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  • 1990-1994  (3,688)
  • 1980-1984  (1,920)
  • Engineering  (4,698)
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  • 101
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 209-221 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: A theoretical analysis has been developed to study the crosstalk in crossed bundles of parallel lines. The model is based on the theory of the coupled transmission lines and the resulting system of differential equations has been solved by means of the finite difference, time-domain (FDTD) method. The frequency response of the network has been achieved by the discrete fourier transform (DFT) algorithm; measurements, performed with a vectorial network analyser, show a good agreement with numerical simulation.
    Additional Material: 8 Ill.
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  • 102
    Electronic Resource
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 35-41 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The eigenmodes in electromagnetic cavities, loaded with arbitrarily shaped dielectric materials, are computed by the edge element method. The computation shows that the well known ‘spurious modes’ no longer appear. Formulae are given and verified so that the number of zero eigenvalues, which come from ∇ × H = 0, may be accurately predicted. Formulae for the order and density of the global matrices are given for a rectangular cavity regularly divided into bricks and tetrahedra, allowing an associated comparison between the contrasting edge and nodal element formulations. Comparison of the computed results with available theoretical and previously published data show the edge element approach to be a robust, accurate and effective method.
    Additional Material: 1 Ill.
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  • 103
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 253-265 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: A numerical frequence-domain modelling of two-terminal, non-linear microwave circuits is presented. It basically relies on a process allowing the solution of the frequency-domain curcuit harmonic balance equations while accounting for the semiconductor device by means of an accurate numerical macroscopic physical model. In its present state of development, the model allows the study of a single two-terminal device circuit operating in harmonic mode. Its capabilites are illustrated by means of the results of a study devoted to the optimization of the load curcuit configuration of a millimetre-wave avalanche diode frequency multiplier. The influence of the output load impedance level on the circuit output RF performance has been investigated for different input power levels in direct frequency multiplication mode and in the presence of additional circuit tunings at low harmonic rank idler frequencies.
    Additional Material: 10 Ill.
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  • 104
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994) 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Type of Medium: Electronic Resource
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  • 105
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 309-319 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: This paper describes a rigorous and systematic procedure to derive a non-linear distributed FET model that an easily be implemented in CAD routines of simulators based on harmonic balance techniques. The new model is derived from a knowldge of the conventional linear lumped equivalent circuit, from non-linear current sources extracted with pulsed measurements, and from the physical dimensions of the FET.For fundamental and haromonic requencies, the FET is modelled by N identical cells. Each cell is made up of a non-linear two-port section inserted between two linear four-port sections that simulate the coupling and the distributed effects along the electrodes of the FET in the width direction only. This non-linear distributed scaling approach to FET modelling has been applied to the analysis of a submicrometre-gate GaAs FET at Millimetre-wave frequencies, and the results were compared to the non-linear lumped element approach. This approach can be applied to other transistors used in non-linear regions at microwave and millimetre-wave frequencies.
    Additional Material: 7 Ill.
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  • 106
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 375-375 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Type of Medium: Electronic Resource
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  • 107
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. ii 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Type of Medium: Electronic Resource
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  • 108
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 399-405 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Symbolic computational systems introduce some unique features in computational engineering. There have been several papers published on the solution of differential equations under given boundary conditions by symbolic systems. The finite element formalism has received prime attention in the course of development of symbolic computation in engineering. The main idea has been to develop a symbolic FEM package to reduce the burden of manual algebra, eliminate errors introduced by numerical quadrature, and improve the efficiency of element generation.This work discusses a symbolic solution to electromagnetic linear antenna problems. The solution is a method of moments that transforms Pocklington's integral equation to a matrix equation. The symbolic system is used to produce (1) analytical integration, (2) the parametric expression for the input impedance and (3) computational code for forward and reverse problem of the input impedance.
    Additional Material: 5 Ill.
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  • 109
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 419-432 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: This paper presents a new finite element formulation in the Laplace domain for both diffusion and wave equations with applications in the field of electrical engineering. With the aid of congruence transformation of matrices, the finite element equations in the Laplace domain are solved and time-domain results can be obtained through the inverse Laplace transform. In a test problem, good agreement between the numerical results derived with the present method and the analytical solutions has been found. For applications in which only Dirichlet and Neumann boundary conditions are involved, this new finite element approach can be applied and provide both frequency-domain and time-domain results in one run without any timestepping scheme. The limitations of using the congruence transformation in solving propagation problems are also addressed in this paper.
    Additional Material: 5 Ill.
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  • 110
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 433-452 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: A hybrid method obtained as a combination of the coupled-mode method (CMM) and the mode-matching method (MMM) is developed and applied in the analysis of multiple dielectric and magnetic discontinuities in rectangular waveguides. As both are moment methods, some kind of truncation has to be carried out in the computer implementation. It is shown that selection of a different number of modes in the two methods is not necessary, unless low-permittivity meida inside the waveguide are considered. As a consequence, the procedure for slecting the number of basis functions is only done in one of the methods. Numerical examples are presented showing the behaviour of the method and the proofs of convergence. Examples are included illustrating the power of this hybrid technique, especially in relation to non-reciprocal structures containing magnetized ferrites.
    Additional Material: 14 Ill.
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  • 111
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1481-1497 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A procedure for the optimization of stretched triangular grids is described. The method is based on the construction and minimization of a function that represents a generalized version for stretched grids of a non-linear spring system. The function is minimized using a gradient method based on the steepest descent. Examples are provided to show the applicability of the method to computational fluid dynamics problems.
    Additional Material: 15 Ill.
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  • 112
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1465-1480 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Multigrid method is used to accelerate the convergence of the numerical solution of the set of partial differential equations for generating the Body-Fitted Co-ordinate system (BFC) for both simply and doubly connected domain problems. The multigrid method is based on the full approximation scheme with bilinear interpolation as prolongation operator. The other components of the multigrid method such as the relaxation method, restriction operator, number of relaxation sweeps per cycle and direction of relaxation sweeps are varied with a view to obtaining the general principle in implementing an efficient multigrid algorithm for the generation of the BFCs.
    Additional Material: 11 Ill.
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  • 113
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1531-1555 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In Part I of this work, Paulino et al.1 have presented an algorithm for profile and wavefront reduction of large sparse matrices of symmetric configuration. This algorithm is based on spectral properties of a Finite Element Graph (FEG), An FEG has been defined as a nodal graph G, a dual graph G* or a communication graph G· associated with a generic finite element mesh. The novel algorithm has been called Spectral FEG Resequencing (SFR). This algorithm has specific features that distinguish it from previous algorithms. These features include (1) use of global information in the graph, (2) no need of a pseudoperipheral vertex or the endpoints of a pseudodiameter, and (3) no need of any type of level structure of the FEG. To validate this algorithm in a numerical sense, extensive computational testing on a variety of problems is presented here. This includes algorithmic performance evaluation using a library of benchmark test problems which contains both connected and non-connected graphs, study of the algebraic connectivity (λ2) of an FEG, eigensolver convergence verification, running time performance evaluation and assessment of the algorithm on a set of practical finite element examples. It is shown that the SFR algorithm is effective in reordering nodes and/or elements of generic finite element meshes. Moreover, it computes orderings which compare favourably with the ones obtained by some previous algorithms that have been published in the technical literature.
    Additional Material: 13 Ill.
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  • 114
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1557-1572 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To exploit the benefits of parallel computer architectures for multibody system simulation, an interdisciplinary approach has been pursued, combining knowledge of the three disciplines of dynamics, numerical mathematics and computer science. An analysis of the options available for the formulation and numerical solution of the dynamical system equations yielded a surprising result. A method initially proposed to solve the inverse problem of dynamics is the best choice to generate the system equations required for solving the simulation problem, when relying on implicit integration routines. Such routines have the particular advantage of handling stiff systems, too. The new O(N)-residual formalism, generating the system equations in a form required for implicit numerical integration, has a high potential to benefit from parallel computer architectures. Two strategies of medium and coarse grain parallelization have been implemented on a Transputer network to obtain a package for parallel multibody simulation. An analysis of the performance of this package demonstrates for typical multibody simulation problems that the new code is five times faster than existing codes when implemented on a serial computer. An additional speed-up by the same order of magnitude is obtained when the code is implemented on a Transputer network.
    Additional Material: 14 Ill.
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  • 115
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 181-201 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general Finite Volume Method (FVM) for the analysis of structural problems is presented. It is shown that the FVM can be considered to be a particular case of finite elements with a non-Galerkin weighting. For structural analysis this can readily be interpreted as equivalent to the unit displacement method which involves mainly surface integrals. Both displacement and mixed FV formulations are presented for static and dynamic problems.
    Additional Material: 12 Ill.
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  • 116
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 229-256 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems. In this method, moving least-squares interpolants are used to construct the trial and test functions for the variational principle (weak form); the dependent variable and its gradient are continuous in the entire domain. In contrast to an earlier formulation by Nayroles and coworkers, certain key differences are introduced in the implementation to increase its accuracy. The numerical examples in this paper show that with these modifications, the method does not exhibit any volumetric locking, the rate of convergence can exceed that of finite elements significantly and a high resolution of localized steep gradients can be achieved. The moving least-squares interpolants and the choices of the weight function are also discussed in this paper.
    Additional Material: 26 Ill.
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  • 117
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 37-48 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A pseudo-transient (static) linear, geometric, material and combined geometric and material non-linear analyses of composite laminates are presented. A nine-noded isoparametric quadrilateral finite element belonging to the Lagrangiar family is used in space discretization. An explicit time marching scheme is employed for time integration of the resulting discrete ordinary differential equations with the special forms of diagonal fictitious mass and/or damping matrices. Elasto-plastic material behaviour is incorporated using the flow theory of plasticity. In particular, a modified version of Hill's initial yield criterion is used in which anisotropy parameters of plasticity are introduced. The shear deformation is accounted for by assuming a constant transverse shear strain across the thickness of the laminate and the geometric non-linearity is considered in the sense of von Karman strains. The layered element approach is adopted for the treatment of plastic behaviour through the thickness. A wide range of numerical examples is presented to demonstrate the validity and efficiency of the present approach. The results for combined non-linearity are also presented. The variety of results presented here, which are based on realistic material properties of often-used advanced laminated composite plates, and especially those for combined non-linear analysis, should serve as a reference for future investigations.
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  • 118
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 91-105 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A variationally coupled finite element-boundary element method is developed for transient problems. A single variational statement is obtained for the entire domain and the unknown tractions, which may be discontinuous on the interface and are often a source of difficulties, are eliminated. Moreover, no interface conditions need be taken into consideration at the level of the discretized equation. The discrete equations for the coupled system can be obtained directly without any intermediate steps. The method generalizes a coupling method previously developed by the authors for statics. Numerical examples show that the solutions obtained by the present method agree very well with those obtained by analytical solutions.
    Additional Material: 8 Ill.
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  • 119
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 431-455 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A six-node triangle plate/shell element is developed for the analysis of laminated composite structures. This model is formulated using Hamilton's principle along with a first-order (Reissner/Mindlin) shear deformation theory. The element is based upon an isoparametric representation along with an interdependent interpolation strategy; bicubic polynomials for the transverse displacement and biquadratic polynomials for the element geometry, in-plane displacements and rotations. The resulting element, which is evaluated using exact numerical integration, has correct rank and is free of shear ‘locking’. Numerical results are presented that validate the new element and prove its outstanding convergence capabilities in comparison to existing triangular elements using standardized test problems (elastic eigenvalue analysis, patch test, static simply supported square-plate solutions) and experimentally measured vibration data of cantilevered isotropic and composite plates.
    Additional Material: 13 Ill.
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  • 120
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 475-496 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The collapse of ordinary finite elements to generate the desired strain singularity at the crack tip for fracture mechanics applications can lead to unwanted additional singularities in that area. Although neither the quarter-point nor the half-point 8-node two-dimensional (2-D) and 20-node three-dimensional (3-D) elements exhibit this behaviour, the present article proves that arbitrarily small deviations from the quarter-point element can be constructed which do have additional singularities. Since the general behaviour of the half-point element is not affected by small modifications, this element is better suited to match complex body geometries.
    Additional Material: 9 Ill.
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  • 121
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 537-538 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 122
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 517-536 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The superconvergent patch derivative recovery method of Zienkiewicz and Zhu is enhanced by adding the squares of the residuals of the equilibrium equation and natural boundary conditions. In addition, a new conjoint polynomial for interpolating the local patch stresses over the element which significantly improves the local projection scheme is presented. Results show that in the 4-node quadrilateral, the equilibrium and boundary condition residuals usually improve accuracy but not the rate of convergence, whereas in the 9-node quadrilateral, results are mixed. The conjoint polynomial always improves the accuracy of the derivative field within the element as compared to the standard nodal interpolation, particularly in 4-node quadrilaterals.
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  • 123
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 279-296 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An hybrid stress element formulation based on internal, incompatible displacements is used to develop efficient Mindlin plate elements. The 4-node quadrilateral Mindlin plate element is derived from a modified energy functional. Both displacements and stresses are defined in the natural co-ordinate interpolation system. The assumed stress field is obtained by tensor transformation and so chosen as to ensure that the element is co-ordinate invariant and stable. Shear locking is avoided through an appropriate identification of the internal, incompatible displacement field. The role played by incompatible displacements in the formulation of hybrid stress elements for thin and moderately thick plates is discussed. Numerical applications are presented to illustrate the accuracy and reliability of the suggested Mindlin plate element.
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  • 124
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 605-621 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the present paper, we analyse the computational performance of the Lanczos method and a recent optimization technique for the calculation of the p (p ≤ 40) leftmost eigenpairs of generalized symmetric eigenproblems arising from the finite element integration of elliptic PDEs. The accelerated conjugate gradient method is used to minimize successive Rayleigh quotients defined in deflated subspaces of decreasing size. The pointwise Lanczos scheme is employed in combination with both the Cholesky factorization of the stiffness matrix and the preconditioned conjugate gradient method for evaluating the recursive Lanczos vectors. The three algorithms are applied to five sample problems of varying size up to almost 5000. The numerical results show that the Lanczos approach with Cholesky triangularization is generally faster (up to a factor of 5) for small to moderately large matrices, while the optimization method is superior for large problems in terms of both storage requirement and CPU time. In the large case, the Lanczos-Cholesky scheme may be very expensive to run even on modern quite powerful computers.
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  • 125
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 387-411 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new eight-node quadrilateral shear-bending Reissner-Mindlin plate finite element for the very thin and thick plates without locking and spurious zero-energy modes is presented. The element has very good convergence characteristics both for thin and thick plates, is hardly insensitive to mesh distortions, and passes the patch tests. The formulation of the element is derived from a displacement variational principle and some general criteria to compute inconsistent transverse shear strains. These criteria have been applied with success to four- and eight-node quadrilateral plate finite elements and could be applied to construct triangular elements. The eight-node quadrilateral shear-bending plate finite element proposed has been found to be very efficient.
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  • 126
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 457-474 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A theory is proposed in this paper to explain, in a unified manner, the three rational approaches using the incompatible displacements uλ in the hybrid element formulation. Limited to the plane stress case, the theory suggests that the introduction of uλ is to constrain the total value of the invariant I2(= σxσy - τxy2) of the assumed stresses over the element to zero. In the plane stress case, this is the well-known condition for the stress distributions to be independent of the elastic constants of the material. The theory proposed is also used to explain the closeness of the performances of the four 4-node hybrid stress membrane elements, 5β-I, 5β-II, 5β-A and 5β-C, that have been developed previously. The differences among them are shown to be of the second degree in the distortion measures of the element shape, when they are compared on the basis of the non-vanishing total value of I2 of their respectively adopted assumed stress field. Several numerical examples are used to verify and to illustrate the proposed theory.
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  • 127
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 128
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1825-1840 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a boundary element formulation for the permanent Navier-Stokes equations in which the well-known closed-form fundamental solution for the steady Stokes equations is employed. In this way, from the integral representation formulae for the Stokes' equations, an integral equation is found in which the original non-linear convective terms of the Navier-Stokes equations appear as a domain integral. Additionally, the method of dual reciprocity is used to transform the domain integral to boundary integrals (this method is closely related to the method of particular integrals also used in the literature to transform domain integrals to boundary integrals). Numerical results are presented for the three-dimensional internal flow in a cylindrical container with a rotating cover, in which the accuracy of the method is shown.
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  • 129
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 2291-2309 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The helicoidal beam model developed in the first part of this work is applied here to the development of a mixed finite element for space-curved and twisted beams undergoing large displacements and finite rotations. Starting from the governing weak form expressed by the principle of virtual work, a consistent linearization is obtained in the following and a novel updated Lagrangian finite element implementation is thoroughly discussed.The unique features and the distinguishing properties previously claimed for the helicoidal model are shown here to imply remarkable numerical consequences. For this purpose, meaningful example problems regarding the non-linear static response of beams are addressed in the following and the results are compared with those available from the literature.Furthermore, a finite element in time for the rigid body dynamic problem is developed within the framework of the helicoidal geometry. The underlying philosophy of this novel finite element for dynamics is the realization of the helicoidal decomposition of the rigid body motion within a time step.
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    International Journal for Numerical Methods in Engineering 37 (1994) 
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2311-2335 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A finite element approach for shape optimization in two-dimensional (2-D) frictionless contact problems is presented in this work. The goal is to find the shape that gives a constant distribution of stresses along the contact boundary.The whole formulation, including mathematical model for the unilateral problem, sensitivity analysis and geometry definition is treated in a continuous form, independently of the discretization in finite elements. Shape optimization is performed by direct modification of geometry through B-spline curves and an automatic mesh generator is used at each new configuration to provide the finite element input data for numerical analysis and sensitivity computations. Using augmented-Lagrangian techniques (to solve the contact problem) and an interior-point mathematical-programming algorithm (for shape optimization), we obtain several results reported at the end of the article.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2337-2338 
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 1881-1896 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper presents the first endeavour to exploit a generalized differential quadrature method as an accurate, efficient and simple numerical technique for structural analysis. Firstly, drawbacks existing in the method of differential quadrature (DQ) are evaluated and discussed. Then, an improved and simpler generalized differential quadrature method (GDQ) is introduced to overcome the existing drawback and to simplify the procedure for determining the weighting coefficients. Subsequently, the generalized differential quadrature is systematically employed to solve problems in structural analysis. Numerical examples have shown the superb accuracy, efficiency, convenience and the great potential of this method.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 3015-3018 
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 3019-3021 
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    International Journal for Numerical Methods in Engineering 37 (1994) 
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 3005-3014 
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    Notes: Since Soize introduced the concept of fuzzy structures in structural acoustics there has been little activity clarifying the basic elements which underlie his theory. Soize's papers are not easy reading due to the high level of mathematical formalism. In addition Soize simultaneously bases this fuzzy structure theory on two components: (1) a model for one Degree Of Freedom (DOF) fuzzy oscillators, and (2) a medium frequency solution method developed previously. It is unclear as to the role of the two components, although others have already undertaken a study of the medium frequency method by itself.In the present paper a fundamental analysis of the first component, the one-DOF fuzzy oscillators, is undertaken. The symbolic manipulation program Mathematica is utilized to gain insight into this component of Soize's fuzzy theory. The resulting Mathematica simulations are easy to use and interpret, and they provide valuable insight into the parameters composing Soize's fuzzy oscillators. It is determined that in many cases of structural acoustics, where there is small damping and a medium to high modal density, the fuzzy mass primarily determines what effect a discrete fuzzy oscillator will have as an attachment.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 3023-3036 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A new numerical approach has been devised for performing accurate absorbing-emitting non-scattering radiation calculations for Cartesian co-ordinate based problems with one ordinate symmetry using only the solution plane formed by the other two ordinates. To accomplish this, the method makes use of ‘effective intensity rays’ which only exist and have meaning in the solution plane of the problem but which are made, through a special procedure, to contain the information of the third dimension. This novel procedure thus eliminates the problem of solid angles and greatly reduces both the complexity and computational expense involved in the solution of such problems. Yet it can do this without producing loss in accuracy. The approach is ultimately intended for use in combustion problems involving high temperatures and optically thin media. For verification purposes the method is applied to the problem of heat exchange in infinitely long rectangular enclosures and is found to give excellent results over a optical thickness range that includes the optically very thin case.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 1978-1979 
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2525-2525 
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2005-2039 
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    Notes: A method is described which constructs three-dimensional unstructured tetrahedral meshes using the Delaunay triangulation criterion. Several automatic point creation techniques will be highlighted and an algorithm will be presented which can ensure that, given an initial surface triangulation which bounds a domain, a valid boundary conforming assembly of tetrahedra will be produced. Statistics of measures of grid quality are presented for several grids. The efficiency of the proposed procedure reduces the computer time for the generation of realistic unstructured tetrahedral grids to the order of minutes on workstations of modest computational capabilities.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2109-2123 
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    Notes: A coupled transient thermoelastic behaviour of an axial-cracked hollow circular cylinder subjected to a sudden heating is investigated in this study. It is shown that surface heating may induce the compressive thermal stress near the inner surface of the cylinder which in turn may force the cracked surfaces to close together. Assuming that the existence of the crack does not alter the temperature distribution, we can divide this problem into two parts and solve it by the principle of superposition. First, the temperature and transient thermal stress distributions along the axisymmetric surface of the imaginary cylinder without crack are obtained by finite element implicit time integration method Secondly, the opposite sense of the stress distributions along the cracked surfaces, which is obtained previously, is treated as the traction boundary conditions; the contact length and contact pressure of the real cracked cylinder are obtained by modified elimination finite element scheme. Finally, we also obtained the normalized stress intensity factor for the crack tip of the cylinder. It is concluded that the effect due to thermoelastic coupling term on stress intensity factor becomes more important for higher coupling coefficient, and this coupling term also results in a small time lag in temperature, thermal stress and stress intensity factor.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2149-2150 
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2699-2700 
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2583-2608 
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    Notes: In continuum mechanics within specific classes of problems, one- or two-dimensional theories are often simpler to apply than the more complete three-dimensional one. This is, for example, the case of thin bodies, such as plates or shells, which may be studied using appropriate two-dimensionai theories.Within this approach, the reduction of the dimension is traded for a loss of information relative to the motion in the transverse direction. For example, in the case of non-linear material behaviour, classical plasticity plate theories are usually not able to model the effects related to the spreading of plasticity through the cross-section.In the present paper we discuss a generalized plasticity plate model, which can be used to reproduce some of the three-dimensional effects in a two-dimensional setting. We present the continuous and the discrete time model, including both isotropic and kinematic hardening mechanisms; moreover, the form of the tangent matrix consistent with the discrete model is addressed.Finally, some examples (cantilever beam, clamped circular plate and clamped square plate under monotonic and cyclic loading) are studied numerically using a three-dimensional classical plasticity theory, a classical plasticity plate theory and the proposed plate theory. The generalized plasticity plate model matches the three-dimensional response with greater accuracy, than the classical plasticity plate model.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2679-2697 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The dynamic behaviour of liquid-filled shells of revolution is investigated considering the soil-structure interaction and the fluid-structure interaction, respectively. In the circumferential direction the loads and variables are approximated by Fourier series. The shell is modelled through shell ring elements including non-linear behaviour, coupled with isoparametric continuum ring elements and special infinite elements for the soil and isoparametric pressure ring elements for the fluid. Transient loadings like earthquake excitation and the non-linearities of the shell and the soil require an analysis in the time domain. To reduce the size of the problem, linear parts of the system are condensed by the substructure technique. The soil region is divided into two parts, a near field permitting non-linearities like plastification or uplifting of the shell, and a far field for the treatment of radiation of energy.The boundary conditions for the shell footing have a strong influence on the distribution of the axial membrane forces and, hence, on the stability limit, which is mostly governed by plastic collapse and caused by the dynamically activated pressure acting on the tank wall. It is shown how the soil properties influence the dynamic stability of the shell under harmonic excitation and under realistic earthquake motion.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2701-2702 
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    International Journal for Numerical Methods in Engineering 37 (1994) 
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 2717-2733 
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    Notes: This paper presents a Wave Equation Model (WEM) to solve advection dominant Advection-Diffusion (A-D) equation. It is known that the operator-splitting approach is one of the effective methods to solve A-D equation. In the advection step the numerical solution of the advection equation is often troubled by numerical dispersion or numerical diffusion. Instead of directly solving the first-order advection equation, the present wave equation model solves a second-order equivalent wave equation whose solution is identical to that of the first-order advection equation. Numerical examples of 1-D and 2-D with constant flow velocities and varying flow velocities are presented. The truncation error and stability condition of 1-D wave equation model is given. The Fourier analysis of WEM is carried out. The numerical solutions are in good agreement with the exact solutions. The wave equation model introduces very little numerical oscillation. The numerical diffusion introduced by WEM is cancelled by inverse numerical diffusion introduced by WEM as well. It is found that the numerical solutions of WEM are not sensitive to Courant number under stability constraint. The computational cost is economical for practical applications.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 3825-3842 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A flat shell element based on the free-formulation finite element concept is developed for analysing geometrically non-linear thin composite shells. A corotational form of the updated Lagrangian formulation is utilized. Numerical results for typical validation problems are presented in order to demonstrate the accuracy and validity of this element. These results are obtained by solving the incremental equilibrium equations through the cylindrical arc-length method.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 3809-3823 
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    Notes: In this paper we investigate the additional storage overhead needed for a parallel implementation of finite element applications. In particular, we compare the storage requirements for the factorization of the sparse matrices that would occur on a parallel processor vs. a uniprocessor. This variation in storage results from the factorization fill-in. We address the question of whether the storage overhead is so large for parallel implementations that it imposes severe limitations on the problem size in contrast to the problems executed sequentially on a uniprocessor. The storage requirements for the parallel implementation are based upon a new ordering scheme, the combination mesh-based scheme. This scheme uses a domain decomposition method which attempts to balance the processors' loads and decreases the interprocessor communication. The storage requirements for the sequential implementation is based upon the minimum degree algorithm. The difference between the two storage requirements corresponds to the storage overhead attributed to the parallel scheme.Experiments were conducted on regular and irregular, 2-D and 3-D problems. The meshes were decomposed into 2-256 subdomains which can be executed on 2-256 processors, respectively. The total storage requirements or fill-in for most of the 2-D problems were less than a factor of two increase over the sequential execution. In contrast, large 3-D problems had zero increase in storage or fill-in over the sequential execution; the fill-in was less for the parallel execution than the sequential execution. Thus, we conclude that the storage overhead attributed to the use of parallel processors will not impose severe constraints on the problem size. Further, for large 3-D applications, the combination mesh-based algorithm does better than minimum degree for reducing the fill-in.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 3843-3868 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Incrementally objective integration schemes are proposed for the accurate and efficient determination of design sensitivity coefficients (DSCs) for solid mechanics problems with both material and geometrical non-linearities. The derivation of these schemes are based on the direct differentiation of objective schemes that are used in stress analysis for problems of this class. Two widely used objective stress rates, the Jaumann rate and the Green-Naghdi rate, are considered here within the same setting with only minor changes of the integration scheme. Numerical results are presented for a simple shear problem with different material constitutive laws, including a hypoelastic model and a unified isotropic viscoplastic model, for these two objective rates. The numerical results are compared with analytical solutions or direct integration solutions. The close agreement among these solutions demonstrates the accuracy and efficiency of the proposed scheme.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 3869-3903 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Development of a finite deformation elasto-plasticity model based on the multiplicative decomposition of the deformation gradient is presented and discussed in detail. The formulation presented in this paper includes the derivation of the full set of equations for the Drucker-Prager yield criterion. The equations, which are not available elsewhere, are developed within a framework using a spectral decomposition approach. Further, expressions for the consistent (algorithmic) tangent moduli in the finite strain regime are developed. Since the finite deformation framework employed to obtain the expressions presented here collapses to the classical infinitesimal plasticity framework when the finite strain assumption is no longer necessary, the finite deformation consistent tangent moduli are compared to the consistent tangent moduli valid for use with infinitesimal plasticity. Validation of the implemented finite deformation elasto-plastic Drucker-Prager model is performed through the solution of the concrete slump test. Comparisons between an existing approximate analytical solution and experimental data are presented, and results are discussed in detail.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 3905-3919 
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    Notes: This paper presents a parallel implementation of the boundary element method for MIMD computer architectures to determine the effective properties of two heterogeneous physical systems. The first physical system is comprised of spheres sedimenting in a viscous fluid at low Reynolds numbers. The effective property is characterized by the hindered settling function which is a measure of the average sedimentation velocity. The second physical system is a short-fibre reinforced composite. The effective property for this system is the composite modulus. The determination of effective properties of heterogeneous media requires performing statistical analyses of several realizations of physical systems based on defining characteristics of the media. The boundary element method is particularly well suited for studying such systems because of the simplification in the discretization associated with the method. However, as the number of heterogeneities to be modeled is increased so are the computational demands. Parallel computation offers the opportunity to model systems of greater complexity. We discuss a parallel boundary element formulation based on the torus-wrap mapping. In this approach, blocks of the coefficient matrix associated with the discretized boundary element equations are assigned to processors as opposed to more traditional parallel boundary element implementations where rows or columns are assigned to processors. The torus-wrap mapping can be shown to minimize communication volume between processors during the LU factorization. Therefore, the present formulation scales well with increases in the number of processors.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 4263-4284 
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    Notes: The use of inconsistent displacement fields for Mindlin plate elements causes unmatched coefficients to appear in shear strain interpolations. The role of the numerical integration order in relation to these unmatched coefficients, and the existence of optimal stress points are explained through the use of the reduced minimization concept. This concept makes it possible to test whether assumed displacement fields or shear strain fields result in inconsistent strain fields which contain spurious constraints. We have included applications of reduced minimization to the conventional C0-continuous elements, which employ reduced integration, and to quadrilateral Mindlin plate elements of Hinton and Huang to demonstrate how these elements alleviate shear locking.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 715-716 
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 693-713 
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    Notes: A method using techniques of computational geometry for generating tetrahedral finite element meshes in three-dimensional polyhedral regions is presented. The input to the method consists of the boundary faces of the polyhedral region and possibly internal and hole interfaces, plus the desired number of tetrahedra and other scalar parameters. The region is decomposed into convex polyhedra in two stages so that tetrahedra of one length scale can be generated in each subregion. A mesh distribution function, which is either automatically constructed from the first-stage convex polyhedron decomposition or supplied by the user, is used to determine the tetrahedron sizes in the subregions. Then a boundary-constrained triangulation is constructed in each convex polyhedron, with local transformations being used to improve the quality of the tetrahedra. Experimental results from triangulations of three regions are provided.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 763-775 
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    Notes: The aim of the present study is to show that the developed particle dynamics method is able to describe important characteristics of powder assemblies. In the method, the interaction forces that are introduced between the particles are electrostatic attractive forces and elastic repulsive forces. Energy dissipation by friction at contact surfaces and damping during cohesive collision were also considered. Several numerical experiments on the angle of repose, packing and compaction are carried out. The initial position and the size of the particles are randomly distributed based on the Monte-Carlo method. The simulation results show that the method can be used to evaluate the effect of particle characteristics on flowability of powder assemblies.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 737-762 
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    Notes: An iterative and incremental algorithm is presented for the Design Sensitivity Analysis (DSA) of elastoplastic structures. Geometrical non-linearity is included in the formulation, and the structure may be subjected to a cyclic loading. The key concept is discussed using an elastoplastic truss. It is shown that the Design Sensitivity Coefficients (DSCs) are path-dependent and discontinuous at the time at which yielding takes place in a member (yield time). In the proposed algorithm, the yield time is considered to be a function of the design variables. In this way, the discontinuity in the DSCs at the material transition points can be overcome in a simple and routine way. Incremental response analysis and DSA are carried out simultaneously using the Newton-Raphson type iterative procedure. Since the proposed algorithm is completely consistent with the analysis procedure, it can be implemented into an existing code for structural analysis. Application to distributed parameter structures with kinematic and/or isotropic hardening is discussed using the von Mises yield condition and the elastic-predictor radial-return method. DSA is carried out for a ten-bar truss with a piecewise linear constitutive relation. It is shown that the DSCs found using the proposed method agree quite well with those calculated by the central difference method. Finally, an alternate method without any iteration for DSA is proposed and the results from the two methods are compared.
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  • 162
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 717-735 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Sheet metal forming is simulated by finite element methods using a stress resultant constitutive law in this paper. A Lagrangian description of axisymmetric and plane-strain shell deformation is first reviewed. Then a stress resultant constitutive law in rate form is presented, where the effect of thickness reduction due to large plastic deformation is considered. A finite element formulation in terms of stress resultants and their work-conjugate generalized strain rates is derived based on the virtual work principle. A hemispherical punch stretching operation and a plane-strain draw operation are simulated by a finite element program based on the finite element formulation. The results of these finite element simulations are in good-agreement with those using the through-the-thickness integration method. The results of the hemispherical punch stretching simulation suggest that the coupling term of moments and membrane forces of the modified Ilyushin yield function should be eliminated to avoid numerical instability under stretching-dominated conditions for this rate-independent plasticity formulation. Further, the results suggest that the hardening rule in a power-law form based on the small-strain approach must be modified to take account for finite deformation effects of combined stretching and bending. Under the plane-strain draw operation, the sheet experiences a large amount of bending before the final stretching. The simulation based on the stress resultant constitutive law can produce this essential aspect of deformation pattern as that of the through-the-thickness integration method, whereas a simulation based on a membrane theory cannot. In conclusion, the results of these simulations indicate that a finite element program based on the stress resultant constitutive law can simulate sheet-forming processes with much shorter computational time than that based on the through-the-thickness integration method.
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  • 163
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 813-826 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A return mapping algorithm is presented for the numerical time integration of the constitutive equations for elastoplasticity with isotropic yield surfaces, constructed from all three invariants of the stress tensor. Based on the first-order backward Euler difference formula (BDF), the governing equations for the stresses are solved in the space of the invariants and the discretized persistence parameter. The stresses are recovered afterwards. The solution concept is applied to a pressure-independent yield function, expressed in terms of the second and third invariant of the stress tensor. The numerical performance of the method is demonstrated with two examples.
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  • 164
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 793-812 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A technique for refining three-dimensional tetrahedral meshes is proposed in this paper. The proposed technique is capable of treating arbitrary unstructured tetrahedral meshes, convex or non-convex with multiple regions resulting in high quality constrained Delaunay triangulations. The tetrahedra generated are of high quality (nearly equilateral). Sliver tetrahedra, which present a real problem to many algorithms are not produced with the new method. The key to the generation of high quality tetrahedra is the iterative application of a set of topological transformations based on the Voronoi-Delaunay theory and a reposition of nodes technique. The computational requirements of the proposed technique are in linear relationship with the number of nodes and tetrahedra, making it ideal for direct employment in a fully automatic finite element analysis system for 3-D adaptive mesh refinement. Application to some test problems is presented to show the effectiveness and applicability of the new method.
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  • 165
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 1027-1038 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The stiffness matrix of a plane four-node quadrilateral finite element is given in closed form. When expressed as a FORTRAN subroutine and compared with the classical method of forming the stiffness matrix using Gaussian integration, the approach gives a CPU time speed-up of the order of 2-3 on a vector machine and of the order of 4-5 on a scalar machine. The technique used to generate the terms of the stiffness matrix made use of a computer algebra system which could clearly be extended to generate the matrices for other elements types.
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  • 166
    ISSN: 0003-276X
    Keywords: Ultrastructure ; Human inner ear ; Melanocytes ; Melanosomes ; Gap junctions ; Isolated cilia ; Annulate lamellae ; Fusiform banded structures ; Life and Medical Sciences ; Cell & Developmental Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Background: It is known that melanocytes exist in almost all parts of the inner ear, such as the cochlear duct, stria vascularis, Reissner's membrane, modiolus, vestibular organs in the region surrounding the cristae and maculae, semicircular canals, and pars rugosa of the endolymphatic sac. But there have been few studies using human materials, because of the difficulty of obtaining materials. We attempted to investigate the detailed ultrastructure of melanocytes in the vestibular organs of human inner ear.Methods: Eight surgical specimens obtained from patients with vestibular schwannoma were studied by light microscopy and electron microscopy.Results: Melanocytes were found in the subepithelial layer of the dark cell area. Melanocytes had round or spindle-shaped nuclei and clear cytoplasm with brown pigment granules. Besides melanocytes, there were melanophages, fibroblasts, and small blood vessels. Through electron microscopy we found melanocytes with round-shaped melanosomes in various stages of pigmentation, well-developed Golgi apparatus and endoplasmic reticulum in the cytoplasm, and many cytoplasmic processes. Gap junctions were occasionally found between the cytoplasmic processes. And there were pinocytotic vesicles just under the limiting membrane of melanocytes, and intermediate filaments were abundant in the cytoplasm. Isolated cilia of melanocytes, annulate lamellae, and fusiform banded structures in the connective tissue area around melanocytes were found.Conclusions: Melanocytes in human vestibular organs actively synthesize melanosomes. Frequent findings of isoalted cilia and fusiform banded structures and the incidental existence of annulate lamellae may be an indicator of this metabolically activated state of melanocytes. Moreover, monitoring environmental changes by isolated cilia, melanocytes in the human inner ear could act not only as one cell but also as a group to achieve their physiological functions by means of information transmission through gap junctions. © 1994 Wiley-Liss, Inc.
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  • 167
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    The @Anatomical Record 238 (1994), S. 425-436 
    ISSN: 0003-276X
    Keywords: Amelogenesis ; Tooth ; Rat ; Mouse ; Cryofixation ; Freeze-substitution ; Ultrastructure ; Enamel proteins ; Immunocytochemistry ; Life and Medical Sciences ; Cell & Developmental Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Background: Cryofixation rapidly immobilizes cell and tissue components in their native state, thereby resulting in an ultrastructural preservation very close to the living situation. We have applied this approach to examine the morphology of secretory stage ameloblasts and the distribution of enamel proteins in these cells.Methods: Molar and incisor tooth germs from newborn mice and/or rats were quickly dissected and divided into segments. The segments were then rapidly frozen using slam, plunge or pressure freezing, freeze-substituted and embedded in Epon. In addition, incisors from older rats were chemically fixed by vascular perfusion and also dehydrated by freeze-substitution.Results: Well-preserved ameloblasts were obtained with all four tissue processing methods. However, slam freezing often showed mechanical damage to the ameloblasts, particularly at the level of the distal portion of Tomes' processes which appeared severed or distorted. Plunging into liquid nitrogen-cooled liquid propane resulted in comparatively less tissue distortion. High pressure freezing gave a relatively higher yield of well-preserved specimens, although displacement of organelles in ameloblasts was sometimes observed, probably resulting from hydrostatic pressure. Minimal ice crystal and mechanical damage was observed in chemically fixed tooth samples processed by freeze-substitution since such specimens are cryoprotected and their examination is not restricted to a surface layer. With all of the above cryopreparation methods, the ultrastructure of well preserved ameloblasts was, in general, similar to that obtained following conventional chemical fixation, and immunocytochemistry with an anti-amelogenin antibody indicated no profound differences in the distribution of enamel proteins.Conclusions: These results indicate that, despite some limitations, it is possible to adequately cryofix tooth organs while preserving the architecture of ameloblasts and permitting immunolocalization of enamel proteins. Furthermore, they confirm the general morphology of secretory stage ameloblasts as currently derived from conventional chemical tissue processing. © 1994 Wiley-Liss, Inc.
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  • 168
    ISSN: 0003-276X
    Keywords: Cartilage ; Osteoarthrosis ; Human ; Ultrastructure ; Histochemistry ; Life and Medical Sciences ; Cell & Developmental Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: Background: Ageing and osteoarthritic (OA) cartilage show characteristic alterations in chondrocyte morphology and in the composition and content of matrix proteoglycans (PGs). Data concerning matrix components are mostly of biochemical nature. Ultrastructural histochemistry is needed to gain more information about distribution of these altered matrix components.Methods: We used the cationic dye polyethyleneimine (PEI) to visualize at the EM level alterations in the distribution and dimensions of PGs of human healthy young, healthy aged, and OA articular cartilage.Results: Young cartilage contained PEI-positive granules in the superficial layer and big winding PEI-positive structures in the deeper layers. In the healthy aged tissue, PEI-positive granules were observed throughout the matrix and smaller winding structures were present in the deeper layer. In OA cartilage both types of PEI-positive structures were absent in the superficial layer. Deeper in the matrix PEI-positive granules could be demonstrated. Moreover, PEI-positive angular structures were observed in the deeper zones.Conclusions: The differences in PEI-positive structures are a good reflection of the differences in PGs between young, ageing, and OA cartilage as demonstrated in biochemical studies. PEI, used at the EM level, gave more precise information concerning the localized changes in quality, quantity, and location of PGs in articular cartilage during ageing and disease. © 1994 Wiley-Liss, Inc.
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  • 169
    ISSN: 1059-910X
    Keywords: Sinus afferent pathway ; SP interneurons ; Double immunocytochemistry ; Ultrastructure ; Life and Medical Sciences ; Cell & Developmental Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Natural Sciences in General
    Notes: The ultrastructure of substance P-containing nerve terminals synapsing on catecholamine neurons in the rat commissural subnucleus of the nucleus tractus solitarii (NTScom) was studied using a double immunocytochemical labeling technique. Although there were numerous tyrosine hydroxylase-immunoreactive (TH-I) somata present, substance P immunoreactive (SP-I) cell bodies were only occasionally found in the NTScom. At the light microscopic level, many SP-I terminals were seen closely associated with TH-I dendrites and somata. At the electron microscopic level, SP-I terminals synapsing on TH-I structures were also readily encountered. SP-I terminals contained small, clear, and predominantly spherical vesicles (32 ± 4 nm diameter), as well as large dense-cored vesicles approximately 100 nm in diameter. Postsynaptic TH-I dendritic profiles of various calibers and somata were encountered. These postsynaptic TH-I structures often showed postsynaptic densities. The morphological features of the SP-TH synapses in the present study, that is, the size of synaptic vesicles and the presence of postsynaptic densities, are quite different from those of central carotid sinus afferent synapses reported in our previous study [Chen et al. (1992), J. Neurocytol., 21:137-147]. Therefore, most of the SP terminals of the SP-TH synapses in the NTScom appear not to originate from the carotid sinus afferents. SP-I second-order neurons of the carotid sinus afferent pathway [Chen et al. (1991), J. Auton. Nerv. Syst., 33:97-98] may be one of the possible sources of such terminals. © 1994 Wiley-Liss, Inc.
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  • 170
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    Numerical Linear Algebra with Applications 1 (1994), S. 75-101 
    ISSN: 1070-5325
    Keywords: Variable-step preconditioners ; Nonlinear preconditioning ; Generalized conjugate gradient method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: When solving large size systems of equations by preconditioned iterative solution methods, one normally uses a fixed preconditioner which may be defined by some eigenvalue information, such as in a Chebyshev iteration method. In many problems, however, it may be more effective to use variable preconditioners, in particular when the eigenvalue information is not available.In the present paper, a recursive way of constructing variable-step of, in general, nonlinear multilevel preconditioners for selfadjoint and coercive second-order elliptic problems, discretized by the finite element method is proposed. The preconditioner is constructed recursively from the coarsest to finer and finer levels. Each preconditioning step requires only block-diagonal solvers at all levels except at every k0, k0 ≥ 1 level where we perform a sufficient number ν, ν ≥ 1 of GCG-type variable-step iterations that involve the use again of a variable-step preconditioning for that level.It turns out that for any sufficiently large value of k0 and, asymptotically, for ν sufficiently large, but not too large, the method has both an optimal rate of convergence and an optimal order of computational complexity, both for two and three space dimensional problem domains.The method requires no parameter estimates and the convergence results do not depend on the regularity of the elliptic problem.
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  • 171
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    Numerical Linear Algebra with Applications 1 (1994), S. 65-74 
    ISSN: 1070-5325
    Keywords: Elasticity ; Finite elements ; preconditioning ; Multilevel ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The basic theory of the strengthened Cauchy-Buniakowskii-Schwarz (C.B.S.) inequality is the main tool in the convergence analysis of the recently proposed algebraic multilevel iterative methods. An upper bound of the constant γ in the strengthened C.B.S. inequality for the case of the finite element solution of 2D elasticity problems is obtained. It is assumed that linear triangle finite elements are used, the initial mesh consisting of right isosceles triangles and the mesh refinement procedure being uniform. For the resulting linear algebraic systems we have proved that γ2〈0.75 uniformly on the mesh parameter and on Poisson's ratio ν ∊ (0, 1/2). Furthermore, the presented numerical tests show that the same relation holds for arbitrary initial right triangulations, even in the case of degeneracy of triangles.The theoretical results obtained are practically important for successful implementation of the finite element method to large-scale modeling of complicated structures. They allow us to construct optimal order algebraic multilevel iterative solvers for a wide class of real-life elasticity problems.
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  • 172
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    Numerical Linear Algebra with Applications 1 (1994), S. 247-263 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper presents a row relaxation method for solving the regularized ℓp least norm problem \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm minimize}P({\rm x}) = \frac{1}{2}\varepsilon \parallel {\rm x}\parallel _{\rm 2}^{\rm 2} + \parallel A{\rm x} - {\rm b}\parallel _p^p /p $$\end{document} where e and p are positive constants, 1〈p〈∞ The interest that we have in this problem lies in the observation that for small values of E the minimizer of P (X ) is a good substitute for a minimizer of the unregularized problem \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm minimize }U({\rm x}) = \parallel A{\rm x} - {\rm b}\parallel _p^p /p $$\end{document} It is shown that the dual of the regularized problem has the form \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm minimize }D({\rm y}) = {\rm b}^T {\rm y} - \frac{1}{2}\varepsilon \parallel A^T {\rm y/}\varepsilon \parallel _2^2 - \parallel {\rm y}\parallel _q^q /q $$\end{document} where q = p /(p - 1). Moreover, if y solves the dual problem then X = ATy/∊ solves the primal problem and P(ATy/∊) = D(y). Maximizing the dual objective function by changing one variable at a time results in a row relaxation method that resembles Kaczmarz's method. This feature makes the new method suitable for solving large sparse C, problems that arise in computerized tomography, geophysics, and groundwater hydrology. Numerical experiments illustrate the feasibility of our ideas.
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  • 173
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    Numerical Linear Algebra with Applications 1 (1994), S. 331-333 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 174
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    Numerical Linear Algebra with Applications 1 (1994), S. 313-329 
    ISSN: 1070-5325
    Keywords: Discretization method ; Nonlinear ABS class ; Newton-type method ; Quadratic convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we give a class of algorithms for solving nonlinear algebraic equations using difference approximations of derivatives. The class is a modification of the original ABS class with the advantage of requiring less function evaluations. Special cases include the methods of Brown and Brent and the discretized Newton method, which is formulated in a way requiring fewer function evaluations per iteration.
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  • 175
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    Numerical Linear Algebra with Applications 1 (1994), S. 287-311 
    ISSN: 1070-5325
    Keywords: Linear systems ; Incomplete factorizations ; Parallel computation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper two new implementations of SSOR and incomplete factorization preconditioners are given, for shared memory and distributed memory parallel computers respectively. These new implementations give increased solution speeds for matrix problems such as those arising from discretized partial differential equations with natural ordering of the grid points, for which it is well-known that the standard implementation of these preconditioners is difficult to parallelize effectively. For shared memory machines, a new technique is presented here which decreases the number of synchronization points in each preconditioning step and thus allows better parallel speedups. For distributed memory machines, an implementation based on block cyclic reduction is given which circumvents the problem of idle processors during the preconditioning phase. Descriptions of the implementations are given, and numerical comparisons are given for a model diffusion problem on the Cray Y-MP and the CM-2 Connection Machine.
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  • 176
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    Numerical Linear Algebra with Applications 1 (1994), S. 511-532 
    ISSN: 1070-5325
    Keywords: Iterative methods for linear systems ; Acceleration of convergence ; Preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new incomplete factorization method is proposed, differing from previous ones by the way in which the diagonal entries of the triangular factors are defined. A comparison is given with the dynamic modified incomplete factorization methods of Axelsson-Barker and Beauwens, and with the relaxed incomplete Cholesky method of Axelsson and Lindskog. Theoretical arguments show that the new method is at least as robust as both previous ones, while numerical experiments made in the discrete PDE context show an effective improvement in many practical circumstances, particularly for anisotropic problems.
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  • 177
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    Numerical Linear Algebra with Applications 1 (1994), S. 571-581 
    ISSN: 1070-5325
    Keywords: GMRES ; GMRES(m) ; Large-scale nonsymmetric linear systems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The generalized minimal residual (GMRES) method is widely used for solving very large, nonsymmetric linear systems, particularly those that arise through discretization of continuous mathematical models in science and engineering. By shifting the Arnoldi process to begin with Ar0 instead of r0, we obtain simpler Gram-Schmidt and Householder implementations of the GMRES method that do not require upper Hessenberg factorization. The Gram-Schmidt implementation also maintains the residual vector at each iteration, which allows cheaper restarts of GMRES(m) and may otherwise be useful.
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  • 178
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    Numerical Linear Algebra with Applications 1 (1994), S. 555-570 
    ISSN: 1070-5325
    Keywords: Linear system of equations ; Iterative method ; Fast algorithm ; Arnoldi process ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new iterative scheme is described for the solution of large linear systems of equations with a matrix of the form A = ρU + ζI, where ρ and ζ are constants, U is a unitary matrix and I is the identity matrix. We show that for such matrices a Krylov subspace basis can be generated by recursion formulas with few terms. This leads to a minimal residual algorithm that requires little storage and makes it possible to determine each iterate with fairly little arithmetic work. This algorithm provides a model for iterative methods for non-Hermitian linear systems of equations, in a similar way to the conjugate gradient and conjugate residual algorithms. Our iterative scheme illustrates that results by Faber and Manteuffel [3,4] on the existence of conjugate gradient algorithms with short recurrence relations, and related results by Joubert and Young [13], can be extended.
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  • 179
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    Numerical Linear Algebra with Applications 1 (1994), S. 583-587 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 180
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    Communications in Numerical Methods in Engineering 10 (1994), S. 373-384 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper demonstrates an approach to generate three-dimensional boundary-fitted computational meshes efficiently. One basic idea underlying the present study is that often similar geometries have to be meshed, and therefore an efficient mesh-adaption method, which allows adaptation of the topological mesh to the specific geometry, would be more efficient than generating all new meshes. On the other hand the mesh generation for Cartesian topologies has been shown to be a very simple task. It can be executed by connecting and removing brick elements to a basic cube. In connection with a so-called ‘Macro Command Language’, a high degree of automation can be reached when adapting topologically defined meshes to a surface. Furthermore, a high mesh quality has proved to be the key to good simulation results. During the mesh generation it is important to provide the possibility of modifiying the mesh quality and also the mesh density at any time of the meshing process. Using this generation method the meshing time is reduced - e.g. a computational mesh for a two-valve cylinder head can be generated within a few hours.
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  • 181
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    Communications in Numerical Methods in Engineering 10 (1994), S. 393-401 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we present numerical experiments made to investigate the behaviour of the Newmark time-stepping scheme applied to non-linear dynamic systems. Our attention is focused on the instability and chaos in the Newmark scheme when it is applied to the equation ü + P(u) = 0, representing a non-linear elastic spring. Some unusual modes of behaviour, which are of substantial interest, have been observed. In the first case, a stable but chaotic solution is found. In the second case, while a stable solution is obtained with a certain time step, an unstable solution is found by decreasing the time step. In the third case, instability is triggered by neglecting the initial acceleration. A simple modification of the Newmark scheme is proposed which keeps the energy constant for the equation ü + P(u) = 0 and thereby guarantees unconditional stability. Numerical examples in support of such an energy-conserving scheme are presented.
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  • 182
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    Communications in Numerical Methods in Engineering 10 (1994), S. 421-423 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A note on the effects of a weak discontinuity in the forcing function g(x) of a singular, integral equation of the first kind and the resulting strong discontinuity that can appear in the solution f(x) is presented.
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  • 183
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    Communications in Numerical Methods in Engineering 10 (1994), S. 427-435 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a new method for the numerical solution of transient linear heat conduction problems. In the proposed method, the transient linear heat conduction equation is first integrated with respect to time over subsequent intervals. Then the resulting set of elliptic equations is discretized in space according to a finite-element procedure. The method is unconditionally stable. At the end of the paper, the effectiveness of the proposed method is assessed through some numerical examples.
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  • 184
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    Communications in Numerical Methods in Engineering 10 (1994), S. 453-460 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In finite-element analysis of transient heat conduction, oscillatory results are quite common. Several criteria for eliminating oscillation which permit choice of time step length and/or element mesh and type are sensibly derived and proved with a different methodology from those of previous work. Numerical examples are presented to show their validity and usefulness.
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  • 185
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    Communications in Numerical Methods in Engineering 10 (1994), S. 437-451 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper a computation code based on the finite-element method for temperature evolutions in composite elements with internal cavities is presented. It is suitable for the analysis of various thermal problems encountered in mechanical and civil engineering such as fire risk assessment. It is based on a plane isoparametric triangular element with six nodes allowing the modelling of curved boundaries. In order to analyse composite steel-concrete elements and to take into account the non-linearities coming from the temperature-dependent material properties and from the boundary conditions, an implicit integration scheme is used. Another advantage of the program is the possibility of describing internal cavities with convection and radiation exchanges. In order to show the capacity of the program two examples are presented. Comparisons have been made with experimental and other numerical results, exhibiting very good agreement.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 461-468 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A speculation is presented to explain in physical terms the biblical story in which the withdrawal and return of the sea saved the Hebrews but drowned the army of Pharaoh. The explosion of the volcano on the island of Thira (Santorini) is speculated to be connected with this biblical story.To support our proposition concerning depression and flooding waves, we have made a numerical calculation with a highly accurate computer code and provided an outline of the PLIM method (piecewise linear interpolation method) used. This calculation is numerically very challenging because the volcano is located far from the shore and hence detailed discretization is not practical. In addition, we show that if a less accurate numerical method is used, the whole phenomenon is lost because of numerical errors.Our simple approach provides a withdrawal and return of the water to the shore that is sufficiently large, but the duration of this occurence is only a few minutes. The opportunity for a much longer duration as a consequence of other phenomena has not been excluded, however.
    Additional Material: 8 Ill.
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  • 187
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    Communications in Numerical Methods in Engineering 10 (1994), S. 489-496 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The possibility of improving heat transfer rates by the imposition of a wavy boundary led to this extension of direct simulation of heat transfer in turbulent flow in a channel. This part of the paper shows how a pattern of micro-riblets on the surface and parallel to the flow is incorporated into the solution of the Navier-Stokes and temperature equations. The channel is two-dimensional with walls at different but uniform temperatures, and the fluid properties are constant. The presence of the patterns presents a considerable computational problem that can be largely overcome by the use of a discrete Green function technique. The method is illustrated by making short-time calculations of the velocity and temperature fields for a Prandtl number of 0.72, a Reynolds number based on channel half-width and bulk velocity of 2800, and a sinusoidal pattern with a height of 5 wall units.
    Additional Material: 3 Ill.
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  • 188
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    Communications in Numerical Methods in Engineering 10 (1994) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 189
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    Communications in Numerical Methods in Engineering 10 (1994), S. 511-521 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the present study a hybrid boundary-element and finite-element method is developed for the non-linear analysis of two-dimensional elastic media with inclusions, and it is utilized in defining the micro-mechanical stress field in composite materials. The linear elastic, isotropic and homogeneous matrix is treated with the BEM, while the non-linear elastic and orthotropic inclusions (fibres) are treated with the FEM.
    Additional Material: 12 Ill.
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  • 190
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    Communications in Numerical Methods in Engineering 10 (1994), S. 501-510 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite-element solution for elastohydrodynamic lubrication (EHL) of spherical bodies undergoing elastic deformation is presented. The Galerkin finite-element approach is employed and the domain under investigation is discretized using isoparametric quadrilateral elements. Isothermal conditions are assumed and the generation of the pressure is assumed to be governed by the Reynolds equation. The viscosity and the density of the oil are assumed to be functions of the pressure. It is assumed that the underlying surface deforms elastically under the hydrodynamic pressure distribution. The accuracy of the technique is illustrated in particular examples.
    Additional Material: 12 Ill.
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  • 191
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    Communications in Numerical Methods in Engineering 10 (1994), S. 523-530 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient algorithm is developed for the formation of a minimal cycle basis of a graph. This method reduces the number of cycles to be considered as candidates for being the elements of a minimal basis and makes practical use of the Greedy algorithm feasible. A comparison is made between the existing methods and the present algorithm. A counter-example is presented for Kaveh's algorithm from planar graphs.
    Additional Material: 5 Ill.
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  • 192
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    Communications in Numerical Methods in Engineering 10 (1994) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 193
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    Communications in Numerical Methods in Engineering 10 (1994), S. 711-716 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We derive explicit expressions of shape functions for the 8-node serendipity element with bilinear element geometry, which is modified so that it can represent any quadratic fields in Cartesian co-ordinates. The modification is similar to the one by MacNeal and Harder, but is slightly different and based on our own idea. We also show that the usual 6-node triangular element can be obtained by applying the node degeneration technique to this modified element.
    Additional Material: 1 Ill.
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  • 194
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    Communications in Numerical Methods in Engineering 10 (1994), S. 673-681 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Timoshenko beam elements have been the subject of numerous publications. The difficulty was that of arriving at a superconvergent element with four degrees of freedom, as is the case for the Bernuli-Euler classical beam element. Two different approaches are presented here for the derivation of the shape functions. The first is based on the flexibility matrix, where utilizing the unit load method, including the term that accounts for the shear deformations in the virtual work expression, the stiffness matrix is derived. Then, a second method is presented to derive the exact shape functions, directly from the differential equations of the Timoshenko beam theory. The resulting shape functions are the same in both methods.
    Additional Material: 1 Ill.
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  • 195
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    Communications in Numerical Methods in Engineering 10 (1994), S. 683-697 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The convergence of stress maxima, computed directly from finite element solutions, is investigated with respect to a family of exact solutions characterized by varying degrees of smoothness. The performances of h- and p-extensions and the product and trunk spaces are evaluated and documented with respect to a family of benchmark problems. In uniform p-extensions a characteristic pattern in the convergence of stress maxima was observed. There does not appear to be a clear-cut advantage of the product space over the trunk space in this respect. The much faster convergence of stress maxima in the case of p-extensions, as compared with h-extensions, is evident from the results.
    Additional Material: 10 Ill.
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  • 196
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    Communications in Numerical Methods in Engineering 10 (1994), S. 699-709 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Enhanced 8-node three-dimensional solid and 4-node shell elements are proposed in the paper. Improvement of the response of the 3-D solid is achieved through additional strains corresponding to generalized displacements incompatible between elements. In the case of the 4-node shell, the membrane behaviour is improved through addition of incompatible membrane strains.Some linear and geometrically non-linear examples demonstrate significant improvements of the elements. Results are compared with solutions obtained with the standard, displacement-based elements and with results available in the literature.
    Additional Material: 5 Ill.
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  • 197
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    Communications in Numerical Methods in Engineering 10 (1994), S. 717-730 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Factorization procedures for the efficient solution of large sparse linear finite difference systems have been introduced recently. In these procedures the large sparse symmetric coefficient matrix of a certain structure is factorized exactly, yielding a direct solution method. Furthermore, approximate factorization procedures yeild implicit preconditioning iterative methods for the finite difference solution. The numerical implementation of these algorithms is presented and Fortran subroutines for the efficient solution of the resulting sparse symmetric linear system of algebraic equations are given.
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  • 198
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    Communications in Numerical Methods in Engineering 10 (1994), S. 731-734 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is well known that the finite element discretization with a distributed mass matrix gives overstimates of the natural frequencies of a system. The note shows that these do not necessarily become progressively worse as the frequency increases.
    Additional Material: 2 Tab.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 751-758 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Semi-discretization methods with iterated corrections are considered for solving the heat equation with boundary conditions containing integrals over the interior of the interval. The given problem is transformed into an ordinary differential system of equations, when we substitute the spatial derivative by finite differences. Such a system is then solved with an implicit integrator together with a quadrature method for the boundary integrals and, for each time step, the numerical scheme - implicit integrator and quadrature method - is repeated iteratively in order to achieve a given accuracy. The extra work we need with the iterated corrections enables us to take care of the interrelation of the solution u(x, t) at the interior and at the boundary points and also to start the numerical process with rough approximations of u(0, t) and u(1, t).An improvement of the results is achieved when we estimate the local spatial truncation error and make the injection of that estimation into the ordinary differential system. Numerical experiments are presented.
    Additional Material: 1 Ill.
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  • 200
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    Communications in Numerical Methods in Engineering 10 (1994), S. 735-742 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A technique is presented whereby numerical calculations of vibration modes can be improved. The paper looks at the classical two-dimensional wave equation using finite difference approximations. Analysis of the numerical dispersion of the approximations is used to develop a correction method. In general the numerical dispersion is dependent upon both the frequency and the direction of a wave, but if a 9-point formula is used the directional dependence is much reduced. This enables correction factors to be obtained using only the frequency of a vibration mode. The method was tested on the vibration of a square membrane and of an L-shaped region; in both cases a marked improvement in accuracy was obtained, at very little computational cost.
    Additional Material: 5 Ill.
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