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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper presents an exponentially fitted finite difference scheme of order one for the singularly peturbed Riccati equation εu′ (t) = c(t)u2(t) + d(t)u(t) + e(t), t>0, u(0) = φ with a small parameter ε multiplying the first derivative. The scheme is a modified form of Carroll's scheme (1986). The scheme is both optimal and uniform with respect to the small parameter ε, that is, the solution of the difference scheme satisfies error estimates of the form | u(ti) - ui | ≤ C min(h,ε) where C is independent of i, h and ε. Here h is the mesh size and ti is any mesh point. The scheme is explicit in nature and so no iteration is involved for the convergence of the solution. The scheme presented in this paper is new and it is different from the uniform schemes of order one available in the literature. Finally, numerical experimetns are presented. [ABSTRACT FROM AUTHOR]

PISO (pressure-implicit with splitting of operators) is an algorithm devised to solve the transient incompressible Navier-Stokes and energy equations. In that it uses separate equations for each of two pressure corrections, velocity components and transported scalars, PISO is known as a segregated solution procedure. Preconditioned, generalized conjugate gradient (GCG) methods in combination with schemes for vectorization and storage minimization are described in the paper for the purpose of solving both the symmetric and non-symmetric algebraic equation systems that result from the PISO algorithm. Of particular interest in the paper is a comparison of the present procedure with a procedure described by Chin et al. (1992) in which preconditioned conjugate gradient methods are used to solve the Jacobian matrix used in the Newton iteration of the fully coupled non-linear equations. The two methods are similar in that both techniques are based on a discretization using staggered control volumes with the power-law method for modelling advection-diffusion transport. [ABSTRACT FROM AUTHOR]

The paper presents finite difference schemes of order two for stiff initial-value problems, with a small parameter ∊ multiplying the first derivative. The schemes are a modified form of the classical trapezoidal rule. They are both optimal and uniform with respect to the small parameter ∊, that is, the solution of the difference schemes satisfies error estimates of the form | u(ti)-ui| ⩽ C min(h²,∊) where C is independent of i, h and ∊. Here h is the mesh size and ti is any mesh point. The schemes presented in this paper are different from the scheme of order two available in the literature. Finally, numerical experiments are presented. [ABSTRACT FROM AUTHOR]

In a recent paper we presented a data structure to be used with multigrid techniques on non- homogeneously refined FEM meshes. This paper focuses on the adaptive refinement techniques used there. The error estimate is obtained from standard Taylor series. For each element we compute its efficiency in terms of the size, the norm of the second derivatives of the unknown and the parameter p, where Lp is the chosen norm. The way the norm influences the optimal mesh is studied. The number of elements to be refined at each step is such to produce a fast convergence to the optimal mesh, followed by successive homogeneous refinements. We hope that the analysis of these two subjects could be of value for people working with other (perhaps very dissimilar) adaptive refinement techniques (error estimate and data structure, for instance). [ABSTRACT FROM AUTHOR]

This paper examines the suitability of three-dimensional finite elements to model accurately problems involving material incompressibility, using the displacement finite element method and exact numerical integration. The previously used method for classification of element suitability is presented and extended to the three-dimensional case. However, an alternative approach for examining suitability, quantified in terms of free degrees of freedom (equal to the degrees of freedom minus the incompressibility constraints), is introduced. This is used to examine Lagrangian cubic, serendipity cubic and tetrahedral three-dimensional elements configured in a regular cubic arrangement. The findings of this paper are substantiated by a number of three-dimensional numerical experiments and comparison with a separate two-dimensional study. All serendipity cubic elements are found to be unsuitable. The linear strain tetrahedron is on the borderline of suitability in a 6-tetrahedra-per-cube arrangement, and is thought to be only suitable if the mesh boundary nodes are not over-constrained. The same element in a 5-tetrahedra-per-cube arrangement, and higher order tetrahedra (quadratic strain etc), are suitable. The Lagrangian cube elements of higher order than the 27-node cube are suitable, but are probably not as efficient computationally as the tetrahedral elements of the same order. [ABSTRACT FROM AUTHOR]

When solving parabolic partial differential equations using finite difference non-overlapping domain decomposition methods, one often uses the stripwise decomposition of spatial domain and it can be extended to the rectangular decomposition without further analysis. In this paper, we analyze the rectangular decomposition when the modified implicit prediction (MIP) algorithm is used. We show that the performance of the rectangular decomposition and the stripwise decomposition is different. We compare spectral radius, maximum error, efficiency, and total operations of the rectangular and the stripwise decompositions. We investigate the accuracy of the interface of the rectangular decomposition and the effects of the correction phase of the rectangular decomposition. Numerical experiments have been done in both two and three spatial dimensions and show that the rectangular decomposition is not better than the stripwise decomposition. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents the reason why Barlow points do not coincide with the reduced Gauss quadrature points for higher-order finite elements. Based on the numerical implementation for one-dimensional bar by finite elements, it is found that the reason for noncoincidence of Barlow points and the reduced Gauss quadrature points for higher-order elements is due to the mismatch of nodal displacements by FEM with the exact solution. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper an efficient method is developed for the formation of null bases of finite element models (FEMs) composed of tetrahedron elements, corresponding to highly sparse and banded flexibility matrices. This is achieved by associating special graphs with the FEM and selecting appropriate subgraphs and forming the self-stress systems on these subgraphs. The efficiency of the present method is illustrated through two examples. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The method proposed by J.C. Houbolt in 1950 is one of the pioneering methods of time integration. Nevertheless, especially due to its multi-step fashion and not having a well-defined starting procedure, the method has not met considerable acceptance. The conversion of the Houbolt method to a one-step method is reported in the literature. However, the resulting method still lacks an appropriate starting procedure for all practical cases. In this paper, a parameter-less unified starting procedure is proposed for time integration with the Houbolt method. Copyright © 2006 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, 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, the problems involved in the process of degeneration of quadrilateral element into triangular element are thoroughly analysed. The contents include the formulation of the geometry mapping induced by collapsing one side of the quadrilateral element and the construction of the shape functions. The study focuses first on a 4-node bilinear quadrilateral (Q4) element to 3-node constant strain triangular (CST) element, and then on a 8-node serendipity (Q8) element to 6-node triangular element (T6). In the analysis, the quadrilateral element and degenerate triangular element are assumed to be enclosed by straight edges. The theoretical results show that there is another better approach to realize the degeneration, and that even for conventional approach of degeneration we can give more reasonable explanation to the unclear problems like the CST property in degenerate CST element and the necessity of the additional terms in degenerate T6 element. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes and compares several effective methods for the numerical solution of one-dimensional Stefan problems. It is not intended to be an exhaustive review but is restricted to a range of problems and geometries including melting in the half-plane, outward cylindrical solidification and outward spherical solidification. From the limited comparison of numerical results obtained, some helpful comments can be made which may prove valuable in the future use of these methods. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An overlay-type rheological model is presented, which is used to introduce viscosity in inviscid elasto-plastic material laws with softening, in order to reduce the mesh-dependency of Finite Element solutions. This model is intended to be an alternative to the well-known visco-plastic formulations of Perzyna and Duvaut–Lions. A time integration algorithm for the visco-elastic model component is presented, being demonstrated in the paper, that it is unconditionally stable and oscillation-free. The algorithm is tested in a problem with slip driven softening (von Mises material) and in a problem with decohesion driven softening (Cam-Clay model). Figures showing the capability of the algorithm to regularize the solution are presented. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a rigorous full-wave analysis of rectangular microstrip patches over ground planes with rectangular apertures in substrates containing isotropic and anisotropic materials is presented. The dyadic Green's functions of the problem are efficiently determined in the vector Fourier transform domain. The integral equations for the unknown patch current and aperture field are solved numerically by applying the Galerkin method of moments. The TM set of modes issued from the magnetic wall cavity model are used to expand the unknown current on the patch. Also, the same basis functions are used for approximating the aperture field in accordance with the concept of complementary electromagnetic structures. The validity of the solution is tested by comparison of the computed results with experimental data. Numerical results show that changes in aperture length can drastically shift the resonant frequency. The aperture width, on the other hand, can be used for a fine adjustment of the operating frequency. Other results also indicate that dielectric anisotropy effect is especially significant when the size of the aperture is similar to that of the patch. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

By following the geometric point of view in mechanics combined with mathematical analysis, a novel expression of the combined hybrid variational principle is introduced to clarify its intrinsic mechanism of enhancing coarse-mesh-accuracy and stability of lower-order displacement schemes. It is pointed out that the combined hybrid scheme achieving energy optimization leads to enhancement of accuracy at coarse meshes. By this mechanism's bringing to light the two factors (adding energy-compatible bubbles and adjusting the combination parameter α) governing this enhancement, this paper presents a sound procedure for optimizing a combined hybrid scheme in a manner independent of the choice of assumed stresses. The effectiveness of the procedure is verified by improving Allman's membrane element with drilling d.o.f.'s. The numerical benchmark tests indicate that the combined hybrid counterpart of Allman's membrane element is capable of attaining the degree of accuracy of linear strain (i.e. 2-order) element at coarse meshes without distortion. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Axisymmetric finite element stress analysis involves repeated integration of a rational polynomial integrand. For elements near the axis of symmetry, such integrals are quasi-singular, are difficult to integrate numerically, and can lead to significant computational errors. This paper describes a Gaussian quadrature procedure to integrate exactly, within computational limits, a class of rational polynomials over undistorted triangular and quadrilateral finite elements. The procedure's accuracy and efficiency are illustrated through a numerical example. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Inflatable structures made of modern textile materials with important mechanical characteristics can be inflated at high pressure (up to several hundreds kPa). For such values of the pressure they have a strong mechanical strength. The aim of the paper is to construct a new inflatable beam finite element able to predict the behaviour of inflatable structures made of beam elements. Experiments and analytical studies on inflatable fabric beams at high pressure have shown that their compliance is the sum of the beam compliance and of the yarn compliance. This new finite element is therefore obtained by the equilibrium finite element method and is modified into a displacement finite element. The stiffness matrix takes into account the inflation pressure. Comparisons between experimental and numerical results are shown and prove the accuracy of this new finite element for solving problems of inflatable beams at high pressure. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents an examination of the methods for the iterative modal perturbation and the application of these methods to the reanalysis of the eigenvalue problem. The iteration is based on the first-order modal perturbation. In two examples, it is shown that the iterative analysis has the advantage of accuracy over the addition of higher-order perturbations and it is an appropriate approach for the reanalysis of the eigenvalue problem in terms of accuracy and computational efficiency. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper the advection of element data which are linearly distributed inside the elements is addressed. Across element boundaries the data are assumed discontinuous. The equations are discretized by the Discontinuous Galerkin method. For stability and accuracy at large step sizes (large values of the Courant number), the method is extended to second order. Furthermore the equations are enriched with selective implicit terms. This results in an explicit and local advection scheme, which is stable and accurate for Courant numbers less than .95 on unstructured triangle meshes. Results are shown of some pure advection test problems. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The lateral buckling of a simply supported symmetric thin-walled member is investigated. An energy equation for the lateral buckling of thin-walled member has been presented in which the effects of torsion and assumed warping are taken into account. Using variation method helps to derive the governing differential equation together with appropriated boundary conditions. The lateral buckling loads are obtained by solving the differential equation numerically using Galerkin's method of weighted residuals. The method presented in this paper yields the formula for computing the lateral buckling load that is very simple and straightforward. By the study, a very complex practical eigenvalue problem can be transformed into a very simple one. The results predicted with the analytical method are in good agreement with the ones obtained by experimental, finite integral, non-linear finite element methods and optimal analysis. The fast convergence of the method makes it possible to write the resulting formulae in a likely closed form which is very simple and very convenient to use. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The standard boundary node method (BNM) uses a (meshless) diffuse interpolation (in terms of neighbouring scattered boundary points) for the primary variables. The method is not ‘truly meshless’, however, since cells on the boundary of a body are used for integration. This paper presents a ‘pure’ version of the BNM in which integration cells are dispensed with. Instead (overlapping), regions of influence (ROIs) of boundary nodes are used for integration. Initial results for 2-D potential theory, presented here, are encouraging. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The question of the accurate numerical evaluation of weakly singular integrals arising in the boundary element method has attracted considerable recent attention. A popular method is to use a non-linear transformation with zero derivative at the singular point to adjust the position of the Gauss–Legendre quadrature points, resulting in a more accurate evaluation of the integral. This paper presents a simple algebraic device to overcome a numerical round-off problem which has limited previous implementations of non-linear transformations. Utilization of this device allows higher orders of transformation to be used, resulting in lower relative errors in the numerical evaluation of the weakly singular integrals. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we review the development of local discontinuous Galerkin methods for elliptic problems. We explain the derivation of these methods and present the corresponding error estimates; we also mention how to couple them with standard conforming finite element methods. Numerical examples are displayed which confirm the theoretical results and show that the coupling works very well. 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]

In this paper, we derive precise eigenvalue upper bounds for the discretized Stokes operator corresponding to two widely used schemes, namely the Q1–P0 mixed finite element and the marker and cell (MAC) finite difference scheme. We also highlight a remarkable property concerning the multiplicity of the eigenvalue μ=1 in the MAC case. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the existence, uniqueness and uniform convergence of the solution of the Carey non-conforming element with non-quasi-uniform partitions is proved for non-self-adjoint and indefinite second-order elliptic problems under a minimal regularity assumption. Furthermore, the optimal error estimate for the solution of Carey non-conforming element method is obtained only under an H2 smoothness hypothesis. Finally, a two-level Schwarz method which suits non-quasi-uniform partitions is proposed and optimal convergence for the pre-conditioned GMRES method is shown. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper discusses implementation strategies for second-order finite difference discretizations of advection. Purely explicit and implicit methods both have disadvantages, and we consider semi-implicit schemes in which the flux is split into a primary implicit part and a secondary explicit correction. One-dimensional scalar advection is used as a model problem to analyse the leading order error terms and the stability of the schemes. Some of the splittings turn out to be unconditionally stable, but accuracy or monotonicity may deteriorate for large time steps. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The serendipity (eight nodes) and Lagrange (nine nodes) plate elements following the Reissner–Mindlin irreducible formulation for the bending of plates are among the most popular in the finite element method. However, reduced integration on the shearing part of the stiffness matrix has to be performed in order to avoid locking of the mesh in the limit of thin plates, where numerical constraints are taking some degrees of freedom in order to be satisfied. This paper explains the competition between those constraints and the degrees of freedom, giving a mean to predict whether a mesh will lock or not. It also shows why the Lagrange element performs better than the serendipity element. Numerical results confirm this analysis. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes the implementation of a parametric optimization process in the field of composite structure design. The application concerns alpine skis. Using a reference ski, the process enables the calculation of the optimum shapes for a complete range of skis and checks their behaviour on snow. The objective function is formulated as a least-squares problem involving nine static bending flexibilities of the ski, considered as a simply-supported beam on nine predetermined spans. The composite cross-section properties and the longitudinal profile of the structure are taken into account in a parametric geometry approach. After the homogenization process, integration of the bending equation is carried out using a finite difference approach. The line search procedure uses the gradient method and the descent parameter optimization is carried out using an adapted linear approximation. The discussion of the results highlights the satisfying compromise between precision and calculation time. The procedure constitutes an original implementation of numerical methods in the area of sports equipment. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents an improved approximation technique for gradient based approximation methods of mathematical programming. The proposed technique prevents oscillations of the sequence of approximate solutions in the optimization process efficiently and preserves the relatively simple form of the approximating functions. The improvement is achieved by adding an appropriate convex term to each conventional approximating function. The theory is illustrated with several numerical examples. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper presents a hybrid Trefftz (HT) element approach for the numerical solution of transient plate bending problems. In the proposed method, the dynamic plate equation is first discretized with respect to time and then the resulting set of elliptic equations is solved by the corresponding time independent hybrid Trefftz element approach. Two examples are considered to assess the effectiveness of the numerical method. [ABSTRACT FROM AUTHOR]

The paper describes a new numerical algorithm for pure advection at large Courant numbers. The DISCUS scheme uses an accurate and proven control volume algorithm (QUICKEST) within a Lagrangian treatment of advection. By being in sympathy with the information flow dictated by characteristic lines, the scheme performs exceedingly well at Courant numbers greater than one. In contrast to existing Lagrangian schemes which use the characteristics to determine the grid points from which concentrations are interpolated, in DISCUS the characteristics are used to determine the appropriate location for the control volume. The scheme is of comparable accuracy to Eulerian schemes at Courant numbers less than one, but it increasingly outperforms them as the Courant number increases. Indeed, the results reported illustrate the futility of using an Eulerian scheme at high Courant numbers. [ABSTRACT FROM AUTHOR]

For elastodynamic problems in an elastic half-space, the idea of describing the displacement variation on the free ground surface outside the region being studied with the fundamental solution in a full space is presented in the paper. Then a corresponding mapped infinite boundary element is constructed for the problems of anti-plane motion. The computed results show that such an element can be applied effectively to obtain high-precision solutions. [ABSTRACT FROM AUTHOR]

In the paper the authors investigate the conditions of optimal mesh, and prove that the element errors in the optimal mesh should be identical for all existing elements. Also, it is shown that the correct mesh refinement formulations should be derived at an element level rather than the global level. Thus the element permissible errors need to be determined. The method to determine these permissible element errors is described. [ABSTRACT FROM AUTHOR]

When solving non-linear algebraic equations resulting from a typical finite element discretization it is quite common that the popular Newton-Raphson iteration fails to converge or requires an excessive number of iterations. To solve this problem, line searches have been proposed in conjunction with load control and quadratic arc-length control, which has proved to be highly successful. In the paper we first review a number of the most popular arc-length controls. Then we highlight the severe drawbacks associated with the coupling of the cylindrical arc-length control and line searches. Next, various other forms of arc-length controls are scrutinized in the light of this coupling. It is shown that for some of the arc-length controls such a combination is extremely simple and straightforward, yet at the same time efficient and effective. For the rest the same complications incurred for the cylindrical arc-length method remain. [ABSTRACT FROM AUTHOR]

Computing the charge density on the surfaces of conductors is fundamental to many electrostatic applications. Difficulties arise in two-dimensional simulation due to the O(log||r||) potential. Fully understanding the 2D potential problem, and reasonably connecting the mathematical formulation with physical interpretation, are key to handling this difficulty properly. In the absence of these factors it is easy for one to propose an ill-posed problem. In this paper, a complete investigation of potential theory, from 3D to 2D, is made for computing charge density on the surfaces of conductors. Various integral formulations are derived - these are applicable in different situations. It is shown that, in general, the electrostatic potential need not be finite valued at infinity for 2D problems. Numerical examples for the 2D case are constructed to show that the formulations are consistent. Criteria for choosing the most appropriate formulation for a given problem are suggested. [ABSTRACT FROM AUTHOR]

The paper presents a new finite difference solution for the 3D non-linear heat equation. This solution is based on the approach of making finite difference substitutions into the solution of the partial differential equation, rather than into the partial differential equation itself, which is the classical approach. Numerical results show that the new FD equation is approximately ten times more accurate than the classical solutions. [ABSTRACT FROM AUTHOR]

Upwind finite difference operators on uniform meshes are well known to be unsuitable for the numerical solution of singularly perturbed partial differential equations, in the sense that, in the neighborhood of the boundary layers, the error in the numerical approximation may increase as the mesh is refined. Recently, on the other hand, it has been predicted theoretically that the use of upwind finite difference operators on specially designed piecewise uniform meshes guarantees the decrease of the nodal error to zero as the number of mesh elements increases. In the paper the general theorem is quoted and its prediction is validated by numerical experiment for a specific linear advection-dominated transport equation in two dimensions. Experimental values of the convergence rate are obtained, which also agree with the theoretical estimates. [ABSTRACT FROM AUTHOR]

In this paper I re-examine the mechanics of the residual bending flexibility correction and show that it is an extravariational trick. [ABSTRACT FROM AUTHOR]

In this paper, I discuss the convergence and divergence rates for a class of generalized matrix multisplitting relaxation methods in a detailed manner. In particular, when the coefficient matrix is an L-matrix, I obtain several sufficient and necessary conditions ensuring the convergence of these methods. [ABSTRACT FROM AUTHOR]

Hybrid shell elements have long been regarded with reserve by the commercial finite element developers despite the high degree of reliability and accuracy associated with such formulations. The fundamental reason is the inherent higher computational cost of the hybrid approach as compared to the displacement- based formulations. However, a noteworthy factor in favor of hybrid elements is that numerical integration to generate element matrices can entirely be avoided by the use of symbolic integration. In this paper, the use of the symbolic computational approach is presented for an assumed-stress hybrid shell element with drilling degrees of freedom, and the significant time saving achieved is demonstrated through an example. [ABSTRACT FROM AUTHOR]

Recent advances in planar mesh generation of arbitrary domains incorporate methods for placing points as well as connecting them into a triangulation. Postprocessing techniques such as Laplacian smoothing and mesh relaxation enhance the shape of triangles in these meshes but do not address the construction of meshes near boundaries or provide a criterion to determine the number of interior points of the initial triangulation. The paper addresses these issues by investigating the construction of degree-6 triangulations, the primary goal of the mesh relaxation 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]