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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Recent work has shown that many ceramic fibres which are increasingly used to line industrial furnaces have highly spectral-dependent emissivities. This paper presents an extension to the standard zone method for radiative heat transfer calculations which directly models spectral variation in surface and gas properties. A short description of the zone method is given along with a summary of the weighted sum of grey gases model. This is often used as a means of representing the temperature dependence of total gas properties brought about because of the spectral non-uniformity of these properties. When surfaces as well as the gas are non-grey, a new approach is required. The method of this paper is based on dividing the spectrum into a number of bands and treating the properties as constant within each band. This method can be used directly if the boundary conditions specify all the zone temperatures. However, if some temperatures are unknown, then an iterative solution technique is required. Results of some sample calculations are presented. These illustrate the importance of directly modelling the spectral behaviour of gas and surface properties. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the problem for evaluating the eigenvalues in the buckling problem and the natural vibration problem of the bending bar is reduced to finding zeros of a function, which is called the target function T(ω) in this paper. The explicit forms of the target functions can be obtained for all possible boundary value problems. The functions depend on the numerical solution of the fundamental problems. The zeros of the target functions will be the required eigenvalues. Finally, several numerical examples are given to demonstrate the use of the suggested method. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents an exact structural static reanalysis method for locally modified structures. Through the introduction of structural rigid body motion eigenvectors, the generalized structural compliance matrix can be obtained and the original stiffness equation is transformed into a linear system of much lower order. The general solution of displacements can be expressed prior to any assignment of boundary conditions. For a structure with given boundary and loading conditions, the displacements can be obtained by solving this linear system. For locally modified structures, the structural compliance matrix can be adjusted quickly. This static reanalysis method can be used for structures with modifications on structural elements, boundary and loading conditions, either independently or in combination. Two test examples are provided in the paper to prove the efficiency of the method. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this review paper we discuss Intelligent Systems for Medicine Laboratory's contributions to mathematical and numerical modelling of brain deformation behaviour for neurosurgical simulation and brain image registration. These processes can be reasonably described in purely mechanical terms, such as displacements, strains and stresses and therefore can be analysed using established methods of continuum mechanics. We advocate the use of fully non-linear theory of continuum mechanics. We discuss in some detail modelling geometry, boundary conditions, loading and material properties. We consider numerical problems such as the use of hexahedral and mixed hexahedral–tetrahedral meshes as well as meshless spatial discretization schemes. We advocate the use of total Lagrangian formulation of both finite element and meshless methods together with explicit time-stepping procedures. We support our recommendations and conclusions with two examples: computation of the reaction force acting on a biopsy needle, and computation of the brain shift for image registration. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach, the matched interface and boundary (MIB) method, for the vibration analysis of rectangular plates with simply supported, clamped and free edges, and their arbitrary combinations. In previous work, the MIB method was developed for three-dimensional elliptic equations with arbitrarily complex material interfaces and geometric shapes. The present work generalizes the MIB method for eigenvalue problems in structural analysis with complex boundary conditions. The MIB method utilizes both uniform and non-uniform Cartesian grids. Fictitious values are utilized to facilitate the central finite difference schemes throughout the entire computational domain. Boundary conditions are enforced with fictitious values—a common practice used in the previous discrete singular convolution algorithm. An essential idea of the MIB method is to repeatedly use the boundary conditions to achieve arbitrarily high-order accuracy. A new feature in the proposed approach is the implementation of the cross derivatives in the free boundary conditions. The proposed method has a banded matrix. Nine different plates, particularly those with free edges and free corners, are employed to validate the proposed method. The performance of the proposed method is compared with that of other established methods. Convergence and comparison studies indicate that the proposed MIB method works very well for the vibration analysis of plates. In particular, modal bending moments and shear forces predicted by the proposed method vanish at boundaries for free edges. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A modified version of the equilibrium on line method (ELM) for imposition of Neumann boundary conditions in collocation methods is presented. In the ELM, equilibrium on lines in the local coordinate systems on the Neumann boundary is satisfied as Neumann boundary condition equations. In other words, integration domains are straight lines for nodes located on the Neumann boundary. Furthermore, the Heaviside function is used as a weight in these integrals. In this paper, a modified procedure for choosing the integration domains is proposed. Also, application of different test functions is examined. The performance of the modified version of the ELM is studied for collocation methods based on two different methods to construct meshless shape functions: moving least-squares approximation and radial basis point interpolation. Also, the effects of these two meshless interpolation parameters are investigated. Numerical examples of two-dimensional linear and generalized nonlinear Poisson's equation, linear elasticity and elasto-plastic analysis are presented to demonstrate the stability, accuracy and convergence of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a two-dimensional frequency domain model for analyzing resonant structures. In this model, the transverse waves in the waveguide cross-section at any point are simulated by superposition of two waves in two perpendicular directions. The relationships between the physical wave parameters and the model parameters are derived. Results for cutoff wave numbers of homogeneous arbitrarily shaped cylindrical waveguides are given to test the validity of the model. These results are compared with available analytical solutions and results given by other published methods. The model proves to give good treatment for boundary conditions and accurate results with smaller matrix size in comparison with other numerical methods. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a new fictitious-domain technique for numerically solving elliptic second-order partial differential equations (PDEs) in complex geometries. The proposed technique is based on the use of integral-collocation schemes and Chebyshev polynomials. The boundary conditions on the actual boundary are implemented by means of integration constants. The method works for both Dirichlet and Neumann boundary conditions. Several test problems are considered to verify the technique. Numerical results show that the present method yields spectral accuracy for smooth (analytic) problems. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, substructuring techniques for the analysis of frame structures by the force method are reviewed. An algorithm is presented for the formation of cycle basis of the graph model of a frame structure. A simple and efficient graph method is proposed for preserving the sparsity of the matrices involved for including the boundary conditions when algebraic and graph force methods are employed. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, an improved procedure for imposing displacement boundary conditions in the direct stiffness method of the finite element analysis is presented. The proposed procedure neither changes the original order of the master stiffness matrix, nor does it require the rearrangement of the coefficient matrix. Consequently, it is easy to be implemented. Especially, the condition numbers of coefficient matrices of the improved procedure are remarkably reduced; hence the sensitivity of the solution to perturbations is considerably lowered. Numerical examples are used to demonstrate the validity of the proposed procedure. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Free-surface boundary is not only unknown in a priori but also the boundary conditions are overspecified. In this paper, the Laplace problem with overspecified boundary conditions on the free surface is solved by using the hypersingular equation instead of singular equation used conventionally in boundary element method. The free surface can be determined using an iterative procedure starting from an initial guess. By introducing the hypersingular equation, the convergence rate of free surface can be accelerated. Finally, numerical examples including rectangular dams and canals were demonstrated and were compared with others to show the validity of the present method. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Collocation methods based on radial basis functions can be used to provide accurate solutions to deterministic problems. For stochastic problems, accurate solutions may not be desirable if they are too sensitive to random inputs. In this paper, four methods are used to solve stochastic Poisson problems by expressing solutions in terms of source terms and boundary conditions. Comparison among the methods reveals that the method based on fundamental solutions performs better than other methods. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a meshfree interpolating moving least squares (IMLS) method based on singular weights for the solution of partial differential equations. Due to the specific singular choice of weight functions, which is needed to guarantee the interpolation, there arises a problem of finding the inverse of the occurring singular matrix. The inverse is carried out using a regularization of weight functions. It turns out that a stable inverse is obtained by considering the vanishing regularization parameter. Moreover, the use of this perturbation technique allows the correct evaluation of all necessary derivatives in interpolation points at a reasonable cost. Unlike standard kernel functions used in EFGM, RKPM, etc., the singular kernel functions lead to really interpolating functions which satisfy the Kronecker-delta property. They can be used for enforcement of Dirichlet boundary conditions when solving boundary value problems. Solution to a model BVP as well as an experimental convergence study of the method to analytical solutions, confirming the mathematical derivations, are given. Copyright © 2006 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]

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]

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]

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]

We study the boundary-value problems for singularly perturbed differential-difference equations with small shifts. Similar boundary-value problems are associated with expected first-exit time problems of the membrane potential in models for activity of neurons (SIAM J. Appl. Math. 1994; 54: 249–283; 1982; 42: 502–531; 1985; 45: 687–734) and in variational problems in control theory. In this paper, we present a numerical method to solve boundary-value problems for a singularly perturbed differential-difference equation of mixed type, i.e. which contains both type of terms having negative shifts as well as positive shifts, and consider the case in which the solution of the problem exhibits rapid oscillations. The stability and convergence analysis of the method is given. The effect of small shift on the oscillatory solution is shown by considering the numerical experiments. The numerical results for several test examples demonstrate the efficiency of the method. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new non-iterative numerical method for solving inverse boundary value problems for linear elliptic equations of second order. Here we assume that the Dirichlet and Neumann boundary conditions are given only on part of the domain, we have to reconstruct the solution and its normal derivative on the unaccessible part of the domain, which is the well-known ill-posed Cauchy problem. We propose to solve such inverse problems directly by using the recently developed radial basis meshless method. Several numerical experiments are given to demonstrate the effectiveness and efficiency of the proposed method. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper a finite-difference method is proposed for the first time for the solution of coupled heat and moisture transfer problems of transient nature in 1-D multilayer building elements. Transient boundary conditions are specified for both heat and moisture transfer at external surfaces, while constant values are assumed for material properties of each layer of the structure. The calculations for a typical three layers wall are conducted to obtain the dynamic distributions of the relative humidity at the interfaces of every layer during 24 h by use of the mentioned method, and the results agree with the transfer function method in (ASHRAE Trans. 1999; 105(2) : 954–961). The method can be extended to 2-D and 3-D coupled heat and moisture transfer problems. Copyright © 2003 John Wiley Sons, Ltd. [ABSTRACT FROM AUTHOR]

Several second-order finite difference schemes are discussed for solving a non-local boundary value problem for two-dimensional diffusion equation with Neumann's boundary conditions. While sharing some common features with the one-dimensional models, the solution of two-dimensional equations are substantially more difficult, thus some considerations are taken to be able to extend some ideas of one-dimensional case. Using a suitable transformation the solution of this problem is equivalent to the solution of two other problems. The former which is a one-dimensional non-local boundary value problem gives the value of μthrough using the unconditionally stable standard implicit (3,1) backward time centred space (denoted BTCS) scheme. Using this result the second problem will be changed to a classical two-dimensional diffusion equation with Neumann's boundary conditions which will be solved numerically by using two unconditionally stable fully implicit finite difference schemes, or using two conditionally stable fully explicit finite difference techniques. For each method investigated the modified equivalent partial differential equation is employed which permits the order of accuracy of the numerical techniques to be determined. The results of a numerical example for all finite difference schemes discussed in this paper are given and computation times are presented. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The method of fundamental solutions (also known as the singularity or the source method) is a useful technique for solving linear partial differential equations such as the Laplace or the Helmholtz equation. The procedure involves only boundary collocation or boundary fitting and hence is a very fast procedure for the solution of these classes of problems. The resulting coefficient matrix, is however ill-conditioned and hence the solution accuracy is sensitive to the location of the source points. In this paper, an alternative solution procedure based on the singular value decomposition of the coefficient matrix is suggested and it is shown that the numerical results are extremely accurate (often within machine precision) and relatively independent of the location of the source points. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper discusses the necessity and handling of non-linear constraint equations to describe the behaviour of properties of the loading system such as, e.g. smooth free-rotating loading platens. An exact, non-linear formulation for a smooth loading platen is derived and its incorporation into the equilibrium equations is presented. For this purpose, the Lagrange multiplier method is used. The solution of the equilibrium equations by means of a Newton–Raphson algorithm is also outlined. The proposed approach is validated on a patch of two finite elements and applied to a compression-bending test on a pre-notched specimen. It is observed that use of a linearized approximation of the boundary constraint can lead to errors in the description of the motion of the constrained nodes. Thus, the non-linear formulation is preferable. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The purpose of this paper is twofold: First, a Nitsche-type method for the treatment of inhomogeneous Dirichlet boundary conditions for the Navier–Stokes equations is proposed. This formulation is then used for discretization of Dirichlet control problems using adaptive finite elements. The mesh adaptation is driven by an a posteriori error estimator for the whole optimization problem. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper introduces an elastic predictor/return mapping integration algorithm for a simplified version of the Lemaitre ductile damage model, whose return mapping stage requires the solution of only one scalar non-linear equation. The simplified damage model differs from its original counterpart only in that it excludes kinematic hardening. It can be used to predict ductile damage growth whenever load reversal is absent or negligible—a condition met in a vast number of practical engineering applications. The one-equation integration scheme proves highly efficient in the finite element solution of typical boundary value problems, requiring computation times comparable to those observed in classical von Mises implementations. This is in sharp contrast to the previously proposed implementations of the original model whose return mapping may require, in the most general case, the solution of a system of 14 coupled algebraic equations. For completeness, a closed formula for the corresponding consistent tangent operator is presented. The performance of the algorithm is illustrated by means of a numerical example. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper numerically studies the effects of boundary conditions of different types on a class of mixed discontinuous finite element methods. The focus of this study is on a reaction–diffusion problem in one space dimension, which arises in the modelling and simulation of fluid flows in porous media. Numerical results show that for boundary conditions of certain types these mixed discontinuous methods produce an optimal rate of convergence; for others they generate a sub-optimal rate of convergence. A lower-order term is included in the reaction–diffusion problem, so the numerical study applies to a time-dependent problem as well. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, to solve the problems of the interaction between the unilateral interface cracks and elastic wave, a new numerical method based on boundary element method (BEM) has been proposed. In this method, an iterating–correcting process of the solution in frequency domain and the correction in time domain has been designed to eliminate the mutual interference between the time and frequency domain. As an illustration to the algorithm, an interface crack between two half-planes under the attack of harmonic plane elastic wave has been analysed in detail. The contact configurations and stress field at the crack surface, and dynamic stress intensity factor (DSIF) at the crack tip have been given. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

One of major difficulties in the implementation of meshless methods is the imposition of essential boundary conditions as the approximations do not pass through the nodal parameter values. As a consequence, the imposition of essential boundary conditions in meshless methods is quite awkward. In this paper, a displacement constraint equations method (DCEM) is proposed for the imposition of the essential boundary conditions, in which the essential boundary conditions is treated as a constraint to the discrete equations obtained from the Galerkin methods. Instead of using the methods of Lagrange multipliers and the penalty method, a procedure is proposed in which unknowns are partitioned into two subvectors, one consisting of unknowns on boundary Γu, and one consisting of the remaining unknowns. A simplified displacement constraint equations method (SDCEM) is also proposed, which results in a efficient scheme with sufficient accuracy for the imposition of the essential boundary conditions in meshless methods. The present method results in a symmetric, positive and banded stiffness matrix. Numerical results show that the accuracy of the present method is higher than that of the modified variational principles. The present method is a exact method for imposing essential boundary conditions in meshless methods, and can be used in Galerkin-based meshless method, such as element-free Galerkin methods, reproducing kernel particle method, meshless local Petrov–Galerkin method. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The conventional boundary integral equation in two dimensions is non-equivalent to its corresponding boundary value problem when the scale in the fundamental solution reaches its degenerate scale values. An equivalent boundary integral equation was recently derived. This equation has the same solution as the boundary value problem of differential equations. This paper presents the boundary contour method based on the equivalent boundary integral equation for two-dimensional linear elasticity. The method requires only numerical evaluation of potential functions and gives correct equivalent results to the boundary value problem of differential equations in two dimensions. Numerical results are presented for some examples. The present approach is shown to give excellent results in illustrative examples. Meanwhile, the traction results from the BCM based on the conventional displacement boundary integral equation are incorrect. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Helically symmetric structures such as helical springs, machine screws and wire rope strands are commonly used structural items. When they are subjected to axial loads (tensile and torsional), these structures may still exhibit the helically symmetric characteristic after loading. If this is the case this feature can be used to substantially simplify the analysis of these structures in numerical simulations. In this paper, the formulation of helically symmetric boundary conditions for finite element (FE) modelling is presented. The helically symmetric relationship is ensured by using constraint equations which relate the displacements of the corresponding nodes on the corresponding artificial boundaries of the model. The application of these helically symmetric equations renders it possible to reduce the finite element model size greatly and improve the accuracy of the results. Examples of a simple circular cross-section bar and wire rope strand are presented which demonstrate the validity of the formulation. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive mesh method is employed to solve a class of singular boundary value problems. The approach is based on an area-preserving map and some mesh shape control in two-dimensional space. Two benchmark problems, which both involve singularities in physical domains, are tested. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a method for the evaluation of boundary stresses directly from the BEM solution of elastostatic problems using the static boundary integral equation is presented. The technique is valid for corners and edges as well as smooth points on the boundary, and involves defining a new interpolation function for continuous elements which incorporate certain continuity conditions arising from the hypersingular nature of the integrals involved. An integration technique based on the singularity subtraction method using series expansions is adopted for the hypersingular intergrals. Results are shown to be more accurate than those obtained with conventional techniques. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper we implement the spatially periodic boundary conditions in finite element solutions of the Navier–Stokes equations based on the streamfunction–vorticity formulation. Periodic boundary conditions are enforced at both inflow/outflow and lower/upper boundaries. As an example of application we consider the fluid flow, at two different Reynolds numbers, through an array of pin fins. The limiting assumption of symmetry conditions at the boundaries parallel to the main flow is shown to yield unphysical-looking configurations. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes a new family of special Trefftz elements in which the boundary conditions on an internal curve (stiffener, hole, etc.) are fulfilled by the least squares procedure. The author anticipates difficulties with conditioning of such elements and therefore proposes a method to improve the aspect. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

With respect to a given boundary value problem, the corresponding conventional boundary integral equation is shown to yield non-equivalent solutions, which are dependent upon Poisson's ratio and geometry. In the paper a systematic method for establishing a necessary and sufficient boundary integral formulation has been proposed for two-dimensional elastostatic problems. Numerical analyses show that the conventional boundary integral equation yields incorrect results when the scale in the fundamental solution approaches a degenerate scale value. However, the results of the necessary and sufficient boundary integral equation are in good agreement with analytical solutions of the boundary value problem. [ABSTRACT FROM AUTHOR]

This paper is concerned with several refinement techniques of finite element meshes for treating elliptic boundary value problems in domains with re-entrant edges and corners. A priori mesh grading is explained, and it is combined with the well-known adaptive finite element method. For two representative examples the numerically determined error norms are recorded, and the different strategies are compared. [ABSTRACT FROM AUTHOR]

A new variational problem corresponding to a three-dimensional eddy-current boundary-value problem is treated in the paper. The equivalence between the variational problem and the boundary-value problem is proved, and so is the uniqueness of the solution. These form the foundation of the H - ψ method. [ABSTRACT FROM AUTHOR]

The success of the finite element method depends on the highly systematic way the analysis is built up, which means that the structure of the theoretical description and the code is transferable between different applications. It is advisable to teach the subject in such a way that this fact is fully exploited. It is a fact that most FE calculations today do not contain a check of the accuracy/quality of the solution. In the teaching of the FE method nothing is more important than the basic knowledge and understanding of the properties and behavior of the obtained FE solution. The paper deals with the methodology in presenting the method, by use of conceptual diagrams. It also discusses the interpretation of the results from a classical FE analysis and the extraction of high quality information. Finally, error estimation and postprocessing are discussed. The detailed description of the boundary conditions is lost in the FE solution. In the postprocessing stage they should be taken into account once more. [ABSTRACT FROM AUTHOR]

In order to make an exact estimation of discretization error for finite/infinite element methods, it is necessary to develop analytical solutions for some transient mass transport problems in infinite media. These transient mass transport problems may be viewed as the benchmark problems for the discretization error estimation of a new numerical method so that they generally have the following characteristics: (1) their initial and boundary conditions can be exactly modeled by the finite/infinite element method; (2) their solutions can be rigorously expressed in a closed form. In this paper, several of the aforementioned problems have been constructed and solved mathematically for transient mass transport problems in both 1D and 2D infinite media. [ABSTRACT FROM AUTHOR]

In the paper we address the problem of 2D adaptive quadrilateral mesh generation by using the variational principles. We first find the variational integral which generates the known grid system of curve-by-curve error equidistributions. We then use the same integral to generate a new adaptive grid system which is superior to the known system in that the new system produces smoother meshes. Moreover, the new integral may be combined linearly with existing smoothness control integrals to yield more robust adaptive grid systems. Numerical results and comparisons are reported. [ABSTRACT FROM AUTHOR]

The diffraction of waves due to the presence of submerged objects in the ocean environment is solved by a relatively novel approach involving the direct boundary integration method (DBIM). Firstly, the method is tested for the case of a submerged circular cylinder and compared with the conventional boundary element method (BEM) results. The agreement between the results using this method and the BEM is good. Further, the DBIM has been applied to the case of a submerged horizontal plate for which the horizontal and vertical force coefficients are computed and compared with a semi-analytical solution using the matched eigenfunction expansion method (EFEM). It is found that the computed results using DBLM are in good agreement with those of EFEM and BEM. Further, the DBIM is found to be computationally more efficient than the BEM for the water wave diffraction problems presented in this paper. [ABSTRACT FROM AUTHOR]

The paper presents a probabilistic boundary element method for analysis of structural responses to static loading, when the shape parameters of structures are considered as random variables. We can use this method to evaluate the mean values and standard deviations of the responses, and estimate the stochastic errors of structural character resulting from manufacturing errors. [ABSTRACT FROM AUTHOR]

We present in this paper a nine-point, fourth-order difference scheme for the numerical solution of the quasilinear Poisson equation in polar co-ordinates, [This equation can not be represented in ASCII.TXT] with appropriate boundary conditions. A separate difference scheme of order four valid at r = 0 has also been obtained. The method is based on five evaluations of the function f. The numerical results of two problems obtained using this scheme are listed. The numerical results demonstrate the fourth-order accuracy of the scheme. [ABSTRACT FROM AUTHOR]

In this paper we present numerical experiments made to investigate the behaviour of the Newmark time- stepping scheme applied to non-linear dynamic systems. Our attention is focused on the instability and chaos in the Newmark scheme when it is applied to the equation ü + P(u) = 0, representing a non-linear elastic spring. Some unusual modes of behaviour, which are of substantial interest, have been observed. In the first case, a stable but chaotic solution is found. In the second case, while a stable solution is obtained with a certain time step, an unstable solution is found by decreasing the time step. In the third case, instability is triggered by neglecting the initial acceleration. A simple modification of the Newmark scheme is proposed which keeps the energy constant for the equation ü + P(u) = 0 and thereby guarantees unconditional stability. Numerical examples in support of such an energy-conserving scheme are presented. [ABSTRACT FROM AUTHOR]

We propose in this paper a nine-point, fourth-order difference method for the numerical solution of the quasilinear Poisson equation Auzz + &frac1r; ur + Burr = f(r, z, u, ur, uz) with appropriate boundary conditions. The method is based on five evaluations of f. The numerical results of four problems obtained using this method are listed. The results demonstrate the fourth-order accuracy of the method. [ABSTRACT FROM AUTHOR]