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This paper represents a macroscopic constitutive law for domain switching effects, which occur in piezoelectric ceramics. The thermodynamical framework of the law is based on two scalar valued functions: the Helmholtz free energy and a switching surface. In the general sense of a kinematic hardening process, the movement of the centre of the switching surface is controlled by internal variables. In common usage, these are the remanent polarization and the irreversible strain. The novel aspect of the present work is to introduce an irreversible electric field, which serves besides the irreversible strain as internal variable. The irreversible electric field has only theoretical meaning, but it makes the formulation very suitable for a finite-element implementation, where displacement and the electric potential are the nodal degrees of freedom. The constitutive model successfully reproduces the ferroelastic and the ferroelectric hysteresis as well as the butterfly hysteresis for piezoelectric ceramics. Furthermore, it accounts for the mechanical depolarization effect, which occurs if the polarized piezoceramic is subjected to a compression stress. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The objective of this paper is the construction of a robust strategy towards adaptively solving Signorini's frictional contact problems. The frictional contact problem between a linearly elastic body and rigid foundation is formulated as a classical boundary value problem of the elastic body but associated with special inequality conditions on the contact surface. A new iterative approach is presented to solve the problem on a given mesh. In the first iteration the candidate nodes are assumed to be in micro-slip contact and then proceeding to update the contact status according to the actual displacements and stresses obtained at the end of each increment. An efficient multigrid method is developed to solve the discrete problems of different iterations. The proposed iterative procedure is integrated with an error indicator and automatic grid generator to construct an adaptive multigrid method. Numerical results of the convergence rates, automatically generated grid sequence, contact stresses and strains as well as two parametric studies are presented to prove the efficiency of the proposal. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The variational indirect boundary element method is widely used in many acoustical problems such as simulation of scattering and radiation phenomena. Although it has many advantageous features in dealing with those problems, it suffers from the singularity problem when the double surface integral is done over the same element. In this paper, a straightforward technique for computing the singularity 1/R over triangular element is presented. It is based on a generalized polar co-ordinates transformation to transform the triangular master element into a square one. The singularity factor is taken as weight function. Consequently, a single straightforward implementation without any special treatment of singularity is possible for meshes involving both quadrilateral and triangular elements of higher order. The efficiency of the proposed method is demonstrated for some numerical examples. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a fully implicit scheme for approximating two-phase flow in heterogeneous porous media. The primary unknowns are the wetting phase pressure and non-wetting phase saturation. At each time step, a Jacobian matrix is computed. Convergence of the scheme is shown via increase of the polynomial degree. No slope limiters are needed. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We develop a numerical method to solve $$L_{\varepsilon} u_{\varepsilon} =- {{\partial} \over {\partial x_{i}}} a_{ij} (x / \varepsilon ) {{\partial} \over {\partial x_{j}}} u_{\varepsilon} = f \quad {\rm in} \, \, \Omega, \quad u_{ \varepsilon} =0 \quad {\rm on} \, \, \partial \Omega $$ where the matrix a(y)=(aij(y)) is symmetric positive definite, whose entries are periodic functions of y with periodic cell Y. More specifically we assume $ a_{ij} \in C^{1, \beta} (\Re^{2}), \quad \beta > 0 $. It is also assumed that there exists positive constants γa and βa such that $ \gamma_{a} ||\xi ||^{2} \le a_{ij} (y) \xi_{i} \xi_{j} \le \beta_{a} ||\xi||^{2} $ for all $ \xi \in \Re^{2} $ and $ y \in {\bar Y} $. The major goal in this paper is to develop a numerical approximation scheme on a mesh size h > ℇ (or h≫ℇ) with quasi-optimal approximation on L2 and broken H1 norms. The new method is based on asymptotic analysis and a careful treatment of the boundary corrector term. This kind of equation has applications in areas such as the study of flow through porous media and composite materials. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper deals with the boundary integral formulation for solution of 3-D axial symmetric problems of stationary thermo-elasticity with including the domain heat sources. The domain integral of heat sources is converted into boundary integrals of a new field variable and another summation term involving the function values of another field variable at isolated interior points. Making use of the triple-reciprocity method, the unknown boundary densities as well as the interior point unknowns are computed by solving the integral equations without the need to use domain cells in discretization. The integral kernels involved in the developed boundary integral formulation for axial symmetric problems are received by angular integration of 3-D kernels with using cylindrical co-ordinates. The explicit expressions of the kernels are collected in appendix and two numerical examples are considered for illustration of the accuracy and efficiency of the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a new algorithm to map a given mesh over a source surface onto a target surface. This projection is determined by means of a least-squares approximation of a transformation defined between the loops of boundary nodes of the cap surfaces in the parametric spaces. Once the new mesh is obtained on the parametric space of the target surface, it is mapped to the target surface according to its parameterization. Therefore, in contrast with the usual techniques, the developed algorithm does not require solving any root finding problem to ensure that the projected nodes are on the target surface. Finally, this projection algorithm is extended to three-dimensional cases and included in a sweep meshing tool in order to generate the inner layers of elements in the physical space. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper reports on the non-linear static analysis of 2D concrete structures using an hybrid-mixed stress formulation and continuum damage mechanics. The finite element model adopted is based on the direct and independent approximation of three fields: the effective stress and displacement fields in the domain of each element and the displacement field on the static boundary. The non-linear behaviour of the material is modelled with a non-local isotropic damage model. A set of numerical examples are presented to illustrate and validate the use of such numerical technique. The performance of the model is assessed by comparison with results obtained using other numerical schemes presented in the literature and also with experimental results. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper reports a new Chebyshev spectral collocation method for directly solving high-order ordinary differential equations (ODEs). The construction of the Chebyshev approximations is based on integration rather than conventional differentiation. This use of integration allows the multiple boundary conditions to be incorporated more efficiently. Numerical results show that the proposed formulation significantly improves the conditioning of the system and yields more accurate results and faster convergence rates than conventional formulations. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a new principle of geometric design for blade's surface of an impeller is established. This is a thorough mathematical investigation of a shape control problem for the optimal design of an impeller's blade while 3D rotating Navier–Stokes equations are as the state equations in the control problem. The objective is to design the blade such that the viscous drag is minimized. Establishing a new curvilinear coordinate system, we depart from a standard domain transformation commonly used in the engineering literature and utilizing it we rephrase the design problem in one on a fixed domain. Certain advantages of our approach as no need for mesh regeneration and node redistribution and 3D mesh quality improvement are evident. Furthermore, in new coordinate system, it is easy to obtain gradient of optimal functional with respect to the surface of blade and to derive Euler–Lagrange equations for optimal solution which is an elliptic boundary value problem of fourth order. Moreover, we give the conjugate gradient algorithm for the control problem. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we present and analyse some local and parallel covolume algorithms for second-order elliptic problems. We first prove some local a priori error estimates for covolume method. With these results, we shall apply the two-grid strategy to covolume approximation to give two novel covolume algorithms, and show that the convergence rates of these algorithms are optimal in piecewise H1-norm. Numerical results confirming the theory are also provided. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a numerical method for determination of reworking or scraping defective items in a finite production rate model with backlogging permitted. In most practical manufacturing settings, due to process deterioration or other factors, generation of defective items is inevitable. The defective items can either be repaired or be discarded. In the finite production model we studied, the defective rate is assumed to be a random variable and the rework process can start immediately when regular production ends. The optimal lot sizes and the expected annual inventory costs for the cases of production systems with the rework process and without the rework process are compared and analysed. A set of numerical equations are developed to assist in determining on whether or not it is beneficial to rework defective items. A numerical example is provided to demonstrate their practical usages. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

It is well known that numerical methods designed to solve the compressible Euler equations, when written in terms of conservation variables behave poorly in the incompressible limit, that is, when density variations are negligible. However, a change to pressure based variables seem to, partly, eliminate the problem by making the Jacobian matrices fully invertible whatever the flow regime may be. Despite this apparent benefit, the stabilization matrix plus discontinuity capturing operator (for the compressible regime) still need attention, since they tend to be ill behaved for either conservation or pressure variables. In this paper, we introduce a simple way of balancing two stabilizing matrices, one of them suitable for low Mach flows and the other one for supersonic flows, so that a wide range of flow regimes are covered with only one formulation. Comparison between conservation and pressure variables is made and numerical examples are shown to validate the method. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the famous Adini's non-conforming finite element for plate-bending problems on anisotropic meshes. Without the regular assumption on the meshes, the interpolation error and consistency error estimates are both of order O(h2) (h is the maximum diameter of elements), which improves the conventional results of this element. Lastly, a numerical test is carried out, which coincides with our theoretical analysis. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, Newton-like iteration methods for solving non-linear equations or improving the existing iteration methods are proposed. The iteration formulae are obtained by applying the homotopy perturbation method which contains the well-known Newton iteration formula in logic, so those improving the Newton method. The orders of convergence of some of those iteration formulae are derived analytically and by applying symbolic computation of Maple. Some numerical illustrations are given. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents two sets of the Hamiltonian for checking errors of approximated solutions. The first set can be applied to those problems having any number of independent and dependent variables. This set of the Hamiltonian can effectively indicate the errors of approximated solutions when requiring a high accuracy. The second set of the Hamiltonian has the invariant property when the Lagrangian is not an explicit function of time, even for non-conservative systems. Both sets can be formulated as error indicators to check errors of approximated solutions. Three illustrative examples demonstrate the error analyses of finite element solutions. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with static reanalysis of a structure with added degrees of freedom where the nodes of the original structure form a subset of the nodes of the modified structure. A preconditioned conjugate-gradient approach is developed. The preconditioner is constructed, and the implementation of the approach involves only decomposition of the stiffness matrix corresponding to the newly added degrees of freedom. In particular, the approach can adaptively monitor the accuracy of approximate solutions. The approach is applicable to the reanalysis of the structural layout modifications for the case of addition of some nodes, deletion and addition of elements and further changes in the geometry as well as to the local mesh refinements. Numerical examples show that the condition number of the selected preconditioned matrix is largely reduced. Therefore, the fast convergence and accurate results can be achieved by the approach. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The geometrical view (configuration) factor plays a crucial role in radiative heat transfer simulations and several methods, such as integration, the Monte Carlo and the hemi-cube method have been introduced to calculate view factors in recent years. In this paper the Monte Carlo method combined with the finite element (FE) technique is investigated. Results describing the relationships between different discretization schemes, number of rays used for the view factor calculation, CPU time and accuracy are presented. The interesting case where reduced accuracy is obtained with increased refinement of FE mesh is discussed. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We developed in this paper a variational formulation of heat diffusion equation applicable to the flat shell context and cellular structures. For this purpose, we introduce the average mid-surface temperature field, through-the-thickness gradient and their dual generalized fluxes. Moreover, we introduced radiative heat exchange in the same way, which leads to a non-linear and unsymmetrical thermal discrete problem. The model performance is illustrated by several numerical examples concerning cellular structures like hollow clay bricks submitted to thermal loading. Thermo-mechanical coupling for such structure which is well adapted to the shell-like modelling approach, is presented in the elastic regime with the numerical results concerning temperature field and forces. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the properties of previously developed Form II symmetry (Commun. Numer. Meth. Engng 2003; 19:125–136; 2004; 20:133–146) is further investigated. Additivity properties of graphs with this form are formulated, and the effect of adding or deleting members on the eigenvalues of the Laplacian matrices of the corresponding graphs, is studied. Depending on the category of the added or deleted members, the condensed submatrices on which changes occur are identified, and the necessary modifications are suggested. A mass-spring dynamic system is presented to illustrate a typical application of the latter approach. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The correct design of flexible and rigid supports improves the performance of structures, by reducing deflections or increasing natural frequencies. The optimization of the location of rigid supports is difficult because the support reduces the number of modelled degrees of freedom. This paper introduces efficient methods for the analysis of models where the support occurs within the element. This allows a single relatively coarse element mesh to be used, while still providing accurate predictions of the effect of the support on the structure's static and dynamic response. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Runoff regulation of hydropower station is always an important point and difficult issue for researchers and engineers, and different methods have been advanced for obtaining simple and accurate results, but they do not often do good work. In this paper a new approach is presented to regulate runoff of hydropower station that through iterative equation for turbine discharge and construct numerical computation for runoff regulation of hydropower station. A case shows that the solution is simple, accurate and easy to use in practice. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper delivers an efficient solution technique for the numerical simulation of crack propagation of 2D linear elastic formulations based on finite elements together with the conjugate gradient method in order to solve the corresponding linear equation systems. The developed iterative numerical approach using hierarchical preconditioners has the interesting feature that the hierarchical data structure will not be destroyed during crack propagation. Thus, it is possible to simulate crack advance in a very effective numerical manner, including adaptive mesh refinement and mesh coarsening. Test examples are presented to illustrate the efficiency of the given approach. Numerical simulations of crack propagation are compared with experimental data. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An algorithm combining the numerical execution in time of implicit and explicit methods of solution is presented in this paper. The algorithm swaps between both methods as required for the analysis. The whole mesh is solved for an unique method at once, i.e. there are no partitions of the mesh for separate implicit or explicit treatment of the solution. The combination is in-time, in such a manner that if the implicit method starts diverging the explicit one is initiated by appropriate conditions of transition. The formulation is presented first and its implementation is validated by the analysis of a key numerical example. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Unstructured mesh based discretization techniques can offer certain advantages relative to standard finite difference approaches which are commonly used in reservoir simulation, due to their flexibility to model complex geological features and to their ability to easily incorporate mesh adaptation. Within such class of methods the most frequently used are the finite element method (FEM) and the finite volume method (FVM). The latter is particularly attractive in reservoir problems due to its local and global conservation properties. The main goal of the present paper is to describe an unstructured edge-based FVM formulation which is used to solve the partial differential equations resulting from the modelling of two-phase fluid flow of oil and water in homogeneous porous media, when an IMPES (IMplicit Pressure Explicit Saturation) approach is used. This finite volume formulation is similar to the edge-based FEM formulation when linear triangular or tetrahedral elements are employed. Some model examples are presented in order to validate the presented formulation. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We present a rotation-free, subdivision-based, isoparametric quadrilateral finite element for the analysis of doubly-curved thin shells. The element is a generalization of spline-based C1 finite elements to curved domains, and general mesh connectivity. It uses semi-local basis functions that span the two-neighbourhood of a node. The traditional difficulty with this class of elements comes from the fact that these basis functions depend on the valence of the nodes of the element. For elements with 4-valence nodes the basis functions are bicubic polynomials, but there are no simple closed-form expressions for them when the nodes have general connectivity patterns. In the paper, we show how the basis functions for the general case may be efficiently evaluated as linear combinations of translation and scaling transformations of the bicubic polynomials. The performance of the resulting element is illustrated on a hemispherical shell model problem. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the discontinuous Galerkin (DG) finite element method is applied to simulate high-temperature equilibrium airflows. Two approximate Riemann solvers are used to compute the advective flux. A second-order TVD Runge–Kutta time integration scheme is employed to march the solution in time. The extension to equilibrium chemistry is implemented by using the effective &gamma approach. The effective &gamma is obtained through a polynomial curve fit. With this approach, the computation of the species composition of the equilibrium air can be completely separated from the main solver. Several numerical examples are provided to demonstrate the effectiveness and accuracy of the DG method in chemically reacting airflows. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper exposes an interior-point method used to solve convex programming problems raised by limit analysis in mechanics. First we explain the main features of this method, describing in particular its typical iteration. Secondly, we show and study the results of its application to a concrete limit analysis problem, for a large range of sizes, and we compare them for validation with existing results and with those of linearized versions of the problem. As one of the objectives of the work, another classical problem is analysed for a Gurson material, to which linearization or conic programming does not apply. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper a high-order discontinuous Galerkin method is used to solve steady-state isothermal line contact elastohydrodynamic lubrication problems. This method is found to be stable across a wide range of loads and is shown to permit accurate solutions using just a small number of degrees of freedom provided suitable grids are used. A comparison is made between results obtained using this proposed method and those from a very large finite difference calculation in order to demonstrate excellent accuracy for a typical highly loaded test problem. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Groundwater modelling is made difficult by the large uncertainties on the different modelling components: structural errors related to the model parameterization, parameter uncertainty, and errors in the forcing terms. This paper proposes an approach to parameter identification of the leakage aquifer using the model of coupled finite element method and Kalman filter. The method considers the uncertainty of groundwater flow system. Therefore, the stochastic and deterministic parameters are identified in numerical simulation processes. Statistical tests, the Student's test and Chi-square test are applied to examining the mean and deviance values between the observed and simulated heads at specified confidence interval. A case study for parameter identification of a leakage aquifer system in Daqing region of China shows that the reliability of parameter estimation reaches 90%. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An efficient and accurate locking-free corotational beam finite element for the analysis of large displacements and small-strain problems is developed in this paper. Three different finite element models based on three different beam theories, namely, the Euler–Bernoulli, Timoshenko, and simplified Reddy theories are presented. In order to develop a single corotational finite element that incorporates the kinematics of all three theories, the unified linear finite element model of beams developed by Reddy (Comm. Numer. Meth. Eng. 1997; 13:495–510) is included in the formulation. An incremental iterative technique based on the Newton–Raphson method is employed for the solution of the non-linear equilibrium equations. Numerical examples that demonstrate the efficiency and large rotation capability of the corotational formulation are presented. The element is validated by comparisons with exact and/or approximate solutions available in the literature. Very good agreement is found in all cases. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a method for generating multi-resolution adaptive triangulations of non-manifold 3D objects composed of several regions with arbitrary geometry. The process first immerses the input boundary elements inside a semi-regular adaptive tetrahedral mesh known as a BMT triangulation. The mesh elements are then pushed towards the boundary by means of a physically based compression scheme, more specifically, a mass-spring system. The final triangulation has no degenerated tetrahedra and provides an approximation of the boundary based on a chosen resolution. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The computational significance of the case of two or three equal principal stretches in large deformation analysis is investigated in this paper. A detailed analytical study shows that the previously suggested solutions, based on numerical perturbations, are not adequate and might lead to erroneous results. A number of examples are presented to illustrate the approach. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, incorporating the hybrid method and the mixed interpolation method into a unified optimization framework, a 4-node quadrilateral plate element with bilinear displacement approximations is proposed. By an energy optimization tactic, among all of assumed linear bending moment modes, a 5-parametric optimal bending moment mode is selected. Using the optimal bending moment mode to improve the well-known plate element MITC4, the optimized plate element numerically possesses high accuracy at the coarse meshes in the analysis of thin/thick plates. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper new forms are introduced for efficient eigensolution of special tri-diagonal and five-diagonal matrices. Applications of these forms are illustrated using problems from mechanics of structures. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper presents a formulation for geometrically non-linear anisotropic elastic material behaviour. To this end the space of symmetric second order tensors related to the undeformed reference configuration is decomposed into invariant subspaces characterizing the symmetry conditions of the specific material. The subspaces are equipped with tensor bases, which have been determined in the literature for several material classes, such as cubic symmetry, transverse isotropy and complete isotropy. Upon formulating a free energy function in terms of generalized Seth–Hill strain tensors projected onto the subspaces, the symmetry conditions characterizing the specific material are satisfied a priori. From standard results of continuum mechanics the corresponding Lagrangian stress tensor and elastic moduli are obtained by straightforward application of the chain rule. Representative examples in one-dimensional loading illustrate the material behaviour of cubic symmetry for elastic materials. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper investigates the applicability of a recently proposed global functional set based on ‘3-D Coons' interpolation formula’, in the static and dynamic analysis of box-like elastic structures. According to the proposed methodology, only the 12 edges of the entire hexahedral-like structure should be discretized into a small number of nodal points. In this way, the dimensionality of the problem is drastically reduced from three to one, in the sense that instead of the volume, only the control lines being absolutely necessary to define the geometric model should be considered in the analysis. Preliminary results obtained for paralleloidal and cylindrical beams in tension, bending and torsion, as well as an internally pressurized thick-walled cylinder were found to be encouraging for the static analysis. Moreover, the natural frequencies of a rectangular clamped beam were calculated with excellent accuracy. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

It is well known that conforming finite element schemes exhibit Poisson locking in the incompressible limit as the Poisson ratio ν tends to 1/2. A remedy for this is to use a non-conforming method (Math. Comput. 1992; 59:321-328) in which an a priori error bound is proved for the Crouzeix–Raviart scheme. In this paper we derive a new a priori estimate for the error in energy for the Fortin–Soulie finite element method using a method similar to that used in Brenner and Sung. We then illustrate the new error bound by presenting some numerical examples. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a unified method is developed for calculating the eigenvalues of the weighted adjacency and Laplacian matrices of three different graph products. These products have many applications in computational mechanics, such as ordering, graph partitioning, and subdomaining of finite element models. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Imposition of essential boundary conditions in meshfree methods is made difficult because the shape functions used do not possess the ‘delta’ property. Various procedures have been proposed including penalty, Lagrange multipliers and collocation. It is shown in this paper that the success of a procedure depends on the arrangement of the nodal points. Certain methods of imposing boundary conditions are shown not to work for unstructured nodal arrangements. Much previous work has been demonstrated using structured grids thus hiding these drawbacks. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a new iterative solver for least-squares problems, which is developed based on the Levenberg–Marquardt and trust region methods. The proposed iterative solver substantially reduces computing time compared with the conventional Levenberg–Marquardt scheme, and can be efficiently applied to large-scale problems. Three numerical examples are used to demonstrate the effectiveness of the proposed solver. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper we propose a wavelet Taylor–Galerkin method for the numerical solution of time-dependent advection–diffusion problems. The discretization in time is performed before the spatial discretization by introducing second- and third-order accurate generalization of the standard time stepping schemes with the help of Taylor series expansions in time step. Numerical schemes taking advantage of the wavelet bases capabilities to compress both functions and operators are presented. Numerical examples demonstrate the efficiency of our approach. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a rigorous analysis of the tunable circular microstrip patch is performed using a dyadic Green's function formulation. To make the theoretical formulation more general and hence valid for various antennas structures (not only limited to tunable microstrip patch); the dyadic Green's function is derived when the patch is assumed to be embedded in a multilayered dielectric substrate. A very efficient technique to derive the dyadic Green's function in the vector Hankel transform domain is proposed. Using the vector Hankel transform, the mixed boundary value problem is reduced to a set of vector dual integral equations. Galerkin's method is then applied to solve the integral equation where two sets of disk current expansions are used. One set is based on the complete set of orthogonal modes of the magnetic cavity, and the other consists of combinations of Chebyshev polynomials with weighting factors to incorporate the edge condition. Convergent results for these two sets of disk current expansions are obtained with a small number of basis functions. The calculated resonant frequencies and quality factors are compared with experimental data and shown to be in good agreement. Finally, numerical results for the air gap tuning effect on the resonant frequency and half-power bandwidth are also presented. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Physical loading sometimes causes crack face contact and frictional sliding. The relative sliding of the face induces modes II and III types of stress intensities at the crack tip region. This paper discusses domain integral method of calculating the J integral when crack face contact and sliding by friction are considered for general cracked geometries. The scheme of including crack face contact and sliding is implemented in a finite element code. Numerical examples are presented to show the accuracy for J integral value in this case. In addition, we present an approach for mesh design flexibility at the crack tip region to suit complicated engineering geometries. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The problem of the buckling of finite length externally constrained thin circular cylinders is solved to yield a generalized eigenvalue problem with constraint conditions. The solution is based on an inverse iteration procedure in which the non-linear complementary equation is solved by a non-smooth version of Newton's method that saves computer time and space when compared to a linear complementary algorithm. The numerical results show that the method proposed is effective and that the critical buckling load of the constrained cylinder is almost independent of the length of the cylinder, unlike the critical load of free (unconstrained) thin cylinders. In the direction of its axis, the shell is discretized by finite strips which circumferentially use straight bar and beam displacement functions. It is proved that when the widths of the strips approach zero, the geometrical relationships used in this paper approach those of Koiter–Sanders cylindrical shell theory. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A higher-order boundary element method (BEM) recently developed by the current authors (Comput Methods Appl Mech Eng 2003; 192: 4281–4298; 4299–4312; 4313–4335) for time-dependent convective heat diffusion in two-dimensions appears to be a very attractive tool for efficient simulations of transient linear flows. However, the previous BEM formulation is restricted to relatively small time step sizes (i.e. &Deltat⩽4κ/V2) owing to the convergence issues of the time series for the kernel representation within a time interval. This paper extends the boundary element formulation in a way to allow time step sizes several orders of magnitude larger than in the previous approach. We consider an example problem of thermal propagation, and investigate the accuracy and efficiency of BEM formulations for Peclet numbers in the range from 103 to 105. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we develop a non-iterative way to solve biharmonic boundary value problems by using a radial basis meshless method. This is an original application of meshless method to solving inverse problems without any iteration, since traditional numerical methods for inverse boundary value problems mainly are iterative and hence very time-consuming. Numerical examples are presented for inverse biharmonic boundary value problems and corresponding direct problems, since solving direct problems is a preliminary step for inverse problems. All our examples of direct and inverse problems are solved within seconds in CPU time on a standard PC, which makes our proposed technique a great potential candidate for wide-spread applications to other inverse problems. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In variational and optimization problems where the field variable is represented by a series of functions that individually do not satisfy the constraints, penalty functions are often used to enforce the constraint conditions approximately. The major drawback with this approach is that the error due to any violation of the constraint is not known. In a recent publication dealing with the Rayleigh–Ritz method it was shown that, by using a combination of positive and negative penalty parameters, any error due to the violation of the constraints may be kept within any desired tolerance. This paper shows that this approach may also be used in solving partial differential equations using a Galerkin's solution to Laplace's equation subject to mixed Neumann and Dirichlet boundary conditions as an example. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes a finite element solution algorithm for the numerical solution of large size three-dimensional flow problems on a personal computer. To demonstrate the algorithm, the Stokes equations in velocity–vorticity form are solved for a lid-driven cubical cavity problem. The Galerkin's weighted residual form of the governing equations is evaluated for all the elements of the computational domain and kept as element-matrices and element-vectors. This results in a set of simultaneous equations corresponding to the global nodes of each element. Those elements that contain the boundary nodes are modified to incorporate the Dirichlet boundary conditions. A conjugate gradient iterative scheme is employed to solve the simultaneous equations in element form to get the solution at the global nodes. The matrix–vector products used in the conjugate gradient iterative solver are performed in element level, assembling only the element-level vectors to form the global vectors. Since the element-level computation has eluded the formation of global matrices, the numerical solution of three-dimensional Stokes equations using a mesh of size as high as 513 could be achieved on a personal computer. The algorithm is validated by comparing the results for a three-dimensional transient diffusion problem and Stokes flow in a lid-driven cubical cavity. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The shape of grains or of cross-sections of fibres in a two-phase elastic material has an important influence on the overall mechanical behaviour of the composite. In this paper a numerical scheme is devised for determining the optimal shape of a two-dimensional grain or of a fibre's cross-section. The optimization problem is first posed mathematically, using a global objective function, and then solved numerically by the finite element method and a specially designed global optimization scheme. Excellent agreement is obtained with analytical results available for extreme cases. In addition, optimal shapes are obtained under more general conditions. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]