bluuebunny/crossref_metadata_2025 huggingface dataset:
The problem of selecting the shape functions for a p‐type finite element
Authors: Babuška I. , Griebel M. , Pitkäranta J.
Published: August 2005

The paper addresses the question of the optimal selection of the shape functions for p‐type finite elements and discusses the effectivity of the conjugate gradient and multilevel iteration method for solving the corresponding linear system.
Coupled use of reduced integration and non‐conforming modes in quadratic Mindlin plate element
Authors: Choi Chang‐Koon , Kim Sun‐Hoon
Published: August 2005

The applications of the reduced integration technique, and the addition of non‐conforming modes and their coupling to Mindlin plate elements to improve their basic behaviour are reviewed and the establishment of a series of new plate elements by combined use of these schemes is presented in this paper. The element formulation is based upon the quadratic Mindlin plate concept. The results obtained by new elements converge to the exact solutions very rapidly as the mesh is refined and show reliable solutions even for severely distorted meshes. The new elements have the requisite numbers of zero eigenvalues associated with rigid body modes to avoid spurious zero energy modes. These elements are shown to solve the shear locking problem completely so that they are applicable to a wide range of plate problems, giving a high accuracy for both thick and thin plates.
A time–space finite element discretization technique for the calculation of the electromagnetic field in ferromagnetic materials
Authors: Axelsson O. , Maubach J.
Published: August 2005

The stability of time‐stepping methods for parabolic differential equations is mostly a critical issue. Furthermore, solving such equations with a classical time‐stepping approach can be very expensive because many small time‐steps have to be taken if steep gradients occur in the solution, even if these occur only in a narrow part of the space domain. In this paper we present a discretization technique in which finite element approximations are used in time and space simultaneously for a relatively large time period called a ‘time‐slab’. This technique may be repeatedly applied to obtain further parts of the solution in subsequent time‐intervals. It will be shown that, with the proposed method, the solution can be computed cheaply even if it has steep gradients and that stability is automatically guaranteed. For the solution of the non‐linear algebraic equations on each time‐slab fast iterative methods can be used.
Analysis of the Zienkiewicz–Zhu a‐posteriori error estimator in the finite element method
Authors: Ainsworth M. , Zhu J. Z. , Craig A. W. , Zienkiewicz O. C.
Published: August 2005

An a‐posteriori error estimator for finite element analysis proposed by Zienkiewicz and Zhu is analysed and shown to be effective and convergent. In addition we analyse wider classes of estimators of which the Zienkiewicz–Zhu estimator is a special case. It is shown that some of these estimators will be asymptotically exact. Numerical evidence is presented supporting the analysis.
Error estimates and convergence rates for various incompressible elements
Authors: Zienkiewicz O. C. , Liu Y. C. , Huang G. C.
Published: August 2005

This note reports numerical experiments on the efficiency of simple error estimates derived earlier1 applied to incompressible mixed or related penalty type formulations. The rate of convergence and performance of various mixed elements is compared. Numerical results from a driven cavity and an incompressible elastic problem demonstrate that the T6B1/3D and T6/3C elements give a faster rate of convergence than the T6/1D element. However, in the case of a plane extrusion analysis (stronger singularity), the rate of convergence for the T6B1/3D element drops and is inferior to that of the T6/1D, while the T6/3C element still proves superior to the other two elements.
Numerical study of incompressible fluids in unbounded domains
Authors: Razafimahery F.
Published: August 2005

The aim is to build up and test a numerical method to calculate the velocity of stationary two‐dimensional flows. Both inviscid and viscous fluids are considered. They act in the unbounded domain surrounding a given profile and a stream function is introduced. A variational procedure, adapted to unbounded domains, reduces the problem to solving a finite sequence of hormonic equations, posed in bounded domains. Some profiles are tested using a finite element method.
A plate bending element based on a generalized laminate plate theory
Authors: Reddy J. N. , Barbero E. J. , Teply J. L.
Published: August 2005

A plate bending element based on the generalized laminate plate theory (GLPT) developed by the senior author is described and its accuracy is investigated by comparison with the exact solutions of the generalized plate theory and the 3D‐elasticity theory. The element accounts for transverse shear deformation and layer‐wise description of the inplane displacements of the laminate. The element has improved description of the inplane as well as the transverse deformation response. A method for the computation of interlaminar (transverse) stresses is also presented.
Assumed strain formulation for triangular C0 plate elements based on a weak form of the Kirchhoff constraints
Authors: Stolarski H. K. , Chiang M. Y. M.
Published: August 2005

Application of a weak form of the Kirchhoff constraints in the formulation of triangular assumed shear strain C0 plate element is described. It is shown that, compared to a similar formulation of the quadrilateral elements, formulation of the triangles requires some additional considerations which lead to additional terms in the energy expression. With those terms performance of the assumed shear strain triangular elements is comparable to that of the quadrilateral elements.
On updating the structure of sparse matrix factors
Authors: Law Kincho H.
Published: August 2005

Structural analysis often involves the solution of a sparse system of linear equations using matrix factorization. For structural reanalysis problems, the system of equations is progressively changing and matrix factorization is required at each iteration step. In this paper, we study the problem of updating the structure of sparse matrix factors using an ordered‐tree model. The ordered‐tree model provides the information needed to symbolically compute the non‐zero structure of the matrix factor of a sparse matrix. Furthermore, for matrix factor modification problems, this tree model can be used to determine the numerically modified entries in the matrix factor. Examples for modification of a structure and h‐adaptive refinement of a finite element model are given to illustrate the potential application of the procedures developed in this study.
A time domain boundary element method for poroelasticity
Authors: Dargush G. F. , Banerjee P. K.
Published: August 2005

The development of a general boundary element method (BEM) for two‐ and three‐dimensional quasistatic poroelasticity is discussed in detail. The new formulation, for the complete Biot consolidation theory, operates directly in the time domain and requires only boundary discretization. As a result, the dimensionality of the problem is reduced by one and the method becomes quite attractive for geotechnical analyses, particularly those which involve extensive or infinite domains.

The presentation includes the definition of the two key ingredients for the BEM, namely, the fundamental solutions and a reciprocal theorem. Then, once the boundary integral equations are derived, the focus shifts to an overview of the general purpose numerical implementation. This implementation includes higher‐order conforming elements, self‐adaptive integration and multi‐region capability. Finally, several detailed examples are presented to illustrate the accuracy and suitability of this boundary element approach for consolidation analysis.
On the problem of modelling for parameter identification in distributed structures
Authors: Norris Mark A. , Meirovitch Leonard
Published: August 2005

Structures are often characterized by parameters, such as mass and stiffness, that are spatially distributed. Parameter identification of distributed structures is subject to many of the difficulties involved in the modelling problem, and the choice of the model can greatly affect the results of the parameter identification process. Analogously to control spillover in the control of distributed‐parameter systems, identification spillover is shown to exist as well and its effect is to degrade the parameter estimates. Moreover, as in modelling by the Rayleigh–Ritz method, it is shown that, for a Rayleigh–Ritz type identification algorithm, an inclusion principle exists in the identification of distributed‐parameter systems as well, so that the identified natural frequencies approach the actual natural frequencies monotonically from above.
Towards parallel I/O in finite element simulations
Authors: Farhat Charbel , Pramono Eddy , Felippa Carlos
Published: August 2005

I/O issues in finite element analysis on parallel processors are addressed. Viable solutions for both local and shared memory multiprocessors are presented. The approach is simple but limited by currently available hardware and software systems. Implementation is carried out on a CRAY‐2 system. Performance results are reported.
A mixed‐variable continuously deforming finite element method for parabolic evolution problems. Part I: The variational formulation for a single evolution equation
Authors: Kececioglu Ifiyenia , Rubinsky Boris
Published: August 2005

The objective of the research presented here was to develop a generic adaptive computational method for porous media evolution problems that involve coupled heat flow, fluid flow and species transport processes with sharply defined phase‐change interfaces.

In this paper we examine the general least squares variational approach and develop the conceptual framework for a rate least squares variational formulation of a continuously deforming mixed variable finite element method for solving highly non‐linear time‐dependent partial differential equations. In Part II of this paper1 we extend the formulation given here for a single evolution equation to a system of coupled evolution equations. In Part III2 we discuss in detail the numerical procedures that were implemented in a computer program and present several numerical examples that demonstrate the performance of this computational method.
Delaunay triangulation of non‐convex planar domains
Authors: Lo S. H.
Published: August 2005

This paper investigates the possibility of integrating the two currently most popular mesh generation techniques, namely the method of advancing front and the Delaunay triangulation algorithm. The merits of the resulting scheme are its simplicity, efficiency and versatility. With the introduction of ‘non‐Delaunay’ line segments, the concept of using Delaunay triangulation as a means of mesh generation is clarified.

An efficient algorithm is proposed for the construction of Delaunay triangulations over non‐convex planar domains. Interior nodes are first generated within the planar domain. These interior nodes and the boundary nodes are then linked up together to produce a valid triangulation. In the mesh generation process, the Delaunay property of each triangle is ensured by selecting a node having the smallest associated circumcircle. In contrast to convex domains, intersection between the proposed triangle and the domain boundary has to be checked; this can be simply done by considering only the ‘non‐Delaunay’ segments on the generation front.

Through the study of numerous examples of various characteristics, it is found that high‐quality triangular element meshes are obtained by the proposed algorithm, and the mesh generation time bears a linear relationship with the number of elements/nodes of the triangulation.
Axisymmetric contact of an elastic layer underlain by rigid base
Authors: Li Hui , Dempsey J. P.
Published: August 2005

Axisymmetric contact problems of an elastic layer are studied in this paper. The lower surface of the layer is either bonded to or in smooth contact with a rigid base. The upper surface is in tensionless smooth contact with a rigid flat cylinder, a rigid sphere, an elastic sphere or a circular plate, respectively. A general method is developed so that all these related problems are treated in a straightforward and like manner. In comparison to the other methods used in previous papers, the simplicity and high numerical accuracy are the major advantages of this method. The convergence is proved by comparing the numerical values to some available analytical solutions. Extensive numerical results for contact radii, displacements and contact pressures are provided.
Total Lagrangian formulation for the large displacement analysis of rectangular plates
Authors: Chang Bilin , Shabana A. A.
Published: August 2005

In this paper, a method for the non‐linear dynamic analysis of rectangular plates that undergo large rigid body motions and small elastic deformations is presented. The large rigid body displacement of the plate is defined by the translation and rotation of a selected plate reference. The small elastic deformation of the midplane is defined in the plate co‐ordinate system using the assumptions of the classical theories of plates. Non‐linear terms that represent the dynamic coupling between the rigid body displacement and the elastic deformation are presented in a closed form in terms of a set of time‐invariant scalars and matrices that depend on the assumed displacement field of the plate. In this paper, the case of simple two‐parameter screw displacement, where the rigid body translation and rotation of the plate reference are, respectively, along and about an axis fixed in space, is first considered. The non‐linear dynamic equations that govern the most general and arbitrary motion of the plate are also presented and both lumped and consistent mass formulations are discussed. The non‐linear dynamic formulation presented in this paper can be used to develop a total Lagrangian finite element formulation for plates in multibody systems consisting of interconnected structural elements.
An alternative numerical procedure for simulating the dynamical response of non‐linear elastic rods
Authors: Da Gama Rogério martins Saldanha
Published: August 2005

In this paper there is presented an alternative numerical procedure for obtaining approximations to non‐linear conservation laws like those that describe the dynamical behaviour of elastic rods (composed of materials whose stress–strain relation is non‐linear). The above‐mentioned procedure consists of approximating the solution of the Riemann problem (associated with the considered conservation law) by a piecewise constant function (satisfying the jump conditions) and using Glimm's scheme for advancing in time, step by step. The proposed numerical approach eliminates the necessity of solving (in a complete way) the associated Riemann problem, easing and cheapening its computational implementation. This procedure is employed for simulating the dynamical response of an elastic‐non‐linear rod, fixed at its edges, that is left in a non‐equilibrium state. There is presented a comparison between results obtained through a classical procedure and through the procedure proposed in this work.
A non‐proportional loading finite element analysis of continuum damage mechanics for ductile fracture
Authors: Wang June , Chow C. L.
Published: August 2005

This paper presents the development of a finite element analysis based on an anisotropic model of continuum damage mechanics theory proposed recently by the authors for ductile fracture under non‐proportional loading. The condition of non‐proportional loading is formulated by introducing a dynamic co‐ordinate system of principal damage allowing the principal direction of damage during the loading to rotate accordingly.

The finite element analysis developed under non‐proportional loading is applied to predict the crack initiation load of a centre‐cracked plate under uniform loading. The predicted load agrees satisfactorily with those determined experimentally with centre‐cracked thin plates made of aluminium alloy 2024‐T3. The analysis also reveals under non‐proportional loading the hysteresis effect of the principal directions of damage and stress. In addition, the influence of varying anisotropic damage coefficients on the crack initiation load and the crack tip displacement profile is also examined. The larger the degree of the anisotropy, the higher the crack initiation load. The magnitude of the crack tip displacement profile is found to be proportional to the degree of material anisotropy.
The generalized boundary element approach to Burgers' equation
Authors: Kakuda Kazuhiko , Tosaka Nobuyoshi
Published: August 2005

The generalized boundary element method is presented for the numerical solution of Burgers' equation. The new method is based on the set of boundary integral equations derived for each subdomain by using the fundamental solution for the linearized differential operator of the equation. The resulting system of quasi‐non‐linear equations is solved implicitly with use of a simple iterative procedure. The adaptability and the accuracy of the proposed method are demonstrated by three examples and a comparison of the numerical results with the exact solution or other existing solutions is shown for the first example.
Higher derivative explicit one step methods for non‐linear dynamic problems. Part II: Practical calculations and comparisons with other higher order methods
Authors: Hoff C. , Taylor R. L.
Published: August 2005

A generalized explicit one step alogorithm developed in Part I of this paper is presented in the form of a predictor–corrector scheme suitable for arbitrary non‐linear analyses of structural dynamics problems. Convergence results are checked through practical calculations on linear and non‐linear systems. The generalized algorithm proposed is compared with other recently developed higher order one step algorithms. The slight amount of additional computational effort compared to second order methods pays off in linear and weakly non‐linear systems. The behaviour of the methods is also tested on extreme stiffening and softening systems to investigate reliability and robustness of the algorithm.
Studies in anisotropic plasticity with reference to the Hill criterion
Authors: De Borst René , Feenstra Peter H.
Published: August 2005

Algorithms based upon the notion of return mapping have been developed for the Hill yield function of anisotropic plasticity. The relative accuracy of two algorithms is assessed by means of iso‐error maps. The choice of the algorithm turns out to be much more critical for the orthotropic Hill criterion than for the underlying isotropic von Mises plasticity model. A tangent operator that is consistent with the developed integration algorithm is formulated and its efficiency is assessed compared with the classical continuum tangent operator. The model has been applied to three shell/plate structures.
Inelastic transient dynamic analysis of three‐dimensional problems by BEM
Authors: Ahmad S. , Banerjee P. K.
Published: August 2005

A direct Boundary Element formulation and its numerical implementation for inelastic transient dynamic analysis of three‐dimensional solids is presented. The formulation is based on an initial stress approach and is the first ever of its kind in the field of the Boundary Element Method. This formulation employs the Navier–Cauchy equation of motion, Graffi's dynamic reciprocal theorem, Stokes' fundamental solution and the Divergence theorem, together with Kinematical and Constitutive equations to obtain the pertinent integral equations of the problem in the time domain within the context of small displacement theory of elastoplasticity. The boundary integral equations are cast in an incremental form, in which elastoplastic relations of the incremental type are used for the material description. These equations are then solved using a time‐stepping algorithm in conjunction with an iterative solution scheme to satisfy the constitutive relations. Higher order shape functions are used to approximate the field quantities in space as well as in time. Finally, the applicability of this methodology is demonstrated by presenting a few example problems.
Automatic step size correction for non‐associated plasticity problems
Authors: Van Langen H. , Vermeer P. A.
Published: August 2005

The finite element method is used in calculating accurate collapse loads. The behaviour of granular materials is described by the non‐associated Mohr–Coulomb model. The load–displacement path is traced up to and beyond limit points using an accelerated initial stiffness method. The convergence properties of this method are examined, both for associated and non‐associated plasticity.

Step sizes in the incremental iterative procedure are adapted during the iteration process, depending on an estimated number of iterations. The automatic step size control thus obtained proves to be robust and particularly appropriate for non‐associated plasticity. Some soil collapse calculations are discussed to demonstrate the practical application of the method.
A new approach in non‐linear mechanics: The large time increment method
Authors: Boisse Ph. , Bussy P. , Ladeveze P.
Published: August 2005

A new algorithm family taking into account the entire loading process in a single large time increment is proposed to compute structures with physical non‐linearities and is tested on some examples in elastoplasticity. The method considerably reduces the number of transfers between local and global levels, hence the numerical cost of calculation is also diminished.
A finite‐element model of two‐layer ocean circulation
Authors: Bermejo R.
Published: August 2005

A mixed finite‐element formulation is applied to solve the quasi‐geostrophic equations in a two‐layer ocean domain enclosed by solid boundaries. A combination of leap‐frog and θ‐schemes is used to integrate the equations in time. Wood's formula of the wall vorticity is derived in our formulation for the case of square elements adjacent to the boundaries. Long‐term computations with and without lumping have been carried out.
The multigrid method in solid mechanics: Part I—Algorithm description and behaviour
Authors: Parsons I. D. , Hall J. F.
Published: August 2005

A multigrid algorithm is described that can be used to obtain the finite element solution of linear elastic solid mechanics problems. The method is applied to some two dimensional problems to evaluate its strengths and weaknesses. Extensive studies are made to determine the convergence behaviour of the method. In general, this depends on many factors: the number of degrees‐of‐freedom in the discretization, characteristics of the algorithm, Poisson's ratio when it is close to 0·5, the amount of bending deformation in the problem under consideration, and the degree of non‐uniformity in the mesh. Only certain values of the multigrid parameters allow a converged solution to be obtained with a computational effort proportional to the number of degrees‐of‐freedom. These values include the optimum ones, i.e. those that lead to convergence with the least computational effort. The constant of proportionality is only independent of the number of degrees‐of‐freedom and still depends on the other factors listed above.
Contact problems of kinked cracks modelled by a boundary integral method
Authors: Zang W. L. , Gudmundson P.
Published: August 2005

Based on the integral equation for the resultant forces along a crack, a numerical method is developed for the solution of two dimensional kinked crack problems taking crack contact into account. The method is demonstrated by a consideration of an elastic half‐plane containing a piece‐wise straight line crack. Two numerical examples are presented and compared to finite element calculations. The numerical results indicate that the present method can be an effective and reliable tool for investigations of kinked crack problems associated with crack contact.
A finite element formulation for the coupled thermoviscoelastic response of solid–fluid systems
Authors: Lévesque D. , Bertrand L.
Published: August 2005

The coupled thermoviscoelastic response of a solid–fluid system is computed by a finite element formulation which involves only temperature and displacement fields. The Laplace transform with respect to time is applied to the coupled equations. This results in a global matrix in the transform domain that is symmetric and banded and the time response is obtained by numerical inversion of the transformed solution. Also, this formulation permits the use of fractional derivatives to model viscoelastic material behaviour.
Free vibration of axisymmetric solids by BEM using particular integrals
Authors: Wang Hui‐Ching , Banerjee Prasanta K.
Published: August 2005

The free vibration of solids of revolution had never been solved by the Boundary Element Method (BEM) until a previous paper10 by the authors, in which the BEM was combined with the method of particular integrals to solve axisymmetric free vibration problems. In this paper the previously developed analysis is extended to study the non‐axisymmetric free vibration of axisymmetric solids. The developed analysis has been implemented in a general purpose BEM system. Free vibrations of solid and hollow cylinders, a hyperbolic cooling tower and a gas turbine shell are used as examples, and their results are compared with those given by other methods. Except for low modes of very thin shells, good agreement can be seen.
Time‐domain radiation boundary for analysis of plane Love‐wave propagation problem
Authors: Anandarajah A.
Published: August 2005

A new method of modelling the radiation effect in a time‐domain finite element analysis of semi‐infinite solids is proposed. The domain to be analysed is divided into a finite, interior region and a semi‐infinite, exterior region. The standard finite elements are used to model the interior region. An infinite element is used to model the semi‐infinite region. The main feature of the proposed method is the selection of semi‐infinite shape functions to develop the infinite element. A procedure is proposed whereby the necessary shape functions are derived directly from frequency‐domain analytical mode shapes. The interior and exterior regions are coupled by enforcing displacement continuity at the interface. The validity of the method is demonstrated in this paper by analysing a two‐dimensional, linear (damped), anti‐plane, shear‐wave (plane Love‐wave) propagation problem. The results obtained by the proposed method are compared with those obtained by direct finite element analysis with a fixed boundary placed sufficiently far from the location of loading to avoid wave reflections.
Automatic conversion of triangular finite element meshes to quadrilateral elements
Authors: Johnston Bruce P. , Sullivan John M. , Kwasnik Andrew
Published: August 2005

A method is presented for the fully automatic conversion of a general finite element mesh containing triangular elements into a mesh composed of exclusively quadrilateral elements. The initial mesh may be constructed of entirely triangular elements or may consist of a mixture of triangular and quadrilateral elements. The technique used employs heuristic procedures and criteria to selectively combine adjacent triangular elements into quadrilaterals based on preestablished criteria for element quality. Additional procedures are included to eliminate isolated triangles. The methods operates completely without user intervention once the nodal co‐ordinates and element connectivity of the original mesh are supplied.
An adaptive descent method for non‐linear viscoplasticity
Authors: Eggert Geoffrey M. , Dawson Paul R. , Mathur Kapil K.
Published: August 2005

A forming model based on a viscoplastic flow formulation is derived which includes the effects of small elastic strains. A significant feature of the formulation is its reliance on the dominant inelastic material characteristics in the formation of the stiffness matrix for large strain problems. The resultant non‐linear system of equations is solved by an adaptive descent method which combines the rapid convergence of Newton's method near the solution with the robustness of a method of successive approximations. The use of the adaptive descent method effectively extends the viscoplastic flow formulations into the nearly rate‐insensitive range of behaviours exhibited, for example, by metals at low temperature, where slow convergence of the non‐linear solution algorithm has traditionally hampered their use.
Accurate integration of singular kernels in boundary integral formulations for Helmholtz equation
Authors: Ramesh P. S. , Lean M. H.
Published: August 2005

Boundary integral formulations for the 2D Helmholtz equation involve kernels in the form of modified Bessel functions. Accurate schemes for evaluating integrals of the kernels and their derivatives are presented. Special attention is paid to integrals involving singular and near singular kernels. Both boundary and domain integrals are considered. It is shown that, with the use of series expansion functions for the modified Bessel functions, the boundary integrals can be evaluated analytically in the neighbourhood of the singularity. For domain integrals, the behaviour of the kernels in the vicinity of the singularity is used to construct accurate numerical quadrature schemes. A transient heat conduction problem is formulated as a Helmholtz equation, solved, and compared against analytic solution to demonstrate the effectiveness of these schemes in relation to traditional methods. References are made to previous work to advocate the utility of the boundary integral method for non‐linear and time‐transient problems.
Optimization analysis of the four‐level‐time schemes
Authors: Shayya Walid H. , Segerlind Larry J. , Bralts Vincent F.
Published: August 2005

A procedure was implemented to determine some optimum values for the parameters of the four‐level‐time scheme which can be utilized for the numerical solution of a system of ordinary differential equations. A multi‐variable search method was employed to estimate these optimum parameters. Two different optimization studies were performed. The resultant optimum four‐level‐time schemes produced very accurate results, satisfied physical reality, and did not produce any oscillations for the specific problems that were studied. The optimum values for the three parameters α, β and γ in the four‐level‐time scheme were α = 16.72, β = 6.26 and γ = 2.46. The optimum value of θ for the Wilson‐θ method was θ = 1.42. The optimum schemes were compared to some existing four‐level‐time schemes. The outcome demonstrated that the optimum schemes were superior. The Houbolt method and the Galerkin weighting procedure were shown to have greater inaccuracies than the optimum schemes.
On a new iterative approach of component mode synthesis
Authors: Xu Keqin , Luo Zhenhuang , Han Zushun
Published: August 2005

A wholly new concept of intermediate structure is developed in this paper. Based on this, a new component mode iteration (CMI), or subdomain subspace iteration method, is proposed.

In the new CMI method, the ordinarily required step of ensuring interface compatibility is eliminated. An outstanding achievement of this method is that it retains the merit of the standard subspace iteration (SSI) technique concerning the number of vectors required in computation. In the present method iteraton is carried out at subdomain levels. On machines capable of parallel processing, this work can be performed simultaneously.

Numerical examples clearly demonstrate the excellence of this new method.
Application of the boundary element method to transient heat conduction
Authors: Dargush G. F. , Banerjee P. K.
Published: August 2005

An advanced boundary element method (BEM) is presented for the transient heat conduction analysis of engineering components. The numerical implementation necessarily includes higher‐order conforming elements, self‐adaptive integration and a multiregion capability. Planar, three‐dimensional and axisymmetric analyses are all addressed with a consistent time‐domain convolution approach, which completely eliminates the need for volume discretization for most practical analyses. The resulting general purpose algorithm establishes BEM as an attractive alternative to the more familiar finite difference and finite element methods for this class of problems. Several detailed numerical examples are included to emphasize the accuracy, stability and generality of the present BEM., Furthermore, a new efficient treatment is introduced for bodies with embedded holes. This development provides a powerful analytical tool for transient solutions of components, such as casting moulds and turbine blades, which are cumbersome to model when employing the conventional domain‐based methods.
Efficient evaluation of the flexibility of tapered I‐beams accounting for shear deformations
Authors: Vu‐Quoc L. , Léger P.
Published: August 2005

The principle of complementary virtual work is used to evaluate numerically the flexibility matrix of tapered I‐beams accounting for shear deformations. Equilibrium considerations of the top and bottom fibres reveal that the shear stress is not equal to zero at these locations. To correct for this non‐vanishing shear, a statically admissible shear stress field is considered by assuming a parabolic distribution of shear stress which takes non‐zero values at the top and bottom fibres such that the global equilibrium is satisfied within the assumed stress profile. The flexibility matrices of the proposed tapered I‐beam finite element with different slopes are generated using numerical integration based on Gauss quadrature. The results are compared to full‐blown shell finite element models, and stepped beam models constituted by a series of uniform beam elements, to illustrate the effectiveness of the proposed method.
Postintegration methods for numerical integration of non‐linear dynamic equations of motion
Authors: Langer Jan , Klasztorny Marian , El‐Bagalaty' Salah El‐Sayed
Published: August 2005

The paper presents a family of methods with postintegration, for numerical integration of non‐linear dynamic equations of motion of discrete systems. Both explicit and implicit algorithms of these methods are conditionally stable, but can give solutions of accuracy of a few orders higher than the known methods with preintegration, corresponding to them. A general analysis of stability and accuracy of single‐step methods is carried out. The postintegration methods have been tested on a single‐degree‐of‐freedom non‐linear system.
An integration scheme for Prandtl‐Reuss elastoplastic constitutive equations
Authors: Gratacos P. , Montmitonnet P. , Chenot J. L.
Published: August 2005

We investigate the Generalized Midpoint Rule for the time integration of elastoplastic constitutive equations for pressure‐independent yield criteria. The incremental equations are divided into one scalar hydrostatic pressure/dilation rate equation, and a stress deviator/strain rate deviator tensorial equation, the solution of which reduces to one single scalar equation in the plastic multiplier. The existence and uniqueness of an incremental solution is discussed. The pressure/deviator decomposition is the basis for reduced integration of the pressure term in the Principle of Virtual Work, in order to avoid locking and spurious pressure oscillations. It is also shown that an optimal choice of the parameter of the Midpoint Rule can be computed by reference to the analytical solution of the equations assuming no work hardening. A benchmark test shows that this choice allows increased time steps. This formulation is applied to two classical problems: bulging of a tube under internal pressure and tension test on a notched specimen, and a comparison with the analytical solution is performed. Finally, the hypothesis which sustains these formulations of elastoplasticity (constant strain rate during an increment) is discussed with reference to elastic unloading and residual stress computation.
SIMD implementation of a non‐linear transient shell program with partially structured meshes
Authors: Belytschko Ted , Plaskacz Edward J.
Published: August 2005

The implementation of an explicit transient program for the three‐dimensional non‐linear finite element analysis of shells on a massively parallel SIMD computer, the CONNECTION Machine, is described. Particular emphasis is placed on interprocessor communication using router and NEWS schemes. A hybrid communication scheme, where NEWS is used within structured subdomains and the router is used to exchange nodal forces between subdomains, is examined. It is shown that the ‘mesh‐structure index’ of most large meshes is sufficient to make hybrid schemes effective and this is verified by computer runs. Some benchmark non‐linear calculations with 8K to 32K elements are also presented.
Eight nodes or nine?
Authors: Macneal Richard H. , Harder Robert L.
Published: August 2005

The chief advantage claimed for nine‐noded shell elements is that they can pass constant curvature patch tests with bilinear element geometry while eight‐noded shell elements cannot. It is shown that a simple modification of the shape functions of an eight‐noded element can make this advantage disappear. Test results confirm this result and show that the performance of a modified eight‐noded element is similar to that of recently reported nine‐noded elements.
Theoretical development and numerical verification of a geometrically non‐linear, 3‐D based finite element for composite materials
Authors: Anandan Vailore , Bauld Nelson R.
Published: August 2005

A geometrically non‐linear thin shell element made from classical laminated materials is developed from three dimensional continuum concepts that admits arbitrarily large displacements and rotations. The development shows how explicit integration through the thickness of the element can be accomplished without sacrificing significant accuracy of the element.

Computations obtained via the present formulation are compared with four test problems for which numerical data are available. All computations were carried out using the Crisfield–Riks arc length continuation algorithm with a full Newton–Raphson iterative scheme. Excellent agreement is observed for each test problem.
ALE finite element formulation for ring rolling analysis
Authors: Hu Yu‐Kan , Liu Wing Kam
Published: August 2005

In this paper, a ring rolling process is analysed by the Arbitrary Lagrangian Eulerian (ALE) finite element method. Phenomena associated with the process, such as large deformations, elastoplastic material behaviour and the friction on the interface, are included in the analysis. Special modelling on driven, idle and guide rolls is given. Results which include the overall shape of the formed ring, the time histories of roll separating force and driving torque, the distribution of the normal pressure on the ring–roll interface as well as the distribution of effective stresses in the formed ring, are also presented.
The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique
Authors: Zienkiewicz O. C. , Zhu J. Z.
Published: August 2005

This is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation. In this paper, a general recovery technique is developed for determining the derivatives (stresses) of the finite element solutions at nodes. The implementation of the recovery technique is simple and cost effective. The technique has been tested for a group of widely used linear, quadratic and cubic elements for both one and two dimensional problems. Numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent. One order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements. In particular, an O(h4) convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time. The performance of the proposed technique is compared with the widely used smoothing procedure of global L2 projection and other methods. It is found that the derivatives recovered at interelement nodes, by using L2 projection, are also superconvergent for linear elements but not for quadratic elements. Numerical experiments on the convergence of the recovered solutions in the energy norm are also presented. Higher rates of convergence are again observed. The results presented in this part of the paper indicate clearly that a new, powerful and economical process is now available which should supersede the currently used post‐processing procedures applied in most codes.
Method of lines applied to hyperbolic fluid transient equations
Authors: Suwan K. , Anderson A.
Published: August 2005

Flow and pressure transients in single‐phase liquid‐filled closed pipes (i.e. waterhammer) are described by quasi‐linear hyperbolic partial differential equations for which the preferred solution technique is the Method of Characteristics. However, this is not appropriate for control and stability analyses where a lumped‐parameter single independent variable (i.e. time) model is preferred, using, intentionally or otherwise, the Method of Lines (or partial discretization). By empirical comparison of this with Method of Characteristics time‐domain simulation, it has been found that certain implementations introduce avoidable numerical errors or even instabilities. Four aspects have been investigated:

the dependent variables have often been taken as the original primitive variables but Riemann or Allievi characteristic variables are preferable;

for the waterhammer hyperbolic equations at least, a first‐order discrete space interpolating polynomial represents the underlying physics better than higher‐order approximations;

terms in which finite‐differences are used to represent quantities which are integrals rather than derivatives, in particular pipe friction, may introduce numerical instability and require particular care;

for time‐domain simulation, first‐order Euler integration is more accurate than higher‐order methods which introduce errors by violating the hyperbolic equation domain of dependence.
Shear correction factors for plates and shells
Authors: Vlachoutsis Stefanos
Published: August 2005

Multilayered plate and shell finite elements usually have a constant shear distribution across the thickness. This causes a decrease of accuracy, especially for sandwich structures. The problem is overcome by using shear correction factors which are defined by energy considerations. In this paper a study on shear correction factors is presented as well as typical applications. These factors are defined by studying a crossply laminate without midplane symmetry in cylindrical bending. It is possible to define one factor for a given cross section or several ones, one factor per ply. The two ways are equivalent. Special cases are studied: a multilayered plate, a symmetrical sandwich and a structure formed by two plates glued to each other. The importance of shear correction factors is illustrated in the case of plate and shell applications; the results are obtained by using three‐dimensional degenerated shell finite elements.
Rigid body considerations for non‐linear finite element analysis
Authors: Yang Yeong‐Bin , Chou Jung‐Huai , Leu Liang‐Jenq
Published: August 2005

The purpose of the paper is to demonstrate how the concept of rigid body motions can be employed to derive the external stiffness matrix for an initially stressed finite element. Such a matrix is as important as the elastic and geometric stiffness matrices. It can be used not only in an eigenvalue analysis for testing the zero energy modes of a finite element under initial loadings, but for calculating the element forces in a step‐by‐step non‐linear analysis. The two‐dimensional beam element presented in this paper serves as a vehicle to demonstrate the concept involved. The principle of virtual work in its updated Lagrangian form has been adopted as the method of formulation. Several examples are provided to illustrate the adequacy of the present approach.
A numerical model for wave scattering problems in infinite media due to p‐ and sv‐wave incidences
Authors: Zhao Chongbin , Valliappan S. , Wang Y. C.
Published: August 2005

Based on elastic wave motion theory and the superposition concept, a numerical model for wave scattering problems in infinite media due to P‐wave and SV‐wave incidences is presented in this paper. Since this model is based on a coupled system of finite and infinite elements for simulating wave propagation in infinite media, the complexity of geometry and the variability of material properties in the foundation can be realistically simulated. Through a systematic study of the characteristics of a plane harmonic P‐wave and SV‐wave incidences on a fixed boundary, the concept of stress increase factors and stress factors which can be used to calculate the generalized stresses on the wave input boundary due to the SV‐wave and P‐wave incidences is also proposed. The effects of incident wave mode, incident angle and Poisson's ratio in the foundation on the stress increase factors and the stress factors have been studied in detail. Finally, the proposed model has been applied to a half‐plane foundation and a semi‐circular canyon to calculate SV‐wave and P‐wave scattering problems. The numerical results obtained show good agreement with the theoretical results and Wong's analytical results.
A mixed finite element formulation for non‐linear analysis of plane problems
Authors: Liao C. L. , Tsai J. S.
Published: August 2005

Based on the incremental non‐linear theory of solid bodies and the Hellinger‐Reissncr principle, a mixed updated Lagrangian formulation of the large displacement motion of solid bodies is derived, and an associated mixed finite element model is developed. The model contains the displacements and stresses as the nodal degrees of freedom. The model is used for the large deformation elasto‐plastic analysis of plane problems. In solving non‐linear problems, the Newton‐Raphson method with arc‐length control is adopted to trace the post‐buckling response. The computational steps to calculate the elasto‐plastic stress increments at Gauss points in the elasto‐plastic analysis by the present mixed model are described in detail. Numerical results are presented and compared with those of the displacement model and existing solutions to show the accuracy of the present mixed model in the large deformation elasto‐plastic analysis of plane problems.