bluuebunny/crossref_metadata_2025 huggingface dataset:
Coupling of physical and modal components for analysis of moving non‐linear dynamic systems on general beam structures
Authors: Nielsen J. C. O. , Abrahamsson T. J. S.
Published: August 2005

A general, well‐structured and efficient method is advanced for the solution of‐a large class of dynamic interaction problems including a non‐linear dynamic system running at a prescribed time‐dependent speed on a linear track or guideway. The method uses an extended state‐space vector approach in conjunction with a complex modal superposition. It allows for the analysis of structures containing both physical and modal components. The physical components studied here are vehicles modelled as linear or non‐linear discrete mass–spring–damper systems. The modal component studied is a linear continuous model of a track structure containing beam elements which can be generally damped and which can be embedded in a three‐parameter damped Winkler‐type foundation. The complex modal parameters of the track structure are solved for. Algebraic equations are established which impose constraints on the transverse forces and accelerations at the interfaces between the moving dynamic systems and the track. An irregularity function modelling a given non‐straight profile of the non‐loaded track or a non‐circular periphery of the wheels is also accounted for. Loss of contact and recovered contact between a vehicle and the track can be treated. The system of coupled first‐order differential equations governing the motion of the vehicles and the track and the set of algebraic constraint equations are together compactly expressed in one unified matrix format. A time‐variant initial‐value problem is thereby formulated such that its solution can be found in a straightforward way by use of standard time‐stepping methods implemented in existing subroutine libraries. Examples for verification and application of the proposed method are given. The present study should be of particular value in railway engineering.
Using domain decomposition to solve symmetric, positive‐definite systems on the hypercube computer
Authors: Hennigan Gary L. , Castillo Steven , Hensel Edward
Published: August 2005

A distributed method of solving sparse, positive‐definite systems of equations, like those arising from many finite‐element problems, on a hypercube computer is studied. A domain‐decomposition method is introduced wherein the domain of the problem to be solved is physically split into several subdomains. Each of these subdomains is then distributed to a separate processor on the hypercube where the fill, factorization and solution of the system of equations proceeds. This physical split is based on a nodal ordering known as one‐way dissection.4

The method is applied to two‐dimensional electrostatic problems which are governed by Laplace's equation. Since the finite‐element method is used to discretize the problem, the algorithm is developed to take full advantage of the inherent sparsity in the system of equations by using an envelope storage scheme. The method is applied to several geometries, and results as well as performance data for the algorithm will be given.
Modelling of thick composites using a layerwise laminate theory
Authors: Robbins D. H. , Reddy J. N.
Published: August 2005

The layerwise laminate theory of Reddy1 is used to develop a layerwise, two‐dimensional, displacement‐based, finite element model of laminated composite plates that assumes a piecewise continuous distribution of the tranverse strains through the laminate thickness. The resulting layerwise finite element model is capable of computing interlaminar stresses and other localized effects with the same level of accuracy as a conventional 3‐D finite element model. Although the total number of degrees of freedom are comparable in both models, the layerwise model maintains a 2‐D‐type data structure that provides several advantages over a conventional 3‐D finite element model, e.g. simplified input data, ease of mesh alteration, and faster element stiffness matrix formulation. Two sample problems are provided to illustrate the accuracy of the present model in computing interlaminar stresses for laminates in bending and extension.
A generalized forward gradient procedure for rate sensitive constitutive equations
Authors: Wenner Michael L.
Published: August 2005

Many forward gradient schemes have been proposed for the time‐integration of the stiff constitutive equations of rate sensitive solids. It is shown here that one of these methods can be interpreted as a hybrid ordinary differential equation integrator which combines explicit and semi‐implicit Runge‐Kutta methods. This observation permits development of higher order schemes, illustrated here by one of second order. An embedded first order estimate provides a reliable step‐size control. The method is applied to an overstress model and to an internal variable model, and is used in a finite element analysis of hydrostatic bulging of sheet metal.
Axially‐loaded damped Timoshenko beam on viscoelastic foundation
Authors: Chen Yung‐Hsiang , Sheu Jau‐Tsann
Published: August 2005

The study of an axially‐loaded damped Timoshenko beam on a viscoelastic foundation is presented. The effects of the axial force, viscoelastic foundation and all the various damping components to a Timoshenko beam are considered in the formulation. The dynamic stiffness matrix is established and intensively discussed for applications. Free vibrations and the overall dampings are solved accordingly. Examples and discussions are also included.
Multigrid solution of the 3‐D compressible euler equations on unstructured tetrahedral grids
Authors: Peraire J. , Peiro J. , Morgan K.
Published: August 2005

A low storage, computationally efficient algorithm for the solution of the compressible Euler equations on unstructured tetrahedral meshes is developed. The algorithm takes the form of a centred scheme with the explicit addition of a high accuracy artificial viscosity and the solution is advanced to steady state by means of a multi‐stage time stepping method. The side based data structure which is employed enables a clear connection to be established between the proposed algorithm and upwind cell vertex schemes for unstructured meshes. The computational efficiency of the procedure is improved by incorporating an unstructured multigrid acceleration procedure. A number of flows of practical interest are analysed to demonstrate the numerical performance of the proposed approach.
Non‐linear analysis of rectangular laminates under end shortening, using shear deformation plate theory
Authors: Lam S. S. E. , Dawe D. J. , Azizian Z. G.
Published: August 2005

Consideration is given to the prediction of the geometrically non‐linear elastic response of rectangular composite laminates with simply supported ends when subjected to uniform end shortening in their plane. At the loaded ends lateral in‐plane expansion is either allowed freely or is prevented completely. Material properties of the laminates are quite general, encompassing anisotropy and full coupling between in‐plane and out‐of‐plane behaviour. First‐order shear deformation plate theory is used as the mathematical model of laminate behaviour and the non‐linearity is introduced in the strain‐displacement equations in the manner of the von Karman assumptions. The finite strip method is used as the main numerical analysis procedure and subsidiary use is made of the finite element method. Close comparison of results generated using the two methods is demonstrated in applications ranging from isotropic plates to unsymmetric anisotropic laminates. Further comparison with the results of an earlier‐developed finite strip method, wherein properties are based on the use of classical plate theory, shows the effect of through‐thickness shearing action in different situations.
Explicit thickness integration for three‐dimensional shell elements applied to non‐linear analysis
Authors: Mahe M. , Sourisseau J. C. , Ohayon R.
Published: August 2005

The problem of multilayered degenerated 3‐D shell elements for which the numerical integration is performed for each ply is that of the high generation time in non‐linear analysis when the number of plies is important. But these elements give accurate results for thin and moderately thick shells, so in order to reduce the generation time explicit thickness integration is investigated. We first write an expansion of the strain‐displacement matrix in power series of the thickness variable in order to obtain explicit expressions of the tangent stiffness matrix and internal force vector, appearing in the non‐linear formulation. Explicit expressions of non‐linear stiffness matrices are presented, using the explicit integration‐first approximation. Simple expressions of several matrices, sub‐matrices and vectors appearing in the formulation are given here in order to obtain an important computing‐time gain. Next, some numerical validation tests comparing the classical element with numerical thickness integration and this one are discussed to prove validity of this formulation.
An U‐ALE formulation of 3‐D unsteady viscoelastic flow
Authors: Baaijems Frank P. T.
Published: August 2005

The Arbitrary‐Lagrange‐Euler (ALE) formulation is applied to the analysis of unsteady viscoelastic flow of an Upper‐Convected‐Maxwell (UCM) medium. It is shown how the requirement of incremental objectivity affects the stress updating scheme. The current implementation of the ALE formulation uses the Time‐Discontinuous/Galerkin‐Least‐Squares (TD/GLS) method to handle the advective parts of the equations. Further, the ALE formulation is compared with an Updated‐ALE formulation that is shown to give comparable results but is much more cost effective. The technique presented is particularly effective for free surface flows. Three applications are given.
A displacement‐based geometrically non‐linear constant stress element
Authors: Bout A.
Published: August 2005

A triangular geometrically non‐linear constant stress element is presented, applicable to thin‐shell problems involving finite rotations. The element has the same degrees of freedom as the linear element following from the superposition of the constant strain triangle and the constant moment triangle. In the derivation of the non‐linear strain‐displacement relations, special attention is given to the correct representation of the rigid body motions of a patch of elements. Based on a second‐order out‐of‐plane displacement field, an initial deflection is introduced. This improves the effectiveness of the element, since curved shell geometries can be described more accurately. Several demonstrative examples are included.
Static and dynamic analysis of space frames using simple Timoshenko type elements
Authors: Kouhia Reijo , Tuomala Markku
Published: August 2005

In this paper a finite element method for geometrically and materially non‐linear analyses of space frames is described. Beams with both solid and thin‐walled open cross‐sections are considered. The equations of equilibrium are formulated using an updated incremental Lagrangian description. The elements developed can undergo large displacements and rotations, but the incremental rotations are assumed to be small. The material behaviour is described by elastoplastic, temperature‐dependent elastoplastic and viscoplastic models with special reference to metals. Computationally, more economical formulations based on the relationship between stress resultants and generalized strain quantities are also presented. In the case of thin‐walled beams the torsional behaviour is modelled using a two‐parameter warping model, where the angle of twist and the axial variation of warping have independent approximations. This approach yields average warping shear strains directly from the displacement assumptions and no discrepancy between stress and strain fields exists.
Post‐buckling analysis of structures by dynamic relaxation
Authors: Ramesh G. , Krishnamoorthy C. S.
Published: August 2005

The paper presents a displacement incrementation procedure to handle multiple loadings in post‐buckling analysis of structures by Dynamic Relaxation (DR). This procedure is generalized and a ‘variable‐arc‐length’ method is proposed to automate the tracing of load‐deflection path. The resulting algorithm exactly traces limit points and can handle ‘snap‐through’ or ‘snap‐back’ problems. The efficiency of the proposed method is demonstrated by typical examples of truss, beam and shell structures.
On a class of constitutive equations in viscoplasticity: Formulation and computational issues
Authors: Perić Djordje
Published: August 2005

The viscoplastic constitutive model is formulated based on the existence of the dissipation potential which embodies the notion of the gauge (Minkowski) function of the convex set. A perturbation method is used for a solution of stiff differential equations characterizing the associated problem of evolution. It relies on a discrete formulation of viscoplasticity which results from the regularized version of the principle of maximum plastic dissipation. The operator split methodology and the Newton‐Raphson method are used to obtain the numerical solution of the discretized equations of evolution. The consistent tangent modulus is expressed in a closed form as a result of the exact linearization of the discretized evolution equations. For several variants of the flow potential function, including some representative stiff functional forms, numerical tests of the integration algorithm based on iso‐error maps are provided. Finally, a numerical example is presented to illustrate the robustness and the effectiveness of the proposed approach.
A penalty finite element method for non‐Newtonian creeping flows
Authors: Codina Ramon , Cervera Miguel , Oñate Eugenio
Published: August 2005

In this paper we present an iterative penalty finite element method for viscous non‐Newtonian creeping flows. The basic idea is solving the equations for the difference between the exact solution and the solution obtained in the last iteration by the penalty method. For the case of Newtonian flows, one can show that for sufficiently small penalty parameters the iterates converge to the incompressible solution. The objective of the present work is to show that the iterative penalization can be coupled with the iterative scheme used to deal with the non‐linearity arising from the constitutive law of non‐Newtonian fluids. Some numerical experiments are conducted in order to assess the performance of the approach for fluids whose viscosity obeys the power law.
Dynamic analysis of concrete pavements resting on a two‐parameter medium
Authors: Zaman Musharraf , Alvappillai Arumugam , Taheri Michael R.
Published: August 2005

An analysis procedure based on the finite element method is presented to solve moving‐load problems of rigid pavements. The algorithm presented considers the dynamic pavement‐aircraft interaction effects. The pavement‐foundation system is modelled by thin‐plate, non‐conforming finite elements resting on a two‐parameter elastic medium. The moving aircraft loads are represented by masses supported by a spring‐dashpot system moving at a specified initial horizontal velocity and acceleration. The accuracy of the finite element program developed is verified by comparing the numerical results of a static problem with the available solution. A parametric study is conducted to determine the effects of the various parameters on the dynamic response of pavements. Emphasis is placed on identifying the influence of fictitious edge and corner forces acting on the plate due to the deformation of the soil medium outside the plate.
Transient analysis of geometrically linear and non‐linear structures by a combined finite‐element‐Riccati‐transfer substructure method
Authors: Zhu Jinghua , Xue Huiyu
Published: August 2005

The combined finite‐element‐Riccati‐transfer substructure method is applied to the transient analysis of the structures under various excitations with small and large displacements, respectively. The advantages include reductions in the order of standard transfer equation systems, in the computational efforts, and in the propagation of round‐off errors produced in recursive multiplications of the transfer matrices. Meanwhile, a methodology for analysing transfer substructures is, in combination with exact dynamic condensation and generalized Riccati transformation, proposed to develop the finite element and transfer matrix (FETM) techniques. The Newmark method and Wilson‐θ method are used for time integrations with respect to linear and non‐linear problems. The modified Newton‐Raphson method is employed for equilibrium iteration in each time step.

Numerical examples are presented to demonstrate the high efficiency and accuracy of the proposed method for the transient responses of plates. The results from these examples agree well with those obtained by other methods.
Hybrid hexahedral element for solids, plates, shells and beams by selective scaling
Authors: Sze K. Y. , Ghali A.
Published: August 2005

A robust two‐field hexahedral element capable of handling plate/shell, beam and nearly incompressible material analyses without locking are presented. Starting with the assumed stress element of Pian and Tong,7 parasitic strain components leading to locking in plate, shell and beam analyses are first identified. Locking can be alleviated by scaling down selectively the parasitic strain components in the leverage matrix. Unfortunately, the element then fails the patch test. However, patch test correction and reduction in computation can be achieved by the recently proposed admissible matrix formulation. The resulting element is lock‐free and very efficient. All matrices involved in constructing the stiffness matrix can be derived explicitly. The accuracy of the element is tested by popular bench‐mark problems.
A survey of quasi‐Newton methods with reduced storage
Authors: Papadrakakis M. , Pantazopoulos G.
Published: August 2005

A family of non‐linear solution methods is investigated based on limited‐memory quasi‐Newton updates. Depending upon the number of updates and the updating formula, a number of solution schemes may be constructed such as the conjugate‐ and secant‐Newton methods, the conventional and modified Newton‐Raphson methods and a variety of quasi‐Newton updates. Under the proposed implementation, the preconditioned truncated Lanczos method is used for the solution of the linearized problem in each non‐linear iteration. The complete factorization of the stiffness matrix is avoided and large‐scale problems can be solved efficiently both in terms of computing time and storage. The non‐linear iterative scheme is properly modified to account for loading variation inside the increment in order to be able to trace post‐critical equilibrium paths.
Analysis of the anisotropic viscoplastic‐damage response of composite laminates—continuum basis and computational algorithms
Authors: Saleeb A. F. , Wilt T. E.
Published: August 2005

The mathematical structure underlying the rate equations of a recently‐developed constitutive model for the coupled viscoplastic‐damage response of anisotropic composites is critically examined. In this regard, a number of tensor projection operators have been identified, and their properties were exploited to enable the development of a general computational framework for their numerical implementation using the Euler fully‐implicit integration method. In particular, this facilitated (i) the derivation of explicit expressions of the (consistent) material tangent stiffnesses that are valid for both three‐dimensional as well as subspace (e.g. plane stress) formulations, (ii) the implications of the symmetry or unsymmetry properties of these tangent operators from a thermodynamic standpoint, and (iii) the development of an effective time‐step control strategy to ensure accuracy and convergence of the solution. In addition, the special limiting case of inviscid elastoplasticity is treated. The results of several numerical simulations are given to demonstrate the effectiveness of the schemes developed.
A new family of continuous/discontinuous three‐dimensional boundary elements with application to acoustic wave propagation
Authors: Silva J. J. Rêgo , Wrobel L. C. , Telles J. C. F.
Published: August 2005

This paper presents a new family of continuous/discontinuous three‐dimensional boundary elements which has been implemented in a computer system for acoustic wave propagation in the frequency domain. The system includes elements of different geometrical shapes, 'order of interpolation and degree of continuity. Results of several tests are included to show the efficiency of the family of elements.
Superelement method for transient dynamic analysis of structural systems
Authors: Belyi M. V.
Published: August 2005

A superelement algorithm for the transient dynamic analysis of structural systems is presented. The method represents a generalization of existing static and dynamic superelement (substructure) algorithms. Natural frequencies and modal shapes of a fixed boundary substructure are used to obtain equations of motion of a superelement. An implicit time‐stepping algorithm is presented for the numerical solution of a resulting superelement system of equations of motion. Numerical examples are given to illustrate the presented approach. The method is believed to be effective for large‐scale problems of structural analysis.
Neural networks for computing in structural analysis: Methods and prospects of applications
Authors: Kortesis S. , Panagiotopoulos P. D.
Published: August 2005

A neural network model is proposed and studied for the treatment of structural analysis problems. Both the cases of bilateral and unilateral constraints are considered and Hopfield‐like neural models are proposed. Moreover, new results, generalizing the results of Hopfield and Tank,10 are obtained.

Numerical applications illustrate the theory and show clearly the advantages of the neural network approach. Finally, the parameter identification problem is formulated and solved as a ‘learning’ problem for a neural network.
Curvilinear fatigue crack reliability analysis by stochastic boundary element method
Authors: Lua Yuan Jie , Liu Wing Kam , Belytschko Ted
Published: August 2005

In this paper, the stochastic boundary element method, which combines the mixed boundary integral equations method explored in Reference 1 with the first‐order reliability method, is developed to study probabilistic fatigue crack growth. Due to the high degree of complexity and non‐linearity of the response, direct differentiation coupied with the response‐surface method is employed to determine the response gradient. Three random processes, the mode I and mode II. stress intensity factors and the crack direction angle, are included in the expression of the response gradient. The sensitivity of these random processes is determined using a first‐order response model. An iteration scheme based on the HL‐RF method2 is applied to locate the most probable failure point on the limit‐state surface. The accuracy and efficiency of the stochastic boundary element method are evaluated by comparing the cumulative distribution function of the fatigue life obtained with Monte Carlo simulation. The reliability index and the corresponding probability of failure are calculated for a fatigue crack growth problem with randomness in the crack geometry, defect geometry, fatigue parameters and external loads. The response sensitivity of each primary random variable at the design point is determined to show its role in the fatigue failure. The variation of each primary random variable at the design point with the change of probability of failure is also presented in numerical examples.
Fragmentation algorithm for finite element failure simulation and analysis
Authors: Rice Darren L. , Ting Edward C.
Published: August 2005

An algorithm which combines the techniques of numerical analysis and numerical simulation in the study of transient dynamic structural response is proposed. This is achieved by incorporating the ability to create new surfaces and separate fragments according to a defined failure criterion into a finite element procedure which uses explicit time integration. Thus, the algorithm not only provides accurate prediction of the structural failure and fragmentation pattern, but also evaluates accurate stress, velocity, acceleration and displacement values of each fragmented component.

To develop a viable fragmental algorithm, other than the expected modification in storage and node bookkeeping, we found it necessary to introduce an efficient algorithm to handle extremely large displacements resulting from the fracture. In that regard, an updated corotational approach is introduced.
An analysis of some higher‐order triangular elements and their susceptibility to hourglassing in Lagrangian fluid simulations
Authors: Priestley A.
Published: August 2005

In Lagrangian codes two of the main problems are hourglassing with bilinear quadrilateral elements and mesh locking with linear triangular elements. Higher‐order triangular elements, with their greater number of degrees of freedom, should not suffer from mesh locking, Hourglassing, though, is caused by the interaction of the element and the quadrature used to evaluate the integrals of the derivatives on it. Higher‐order triangular elements, as we shall see, unlike their linear counterparts, also suffer from this spurious mode. A higher‐order element/quadrature combination is found that does not suffer from hourglassing. The main fault of this combination is the extra cost involved over the more usual linear or bilinear element with centroid quadrature combination. A short discussion is given regarding this point.
Geometrically non‐linear method of incompatible modes in application to finite elasticity with independent rotations
Authors: Ibrahimbegović Adnan , Frey Francois
Published: August 2005

We discuss a geometrically non‐linear method of incompatible modes. The model problem chosen for the discussion is the finite elasticity with independent rotations. The conditions which ensure the convergence of the method and the methodology to construct incompatible modes are presented. A detailed derivation of variational equations and their linearized form is given for a two‐dimensional plane problem. A couple of geometrically non‐linear two‐dimensional elements with independent rotational freedoms are proposed based on the presented methodology. The elements exhibit a very satisfying performance over a set of problems in finite elasticity.
Configuration design sensitivity analysis of built‐up structures part II: Numerical method
Authors: Twu Sung‐Ling , Choi Kyung K.
Published: August 2005

A numerical method is presented for structural configuration design sensitivity calculations using established finite element analysis codes. The theoretical foundation of the configuration design sensitivity analysis is given in Part I of this paper1 using the continuum elasticity formulation. A linear approximation between design parameterizations and design velocity fields is derived for line and surface design components. A regular design velocity that avoids the calculation of corner terms at the boundary is implemented to show a unified configuration design sensitivity analysis. The design sensitivity analysis method is demonstrated using the post‐processing data of an existing finite element code. Configuration design sensitivity results of displacement, stress and eigenvalue performance measures are illustrated for several built‐up engineering structures.
Boundary integral equations for thin bodies
Authors: Krishnasamy Guna , Rizzo Frank J. , Liu Yijun
Published: August 2005

A boundary integral equation formulation for thin bodies which uses CBIE (conventional BIE) only is well known to be degenerate. A mixed formulation for a thin rigid scatterer which combines CBIE and HBIE (hypersingular BIE) is motivated by examining the discretized form of the integral equations, and this formulation is shown to be non‐degenerate for thin non‐rigid inclusion problems. A near‐singular integration procedure, useful for singular integrals as well, is presented. Finally, numerical examples for acoustic wave scattering from rigid and soft scatterers are presented.
Higher‐order finite element modelling of laminated composite plates
Authors: Ahmed Nesar U. , Basu Prodyot K.
Published: August 2005

P‐version finite elements based on higher‐order theory are developed for the two‐dimensional modelling of general bending and cylindrical bending of thin‐to‐thick laminated composite plates. In the case of general laminated plate elements, three displacement fields are used. In the special case of cylindrically bent laminated plate elements, two displacement fields are needed. In each case the displacement is expressed as the product of two functions—one in terms of out‐of‐plane co‐ordinates alone and the other in terms of in‐plane co‐ordinates. The shape functions used to build the displacement fields are based on integral of Legendre' polynomials. The quality and performance of the elements are evaluated in terms of convergence characteristics of displacements and stresses. The predicted response quantities are compared with those available in the published literature based on analytical as well as conventional finite element models.
Design of optimal process parameters for non‐isothermal forging
Authors: Cheng Huaining , Grandhi Ramana V. , Malas James C.
Published: August 2005

This paper presents a state space model and an optimal design scheme for non‐isothermal metal forming processes. By selecting nodal velocity and temperature as the state variables, a non‐isothermal state equation with coupled deformation and thermal terms is established. Based on this state space model, a control design scheme is developed to obtain the optimal die velocity and initial die temperature which will ensure that the effective strain‐rate and temperature satisfy the design requirements. A titanium alloy engine disk forging is used to demonstrate two design examples. The results show that the proposed model and design scheme behave well for different design requirements.
An accurate shear‐deformable six‐node triangular plate element for laminated composite structures
Authors: Kosmatka J. B.
Published: August 2005

A six‐node triangle plate/shell element is developed for the analysis of laminated composite structures. This model is formulated using Hamilton's principle along with a first‐order (Reissner/Mindlin) shear deformation theory. The element is based upon an isoparametric representation along with an interdependent interpolation strategy; bicubic polynomials for the transverse displacement and biquadratic polynomials for the element geometry, in‐plane displacements and rotations. The resulting element, which is evaluated using exact numerical integration, has correct rank and is free of shear ‘locking’. Numerical results are presented that validate the new element and prove its outstanding convergence capabilities in comparison to existing triangular elements using standardized test problems (elastic eigenvalue analysis, patch test, static simply supported square‐plate solutions) and experimentally measured vibration data of cantilevered isotropic and composite plates.
A unified theory for formulation of hybrid stress membrane elements
Authors: Yuan Kuan‐Ya , Wen Jyh‐Chung , Pian Theodore H. H.
Published: August 2005

A theory is proposed in this paper to explain, in a unified manner, the three rational approaches using the incompatible displacements uλ in the hybrid element formulation. Limited to the plane stress case, the theory suggests that the introduction of uλ is to constrain the total value of the invariant I2(= σxσy – τ) of the assumed stresses over the element to zero. In the plane stress case, this is the well‐known condition for the stress distributions to be independent of the elastic constants of the material. The theory proposed is also used to explain the closeness of the performances of the four 4‐node hybrid stress membrane elements, 5β‐I, 5β‐II, 5β‐A and 5β‐C, that have been developed previously. The differences among them are shown to be of the second degree in the distortion measures of the element shape, when they are compared on the basis of the non‐vanishing total value of I2 of their respectively adopted assumed stress field. Several numerical examples are used to verify and to illustrate the proposed theory.
An upwind kinetic flux vector splitting method on general mesh topologies
Authors: Weatherill N. P. , Mathur J. S. , Marchant M. J.
Published: August 2005

An upwind flux vector splitting algorithm which utilizes the moments of the Boltzmann equation to derive the Euler equations for inviscid compressible flow has been used with a variety of grid types. Although the upwind approach offers the potential for accurate flow simulations, it is necessary to ensure that such procedures can be utilized on realistic grids. In this paper, an upwind algorithm is used with structured multiblock grids, unstructured grids of triangles and hybrid structured/unstructured grids to solve realistic compressible flow problems in two dimensions.
On stress interpolation for hybrid models
Authors: Bouzeghoub M. C. , Gunn M. J.
Published: August 2005

A technique is proposed for the selection of stress interpolations for hybrid models. The present paper applies this approach to plane problems. The stiffness matrix is derived using the Hellinger–Reissner variational principle. This formulation uses infinitesimal equilibrium relationships and divides the assumed stress into its lower‐order and higher‐order parts. The patch test can be passed and the resulting elements are generally invariant. A plane four‐node quadrilateral element is described and compared with existing elements. Numerical studies show that the accuracy of the element is generally good.
Locking‐free curved beam element based on curvature
Authors: Lee Pal‐Gap , Sin Hyo‐Chol
Published: August 2005

The formulation of a curved beam element with 3 nodes for curvature to eliminate the shear/membrane locking phenomenon is presented. The element is based on curvature so that it may represent the bending energy fully, and the shear/membrane strain energy is incorporated into the formulation by the equilibrium equations. To deal with general boundary conditions, a transformation matrix between nodal curvature and nodal displacement vector is introduced. Several examples are presented in order to verify the element formulation and its analytical capability. The solutions obtained reveal that the element describes the curved beam behaviour quite correctly and efficiently, showing no locking phenomena, and that it is also applicable to the analysis of both thin and thick curved beams.
Linked interpolation for Reissner‐Mindlin plate elements: Part III—An alternative quadrilateral
Authors: Xu Z. , Zienkiewicz O. C. , Zeng L. F.
Published: August 2005

An alternative quadrilateral element for Reissner—Mindlin plates, which extends the mixed formulation described in Part 1 using linked interpolations, is presented. Differently from element Q4BL presented in Part I, this element (Q4BLa) employs four internal rotation nodes and a linear approximation for transverse shear forces. It is shown that the element passes various patch tests, it does not possess any zero‐energy mode and its performance is good for both thick and thin plates.
Pre‐ and postbuckling response of curved, thin, composite panels with cutouts under compression
Authors: Madenci E. , Barut A.
Published: August 2005

Analytical predictions of the postbuckling response of curved composite panels are difficult, especially under in‐plane compression, because of the presence of snap‐back with a steep negative slope beyond the bifurcation point. In this study, the pre‐ and postbuckling response of curved laminated panels with cutouts is investigated by developing a new finite element based on the free formulation. This trianguiar, flat, shell element, in conjunction with the updated Lagrangian form of the co‐rotational approach, accounts for the coupling terms arising from general material anisotropy, as well as large displacements and rotations. The analysis predictions correlate well with the corresponding experimental data available in the literature. Review of the studies in this subject area reveal that none of the available methods, including the STAGS‐C1 finite element program, is capable of providing the full description of the postbuckling phenomenon beyond bifurcation for curved composite panels with small cutouts.
Node and element resequencing using the Laplacian of a finite element graph: Part I—General concepts and algorithm
Authors: Paulino Glaucio H. , Menezes Ivan F. M. , Gattass Marcelo , Mukherjee Subrata
Published: August 2005

A Finite Element Graph (FEG) is defined here as a nodal graph (G), a dual graph (G*), or a communication graph (G˙) associated with a generic finite element mesh. The Laplacian matrix (L(G),L(G*) or L(G˙)), used for the study of spectral properties of an FEG, is constructed from usual vertex and edge connectivities of a graph. An automatic algorithm, based on spectral properties of an FEG (G, G* or G˙), is proposed to reorder the nodes and/or elements of the associated finite element mesh. The new algorithm is called Spectral PEG Resequencing (SFR). This algorithm uses global information in the graph, it does not depend on a pseudoperipheral vertex in the resequencing process, and it does not use any kind of level structure of the graph. Moreover, the SFR algorithm is of special advantage in computing environments with vector and parallel processing capabilities.

Nodes or elements in the mesh can be reordered depending on the use of an adequate graph representation associated with the mesh. If G is used, then the nodes in the mesh are properly reordered for achieving profile and wavefront reduction of the finite element stiffness matrix. If either G* or G˙ is used, then the elements in the mesh are suitably reordered for a finite element frontai solver, A unified approach involving FEGs and finite element concepts is presented. Conclusions are inferred and possible extensions of this research are pointed out.

In Part II of this work,1 the computational implementation of the SFR algorithm is described and several numerical examples are presented. The examples emphasize important theoretical, numerical and practical aspects of the new resequencing method.
Node and element resequencing using the Laplacian of a finite element graph: Part II—Implementation and numerical results
Authors: Paulino Glaucio H. , Menezes Ivan F. M. , Gattass Marcelo , Mukherjee Subrata
Published: August 2005

In Part I of this work, Paulino et al.1 have presented an algorithm for profile and wavefront reduction of large sparse matrices of symmetric configuration. This algorithm is based on spectral properties of a Finite Element Graph (FEG), An FEG has been defined as a nodal graph G, a dual graph G* or a communication graph G˙ associated with a generic finite element mesh. The novel algorithm has been called Spectral FEG Resequencing (SFR). This algorithm has specific features that distinguish it from previous algorithms. These features include (1) use of global information in the graph, (2) no need of a pseudoperipheral vertex or the endpoints of a pseudodiameter, and (3) no need of any type of level structure of the FEG. To validate this algorithm in a numerical sense, extensive computational testing on a variety of problems is presented here. This includes algorithmic performance evaluation using a library of benchmark test problems which contains both connected and non‐connected graphs, study of the algebraic connectivity (λ2) of an FEG, eigensolver convergence verification, running time performance evaluation and assessment of the algorithm on a set of practical finite element examples. It is shown that the SFR algorithm is effective in reordering nodes and/or elements of generic finite element meshes. Moreover, it computes orderings which compare favourably with the ones obtained by some previous algorithms that have been published in the technical literature.
The benefits of parallel multibody simulation
Authors: Eichberger A. , Führer C. , Schwertassek R.
Published: August 2005

To exploit the benefits of parallel computer architectures for multibody system simulation, an interdisciplinary approach has been pursued, combining knowledge of the three disciplines of dynamics, numerical mathematics and computer science. An analysis of the options available for the formulation and numerical solution of the dynamical system equations yielded a surprising result. A method initially proposed to solve the inverse problem of dynamics is the best choice to generate the system equations required for solving the simulation problem, when relying on implicit integration routines. Such routines have the particular advantage of handling stiff systems, too. The new O(N)‐residual formalism, generating the system equations in a form required for implicit numerical integration, has a high potential to benefit from parallel computer architectures. Two strategies of medium and coarse grain parallelization have been implemented on a Transputer network to obtain a package for parallel multibody simulation. An analysis of the performance of this package demonstrates for typical multibody simulation problems that the new code is five times faster than existing codes when implemented on a serial computer. An additional speed‐up by the same order of magnitude is obtained when the code is implemented on a Transputer network.
The variational formulation and solution of problems of finite‐strain elastoplasticity based on the use of a dissipation function
Authors: Eve R. A. , Reddy B. D.
Published: August 2005

The solution of initial‐boundary value problems involving finite elastoplastic deformations is discussed. The formulation considered differs from conventional formulations in that the evolution law is expressed in terms of the dissipation function. A generalized midpoint rule is used to obtain an incremental problem, a variational form of which is derived. The finite element method is used for spatial discretization, and an algorithm to solve the resulting discrete problem is developed. This algorithm has the predictor–corrector structure common to most solution procedures for problems in plasticity. Methods for imposing the plastic incompressibility constraint are investigated. Solutions to two axisymmetric examples obtained using the proposed algorithm are presented and compared with those obtained by other authors.
The use of Stokes' fundamental solution for the boundary only element formulation of the three‐dimensional Navier–Stokes equations for moderate Reynolds numbers
Authors: Power Henry , Partridge Paul W.
Published: August 2005

This paper presents a boundary element formulation for the permanent Navier–Stokes equations in which the well‐known closed‐form fundamental solution for the steady Stokes equations is employed. In this way, from the integral representation formulae for the Stokes' equations, an integral equation is found in which the original non‐linear convective terms of the Navier–Stokes equations appear as a domain integral. Additionally, the method of dual reciprocity is used to transform the domain integral to boundary integrals (this method is closely related to the method of particular integrals also used in the literature to transform domain integrals to boundary integrals). Numerical results are presented for the three‐dimensional internal flow in a cylindrical container with a rotating cover, in which the accuracy of the method is shown.
Aspects of three‐dimensional constrained Delaunay meshing
Authors: Wright Julian P. , Jack Alan G.
Published: August 2005

Presented in this paper are the theoretical aspects of node addition to a non‐convex, multiboundary mesh of tetrahedral elements as used in finite element modelling. The method used is derived from Watson1 and Shenton and Cendes2 and is extended to deal with node addition on inter‐material boundaries. Several situations are identified that result in an illegal insertion polyhedron (IP), these could be caused by the ‘constrained’ nature of the mesh, adjacent objects with different material properties, or degenerate node configurations. A new Delaunay algorithm is described that checks for illegal cases of the IP and then corrects them, this checking relies on the consistent ordering of the element nodes. It is shown that a particular type of illegal IP can easily be identified and corrected using this technique. The Delaunay algorithm is then applied to automatic mesh generation, and modification to the basic Delaunay algorithm is described so that previously meshed edges and faces of the current object being meshed are not deleted during the addition of subsequent nodes. This ‘protection’ method only becomes viable by recognizing the node ordering sense of the IP faces.
A co‐rotational element/time‐integration strategy for non‐linear dynamics
Authors: Crisfield M. A. , Shi J.
Published: August 2005

New procedures are proposed for implicit dynamic analysis using the finite element method. The main aim is to give stable solutions with significant rigid‐body motions, in particular rotations. In contrast to most conventional approaches, the time‐integration strategy is closely linked to the ‘element technologies’ with the latter involving a form of co‐rotational procedure. For the undamped situation, one of the solution procedures leads to an algorithm that exactly conserves energy when constant external forces are applied (i.e. with gravity loading).
Coupled transient thermoelastic contact problems for axial cracks in hollow cylinders
Authors: Chen Cháo‐Kuang , Kuo Bor‐Lih
Published: August 2005

A coupled transient thermoelastic behaviour of an axial‐cracked hollow circular cylinder subjected to a sudden heating is investigated in this study. It is shown that surface heating may induce the compressive thermal stress near the inner surface of the cylinder which in turn may force the cracked surfaces to close together. Assuming that the existence of the crack does not alter the temperature distribution, we can divide this problem into two parts and solve it by the principle of superposition. First, the temperature and transient thermal stress distributions along the axisymmetric surface of the imaginary cylinder without crack are obtained by finite element implicit time integration method Secondly, the opposite sense of the stress distributions along the cracked surfaces, which is obtained previously, is treated as the traction boundary conditions; the contact length and contact pressure of the real cracked cylinder are obtained by modified elimination finite element scheme. Finally, we also obtained the normalized stress intensity factor for the crack tip of the cylinder. It is concluded that the effect due to thermoelastic coupling term on stress intensity factor becomes more important for higher coupling coefficient, and this coupling term also results in a small time lag in temperature, thermal stress and stress intensity factor.
Automatic directional refinement in adaptive analysis of compressible flows
Authors: Zienkiewicz O. C. , Wu J.
Published: August 2005

In such local phenomena as shocks and boundary layers, etc, the discretization errors are directional and the use of elongated elements is obvious if economy is to be achieved. Although facilities for local mesh elongation have been incorporated into earlier codes in generating unstructured meshes, these do not permit the use of very high stretch ratios required for the analysis of such problems as boundary layers. Here the use of locally introduced structured meshes has been practised involving much manual interaction and loss of error control. In the paper we present a procedure which achieves the combination of such locally structured meshes with a general unstructured mesh generator in an automatic and fully adaptive manner. The procedure is illustrated in the context of compressible, viscous and inviscid, flows but has obvious applications in other (solid mechanics) problems involving localization.