bluuebunny/crossref_metadata_2025 huggingface dataset:
Preconditioned conjugate gradient technique for the analysis of symmetric anisotropic structures
Authors: Noor Ahmed K. , Peters Jeanne M.
Published: August 2005

An officient preconditioned conjugate gradient (PCG) technique and a computational procedure are presented for the analysis of symmetric anisotropic structures. The technique is based on selecting the preconditioning matrix as the orthotropic part of the global stiffness matrix of the structure, with all the nonorthotropic terms set equal to zero. This particular choice of the preconditioning matrix results in reducing the size of the analysis model of the anisotropic structure to that of the corresponding orthotropic structure. The similarities between the proposed PCG technique and a reduction technique previously presented by the authors are identified and exploited to generate from the PCG technique direct measures for the sensitivity of the different response quantities to the non‐orthotropic (anisotropic) material coefficients of the structure. The effectiveness of the PCG technique is demonstrated by means of a numerical example of an anisotropic cylindrical panel.
An expert system for the optimal mesh design in the hp‐version of the finite element method
Authors: Rank Ernst , Babuška Ivo
Published: August 2005

This paper suggests a simple expert system frame and provides the domain knowledge for the optimal mesh design and the prediction of the error in the energy norm for the problem of plane elasticity using the hp‐extension in the finite element method. The expert system monitors the progress of the analysis, guides the user through the various steps and is able to reason about its own advice. In an example the user–expert communication is shown and the superiority of the results is demonstrated.
Finite element calculation of three‐dimensional hot forging
Authors: Surdon G. , Chenot J. L.
Published: August 2005

A three‐dimensional finite, element model for the simulation of isothermal hot forging is presented.

The material behaviour is assumed to be incompressible visco‐plastic (Norton–Hoff law), with the associated friction law. The velocity field is calculated with a finite element approximation using eight node hexahedral or six node prismatic elements. An explicit Euler scheme is used for time integration. Simulations of compression of a cubic block and horizontal cylinder are performed. The computed results are compared with experimental measurements made on special Plasticine.
Boundary elements for three‐dimensional elastic crack analysis
Authors: Luchi M. Laura , Rizzuti Sergio
Published: August 2005

In this paper 8‐node traction singular boundary elements are employed to represent displacement and traction variations in the vicinity of the crack front in three‐dimensional geometries. The numerical procedure suggested for evaluating the singular integrals extending over these special elements is described. The efficiency and accuracy of the special elements and integration procedure are demonstrated by the results obtained in a simple test problem whose analytical solution is known. The interaction of two circular coplanar cracks embedded in an infinite medium under uniform tension loading is also analysed. Finally, the stress intensity factor variation computed for a semi‐circular inner surface crack in a pressurized cylinder is presented.
Dynamics of the bilinear Mindlin plate element
Authors: Brockman R. A.
Published: August 2005

Plate 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

This 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

In 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

In 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

Comparison 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

The 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

A 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

An 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

This 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

The 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

A 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

Determination 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

In 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

In 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

The 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

A 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

Surf 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

The 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

Chebyshev 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

The 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

The 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

When 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

One 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

A 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.
A mixed finite element model for the elastic contact problem
Authors: Gallego F. J. , Anza J. J.
Published: August 2005

The static elastic contact problem is approached using Lagrange multipliers, leading to a mixed finite element problem. A non‐linear friction law is introduced explicitly and the non‐local character of the friction phenomena is implicitly assumed. In order to avoid stress oscillations near singular points, a perturbed Lagrangian functional is considered. The algorithms herein proposed do not impose nodal dependencies over the contact surfaces, allowing for the independent discretization of both bodies. The method is able to model simultaneous contact over different regions of any geometrical shape. Computer code, examples and results presented here are restricted to axisymmetrical and bidimensional cases.
Preconditioned conjugate‐ and secant‐Newton methods for non‐linear problems
Authors: Papadrakakis M. , Gantes C. J.
Published: August 2005

The preconditioned conjugate gradient (CG) method is becoming accepted as a powerful tool for solving the linear systems of equations resulting from the application of the finite element method. Applications of the non‐linear algorithm are mainly confined to the diagonally scaled CG. In this study the coupling of preconditioning techniques with non‐linear versions of the conjugate gradient and quasi‐Newton methods creates a set of conjugate‐ and secant‐Newton methods for the solution of non‐linear problems. The preconditioning matrices used to improve the ellipticity of the problem and to reduce the computer storage requirements are obtained by the application of the partial preconditioning and the partial elimination techniques. Both techniques use a drop‐off parameter ψ to control the computer storage demands of the method, making it more versatile for any computer hardware environment. Consideration is given to the development of a highly effective stability test for the line search minimization routine, which computes accurate values without much effort. This results in a beneficiary effect not only on the convergence properties of the methods but on their efficiency as well.
On linear constraints for Newton–Raphson corrections and critical point searches in structural F.E. problems
Authors: Eriksson Anders
Published: August 2005

The paper discusses the introduction of constraining equations in the tangential stiffness relation used to calculate the responses to different load cases in solution algorithms for non‐linear mechanical Finite Element (F.E.) problems. An alternative to the normal two‐phase solution method is discussed. This method is used to represent different iteration constraints, and in conjunction with the search for critical solution points. Numerical tests are presented, evaluating the efficiency of different iteration constraints for a model problem. Practically useful criteria for critical points are discussed. The basic methods for search of such points and some numerical aspects are discussed and evaluated for three different problems.
Adaptiveh‐,p‐ andhp‐versions for boundary integral element methods
Authors: Rank Ernst
Published: August 2005

Recently very promising results in a so‐calledhp‐version of the finite element method have been obtained. The basic idea is a balanced combination of mesh refinement and increase of the polynomial degree of the shape functions. This idea is applied to a boundary collocation method in this paper. The new method is compared with adaptiveh‐ andp‐versions and it is shown in numerical examples that even in the presence of singularities in the exact solution exponential convergence is obtained.
On a mixed finite element method for clamped anisotropic plate bending problems
Authors: Gopalsamy S. , Balasundaram S. , Bhattacharyya P. K.
Published: August 2005

The paper deals with a new mixed finite element method of solution of the bending problem of clamped anisotropic/orthotropic/isotropic plates with variable/constant thickness. This new mixed method gives simultaneous approximations to displacement u and bending and twisting moment tensor (ψij)1 ≤ i, j ≤ 2. Computer implementation procedures for this mixed method are given along with results of numerical experiments on a good number of interesting problems.
An efficient 3‐D infinite element for water wave diffraction problems
Authors: Lau S. L. , Ji Z.
Published: August 2005

An efficient and simple infinite element for modelling the far field potential of water wave diffraction problems is presented. The shape functions in the radial direction comprise the first two terms of the asymptotic expansions of Hankel functions. The integrals with infinite limit for calculating the coefficient matrix have been worked out. Numerical tests on the diffraction by a surface‐piercing circular cylinder give surprisingly accurate resultant forces even if the infinite elements are placed very near to the cylinder. Other typical three dimensional examples also show that satisfactory results can be obtained by the use of this simple infinite element. A computer program, WALOAD, has been developed for computing the wave forces on fixed two and three dimensional bodies.
Adaptive 2D finite element simulation of metal forming processes
Authors: Yang Henry T. Y. , Heinstein Martin , Shih J.‐M.
Published: August 2005

The development and integration of available current methods and the development of new methods for an adaptive finite element analysis of metal forming processes are presented. The analysis includes large‐strain, elastic–plastic, and thermal effects. Many numerical methods such as mesh generation, simulation of the contact between the workpiece and tool and die, and optimization of the finite element mesh are integrated and incorporated. In addition, an algorithm is developed which can detect certain severely distorted elements where the area of integration is approaching zero. The advantage of correcting these regions of locally distorted elements is demonstrated. These numerical methods are implemented in a finite element program developed for simulating metal forming processes, with the emphasis on automating the analysis. Examples include an axisymmetric stress simulation of a coldheading process, a plane strain simulation of an extrusion process and a plane strain simulation of orthogonal metal cutting, all with noticeable thermal effects. The orthogonal cutting forces and feed forces calculated are compared with two sets of experimental data, with good agreement.
A parallel mesh generation algorithm based on the vertex label assignment scheme
Authors: Cheng Fuhua , Jaromczyk Jerzy W. , Lin Junnin‐Ren , Chang Shyue‐Shian , Lu Jei‐Yeou
Published: August 2005

In this article a new mesh generation algorithm is presented. The algorithm is based on a new approach called the vertex label assignment scheme to provide the information for the mesh generation so that parallel processing becomes possible. The algorithm generates 2D meshes of quadrilaterals on the basis of individual faces; conformity and smoothness of the resultant mesh are automatically assured. Local and selective mesh‐refinements are also supported. A regular quadrilateral network which defines the geometry of the problem and an associated subdivision level assignment which specifies mesh density data on the network are the only input information.
Development and applications of two singular points finite elements
Authors: Dutta B. K. , Maiti S. K. , Kakodkar A.
Published: August 2005

An element formulation is suggested to obtain variable order singularities simultaneously at the two neighbouring corner nodes of a 4‐noded quadrilateral. The element is useful for modelling a kinked crack with small kink length. The accuracy is good and this is obtained at a substantially reduced computational cost. Case studies are presented to illustrate the usefulness and the accuracy obtainable.
More on optimal stress points—reduced integration, element distortions and error estimation
Authors: Barlow John
Published: August 2005

The presented work addresses the relationships between optimal sampling points, reduced integration and geometric distortion with the objective of estimating errors in terms of those considerations. Isoparametric quadratic plane and solid elements are used as a vehicle for the study. Geometric distortion measures and evaluation conditions, based on convergence requirements, are first defined in terms of the polynomial orders of the geometry and applied strain. Using these, the concept of optimal stress sampling, already established for undistorted elements, is extended to distorted geometry and shown to be effective over a range of geometries and strains. Errors in the strain‐displacement relationship and numerical integration of the strains are used to estimate the total response error and to rationalize the connection between optimal stress points and reduced integration. Enhanced convergence, by extension to the representation of linear strains in elements with quadratic geometry, is identified as the main advantage of reduced integration. The applicability of the proposed, and other, distortion parameters to vetting of element geometry and error prediction is discussed.
Softening and snap‐back instability in cohesive solids
Authors: Carpinteri Alberto
Published: August 2005

The nature of the crack and the structure behaviour can range from ductile to brittle, depending on material properties, structure geometry, loading condition and external constraints. The influence of variation in fracture toughness, tensile strength and geometrical size scale is investigated on the basis of the π‐theorem of dimensional analysis. Strength and toughness present in fact different physical dimensions and any consistent fracture criterion must describe energy dissipation per unit of volume and per unit of crack area respectively. A cohesive crack model is proposed aiming at describing the size effects of fracture mechanics, i.e. the transition from ductile to brittle structure behaviour by increasing the size scale and keeping the geometrical shape unchanged.

For extremely brittle cases (e.g. initially uncracked specimens, large and/or slender structures, low fracture toughness, high tensile strength, etc.) a snap‐back instability in the equilibrium path occurs and the load–deflection softening branch assumes a positive slope. Both load and deflection must decrease to obtain a slow and controlled crack propagation (whereas in normal softening only the load must decrease). If the loading process is deflection‐controlled, the loading capacity presents a discontinuity with a negative jump. It is proved that such a catastrophic event tends to reproduce the classical LEFM‐instability (KI = KIC) for small fracture toughnesses and/or for large structure sizes. In these cases, neither the plastic zone develops nor slow crack growth occurs before unstable crack propagation.
A comparison between isoparametric Lagrangian elements in 2D BEM
Authors: Deb A. , Banerjee P. K.
Published: August 2005

A comparison between a family of isoparametric C°‐continucus elements in the context of two‐dimensional elastostatics using the direct boundary element method is presented. The elements studied use Lagrangian shape functions of orders quadratic, cubic and quartic. The relative efficiencies of these elements from the viewpoint of accuracy of solution as well as cost effectiveness are examined through certain selected problems. It emerges from the present study that the quartic element is more reliable in accuracy than the lower members of the family without being necessarily more expensive.
PCG methods in transient FE analysis. Part II: Second order problems
Authors: Wong S. W. , Smith I. M. , Gladwell I.
Published: August 2005

In the Part I companion paper, various PCG (preconditioned conjugate gradient) strategies for solving the first order time dependent problem Mu̇ + Ku = f were compared. In all cases M was assumed to be the consistent ‘mass’ matrix arising out of conventional finite element semi‐discretization of the partial differential equation, and not its lumped approximation. In the present paper, similar PCG strategies are applied to the second order time dependent problem Mü + Cu̇ + Ku = f. Again consistent M and C can be retained. Various global and element level preconditioners are compared and optimized.
Assumed stress function finite element method: Two‐dimensional elasticity
Authors: Sarigul Nesrin , Gallagher Richard H.
Published: August 2005

A complementary energy‐based finite element formulation, using assumed stress functions as the approximating functions, is developed for the linear elastic two‐dimensional stress analysis. It features the use of blending function interpolants, enabling the convenient representation of traction boundary conditions, which in the past have posed difficulties. A family of rectangular elements is constructed. Numerical results assessing the behaviour of these elements are presented. An advantage of this approach is in the accurate prediction of stress distributions.
Loading, unloading and reloading of a generalized plane plastica
Authors: Coulter Brett A. , Miller Robert E.
Published: August 2005

This article presents a shooting‐type numerical procedure for the analysis of a planar, continuous and flexible member where the material is permitted to unload and reload plastically. A kinematic type of strainhardening rule is employed, and large displacements, large rotations and general cross section shapes are admitted. Though numerical and semi‐analytical solutions exist in the literature for specific problems where the internal and external loads increase monotonically (see, for example, References 1–4), little attention has been paid to problems where these loads (specifically internal loads) are permitted to decrease or reverse direction. In the present work a comparison is made with the solution to one such problem found in the literature, and the solution to four additional problems is given to show the versatility and usefulness of the method.
Reusable intrinsic sample point (RISP) algorithm for the efficient numerical integration of three dimensional curved boundary elements
Authors: Kane J. H. , Gupta A. , Saigal S.
Published: August 2005

This paper presents an algorithm that provides an order of magnitude gain in the computational performance of the numerical integration of the boundary integral equations for three dimensional analysis. Existing algorithms for numerical integration have strategically clustered integration sample points based on the relative proximity of the load points to the boundary element being integrated using element subdivision or element co‐ordinate transformation. The emphasis in these techniques has been on minimizing the number of sample points required to obtain a given level of accuracy. The present algorithm, while closely following the spirit of these earlier approaches, employs a discrete number of sets of predetermined, customized, near‐optimum, sample point quantities associated with the intrinsic boundary element. The ability created by this approach to reuse sample point geometric information of the actual element allows for the realization of substantive computational economy. This algorithm provides accurate and efficient numerical results both when load points are far from, and when they are on the boundary element being integrated. Numerical results are provided to demonstrate the substantial economy achieved through the use of the present algorithm.
3‐D boundary element method for cracks in a plate
Authors: Fares N. , Li V. C.
Published: August 2005

New fundamental solutions which automatically satisfy boundary conditions at the interfaces of an elastic plate perfectly bonded to two elastic halfspaces are implemented in a 3‐D boundary element method (BEM) for crack problems. The BEM features a new integration scheme for highly singular kernels. The capability is achieved through a part analytic and part numerical integration procedure, such that the analytic part of the integration is similar for all slip/opening variations, ‘Part‐through’ elliptic cracks in an elastic plate with traction‐free surfaces are analysed and the stress intensity factor (SIF) values along the crack front are found to compare favourably with widely accepted numerically obtained SIF results by Raju and Newman.1
A special beam element for the analysis of thin‐walled structural components
Authors: Ali M. Ashraf , Sridharan Srinivasan
Published: August 2005

A new beam element is described which is capable of depicting the non‐linear elastic mode interaction of overall bending/buckling with local buckling in thin‐walled beam‐columns. In addition to being capable of describing overall biaxial bending and twisting, the element has shape functions which contain implictly the relevant local buckling deformation. The mode interaction occurs by virtue of the non‐linear coupling of the overall and local buckling deformation. The local and post‐local buckling displacement fields are computed a priori in an efficient manner using the finite strip technique. The modulation of the local buckling amplitudes is also accounted for in the element. In general, the beam element incorporates three companion local modes, all of which may become important in the process of interaction. Examples are presented which illustrate the efficacy of the element for problems involving interaction of local and flexural buckling modes and the combined interaction of local, flexural and flexural‐‐torsional modes.
A consistent tangent stiffness matrix for three‐dimensional non‐linear contact analysis
Authors: Parisch H.
Published: August 2005

A consistent tangent stiffness matrix for the analysis of non‐linear contact problems is presented. The associated element has three or four nodes and establishes contact between three‐dimensional structures like solids and shells. It accounts for the non‐linear kinematics of large deformation analysis and guarantees a quadratic convergence rate. Two formulations, the penalty method and the Lagrange multiplier method, are investigated.
Application of the Ritz method to plane elasticity problems for composite sheets with variable fibre spacing
Authors: Martin A. F. , Leissa A. W.
Published: August 2005

The plane stress problem of a parallel fibre, rectangular composite sheet with variable fibre content is investigated. The resulting sheets are governed by partial differential equations that have variable coefficients, which are generally unsolvable exactly. A Ritz method is used to approximate the solution and is checked against known problems having exact solutions. The method is found to determine closely both the displacements and the stresses with fewer than 200 degrees of freedom. It is then applied to two interesting problems for which no exact solutions exist, including that of uniform normal stress applied in the direction of the fibres.
Eigensolutions of non‐conservative continuous mechanical systems computed by use of a matrix iteration method
Authors: Abrahamsson T. J. S. , Sällström J. H.
Published: August 2005

Two‐sided Ostrowski matrix iteration is applied to solve eigenproblems of non‐conservative continuous systems in structural dynamics starting from known eigensolutions of a related conservative system. Eigensolution paths are followed as the parameters of the system governing its non‐conservative behaviour are increased from zero. No discretization is performed and no truncation errors are introduced. The real eigenvalues of the related conservative problem are calculated by use of the Wittrick–Williams algorithm. The corresponding eigenvectors are obtained with an inverse iteration method using eigenfrequency‐dependent trial eigenvectors. Residues of system harmonic transfer functions are computed using the eigenvalues and eigenvectors together with eigenvector normalization constants (modal Foss dampings). These residues are needed in a transient analysis. The method is applied to the generalized Beck column stability problem. Critical loads are calculated. Harmonic flexibilities of subcritically loaded columns in transverse vibration are studied. Applications to control problems are foreseen.
On the accuracy of some domain‐by‐domain algorithms for parallel processing of transient structural dynamics
Authors: Hajjar Jerome F. , Abel John F.
Published: August 2005

Two domain‐by‐domain algorithms, suitable for coarse‐grained parallel processing analysis of the transient structural dynamics equation, are investigated for accuracy. The application under specific consideration is the analysis of three‐dimensional framed structures subjected to time‐varying loading. The domain‐by‐domain approaches attempt to include the advantageous aspects of both conditionally stable explicit algorithms, which require no simultaneous solution of equations and employ simple communication, and unconditionally stable implicit algorithms, which permit large time steps. The alternating group explicit algorithm is developed for finite element analysis, and its accuracy is investigated for a linear formulation. The group implicit algorithm is extended to non‐linear finite element analysis, and its accuracy is investigated for the frame dynamics application. Both algorithms are shown to provide inadequate accuracy for practical time step sizes.