the equations of two‐dimensional incompressible laminar flow over bluff obstructions by finite differences. Arbitrary conditions at the corner are removed by this method. Results for a backward‐facing step are in reasonable agreement with those obtained with conventional mesh systems, and the differences are explained. A treatment of a channel expansion, in comparison with empirical data, is also included. The capability of the present method to handle arbitrary two‐dimensional geometries is stressed and demonstrated, using a triangle and a semi‐circle as examples.
An algorithm based on the boundary element method for problems in engineering mechanics
Authors: Vable Madhukar 
Published: August 2005

AbstractThe solution to a two‐dimensional problem using the boundary element method requires the evaluation of a line integral over the boundary. The integrand ot this line integral is a product of a known Green's function and an unknown function. A large number of Green's functions for two‐dimensional problems can be represented by a linear combination of four singular functions. By approximating the unknown function by a linear combination of known polynomials, integrals are generated whose integrand is a product of the polynomiais and one of the four singular functions. To evaluate these integrals analytically, the boundary is approximated by a sum of straight‐line segments. Recursive formulae are established which reduce the generality and the complexity of the integrands to simple expressions. Analytical forms for these simple expressions are found and are used for initiating the algorithm.
Transmission line interpretation of the finite element mesh for a wave propagation problem
Authors: Mason John L. , Anderson William J. 
Published: August 2005

AbstractA one‐dimensional exterior electromagnetic scattering problem is formulated using a differential equation approach followed by a finite element discretization. By interpreting the resulting linear algebraic equations as node voltage equations for a transmission line, a boundary element is obtained which satisfies the requirement of no wave reflection at the edge of the finite element region. Numerical results which show the elimination of non‐physical standing waves from the scattered field are presented and discussed.
Projection and iteration in adaptive finite element refinement
Authors: Carey G. F. , Seager M. 
Published: August 2005

AbstractA local elliptic projection is introduced to provide improved local approximations to the finite element solution of boundary‐value problems. The approach yields a composite global approximation that is more accurate and provides a good starting value for iterative solution methods. The procedure is particularly effective when used in conjunction with adaptive mesh refinement, as illustrated in numerical studies involving two‐point problems of boundary‐layer and interior‐layer type.
Finite element formulations for non‐steady‐state large viscoplastic deformation
Authors: Bohatier Claude , Chenot Jean‐Loup 
Published: August 2005

AbstractDifferent mechanical formulations are employed for calculation of the large deformations occurring in metal forming processes. Eulerian and updated Lagrangian descriptions, valid for viscoplastic materials, are presented. In view of the numerical tests which were carried out, the Eulerian formulation, associated with an implicit integration scheme which proved to be numerically accurate and reliable, is shown to be preferable.
Finite layer analysis of layered viscoelastic materials under three‐dimensional loading conditions
Authors: Booker J. R. , Small J. C. 
Published: August 2005

AbstractA method is presented which enables the calculation of the settlement behaviour of circular or general loadings on horizontally layered soils which undergo secondary or ‘creep’ consolidation. The method of analysis involves the use of Hankel or double Fourier transforms to simplify the equations governing the consolidation process. This leads to great savings in the preparation of data and the amount of computer storage needed to solve problems involving three‐dimensional loadings since such problems are essentially reduced to that of one spatial dimension: Solutions are then obtained by a ‘forward marching’ process where solutions at a particular time are found from those at a previous time. A method is presented which eliminates the need to store the solutions at all previous time steps, and is therefore very efficient. The theory is illustrated by examples of the behaviour of rectangular and circular loadings on layered soil profiles.
Eigenvalues and stable time steps for the bilinear Mindlin plate element
Authors: Belytschko Ted , Lin Jerry I. 
Published: August 2005

AbstractEigenvalues are obtained for the 4‐node Mindlin plate element with one‐point quadrature. Both isotropic and some anisotropic matenals are considered, but for the latter only bounds are obtained on the eigenvalues. These eigenvalues provide stable time steps for explicit time integration algorithms.
Analysis of heat conduction in solids by space‐time finite element method
Authors: Yu J. R. , Hsu T. R. 
Published: August 2005

AbstractA functional in the form of a convolution of the temperature variation in the space–time domain has been derived. It has been used as the basis for a finite element formulation of heat conduction in solids. Numerical illustrations have indicated that the space–time finite element algorithm provides a more rapid convergence to the exact solutions than the usual finite element analysis with discretization in space only.
Fixed‐point iteration to nonlinear finite element analysis. Part I: Mathematical theory and background
Authors: Zeid Ibrahim 
Published: August 2005

AbstractThis paper sets the stage for the implementation of the Fixed‐Point Iteration (FPI) to nonlinear finite element analysis as an alternative to the existing Newton‐Raphson Method (NRM) or its derivatives. The superiority of the former method over the latter one is such that it enables one to obtain nonlinear structural static or dynamic responses without inverting the structural stiffness matrix.In the first part of the paper, a new convergence correction/acceleration factor has been developed for the FPI when applied to a single nonlinear algebraic equation. This new factor causes the iteration function of the equation under consideration to rotate about an axis that passes through one of its fixed points or roots. Using this observation, the slope of the iteration function can be adjusted in the neighbourhood of a specific root to ensure the convergence of the FPI. It is found that the optimum choice of the new factor corresponds to a zero slope, evaluated at the root, of the iteration function. The rate of convergence and the error estimate of this form of the FPI is developed and compared with the NRM. The equilibrium positions of a nonlinear loaded softening spring have been obtained by both methods as an illustrative numerical example to measure the effect of the new factor on the convergence rate.The second part of the paper extends the above concept to find the solution of a linear system of algebraic equations using the FPI. This leads to a better diagonal approximate inverse for the Jacobi iteration, or method of simultaneous displacements. If the elements of the solution vector of a specific system are all equal, the new Jacobi iteration becomes an exact method and the solution is obtained in one iteration. The concept is also extended to the Gauss‐Seidel iteration, or method of successive displacements. Systems involving symmetric as well as nonsymmetric coefficient matrices have been used as numerical examples and are presented. For future implementation to nonlinear finite element analysis, the active column or the skyline (or the non‐zero profile) FPI algorithms are developed for programming considerations.
A new method for evaluating singular integrals in stress analysis of solids by the direct boundary element method
Authors: Li Hong‐Bao , Han Guo‐Ming , Mang Herbert A. 
Published: August 2005

AbstractThe purpose of this paper is to report on a new and efficient method for the evaluation of singular integrals in stress analysis of elastic and elasto‐plastic solids, respectively, by the direct boundary element method (BEM). Triangle polar co‐ordinates are used to reduce the order of singularity of the boundary integrals by one degree and to carry out the integration over mappings of the boundary elements onto plane squares. The method was subsequently extended to the cubature of singular integrals over three‐dimensional internal cells as occur in applications of the BEM to three‐dimensional elasto‐plasticity. For this purpose so‐called tetrahedron polar co‐ordinates were introduced. Singular boundary integrals stretching over either linear, triangular, or quadratic quadilateral, isoparametric boundry elements and singular volume integrals extending over either linear, tetrahedral, or quadratic, hexahedral, isoparametric internal cells are treated. In case of higher order isoparametric boundary elements and internal cells, division into a number of subelements and subcells, respectively, is necessary. The analytical investigation is followed by a numerical study restricted to the use of quadratic, quadrilateral, isoparametric boundary elements. This is justified by the fact that such elements, as opposed to linear elements, yield singular boundary integrals which cannot be integrated analytically. The results of the numerical investigation demonstrate the potential of the developed concept.
Discrete numerical solution of the generalized boussinesq problem
Authors: Gellert M. 
Published: August 2005

AbstractA family of stable algorithms for integration in time of the spatially discretized generalized Boussinesq equation is presented. In space, the finite element approximation is employed enabling arbitrary layout and variable physical properties. Furthermore, the proposed spatial–temporal discretization neither involves inversion of non‐diagonal matrices of large scale nor even their storage. The method is theoretically investigated and numerically tested. Comparison is made with known results.
Taylor expansions for singular kernels in the boundary element method
Authors: Aliabadi M. H. , Hall W. S. , Phemister T. G. 
Published: August 2005

AbstractThe problem treated is the integration of singular functions which arise in three‐dimensional isoparametric formulations of boundary integral equations. A Taylor expansion in the local parametric co‐ordinates is developed for the singular integrand, so allowing singular terms to be integrated in closed form, even for curved surface elements. The remainder integral obtained by subtracting out the worst singularities is integrated by repeated Gaussian quadrature.Two groups of tests are presented. First, the accuracy of the integrations has been checked for plane parallelograms (for which exact solutions have been developed) and for curved elements on a sphere. Secondly, results from complete boundary element calculations based on point collocation have been compared with known analytical solutions to two problems; zonal surface harmonics on a sphere and the capacitance of an ellipsoid. The agreement obtained with few degrees‐of‐freedom suggests that errors which have previously been attributed to point collocation might have arisen in the numerical integration.
The patch test—a condition for assessing FEM convergence
Authors: Taylor R. L. , Simo J. C. , Zienkiewicz O. C. , Chan A. C. H. 
Published: August 2005

AbstractThis paper discusses various forms of the Irons patch test and shows again that its satisfaction is a necessary convergence condition being equivalent to consistency, Further, it is shown that the test can be applied for verification of stability requirements, thus providing also a sufficient condition of convergence. The patch test is useful in testing the order of asymptotic convergence and the satisfaction of the test gives a guide for development of certain incompatible element forms.
A new nine node degenerated shell element with enhanced membrane and shear interpolation
Authors: Huang H. C. , Hinton E. 
Published: August 2005

AbstractA new nine node degenerated shell element is presented in this paper. In the formulation of the new element, an enhanced interpolation of the transverse shear strains in the natural co‐ordinate system is used to overcome the shear locking problem, and an enhanced interpolation of the membrane strains in the local Cartesian co‐ordinate system is applied to avoid membrane locking behaviour. It is shown that the resulting element has the requisite number of zero eigenvalues and associated rigid body modes. The element does not exhibit membrane or shear locking for large span/thickness ratios. To illustrate the good performance of the new element some examples are presented including comparisons with the behaviour of the selectively integrated Lagrangian degenerated shell elements.
Program structure and architecture for a finite element machine
Authors: Norrie D. H. , Norrie C. I. W. 
Published: August 2005

AbstractSuperproblems in finite elements require either general‐purpose or special‐purpose computing machines whose capabilities are very much greater than those currently existing. The advantage of the latter type of machine is that it can be highly optimized for the particular class of problem for which it is designed and can, in principle, for a given generation of hardware, be designed to operate at a higher speed than a corresponding general‐purpose computer. The Parallel Finite Element Machine (PARFEM) investigated at the University of Calgary has an architecture based on the finite element computational algorithms and employs a combination of parallel and vector processing. The overall architecture and program structure is described and the major design considerations outlined.