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Barlow was the first to propose a method to predict optimal stress recovery points in finite elements (FEs). Prathap proposed an alternative method that is based on the variational principle. The optimal points predicted by Prathap, called Prathap points in this paper, have been reported in the literature for linear, quadratic and cubic elements. Prathap points turn out to be the same as Barlow points for linear and quadratic bar elements but different for cubic bar element. Nevertheless, for all the three elements, Prathap points coincide with the reduced Gaussian integration points. In this paper, an alternative implementation of Prathap's best-fit method is used to compute Prathap points for higher-order (viz., 4–10th order) bar elements. The effectiveness of Prathap points as points of accurate stress recovery is verified by actual FE analysis for typical bar problems. Copyright © 2008 John Wiley & Sons, Ltd.

This paper promotes the development of a novel family of finite elements with smoothed strains, offering remarkable properties. In the smoothed finite element method (FEM), elements are divided into subcells. The strain at a point is defined as a weighted average of the standard strain field over a representative domain. This yields superconvergent stresses, both in regular and singular settings, as well as increased accuracy, with slightly lower computational cost than the standard FEM. The one-subcell version that does not exhibit volumetric locking yields more accurate stresses but less accurate displacements and is equivalent to a quasi-equilibrium FEM. It is also subject to instabilities. In the limit where the number of subcells goes to infinity, the standard FEM is recovered, which yields more accurate displacements and less accurate stresses. The specific contribution of this paper is to show that expressing the volumetric part of the strain field using a one-subcell formulation is sufficient to get rid of volumetric locking and increase the displacement accuracy compared with the standard FEM when the single subcell version is used to express both the volumetric and deviatoric parts of the strain. Selective integration also alleviates instabilities associated with the single subcell element, which are due to rank deficiency. Numerical examples on various compressible and incompressible linear elastic test cases show that high accuracy is retained compared with the standard FEM without increasing computational cost. Copyright © 2008 John Wiley & Sons, Ltd.

The phenomenon of failure by catastrophic crack propagation in structural materials poses problems of design and analysis in many fields of engineering. Cracks are present to some degree in all structures. They may exist as basic defects in the constituent materials or they may be induced in construction or during service life. Using the finite element method, a lot of papers deal with the calculation of stress intensity factors for two- and three-dimensional geometries containing cracks of different shapes under various loadings to elastic bodies. In order to increase the accuracy of the results, special elements have been used. They are described together with methods for calculating the stress intensity factors from the computed results. At the vicinity of a crack tip, the strains are not always small, but they may also be large. In this case, the J-integral can also be applied to characterize the cracks in elastic or elastic–plastic bodies. This paper describes the computation of the two-dimensional J-integral for large strains to elastic and elastic–plastic bodies and represents some numerical examples. Copyright © 2007 John Wiley & Sons, Ltd.

The aim of this paper is to develop an efficient method for decoupling joint and elastic accelerations, while maintaining the nonlinear inertia coupling between rigid body motion and elastic body deformation. Almost all of the existing recursive methods for analysis of flexible open-loop and closed-loop multibody mechanical systems lead to dense coefficient matrices in the equations of motion, and consequently there are strong dynamic couplings between the joint and elastic coordinates. When the number of elastic degrees of freedom increases, the size of the coefficient matrix in the equations of motion becomes large and unfortunately the use of these methods for solving for the joint and elastic accelerations becomes less efficient. This paper discusses the problems associated with the inertia projection schemes used in the existing recursive methods, and it is shown that decoupling the joint and elastic accelerations using these methods requires the factorization of nonlinear matrices whose dimensions depend on the number of elastic degrees of freedom of the system. An amalgamated method that can be used to decouple the elastic and joint accelerations is then proposed. In this amalgamated decoupling formulation, the relationships between the absolute, elastic, and joint variables and the generalized Newton–Euler equations are used to develop systems of loosely coupled equations that have sparse matrix structure. Utilizing the inertia matrix structure of flexible manufacturing systems and the fact that the joint reaction forces associated with the elastic coordinates do represent independent variables, a reduced system of equations whose dimension is dependent on the number of elastic degrees of freedom is obtained. This system can be solved for the joint accelerations as well as for the joint reaction forces. The application of the procedure developed in this paper is illustrated using flexible open-loop robotic manipulators and closed-loop crank-slider mechanical systems. Copyright © 2007 John Wiley & Sons, Ltd.

This paper presents a one-dimensional finite element for creep buckling analysis of structures comprised of straight and prismatic beam members. Spatial displacements and rotations are allowed to be large while strains are assumed to be small. Material is assumed to be homogenous and isotropic. The corresponding equilibrium equations are formulated in the framework of co-rotational description, using the virtual work principle. In contrast to conventional co-rotational formulation, which is linear on element level and unable to model Wagner effect, in this paper an additional nonlinear part of stiffness matrix is evaluated and added to standard elastic stiffness. Implementation of developed numerical algorithm is demonstrated through few test problems.

To circumvent the constraint in application of the conventional differential quadrature (DQ) method that the solution domain has to be a regular region, an interpolation-based local differential quadrature (LDQ) method is proposed in this paper. Instead of using regular nodes placed on mesh lines in the DQ method (DQM), irregularly distributed nodes are employed in the LDQ method. That is, any spatial derivative at a nodal point is approximated by a linear weighted sum of the functional values of irregularly distributed nodes in the local physical domain. The feature of the new approach lies in the fact that the weighting coefficients are determined by the quadrature rule over the irregularly distributed local supporting nodes with the aid of nodal interpolation techniques developed in the paper. Because of this distinctive feature, the LDQ method can be consistently applied to linear and nonlinear problems and is really a mesh-free method without the limitation in the solution domain of the conventional DQM. The effectiveness and efficiency of the method are validated by two simple numerical examples by solving boundary-value problems of a linear and a nonlinear partial differential equation. Copyright © 2007 John Wiley & Sons, Ltd.

For an efficient force method of frame analysis, the formation of localized self-equilibrating systems is an important issue. Such systems can be constructed on minimal cycle basis of the graph model of the structure. In this paper, algorithms are presented for the formation of minimal cycle bases of graph products corresponding to sparse cycle adjacency matrices, leading to the formation of highly sparse flexibility matrices. The algorithms presented employ concepts from three graph products namely Cartesian, strong Cartesian and lexicographic products. Though the formulation for the first two products exist, however, efficient implementations are made in this paper. The formulation for the generation of minimal cycle basis is extended to the lexicographic product. Copyright © 2007 John Wiley & Sons, Ltd.

There have been many approaches to solve ordinary differential equations numerically. Even though many numerical methods can provide very good approximate solutions they need considerable calculation effort, often through iterations. The advance of symbolic manipulation packages such as Maple gives the opportunity for new approaches to this type of problems. This paper will discuss an improvement to one of these new approaches enabled by the availability of these packages, to obtain a numerical solution of an initial-value problem governed by a high-order non-linear ordinary differential equation. The method we propose here is based on Zhu and Phan's earlier paper (Commun. Numer. Meth. Engng. 2003; 19:601–614) but we shall show an improved order of accuracy for the case of the highest-order derivative being of an even order. In any case it provides the ability to further increase the order of accuracy under certain conditions of differentiability. Like Zhu and Phan's (Commun. Numer. Meth. Engng. 2003; 19:601–614) original method, an important feature of the new method is that no iterations are needed except in the preparatory phase for some cases. Copyright © 2006 John Wiley & Sons, Ltd.

The existing 1D analytical solution for heat conduction inside structural members plays an important role in the estimation of temperature field and prediction of member strength in fire. In this paper, the novelty lies in a set of proposed analytical formulations for the conduction heat transfer within multi-dimensional (2D and 3D) domains subjected to a particular time-varying boundary condition, i.e. the standard fire conditions. Solutions of multi-dimensional conduction are based on the eigenfunction approach using the technique of separation of variables. The multi-dimensional effect is incorporated by the product of respective solutions of 1D transient heat conduction (1D step functions) of the plate and the infinite cylinder that serve as a set of basis for derivation of analytical solutions. Fire boundary conditions are incorporated using the Duhamel's principle, where the time-varying fire temperature curve is imposed on the step functions. In this paper, the boundary conditions of the first and the third kind are considered, respectively. The analytical solutions are compared with results obtained from finite element analysis for verification. Copyright © 2006 John Wiley & Sons, Ltd.

This paper investigates numerically and experimentally the influence of initial geometric imperfections on the critical loads of initially stretched thick hyperelastic cylindrical shells under increasing uniform internal pressure. Imperfections in shells can have a global or local character. First, two types of local imperfections are considered: (1) a local axially symmetric imperfection in the form of a ring and (2) a small rectangular imperfection. The influence of the imperfection thickness, position and size are analysed in detail. Results show that the critical load decreases as the imperfections increase in size or thickness and as they move from the boundaries to the centre of the shell. The influence of multiple local imperfections is also studied in the present paper. Finally, the influence of global imperfections is considered with the imperfections described as a variation of the shell curvature in the axial direction. The results show that thick hyperelastic shells may be sensitive to local and global imperfections. In all cases the experimental results are in good agreement with the numerical ones, corroborating the conclusions.

This paper is devoted to the parallelization of a new method for solving large, structured eigenvalue problems, which appear in the electromagnetic modal analysis of arbitrarily shaped waveguides, typically present in many modern passive devices. This new method, based on the boundary integral-resonant mode expansion (BI-RME) technique and in the Lanczos method (for solution of the eigenvalue problem), was recently proposed by the authors, showing important advantages in terms of CPU time and memory over previously used solutions. As it will be fully described in this paper, the parallel version of such a new method allows further important savings in the overall CPU computation time. Comparative benchmarks and scalability issues related to the implemented parallel algorithm are discussed. Copyright © 2006 John Wiley & Sons, Ltd.

In this paper, a non-linear recursive formulation is developed for kinematic and dynamic analysis of open-loop mechanical systems. The non-linear equations of motion are developed for deformable links that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars and matrices that depend on the spatial co-ordinates as well as the assumed displacement field, and these time invariant quantities represent the dynamic coupling between the rigid-body modes and elastic deformations. A new recursive formulation is presented for solving equations of motion for open-loop chains consisting of interconnected rigid and deformable open-loop mechanical systems. This formulation is expressed by the recursive relationships and the generalized non-linear equations for deformable mechanical systems to obtain a large system of loosely coupled equations of motion. The main processor program consists of three main modules: constraint module, mass module and force module. The constraint module is used to numerically evaluate the relationship between the absolute and joint accelerations. The mass module is used to numerically evaluate the system mass matrix as well as the non-linear Coriolis and centrifugal forces associated with the absolute, joint and elastic co-ordinates. Simultaneously, the force module is used to numerically evaluate the generalized external and elastic forces associated with the absolute, joint and elastic co-ordinates. Computational efficiency is achieved by taking advantage of the structure of the resulting system of loosely coupled equations. The solution techniques used in this investigation yield a much smaller operations count and can more efficiently implement in any computer. The algorithms and solutions presented in this paper are illustrated by using an industrial robotic manipulator system. The numerical results using this formulation are also presented and discussed in this paper. Copyright © 2006 John Wiley & Sons, Ltd.

The recursive projection schemes used in most existing recursive methods for solid deformable structure dynamic problems lead to dense coefficient matrices in the acceleration equations and consequently there is a strong dynamic coupling between the joint and elastic coordinates. When the number of elastic degrees of freedom increases, the size of the coefficient matrix in the acceleration equations becomes large and consequently the use of these recursive methods for solving for the joint and elastic accelerations becomes less efficient. This paper discusses the problems associated with the recursive projection schemes used in the existing recursive methods, and it is shown that decoupling the joint and elastic accelerations using the nonlinear recursive method requires the factorization of nonlinear matrices whose dimensions are independent of the number of elastic degrees of freedom of the open-loop and closed-loop system. An amalgamated formulation that can be used to decouple the elastic and joint accelerations is then proposed. The use of the nonlinear recursive method developed in this paper is demonstrated using an open-loop free-falling deformable double pendulum system and a closed-loop four-bar mechanism. Copyright © 2006 John Wiley & Sons, Ltd.

This paper deals with a coupled finite element/scaled boundary finite element method (FE/SBFEM) and its application to wave propagation problems in fluids in the time domain. This method is already well established and has proven to be an efficient technique for treating radiation problems. In its application to time domain problems, convolution integrals arise. For each time step ti, i matrix–vector multiplications have to be performed, where the involved influence matrix—due to the non-locality in space—is fully populated. This numerical evaluation becomes a significant, time-consuming task for long time calculations, thus decreasing the attractiveness of the method. In this paper, the application of hierarchical matrices (ℋ-matrices) is to overcome this drawback. ℋ-Matrices represent an octree-based clustered low-rank approximation of the original, fully populated matrix and allow a considerable increase in efficiency for matrix–vector products encountered, e.g. in convolution integrals. The application of ℋ-matrices to this method results in an increase in efficiency without noticeable loss in accuracy. Since convolution integrals arise in various large-scale engineering computations the application of ℋ-matrix techniques might turn out to be a highly promising way to pursue. Copyright © 2005 John Wiley & Sons, Ltd.

This paper presents a new solution strategy for the minimal compliance problem in topology optimization. This problem contains the system of linear elasticity partial differential equations (PDEs) as a constraint resulting in a large scaled optimization problem after the finite element discretization. Due to the repeated solution of the direct field problem given by the PDE constraints, efficient solution techniques are required. In this paper we present a new solution method involving adaptive multilevel techniques combined with a multigrid approach for the direct problem. Topology optimization problems are ill-posed, so regularization is needed. In our algorithm we combine two regularization techniques, in fact filter methods, such that their disadvantages are eliminated and only their positive properties remain. Numerical experiments are performed with several benchmark problems, where our multilevel approach turns out to be quite efficient. For solving the optimization problems arising in each iteration step, the method of moving asymptotes is used. Copyright © 2005 John Wiley & Sons, Ltd.

In the upper bound approach to limit analysis of slope stability based on the rigid finite element method, the search for the minimum factor of safety can be formulated as a non-linear programming problem with equality constraints only based on a yield criterion, a flow rule, boundary conditions, and an energy-work balance equation. Because of the non-linear property of the resulting optimization problems, a non-linear mathematical programming algorithm has to be employed. In this paper, the relations between the numbers of nodes, elements, interfaces, and subsequent unknowns and constraints in the approach have been derived. It can be shown that in the large-scale problems, the unknowns are subject to a highly sparse set of equality constraints. Because of the existence of non-linear equalities in the approach, this paper applies first time a special sequential quadratic programming (SQP) algorithm, feasible SQP (FSQP), to obtain solutions for such non-linear optimization problems. In FSQP algorithm, the non-linear equality constraints are turned into inequality constraints and the objective function is replaced by an exact penalty function which penalizes non-linear equality constraint violations only. Three numerical examples are presented to illustrate the potentialities and efficiencies of the FSQP algorithm in the slope stability analysis. Copyright © 2004 John Wiley & Sons, Ltd.

The spatial oscillation of values in the consolidation analysis when using small time increments has been a common problem for most existing methods. In this paper, the numerical characteristics of a simple finite element formulation for 1-D consolidation analysis recently proposed by the authors have been examined in detail. This paper proves that the commonly encountered phenomenon of spatial oscillation due to small time increments does not occur in the simple finite element formulation. The criterion of minimum time step used in most existing methods can be eliminated at least for linear situations by using the simple formulation proposed by the authors. Thus, the consolidation analysis can be carried easily for many situations, such as the one involving a relatively impermeable clay layer sandwiched between sandy layers. Copyright © 2004 John Wiley & Sons, Ltd.

By using the natural boundary reduction an overlapping domain decomposition method is designed to solve some exterior two-dimensional time-dependent parabolic problems. The governing equation is first discretized in time, leading to a sequence of boundary value problems with respect to time step in an unbounded domain. Then artificial boundaries are introduced. For each time level, an overlapping domain decomposition method, which is based on the natural boundary reduction, is constructed to solve the exterior elliptic boundary value problem on a two-dimensional domain. It is shown that the algorithm is equivalent to Schwarz alternating method. The convergence of this algorithm is given. The contraction factor for the exterior circular domain is also discussed. In the end of this paper, some numerical examples are presented, which illustrate the feasibility and the effectiveness of the proposed methods in this paper. Copyright © 2004 John Wiley & Sons, Ltd.

The objective of this paper is to present and test a simple triangular finite shell element that uses five degrees of freedom at each node. The element is characterized by three position vectors and three unit directors. It depicts the plane stress state version of the element presented (Comput. Struct. 1989; 32(2):379). The element is of the ANS-type (assumed natural strain (J. Appl. Mech. 1981; 48:587). All strains inside the element contain dot products of the six actual element nodal vectors. The construction of the element also allows non-linear material behaviour. Since an enhancement of the membrane strains by the EAS (enhanced assumed strain method) is not possible inside a three node triangle element, the membrane strains perform poor. But via the DKT (discrete Kirchhoff theory) the three directors reveal an excellent bending behaviour for thin shells. The main concern of this paper is to test, if superimposing the CST (constant srain) with the classic DKT leads to good results in standard benchmark tests. Copyright © 2004 John Wiley & Sons, Ltd.

The well-known problem of the height limit of a Tresca or von Mises vertical slope of height h, subjected to the action of gravity stems naturally from Limit Analysis theory under the plane strain condition. Although the exact solution to this problem remains unknown, this paper aims to give new precise bounds using both the static and kinematic approaches and an Interior Point optimizer code. The constituent material is a homogeneous isotropic soil of weight per unit volume γ. It obeys the Tresca or von Mises criterion characterized by C cohesion. We show that the loading parameter to be optimized, γh/C, is found to be between 3.767 and 3.782, and finally, using a recent result of Lyamin and Sloan (Int. J. Numer. Meth. Engng. 2002; 55: 573), between 3.772 and 3.782. The proposed methods, combined with an Interior Point optimization code, prove that linearizing the problem remains efficient, and both rigorous and global: this point is the main objective of the present paper. Copyright © 2003 John Wiley & Sons, Ltd.

In this paper, the implementation of a 3-D parallel CFD code using the meshless method. Reproducing Kernel Particle Method (RKPM) is described. A novel procedure for implementing the essential boundary condition using the hierarchical enrichment method is presented. The Total Arbitrary Lagrangian Eulerian (ALE) formulations using Finite Element Method are developed and implemented in the parallel code. The flow past a cylinder problem served as examples throughout the paper. Both methods have shown promising results compared with analytical solution. Copyright © 2003 John Wiley & Sons, Ltd.

In this paper, a hypersingular integral equation for curved cracks in plane elasticity is formulated and presented. This paper describes a new numerical technique for solution of deep curved cracks in plane elasticity. In this method, the crack curve length is taken as the co-ordinate in the hypersingular integral equation of the curved crack problems. The curved crack configuration maps on the real axis with interval (-a,a), where ‘2a’ is the arc length of the crack. The original hypersingular integral equation is converted into other hypersingular integral equation which is formulated on the curve length co-ordinate, or on (-a,a). The hypersingular integral equation is solved numerically. Numerical examples prove that higher efficiency has been achieved in the suggested method. Copyright © 2003 John Wiley & Sons, Ltd.

The paper presents an algorithm for use with the discrete element method to study possible strain-gradient effects in granular materials. The algorithm produces an intentionally non-uniform displacement pattern by applying external (body) forces to the particles within a simulated granular assembly. The paper describes a method for adjusting the external forces to attain the intended gross displacement pattern, but while allowing individual particles to be in equilibrium among neighbouring particles. The performance of the algorithm is tested in an example of quasi-static deformation, and the algorithm's performance is measured in three respects. The algorithm is shown to enforce the intended displacement pattern, to allow particles to equilibrate among neighbouring particles, and to produce a smooth distribution of the external forces among particles. Copyright © 2003 John Wiley & Sons, Ltd.

In this paper issues related to the imposition of essential boundary conditions in Natural Neighbour Galerkin methods are addressed. Both Sibson and non-Sibson interpolants ability to exactly reproduce essential boundary conditions is investigated and a new analytical condition ensuring linear precision along explicitly described (i.e. CAD) boundaries in both two and three dimensions is presented. The paper is completed with some benchmark numerical examples. Copyright © 2003 John Wiley & Sons, Ltd.

This paper is an extension to an earlier paper dealing with the general problem of integrating special wave elements and specifically deals with quadrilateral elements, which have their own unique problems. The theory for integrating quadrilateral wave finite elements for the solution of the Helmholtz equation for very short waves is presented. The results are compared with those obtained using large numbers of Gauss-Legendre integration points.

A simple method to satisfy the homogeneous boundary condition in the element-free Galerkin method is proposed in this paper. Effectiveness of the method is demonstrated, through free vibration problems of Timoshenko beams. Several case studies involving different slenderness ratios and end conditions are carried out. The results of the present study are compared with those obtained using classical Rayleigh-Ritz and conventional element-free Galerkin method wherein Lagrangian multipliers are employed to satisfy boundary conditions. Eventhough, a one-dimensional problem is considered in the present paper, the validity of the proposed method for the two-dimensional problems is demonstrated theoretically.

Heat sink designers have to balance a number of conflicting parameters to maximize the performance of a heat sink. This must be achieved within the given constraints of size or volume of the heat sink as well as the mass or material cost of the heat sink. This multi-parameter problem lends itself naturally to optimization techniques. Traditionally, an experimental approach was used where different heat sink designs were constructed and their performance measured. This approach is both time consuming and costly. More recently, numerical CFD techniques have been used, but mostly on a trial-and-error basis, and is basically the numerical equivalent of the experimental approach. A better approach is to combine a semi-empirical simulation program with mathematical optimization techniques. This paper describes the use of mathematical optimization techniques to minimize heat sink mass. The simulation uses the Qfin 2.1 code, while the optimization is carried out by means of the DYNAMIC-Q method. This method is extremely robust and specifically designed to handle constrained problems where the objective and/or constraint functions are expensive to evaluate. The paper illustrates how the parameters considered influence the heat sink mass and how mathematical optimization techniques can be used by the heat sink designer to design compact heat sinks for different types of electronic enclosures. Copyright © 2002 John Wiley & Sons, Ltd.

This paper investigates the relationship between the energy- and momentum-conserving time-integration scheme of Simo and Gonzalez (Papers—American Society of Mechanical Engineers—All Series, 1993; 93(4)) and a momentum-conserving time-integration scheme due to Betsch and Steinmann (Int. J. Numer. Meth. Engng 2000; 49: 599) for N-body problems. The schemes are shown to be identical if the potential energy of interaction between masses is a polynomial function of the distances between the masses, of degree two or lower. In addition, they are shown to recover the same relative equilibria. Copyright © 2002 John Wiley & Sons, Ltd.

The paper addresses the development of time-accurate methods for solving transient convection–diffusion–reaction problems using finite elements. Multi-stage time-stepping schemes of high accuracy are used. They are first combined with a Galerkin formulation to briefly recall the time–space discretization. Then spatial stabilization techniques are combined with high-order time-stepping schemes. Moreover, a least-squares formulation is also developed for these high-order time schemes combined with C0 finite elements (in spite of the diffusion operator and without reducing the strong form into a system of first-order differential equations). The weak forms induced by the SUPG, GLS, SGS and least-squares formulations are presented and compared. In a companion paper (Part II of this work), the phase and damping properties of the developed schemes are analysed and numerical examples are included to confirm the effectiveness of the proposed methodology for solving time-dependent convection–diffusion–reaction problems. Copyright © 2002 John Wiley & Sons, Ltd.

Dynamics response of systems to impact or loading may be effectively treated by direct integration. However, it is often difficult to select the time-step of integration properly, especially in the case where the system is badly stiff. Zhong presented an explicit direct integration scheme, HPD, for the homogeneous systems. This paper extends HPD scheme to analyse systems with loading or impact, through Fourier expansion and homogenizing the initial system. Compared with other methods, the new scheme named homogenized high-precision direct integration (HHPD) has a higher precision and wider application and is less time-consuming, and several examples in this paper show HHPD's effectiveness in engineering. Copyright © 2002 John Wiley & Sons, Ltd.

In this paper, it is shown that the symmetric Galerkin boundary element formulation cannot be used in its standard form for multiple connected bodies. This is because the traction integral equation used for boundaries with Neuman boundary condition give non-unique solutions. While this fact is well known from the classical theory of integral equations, the problem has not been fully addressed in the literature related to symmetric Galerkin formulations. In this paper, the problem is reviewed and a general way to deal with it is proposed. The details of the numerical implementation are discussed and an example is solved to demonstrate the effectiveness of the proposed solution. Copyright © 2001 John Wiley & Sons, Ltd.

Logical identification covers a wide range of applications dealing with constrained transformation processes between internal and external models of sequential systems. In this paper, we consider the differential identification approach whose purpose is to measure the influence of minor modifications of the internal or external models of an existing system. This class of identification is dedicated to sensitivity analysis: learning, redesign, diagnosis, etc. Thus, it reveals all its interest for the study of systems which have to adapt themselves to an evolving environment. This paper presents an overall view of the different differential identification approaches and their corresponding applications. We will propose a new resolution technique based on genetic simulation. In a second paper, we will focus on some experiments performed with a genetic identification tool. Copyright © 2001 John Wiley & Sons, Ltd.

This paper reports an intercomparison of three second-order accurate reconstruction schemes to predict 2D steady-state compressible Euler and Navier–Stokes flows on unstructured meshes. The schemes comprise one monotone slope limiter (Barth and Jespersen, A1AA Paper 89-0366, 1989) and two approximately monotone methods: the slope limiter due to Venkatakrishnan and a data-dependent weighting least-squares procedure (Gooch, Journal of Computational Physics, 1997; 133:6–17). In addition to the 1D scalar wave problem, comparisons were performed under two inviscid test cases: a supersonic 10° ramp and a supersonic bump; and two viscous laminar compressible flow cases: the Blasius boundary layer and a double-throated nozzle. The data-dependent oscillatory behaviour is found to be dependent on a user-supplied constant. The three schemes are compared in terms of accuracy and computational efficiency. The results show that the data-dependent procedure always returns a numerical steady-state solution, more accurate than the ones returned by the slope limiters. Its use for Navier–Stokes flow calculations is recommended. Copyright © 2001 John Wiley & Sons, Ltd.

This short paper re-visits an earlier paper by Nagtegaal and Slater in which a quadrilateral shell element was derived which used similar kinematics to that in the Morley facet shell. Because the paper seems to be relatively unknown and also is rather long and involved, we here concentrate on the plate-bending aspects of the element and describe the shape functions. Copyright © 2001 John Wiley & Sons, Ltd.

The idea of the paper is to present theoretical aspects and finite element method implementation of the sensitivity analysis in homogenization of linear elastic fibre composites by the use of effective modules homogenization approach. The deterministic sensitivity approach to the homogenization problem is presented in a general form for n-component composite and is illustrated in the example of two-dimensional fibre-reinforced periodic composite structure. The results of sensitivity analysis shown in the paper confirm the usefulness of the homogenization method to computational analysis of composite materials and may be successfully applied to numerical optimization of engineering composites and to their shape sensitivity studies.

This paper compares the parallel efficiency of three Gram–Schmidt orthonormalization algorithms: modified Gram–Schmidt, classical Gram–Schmidt, and iterated classical Gram–Schmidt. The paper shows how these algorithms can be implemented on a parallel computer, and how their communication overhead can be minimized. In addition, it briefly examines the numerical properties of these algorithms. Finally, it provides some guidelines for selecting the most appropriate algorithm. Copyright © 2000 John Wiley & Sons, Ltd.

This paper describes a new technique to stabilize meshless methods used in conjunction with point-based integration. The method proposed is based on the finite increment calculus (FIC) concepts for convection-dominated problems. In this paper a finite increment gradient operator is defined in such a way that second-order derivatives are included. This operator is then used in the context of a variational formulation of an elliptic problem in order to define a stabilized numerical procedure. For simplicity, the Poisson equation will be used in this paper to illustrate the method, although more general elliptic problems can be equally treated. An eigenvalue analysis will be carried out in order to demonstrate that no mechanisms are present in the resulting equations. Finally, a simple example will illustrate the technique. Copyright © 2000 John Wiley & Sons, Ltd.

SUMMARY In this paper a simple way to describe the eects of microscopic damage on the global behaviour of periodic composite materials is shown. The microscopic damage is interpreted as a local reduction in material stiness as presented in Zohdi et al. [1]. Choosing the damage parameters in an opportune manner a great variety of dierent damage constitutive laws can be studied. The macroscopic constitutive law for damaged periodic composites is obtained with a homogenization procedure described in Pellegrino et al. [2]. A comparison between the results of homogeneous and heterogeneous constitutive models is shown. Copyright ? 2000 John Wiley & Sons, Ltd. In this paper two simple numerical techniques are combined to study the eect of microscopic damage on the global behaviour of a periodic composite material. The microscopic damage is represented, following Zohdi et al. [1], as a reduction of the eigenvalues of the material stiness tensor aecting the point where a given condition is violated. The local consequences of the damage process, such as redistribution of stresses or development of fractures, are not the main objective of this paper. On the contrary, we aim at describing the eect that the local reduction of the stiness has on the global behaviour of a macroscopic structure. Since a precise description of the ne scale material distribution would require an enormous number of nodes, in the nite element model, and therefore a large computer time to solve the problem, a homogenization approach is considered. In this manner a much simpler mesh can be adopted for the global problem to reduce the solution time. The paper is organized as follows: in Section 2 a brief description of the damage model is given followed in Section 3 by some words on the homogenization procedure. Section 4 presents some results which highlight the potentialities of the method and nally some concluding remarks close the paper.

There exist quite a number of published papers showing that BEM/FEM coupling in time domain is a robust procedure leading to great computer time savings for infinite domain analyses. However, in many cases, the procedures presented so far have considered only constant time interpolation for BEM tractions, otherwise one may have (mainly in bounded domains) strong oscillations which invalidate the results. In this paper, such a limitation is overcome by employing the linear 0 method which consists, basically, of computing the response at the time t n+1 from the response previously computed at the time t n+θ , θ ≥ 1.0. This procedure is implicitly incorporated into the BEM algorithm in the coupled BEM/FEM process presented here, i.e. the response is calculated directly at time t n+1 . Proceeding this way, it becomes possible to adopt the Newmark scheme in the FEM algorithm. Two examples are presented in order to validate the formulation.

This paper presents a simplified formula that can be used to obtain the detailed heat transfer rate and temperature distribution on the surfaces of square and non-square cooling channels of a nozzle guide vane (NGV). Due to the three-dimensional shape of the internally cooling channels, the heat transfer rate can vary substantially between the different sides of the channels. This detailed heat flux and resulting temperature distribution on the walls are important to improve the design of the airfoil as well as to determine the expected usable life of the NGV. This detail heat transfer data is usually obtained by means of a complex three-dimensional simulation of the NGV configuration. Therefore, for design purposes, the heat transfer data on the channel surfaces is often assumed to be the average heat transfer rate on the channel walls. The average heat transfer rate can be obtained by using a simplified heat transfer equation, based on the average Reynolds number in the channel. The simplified formula presented in this paper can be used to obtain the detailed heat transfer rate and temperature distribution on the surfaces of square and non-square cooling channels of a nozzle guide vane (NGV). The simplified formula is based on results obtained from three-dimensional simulations of the heat transfer in the channels and was compared to simulated and experimental data over a range in flow rates and channel geometries. In general, it can be concluded that the formulation produces fast and accurate results over a wide range of applications. Copyright © 2000 John Wiley & Sons, Ltd.

In a previous paper (Wang, 1996) an integral equation method was given for the non-linear analysis of U-shaped bellows with uniform wall thickness. However, the wall thickness of a real U-shaped bellows varies along its profile. This paper is a continuation of the previous paper. A U-shaped bellows is still treated as a composite member consisting of circular ring shells and truncated shallow conical shells, but now the wall thickness of the truncated shallow conical shells varies with the radial co-ordinate. By using the Green function method, the non-linear integral equations of the circular ring shells and the truncated shallow conical shells are separately derived. They include four unknown parameters which are determined by junction conditions. The combined numerical procedure and corresponding program, in which the iteration method and the gradient method are respectively applied to solve the non-linear integral equations and to get approximate values of the four unknown parameters, are developed for the non-linear analysis of U-shaped bellows. Numerical results show that it is necessary to consider the wall-thickness variation; thus the decay rate of wall thickness should be taken as an important engineering parameter in the design of bellows. Copyright © 1999 John Wiley & Sons, Ltd.

A linear θ method is used in this paper to improve the stability of the standard time-domain BEM formulation. The time-stepping procedure is similar to that of the Wilson θ method; however, unlike in the FEM, where linear time variation of acceleration (for elastodynamic problems) is assumed, here linear time variation for both potential and flux (for scalar waves) is assumed in the time interval θΔt. A comparison between numerical results obtained from the standard formulation and from the linear θ method studied here shows the latter to be more stable than the former. The effect of varying θ for different values of time steps is also studied in this paper. Copyright © 1998 John Wiley & Sons, Ltd.

In this paper a new technique is presented for transferring the domain integrals in the boundary integral equation method into equivalent boundary integrals. The technique has certain similarities to the dual reciprocity method (DRM) in the way radial basis functions are used to approximate the body force term. However, the resulting integrals are evaluated in a much simpler way. Several examples are presented to demonstrate the validity and accuracy of the proposed paper.

The paper presents a general method of large strain determination over the deformed surface of a sheet metal stamping. It is demonstrated that the conventional degenerated shell element with two normal rotation degrees of freedom is not suitable for large deformation, especially when large element rotation is present. This inaccuracy is primarily caused by the fact that the displacement field description used in the degenerated shell element is only a first-order approximation with respect to the two rotation degrees of freedom, and is therefore suitable only for small rotation angles. The new method presented in this paper replaces the two rotation DOFs with three new degrees of freedom to describe the rotation of the surface normal so that the element deformation can be accurately described with no limitation on the amount of deformation and rotation involved. The advantages of this new method are: (i) a linear and accurate expression of the displacement field in terms of nodal DOFs is obtained; (ii) the formulation is easily incorporated into any existing degenerated shell elements; (iii) the strain calculation is accurate for any amount of element rigid body rotation; (iv) if the method is used in surface grid analysis, the algorithm will not only provide correct surface strains, but also their variation through the thickness direction, i.e. the bending deformation.