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  • Engineering General  (6,759)
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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: finite elements ; automatic generation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element generation methods, such as Delaunay, allow the meshing of shapes from a set of nodes. These nodes must previously exist. The authors present a simple, fast and reliable method to generate them in an unstructured way in N-dimensional space. Its main characteristic is to easily allow variation of the node density by introducing a density function, either analytical or discretized. This function can also be anisotropic. Some nodes can have a pre-fixed position. Inner lines and holes can also be specified in the domain to be meshed. Generated nodes are to be connected according to triangles in 2D and tetrahedrals in 3D.
    Additional Material: 6 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: obstacle problems ; quadratic programming ; finite element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical solution of problems involving frictionless contact between an elastic body and a rigid obstacle is considered. The elastic body may undergo small or large deformation. Finite element discretization and repetitive linearization lead to a sequence of quadratic programming (QP) problems for incremental displacement. The performances of several QP algorithms, including two new versions of a modified steepest descent algorithm, are compared in this context. Numerical examples include a string, a membrane and an Euler-Bernoulli beam, in contact with flat and non-flat rigid obstacles.
    Additional Material: 2 Ill.
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  • 5
    ISSN: 1069-8299
    Keywords: mode-matching ; Helmholtz' equation ; DtN ; finite element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element (FE) mode-matching procedures for the solution of Helmholtz' equation on an unbounded domain are reviewed and a symmetric general formulation is presented. This is a formal restatement of procedures applied previously to computations involving scattering of shallow water waves, acoustic transmission in non-uniform ducts and acoustic radiation from prismatic sheet metal ducts. An essential feature of the method is the use of a Galerkin procedure, rather than collocation, to match a finite computational model to a truncated modal expansion with the desired radiation characteristics. The method produces a symmetric set of linear equations which can be solved to give the unknown nodal values of the dependent variable and the modal coefficients of an outer expansion. Either of these sets of variables can be eliminated prior to solution to yield a reduced set of equations in the remaining parameters. The reduced equations obtained by eliminating the modal coefficients are shown to be identical to those obtained by applying a truncated Dirichlet-to-Neumann (DtN) boundary condition. If applied in this form, mode-matching can therefore be regarded as an alternative to the DtN method for generating this common set of discrete equations while permitting simultaneous solution for the modal coefficients in the outer region.
    Additional Material: 1 Ill.
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  • 6
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The authors study the shape optimization of a complex cracked shell under complex criteria. The shell is one of various cases of a turboshaft, and optimization criteria are associated to the cost, the technology, and above all the working conditions for the turboshaft. The optimization criteria involved are of course the weight of the structure, but also the plastic instability and critical stress intensity factor. All computations have been made with the Ansys finite element program in which an optimization module exists.
    Additional Material: 5 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: mesh generation ; adaptivity ; iterated fractal systems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper the author presents a novel point of view for the refinement and derefinement algorithms of triangular nested meshes using fractal concepts and iterated function systems (IFS). The fractal behaviour can be understood in the sense that these meshes feature a remarkable amplifying invariance under changes of magnification. Here we compare the meshes obtained by the combination of these algorithms with those presented by Bova and Carey (1992). Although both of the meshes are very similar, the current algorithms automatically build and manage sequences of nested irregular discretizations of the domain. The author illustrates here how the application of IFS families is equivalent to the use of an adaptive strategy that combines the refinement procedure with the derefinement one.
    Additional Material: 4 Ill.
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  • 8
    ISSN: 1069-8299
    Keywords: wavelets ; measures ; stability ; domains ; differential equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper investigates the accuracy and numerical stability of a class of wavelet Galerkin formulations on irregular domains. The method of numerical boundary measures is based upon a domain embedding strategy in which the irregular domain of interest is embedded in a larger domain having regular geometry. One advantage of the domain embedding method is that the boundary conditions on the larger, regular domain can be enforced in a straightforward manner, and the solution procedure can exploit the highly structured form of the resulting governing equations. The defining characteristic of this method is that the calculation of integrals along the irregular boundary are carried out using recently derived numerical boundary measures. In addition, the coercive bilinear forms characterizing the boundary value problem of interest must be calculated when restricted to the actual domain. In the case of wavelet Galerkin formulations, this calculation is accomplished with the three term connection coefficients that characterize the numerical boundary measure. The numerical stability and accuracy of the domain embedding procedure is compared to a newly developed wavelet-based finite element formulation.
    Additional Material: 4 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 10
    ISSN: 1069-8299
    Keywords: stretching functions ; mesh refinement ; finite differences ; truncation error ; composite grids ; regularity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this work the truncation-error criteria of Thompson and Mastin (1985) are combined with conditions of vanishing second and higher derivatives at both endpoints for the purpose of deriving new classes of one-dimensional stretching functions for mesh refinement in finite-difference numerics. With these elementary stretching functions, matching of the slopes between adjacent grid patches then automatically confers Cn regularity upon the composite stretching function. Formulated with reference to two conceptions of truncation order (fixed relative distribution against fixed number of nodes) the resulting mappings are shown to provide particularly advantageous node distributions at both ends simultaneously (with concomitantly higher truncation error in between). Viewed overall, the truncation-error functions compare favourably with those for sinh, tanh and erf - mappings whose utility for mesh refinement was established by Thompson and Mastin. The numerical labour of implementing the new stretching functions is only slightly greater than that required for the error function. An illustrative derivation involving Cn patching leads to two-sided stretching functions, which allow the slopes at both ends to be prescribed arbitrarily. This formulation differs from a previous approach described by Vinokur (1983).
    Additional Material: 6 Ill.
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  • 11
    ISSN: 1069-8299
    Keywords: solid-shell structure ; 3D solid element ; degenerated shell element ; DOF expanding ; multipoint constraint equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a degree of freedom expanding method for dealing with the connections of 3D isoparametric solid elements and the degenerated shell elements. By introducing two degrees of freedom to describe the elongation in the normal direction of the shell node linked with solid elements, a series of multipoint constraint equations which provide proper connections of solid and shell nodes are raised. The method gives a complete solution to the problem of connection between 3D isoparametric solid elements and degenerated shell elements even for the thermal elasto-plastic problem. It can adapt to complex junctions and simplify programming. Numerical examples are also presented to demonstrate the accuracy and feasibility in thermal elasto-plastic analysis.
    Additional Material: 6 Ill.
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  • 12
    ISSN: 1069-8299
    Keywords: mesh generation ; Delaunay mesh ; Watsens method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Automated mesh generation using a combined octree/Delaunay approach typically requires that rectangular elements be bounded by other rectangular elements which are not more that one division smaller (i.e. 1/8 the volume in 3D). This limitation is sometimes referred to as the 2 : 1 rule. This paper presents a modification which allows for any level of difference.
    Additional Material: 6 Ill.
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  • 13
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: anisotropy ; finite elements ; layers ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A modification of the usual quadrangle (2D) and brick (3D) finite element for field problems is proposed. It allows the principal directions of the conductivity tensor (anisotropy directions) to be derived from the geometrical shape of the finite element and to change within it. An internal layering is assumed which is parallel to the boundary at two opposite faces (top and bottom) of the element. Without an explicit computation of angles the anisotropy directions are parallel and perpendicular to this layering. An application is the modelling of pore fluid flow in sedimentary basins.
    Additional Material: 4 Ill.
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 15
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 16
    ISSN: 1069-8299
    Keywords: Navier-Stokes ; artificial compressibility methodology ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper considers the problem of laminar incompressible viscous flow through a wavy channel. An artificial compressibility method using the approximate factorization technique is applied to solve the velocity-pressure formulation of the Navier-Stokes equations written in curvilinear non-orthogonal coordinates. The physical domain used was one wavelength of the channel in which appropriate periodicity conditions were applied in order to find a solution independent of entry effects. Flow separation was observed for high Re numbers and/or large wave amplitudes of the channel. The effect of inertia to the velocity profiles was observed, and pressure and shear stress were calculated along the length of the channel. These flows have great interest in industry and medicine such as for the extracorporeal membrane oxygenator.
    Additional Material: 7 Ill.
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  • 17
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: finite element method ; mesh refinement ; adaptivity ; singularities near edges ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: 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.
    Additional Material: 7 Ill.
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  • 18
    ISSN: 1069-8299
    Keywords: symmetrically laminated plates ; anisotropy ; fundamental solutions ; boundary integral equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper the bending problem of moderately thick symmetrically laminated anisotropic plates is considered, based on the first-order transverse shear deformation plate theory. Using the method of plane wave decomposition and Hörmander's operator method, the fundamental solution of the plates is presented. The boundary integral equation of the plates is formulated by taking the fundamental solution presented as the weighted function and using the method of weighted residuals. The numerical calculation of the boundary integral equation presented is discussed in detail. Some examples are presented and compared with the exact solutions and the numerical solutions available in the literature. The numerical results show that the present method has a satisfactory rate of convergence and acceptable accuracy with a reasonable boundary mesh.
    Additional Material: 3 Ill.
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  • 19
    ISSN: 1069-8299
    Keywords: boundary integral equation ; necessary and sufficient condition ; plane elasticity problem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: 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.
    Additional Material: 8 Ill.
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  • 20
    ISSN: 1069-8299
    Keywords: finite volume ; high-order discretization ; non-oscillatory schemes ; pressure interpolation ; non-staggered grid ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper addresses the problem of convection discretization by extension and application of numerical schemes used in compressible flows: SONIC-A, SONIC-B, UNO2, MUSCL and MINMOD to predict steady incompressible recirculating convection dominated flows. A new scheme, SONIC-Q, is proposed together with a third-order non-oscillatory practice for pressure interpolation in non-staggered grids. Finite-volume calculations of the Navier-Stokes equations of a standard 2D driven square cavity standard test case and the laminar flow over a fence using primitive variables and non-staggered grid systems have shown that the schemes are alternatives to the conventional ones used in general algorithms for incompressible recirculating flows. In general these composite high-order schemes have proved to be good candidates to overcome the problems of false-diffusion and unboundedness encountered in non-composite high-order upwind schemes used in incompressible flows.
    Additional Material: 8 Ill.
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  • 21
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 22
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 23
    ISSN: 1069-8299
    Keywords: time integration ; finite element method ; least squares formulation ; multistep methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a formulation and analysis of three and four step least squares algorithms for first order IVPs. The three step algorithm is derived using cubic Lagrangian interpolation, and is found to be third order accurate but only conditionally stable. Fourth order Lagrangian interpolation is used to obtain a four step least squares scheme which is A0-stable but inconsistent.
    Additional Material: 2 Tab.
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  • 24
    ISSN: 1069-8299
    Keywords: two-phase flow ; solute transport ; interphase exchange ; porous media ; finite element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The development of a numerical method for modelling two-phase flows and solute transport, particularly with interphase exchange in porous media, is presented. The governing equations are derived to describe two immiscible and compressible fluids flows such as water-air and two-phase solute transport with interphase exchange. Technically, the standard finite element method and a strongly implicit procedure are employed to solve the fully coupled governing equations. Pressures of two-phase fluids and solute concentrations in two-phase fluids are taken as the primary unknown variables, and the discretized equations are solved by a direct type of solver. Application examples are shown to confirm the applicability of the numerical method.
    Additional Material: 9 Ill.
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  • 25
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: inviscid drops ; coalescence ; boundary element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method is used to simulate the motion of inviscid drops colliding and coalescing at a solid surface. The equations of motion are solved by a boundary element method in which the free surface of the drop is represented by a moving grid. The numerical results include the configuration of the drop during coalescence and the kinetic and potential energies. A numerical example is used to demonstrate the way in which coalescence affects the configuration of the free surface.
    Additional Material: 3 Ill.
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  • 26
    ISSN: 1069-8299
    Keywords: harmonic differential quadrature method ; computational complexity ; differential quadrature ; numerical method ; centrosymmetric matrix ; computational mechanics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The structure of weighting coefficient matrices of harmonic differential quadrature (HDQ) is found to be either centrosymmetric or skew centrosymmetric, depending on the order of the corresponding derivatives. The properties of both matrices are briefly discussed in the paper. It is noted that the computational effort of the harmonic quadrature for some problems can be further reduced by up to 75 per cent by using the properties of the above-mentioned matrices.
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  • 27
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: numerical methods ; constitutive equations ; composite ; mixing formulation ; anisotropic elastoplastic model ; mapping stress tensor space ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general constitutive model adequate for analysis of the thermomechanical response of composite materials is presented. The model is based on the mixture of the basic substances of the composite and allows the evaluation of the interdependence between the constitutive behaviour of different compounding materials. The behaviour of the each compound is modelled by a general anisotropic thermo-elasto-plastic model, termed the ‘base model’. The different base models for each compound are combined using mixing theory to simulate the behaviour of the multiphase material.
    Additional Material: 7 Ill.
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  • 28
    ISSN: 1069-8299
    Keywords: linear polyhedra ; symbolic integration ; polynomial functions ; monomials ; tetrahedron ; hexahedron ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper concerns analytical integration of polynomial functions over linear polyhedra in three-dimensional space. To the authors' knowledge this is a first presentation of the analytical integration of monomials over a tetrahedral solid in 3D space. A linear polyhedron can be obtained by decomposing it into a set of solid tetrahedrons, but the division of a linear polyhedral solid in 3D space into tetrahedra sometimes presents difficulties of visualization and could easily lead to errors in nodal numbering, etc We have taken this into account and also the linearity property of integration to derive a symbolic integration formula for linear hexahedra in 3D space. We have also used yet another fact that a hexahedron could be built up in two, and only two, distinct ways from five tetrahedral shaped elements These symbolic integration formulas are then followed by an illustrative numerical example for a rectangular prism element, which clearly verifies the formulas derived for the tetrahedron and hexahedron elements.
    Additional Material: 5 Ill.
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  • 29
    ISSN: 1069-8299
    Keywords: finite element method ; solid modelling ; optimal interpolation ; a posteriori error estimation ; adaptive interpolation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of approximating functions is considered in a general domain in one and two dimensions using piecewise polynomial interpolation. An error estimator is proposed which shows how to adaptively determine the interpolation degree. Numerical examples are given.
    Additional Material: 1 Ill.
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  • 30
    ISSN: 1069-8299
    Keywords: weight function approach ; edge crack problem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A fundamental field for the edge crack problem is suggested, and the field is composed of the singular displacement field and the complementary regular field. The boundary displacement of the fundamental field plays the role of the weight function in the edge crack problem. After multiplying the boundary traction in the physical problem with the weight function and performing integration along the boundary, the stress intensity factor at the crack tip is obtainable. Numerical examples are given to demonstrate the use of the suggested weight function approach.
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  • 31
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: control volume method ; finite element interpolation ; fluid flow ; upwind schemes ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Together with the finite element method (FEM), the control volume method (CVM) is of particular interest for the numerical solution of partial differential equations. The accuracy of computation of the CVM almost matches that of FEM in contour-adapted co-ordinates or block-structured meshes of a single element type. The CVM is superior to the FEM in terms of physical interpretation and ease of handling. The paper presents an interpretation of the FEM that allows it to be treated like a CVM. This formal CVM, which is based on FEM techniques, combines the advantages of both methods. The method is applied to the discretization of the Navier-Stokes equation.
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  • 32
    ISSN: 1069-8299
    Keywords: non-linear constitutive model ; anisotropy ; finite strains ; axisymmetrical finite elements ; vascular biomechanics ; soft tissue biomechanics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To explore the mechanical non-linear behaviour of anisotropic arterial walls on a computational basis, the formulation of a continuum based elastic potential is a major task and challenge to the analyst. The present communication is concerned with the constitutive modelling and numerical analysis of vascular segments covering finite strains. Special attention is paid to a two term potential that constitutes an essential foundation for accurate simulation within the entire strain domain. Axisymmetrical membrane elements are assembled to match the geometry of blood vessels. Numerical results confirm the theoretical approach by referring to experimental data of different rat arteries.
    Additional Material: 6 Ill.
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  • 33
    ISSN: 1069-8299
    Keywords: hyperbolic equations ; finite-difference methods ; Padé approximants ; sequential and parallel implementation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Techniques for two-time level difference schemes are presented for the numerical solution of first-order hyperbolic partial differential equations. The space derivative is approximated by (i) a low-order, and (ii) a higher-order backward difference replacement, resulting in a system of first-order ordinary differential equations, the solutions of which satisfy recurrence relations. The methods are obtained from the recurrence relations and are tested on three linear problems and one non-linear problem from the literature.
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  • 34
    Electronic Resource
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 35
    ISSN: 1069-8299
    Keywords: frictional contact ; large deformation ; one-pass approach ; master segment ; slave node ; contact constraint ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the context of large deformation analysis for metal forming processes a new one-pass approach for the frictional contact is proposed. This approach eliminates the short comings of traditional one-pass and two-pass approaches both from the constraint requirement and solution convergence points of view. Implemented in an updated Lagrangian framework with the Perturbed Lagrangian formulation of Ju and Taylor for non-linear frictional contact, a patch test and typical examples have been worked out to prove the validity of the proposed approach. It is observed that a finer surface discretization of the slave and master surfaces is no longer needed to enforce contact constraint.
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  • 36
    ISSN: 1069-8299
    Keywords: acoustics ; finite element method ; error estimation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A posteriori error estimation has become very popular, mainly in linear elasticity. A robust implementation of the superconvergent patch recovery technique of O. C. Zienkiewicz and J. Z. Zhu is presented for acoustic finite element analyses: the original concepts are extended to complex variables, and both local and global behaviours of the recovery procedure and the error estimation are studied. The numerical tests confirm the improvement of the rates of convergence for the recovered solution and also show the reliability of the error estimator except at frequencies corresponding either to the analytical or to the finite element eigenfrequencies.
    Additional Material: 13 Ill.
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  • 37
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    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 38
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 39
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: bellows ; shell of revolution ; integral equation method ; compressed angle ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper a U-shaped bellows is treated as a flexible shell of revolution which consists of circular ring shells and truncated shallow conical shells; then the non-linear problem of U-shaped bellows under the action of axial compression force and internal pressure is solved by means of the non-linear theory of shells and the integral equation method. Numerical solutions obtained are compared with previous theoretical and experimental results. The present theory is more appropriate to the analysis of bellows in the light of real profile shape, and shows that the influence of compressed angle on the characteristic relation and peak stresses is noticeable.
    Additional Material: 6 Ill.
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  • 40
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: hybrid-Trefftz element ; plate ; transient analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: 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.
    Additional Material: 4 Ill.
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  • 41
    ISSN: 1069-8299
    Keywords: eigenvalue extraction ; conjugate gradient method ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new conjugate gradient algorithm is presented for extracting eigenvalues from large systems of equations encountered in finite element analysis. The new algorithm involves applying the conjugate gradient method (CGM) to a static problem to generate an equivalent tridiagonal matrix used for eigenvalue computation. The eigenvalues of the tridiagonal matrix are then extracted using a QR factorization. The similarity of the new CGM with the Lanczos method is discussed regarding the need for matrix inversion and reorthogonalization. Several examples using the new method are presented to illustrate its performance.
    Additional Material: 2 Ill.
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  • 42
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    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: finite elements ; moving grids ; moving bodies ; mesh velocity ; ALE ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Laplacian smoothing of the mesh velocities with variable diffusivity based on the distance from moving bodies is introduced. This variable diffusivity enforces a more uniform mesh velocity in the region close to the moving bodies. Given that in most applications these are regions where small elements are located, the new procedure decreases element distortion considerably, reducing the need for local or global remeshing, and in some cases avoiding it altogether.
    Additional Material: 11 Ill.
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  • 43
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three different solution methods for the finite-volume discretized incompressible Navier-Stokes equations have been tested: segregated approaches, built around coupling methods such as SIMPLE, SIMPLER and PISO plus a line Gauss-Seidel linear solver; coupled methods, incorporating a penalty formulation to eliminate zero diagonal elements in the coefficient matrices, plus preconditioned GMRES as a linear solver;- and a FAS-full multigrid algorithm accelerating a classical segregated method based upon SIMPLE and the line Gauss-Seidel solver. Results demonstrate that the coupled method compares favourably to the segregated technique at small grid sizes but becomes too expensive for large problems. The FAS-full multigrid algorithm outperforms the other two methods when large numbers of nodes are employed in the simulation.
    Additional Material: 10 Ill.
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  • 44
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    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: viscoelastic flows ; sphere ; annular flow ; adaptive meshing ; finite elements ; error analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This work describes the implementation of an adaptive procedure for viscoelastic flows. Finite element simulations are conducted using a Taylor-Galerkin/pressure correction scheme. The constitutive equations considered are those for an Oldroyd-B and a Phan-Thien/Tanner model. The adaptive meshing technique is h-refined by grid remeshing, based on a Delaunay procedure. Results are presented for two benchmark problems, namely flow past a sphere in a cylindrical tube and flow in an annular converging tube. It is concluded from the results that the use of an adaptive procedure with mesh regeneration enables an optimized mesh to be devised and a predicted accuracy to be attained.
    Additional Material: 4 Ill.
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  • 45
    ISSN: 1069-8299
    Keywords: Laplace equation ; singularities ; boundary integral method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The authors present a new singular function boundary integral method for the numerical solution of problems with singularities which is based on approximation of the solution by the leading terms of the local asymptotic expansion. The essential boundary conditions are weakly enforced by means of appropriate Lagrange multipliers. The method is applied to a benchmark Laplace-equation problem, the Motz problem, giving extremely accurate estimates for the leading singular coefficients. The method converges exponentially with the number of singular functions and requires a low computational cost. Comparisons are made to the analytical solution and other numerical methods.
    Additional Material: 4 Ill.
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  • 46
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    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: finite elements ; QUAD4 elements ; RBF corrections ; shear force predictions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The residual bending flexibility correction is an extra-variational trick used to enhance the convergence rate of shear flexible beam and plate elements. In the paper we show how this can affect the shear deflection and shear force estimates in the QUAD4 element.
    Additional Material: 3 Ill.
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  • 47
    ISSN: 1069-8299
    Keywords: numerical integration ; Gauss quadrature rules ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The advance of powerful software for symbolic and numerical computations such as Mathematica sheds a new light on a paper by Golub and Welsch from 1969. Based on this paper the author describes a Mathematica procedure for determining the weights and abscissae of a Gauss quadrature rule with a user-defined weight function. After a brief description of the algorithm and its implementation examples demonstrate the usefulness of the procedure. The procedure is extremely useful if one has to compute many integrals with the same, possibly weakly singular, weight function. This might happen, for example, in the boundary element method.
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  • 48
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 49
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 50
    ISSN: 1069-8299
    Keywords: response reanalysis ; structural modifications ; matrix partitioning ; Sherman-Morrison formula ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper lays out an exact method, using the receptance strategy, to calculate the frequency response of a modified structure. A direct inversion of the modified impedance matrix is proposed, which reduces the computation time for successive calculations of an evolving design of the structure.
    Additional Material: 4 Ill.
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  • 51
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    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: finite elements ; isoparametric ; Jacobian ; transformation ; valid ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Isoparametric elements are only valid if the Jacobian determinant of the transformation between a given element and a master element does not change sign within or on the element boundary. Some algorithms are known which analyse Jacobians for various element types. Some necessary conditions are presented for determining the validity of an element.
    Additional Material: 5 Tab.
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  • 52
    ISSN: 1069-8299
    Keywords: RLW equation ; finite element methods ; Petrov-Galerkin ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The RLW equation is solved by a least-squares technique using linear space-time finite elements. In simulations of the migration of a single solitary wave this algorithm is shown to have higher accuracy and better conservation than a recent difference scheme based on cubic spline interpolation functions. In addition, for very small amplitude waves (≤ 0.09) it has higher accuracy than an approach using quadratic B-spline finite elements within Galerkin's method. The development of an undular bore is modelled.
    Additional Material: 5 Ill.
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  • 53
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    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: superconvergence ; isoparametric bilinear finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper the superconvergence property of isoparametric bilinear finite elements is considered. A new superconvergence recovery method for isoparametric bilinear finite elements is discovered on the four vertices and the four midpoints of the edges of the elements for piecewise strongly regular quadrilateral subdivisions.
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  • 54
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    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 55
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    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: iterative methods ; GMRES ; Krylov methods ; incomplete orthogonalization ; quasi-minimization ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We describe a Krylov subspace technique, based on incomplete orthogonalization of the Krylov vectors, which can be considered as a truncated version of GMRES. Unlike GMRES(m), the restarted version of GMRES, the new method does not require restarting. Like GMRES, it does not break down. Numerical experiments show that DQGMRES(k) often performs as well as the restarted GMRES using a subspace of dimension m=2k. In addition, the algorithm is flexible to variable preconditioning, i.e., it can accommodate variations in the preconditioner at every step. In particular, this feature allows the use of any iterative solver as a right-preconditioner for DQGMRES(k). This inner-outer iterative combination often results in a robust approach for solving indefinite non-Hermitian linear systems.
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  • 56
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    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 57
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    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: information ; latent semantic indexing ; low-rank ; orthogonal ; matrices ; metrieval ; singular value decomposition ; sparse ; ULV and URV decompositions ; updating ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Current methods to index and retrieve documents from databases usually depend on a lexical match between query terms and keywords extracted from documents in a database. These methods can produce incomplete or irrelevant results due to the use of synonyms and polysemus words. The association of terms with documents (or implicit semantic structure) can be derived using large sparse {\it term-by-document} matrices. In fact, both terms and documents can be matched with user queries using representations in k-space (where 100 ≤ k ≤ 200) derived from k of the largest approximate singular vectors of these term-by-document matrices. This completely automated approach called latent semantic indexing or LSI, uses subspaces spanned by the approximate singular vectors to encode important associative relationships between terms and documents in k-space. Using LSI, two or more documents may be closeto each other in k-space (and hence meaning) yet share no common terms. The focus of this work is to demonstrate the computational advantages of exploiting low-rank orthogonal decompositions such as the ULV (or URV) as opposed to the truncated singular value decomposition (SVD) for the construction of initial and updated rank-k subspaces arising from LSI applications.
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  • 58
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    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: multigrid ; incomplete Gaussian elimination ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we introduce and analyse a new Schur complement approximation based on incomplete Gaussian elimination. The approximate Schur complement is used to develop a multigrid method. This multigrid method has an algorithmic structure that is very similar to the algorithmic structure of classical multigrid methods. The resulting method is almost purely algebraic and has interesting properties with respect to variation in problem parameters.
    Additional Material: 5 Ill.
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  • 59
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    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: multilevel preconditioning ; Krylov subspace methods ; GMRES, nonsymmetric elliptic problems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The subject of this paper is to study the performance of multilevel preconditioning for nonsymmetric elliptic boundary value problems. In particular, a minimal residual method with respect to an appropriately scaled norm, measuring the size of the residual projections on all levels, is studied. This norm, induced by the multilevel splitting, is also the basis for a proper stopping criterion. Our analysis shows that the convergence rate of this minimal residual method using the multilevel preconditioner by Bramble, pasciak and Xu is bounded independently of the mesh-size. However, the convergence rate deteriorates with increasing size of the skew-symmetric part. Our numerical results show that by incorporating this into a multilevel cycle starting on the coarsest level, one can save fine-level-iterations and, therefore, computational work.
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  • 60
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    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: finite difference discretization ; fast adaptive composite grid method ; convergence rate ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The fast adaptive composite grid (FAC) method is an iterative method for solving discrete boundary value problems on composite grids. McCormick introduced the method in [8] and considered the convergence behaviour for discrete problems resulting from finite volume element discretization on composite grids. In this paper we consider discrete problems resulting from finite difference discretization on composite grids. We distinguish between two obvious discretization approaches at the grid points on the interfaces between fine and coarse subgrids. The FAC method for solving such discrete problems is described. In the FAC method several intergrid transfer operators appear. We study how the convergence behaviour depends on these intergrid transfer operators. Based on theoretical insights, (quasi-)optimal intergrid transfer operators are derived. Numerical results illustrate the fast convergence of the FAC method using these intergrid transfer operators.
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  • 61
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    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: iterative methods ; linear systems ; singular matrices ; block methods ; multisplitting ; two-stage ; non-stationary ; Markov chains ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The use of block two-stage methods for the iterative solution of consistent singular linear systems is studied. In these methods, suitable for parallel computations, different blocks, i.e., smaller linear systems, can be solved concurrently by different processors. Each of these smaller systems are solved by an (inner) iterative method. Hypotheses are provided for the convergence of non-stationary methods, i.e., when the number of inner iterations may vary from block to block and from one outer iteration to another. It is shown that the iteration matrix corresponding to one step of the block method is convergent, i.e., that its powers converge to a limit matrix. A theorem on the convergence of the infinite product of matrices with the same eigenspace corresponding to the eigenvalue 1 is proved, and later used as a tool in the convergence analysis of the block method. The methods studied can be used to solve any consistent singular system, including discretizations of certain differential equations. They can also be used to find stationary probability distribution of Markov chains. This last application is considered in detail.
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  • 62
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    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 63
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    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: diagonally dominant matrix ; determinant ; norm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A property of strictly diagonally dominant matrices and a generalization of a Varga's bound for ∥ A-1∥∞ to the case ∥ A-1B∥∞ are given and the two-sided bounds for the determinants of strictly diagonally dominant matrices are derived
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  • 64
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    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: boundary integral operators ; domain decomposition ; interface operators ; fast elliptic problem solvers ; parallel algorithms ; preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper a method for fast computations with the inverse to weakly singular, hypersingular and double layer potential boundary integral operators associated with the Laplacian on Lipschitz domains is proposed and analyzed. It is based on the representation formulae suggested for above-mentioned boundary operations in terms of the Poincare-Steklov interface mappings generated by the special decompositions of the interior and exterior domains. Computations with the discrete counterparts of these formulae can be efficiently performed by iterative substructuring algorithms provided some asymptotically optimal techniques for treatment of interface operators on subdomain boundaries. For both two- and three-dimensional cases the computation cost and memory needs are of the order O(N logp N) and O(N log2 N), respectively, with 1 ≤ p ≤ 3, where N is the number of degrees of freedom on the boundary under consideration (some kinds of polygons and polyhedra). The proposed algorithms are well suited for serial and parallel computations.
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  • 65
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    ISSN: 1070-5325