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  • 1983  (281)
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  • 101
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    Electronic Resource
    A static infinite element (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1479-1488 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a simple procedure to derive a static infinite element from a linear isoparametric finite element.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620191006
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  • 102
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    Asymptotic rates of convergence of iterative methods applied to finite difference calculations on non-uniform grids (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1489-1506 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper the use of strongly stretched finite difference grids is examined in detail for a simple model equation. Numerical solutions of this equation demonstrate the overall second-order accuracy of the difference approximations. The behaviour of two simple iterative methods, S.O.R. and stationary A.D.I. is discussed for several cases with strong grid stretching and with variable diffusion coefficients. The results show that grid compression near to boundaries can greatly enhance the rates of convergence of these iterative methods, whereas with grid compression in the centre the rate of convergence can be extremely slow. The case of a diffusion coefficient which increases away from the boundaries of a region is analogous to grid compression in the centre and again the convergence rates can degrade considerably.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620191007
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  • 103
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    Unified finite element analysis (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1507-1511 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A special matrix is introduced, the elements of which are zero or first-order differential operators. This matrix is used to define a boundary value problem which covers a wide class of engineering applications. An equivalent variational formulation is found using an extension of the Gauss theorem. From this variational principle the equations of the elements are derived. The unified formulae presented here can be useful for educational purposes and for the design of a finite element system for total analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620191008
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  • 104
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    High-accuracy product integration methods for the Abel equation, and their application to a problem in scattering theory (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1527-1536 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we present orsder three, four and five backward product integration methods for the generalized Abel equation We illustrate their use by silving the small angle deflection problem, and show computationally that these methods are convergent for all ∊ ∊(0,1). The coefficients of order three and four methods are given in Applenidx I.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620191010
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  • 105
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    Optimum synthesis of linkages with autocorrelation concept (modified least squares technique) (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1537-1547 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Correlation is a measure of similarity between two functions. When two functions are exactly similar and equal, the correlation between them is maximum. The correlation concept can be used for system design, e.g. the four-bar mechanism, the slider crank mechanism, etc. The motion generated by four-bar linkage can be expressed as a function of link dimensions, input and output angles. The product of generated function and desired function gives correlation. The best possible design would be when the deviation of actual correlation from its maximum value (i.e. 100 per cent correlation) is least. This concept, in fact, leads to a modified least squares approach and based on this an objective function is formulated and minimized to give link dimensions. The results obtained are better than the least squares technique, and this is illustrated through different numerical examples.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620191011
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  • 106
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    On computing the inverse of a sparse matrix (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1513-1526 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Gauss-Jordan inversion algorithm requires 0(n3) arithmetic operations. In some practical applications, like state estimation or short-circuit calculation in power systems, the given matrix is sparse and only part of the inverse is needed. Most frequently in the diagonal dominant case this is the diagonal. There are two ways to exploit sparsity to determine elements of the inverse: 1Columnwise inversion via the solution of sparse linear systems with columns of the unit matrix as right-hand sides.2Application of the algorithm of Takahashi et al6.The latter algorithm arises very naturally from multiplying the left- and right-hand factors of the Zollenkopf bifactorization in reverse order. We indicate how computing time can be gained in the important symmetric diagonal dominant case if only part of the diagonal is needed and compare computing times of the method of Takahasi et al.6 with several variants of columnwise inversion. Whereas most of the theory holds for general matrices, experiments are performed on the symmetric diagonal dominant case. For band matrices the operation count is 0(n) both for computing a column of the inverse by columnwise inversion and the diagonal by the algorithm of Takahashi et al6.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620191009
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  • 107
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    The consistency and accuracy of the TLM method for diffusion and its relationship to existing methods (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1549-1554 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper investigates the conditions under which a simple transmission-line model for diffusion corresponds to the simple explicit finite difference method and to the method of Du Fort and Frankel. Consideration is also given to the consistency and accuracy of the methods.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620191012
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  • 108
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    Boundary element methods in solid mechanics, S. L. Crouch and A. M. Starfield, George Allen & Unwin, London, 1983. Price: £20. No. pages: 322 (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1579-1579 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620191014
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  • 109
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    Indentation of a half-space with a rigid indentor (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1555-1578 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this work the problem of indentation of a half-space by a spherical rigid indentor is investigated using the finite element method.A system of constitutive equations applicable to elasto-plastic materials subjected to large deformations is used to determine the deformations and stresses for the contact problems. These equations represent the simplest generalization for the large-deformation conditions of the classical theory of plasticity of metals based on the von Mises yield condition and the associated flow rule. The material formulation of the kinematical and dynamical relations will be used. These equations combine the kinematic and the isotropic strain-hardening models.The results obtained from this work are compared with existing solutions for this problem that are confined to small strains and elastic, ideal-plastic materials.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620191013
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  • 110
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    Numerical solution of partial differential equations in science and engineering, L. Lapidus and G. F. Pinder, Wiley-Interscience, New York, 1982, No. of pages: 677. Price: £35.00 (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1580-1580 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620191017
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  • 111
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    Announcements (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1580-1582 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620191018
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  • 112
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    The boundary integral equation method for porous media flow, J. A. Liggett and P. L. F. Liu, George Allen & Unwin, London, 1983. No. pages: 255 (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1579-1579 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620191015
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  • 113
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    Masthead (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983) 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620191101
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  • 114
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    Plasticity of mentals at finites strain: Theory, experimental and computation. Proceedings of Research Workshop held at Stanford University, June 29, 30, July 1, 1981. Editors: E. H. Lee and R. L. Mallett. Published in 1982 by Division of Applied Mechanics, Stanford University and Department Engineering & Mechanics, Rensselaer Polytechnic Institute. ISBN 0-960992-0-5. Library of Congress Catalog Card Number 82-51224 (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1579-1580 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/nme.1620191016
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  • 115
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    A posteriori error analysis and adaptive processes in the finite element method: Part II - adaptive mesh refinement (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1621-1656 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This is a paper presented in two parts dealing respectively with error analysis and adaptive processes applied to finite element calculations. Part I contains the basic theory and methods of deriving error estimates for second-order problems. Part II of the paper deals with the strategy for adaptive refinement and concentrates again on the p-convergent methods. It is shown that an extremely high rate of convergence is reached in practical problems using such procedures. Applications to realistic stress analysis and potential problems are presented.
    Additional Material: 18 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620191104
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  • 116
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    A posteriori error analysis and adaptive processes in the finite element method: Part I - error analysis (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1593-1619 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This is a paper presented in two parts dealing respectively with error analysis and adaptive processes applied to finite element calculations. Part I contains the basic theory and methods of deriving error estimates for second-order problems. Part II of the paper deals with the strategy for adaptive refinement and concentrates on the p-convergent methods. It is shown that an extremely high rate of convergence is reached in practical problems using such procedures. Applications to realistic stress analysis and potential problems are presented.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620191103
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  • 117
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    On the performance of the enthalpy method in the region of a singularity (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1583-1592 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A test problem is presented which provides a realistic challenge for computational techniques designed for the prediction of temperature distributions in melting/freezing processes. It is shown that a suitably modified finite difference implementation of the enthalpy method produces results that are perhaps adequate for practical purposes. However, the best approach to problems typified by the test problem remains to be found.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620191102
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  • 118
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    Stabilization of partitioned solution procedure for pore fluid-soil interaction analysis (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1669-1673 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The conventional staggered solution of pore fluid-soil interaction problems is shown to suffer from stability restriction. This paper presents a stabilized form of the staggered solution procedure of the problem. Computational overhead for this stabilization is shown to be modest and hence this stabilized procedure is recommended for production implementation for pore fluid-soil interaction analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620191106
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  • 119
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    Finite elements for the dynamic analysis of fluid-solid systems (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1657-1668 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Several new finite elements are presented for the idealization of two- and three-dimensional coupled fluid-solid systems subjected to static and dynamic loading. The elements are based on a displacement formulation in terms of the displacement degrees-of-freedom at the nodes of the element. The formulation includes the effects of compressible wave propagation and surface sloshing motion.The use of reduced integration techniques and the introduction of rotational constraints in the formulation of the element stiffness eliminates all unnecessary zero-energy modes. A simple method is given which allows the stability of a finite element mesh of fluid elements to be investigated prior to analysis. Hence, the previously encountered problems of ‘element locking’ and ‘hour glass’ modes have been eliminated and a condition of optimum constraint is obtained.Numerical examples are presented which illustrate the accuracy of the element. It is shown that the element behaves very well for non-rectangular geometry. The optimum constraint condition is clearly illustrated by the static solution of a rigid block floating on a mesh of fluid elements.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620191105
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  • 120
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    A finite element for the analysis of reinforced concrete structures (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1705-1712 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Formulation of a four-node isoparametric element suitable for modelling cracks in reinforced concrete structures is presented. The standard isoparametric element is known to give spurious shear stresses. The conventional remedy of selective integration breaks down in a ‘cracked’ element. It is shown that the proposed formulation gives superior results as compared to both the standard isoparametric element and the conventional selectively integrated element.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620191109
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  • 121
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    Analysis of free surface flows using isoparametric finite elements (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1675-1689 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A theory for free surface flow using variable geometry finite elements is numerically modelled using isoparametric finite elements, for the first time. The resulting nonlinear equations are solved using the Newton-Raphson method. Because a functional is used as the basis of the formulation, the resulting equations are symmetrical. The realistic problem of flow over a Crump weir is solved for a large range of discharges.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620191107
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  • 122
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    Discrete Kirchhoff plate element and work equivalent loads (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1732-1737 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620191111
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  • 123
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    Two bracketing theorems characterizing the eigensolution for the h-version of the finite element method (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1691-1704 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper demonstrates that the classical inclusion principle is in general not valid for the h-version of the finite element method. Whereas the inclusion principle is valid for second-order systems discretized by the h-version of the finite element method, provided linear interpolation functions are used as admissible functions, the principle is not valid for fourth-order systems. To characterize the computed eigenvalues for fourth-order systems discretized by the h-version of the finite element method, this paper formulates two bracketing theorems.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620191108
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  • 124
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    Elementary applied partial differential equations, Richard Haberman, Prentice-Hall International, New Jersey, 1983 (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1738-1738 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620191113
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  • 125
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    A substructuring application of the virtual crack extension method (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1713-1731 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The virtual crack extension method (VCE) is a very effective tool with finite elements for the accurate evaluation of stress intensity factors in two- or three-dimensional structures. The method utilizes the concept of extending any node on the crack profile in any required direction and by any required amount. A new facility stores a relevant substructure of crack tip stiffnesses so that any number of restarts, each with a new set of extensions, can be performed. Different nodes around three-dimensional crack profiles can be considered, either at vertex or midside node positions. The extension of the vertex nodes, in particular, also involves moving adjacent midside nodes along the profile, and different ways of effecting this, together with the calculation of the relevant area change, have been introduced and are described along with illustrative examples.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620191110
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    Mécanique Aléatoire, P. Krée and C. Soize, Dunod, Paris, 1983 (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1738-1738 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/nme.1620191112
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    Hybrid and mixed finite element methods, Editors, S. N. Atluri, R. H. Gallagher and O. C. Zienkiewicz, Wiley, Chichester, 1983, No. of pages: 582. Price: £45·00 (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1739-1739 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620191115
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    Advanced engineering analysis, J. N. Reddy and M. L. Rasmussen, Wiley-Interscience, New York, 1982. No. of pages: 488. Price: $53.00 (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1739-1739 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620191114
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    Announcement (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1740-1740 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620191116
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    Masthead (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983) 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620191201
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    On the suppression of zero energy deformation modes (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1741-1752 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on the Hellinger-Reissner principle and the deformation energy due to assumed stresses and displacements, the problem of the kinematic deformation modes in assumed stress hybrid/mixed finite elements has been examined. Basic schemes are developed for the choice of assumed stress terms that will suppress all kinematic deformation modes. Quadrilateral membrane and axisymmetric elements, and three-dimensional hexahedral elements, are used to illustrate the suggested procedure.
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    How upstream collocation works (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1753-1763 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The smoothing effects of upstream collocation in convective problems are attributable to a dissipative error term analogous to that in upstream-weighted finite differences.
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    Use of the Hankel transform in boundary integral methods for axisymmetric problems (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1765-1769 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
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    Multiple-parameter reduced basis technique for bifurcation and post-buckling analyses of composite plates (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1783-1803 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A multiple-parameter reduced basis technique and a problem-adaptive computational algorithm are presented for the bifurcation and post-buckling analyses of composite plates subjected to combined loadings. The computational algorithm can be conveniently divided into three distinct stages. The first stage is that of determining the stability boundary. The plate is discretized by using displacement finite element models and the analysis region is reduced by exploiting the special symmetries exhibited by the response of the plate. The vector of unknown nodal displacements is expressed as a linear combination of a small number of path derivatives (derivatives of the nodal displacements with respect to path parameters), and a Rayleigh-Ritz technique is used to approximate the finite element equations by a small system of algebraic equations. The reduced equations are used to determine the stability boundary of the plate.In the second stage, a nonllnear solution in the vicinity of the stability boundary is obtained by using a bifurcation buckling mode as a predictor, and a set of reduced equations is generated. In the third stage, the reduced equations are used to trace post-buckling paths corresponding to various combinations of the load parameters.The potential of the proposed approach is discussed and its effectiveness is demonstrated by means of a numerical example of laminated composite plate subjected to combined compressive and shear loadings.
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    On the importance of the discrete maximum principle in transient analysis using finite element methods (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1771-1782 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In transient analysis it is generally thought that small time steps can only improve the accuracy, because standard stability theorems limit the maximum time step for a given mesh size. In finite element approximations, however, small time steps may cause stability problems which lead to physically unreasonable results. It is shown that this is due to the violation of a discrete maximum principle. The influence of lumped and consistent mass matrices on a stable discretization of time and space is presented.
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    Anisotropic cylindrical shell element based on discrete Kirchhoff theory (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1805-1823 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A triangular cylindrical shell element based on discrete Kirchhoff theory is developed. It is a three-node, 27-degrees-of-freedom element using cubic polynomials for the tangential and normal displacement interpolations. The normal rotations are independently interpolated by quadratic polynomials. The formulation is capable of modelling general anisotropy representative of multi-layered, multi-directionally oriented composite construction. The numerical results indicate that the solution for displacements and stresses of cylindrical shells converge monotonically and rapidly to those based on deep shell theory.
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    A posteriori error indicators for the p-version of the finite element method (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1851-1870 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The existence of local a posteriori error indicators for the p-version of the finite element method is demonstrated through numerical examples. The optimal sequence of p-distributions can be closely followed on the basis of the indicators.
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    Announcements (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1881-1884 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/nme.1620191212
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    Numerical methods for fluid dynamics, K. W. Morton and M. J. Baines (eds.) (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1881-1881 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/nme.1620191211
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    Boundary integral equation solution of moving boundary phase change problems (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1825-1850 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Boundary integral equation methods are presented for the solution of some two-dimensional phase change problems. Convection may enter through boundary conditions, but cannot be considered within phase boundaries. A general formulation based on space-time Green's functions is developed using the complete heat equation, followed by a simpler formulation using the Laplace equation. The latter is pursued and applied in detail. An elementary, noniterative system is constructed, featuring linear interpolation over elements on a polygonal boundary. Nodal values of the temperature gradient normal to a phase change boundary are produced directly in the numerical solution. The system performs well against basic analytical solutions, using these values in the interphase jump condition, with the simplest formulation of the surface normal at boundary vertices. Because the discretized surface changes automatically to fit the scale of the problem, the method appears to offer many of the advantages of moving mesh finite element methods. However, it only requires the manipulation of a surface mesh and solution for surface variables. In some applications, coarse meshes and very large time steps may be used, relative to those which would be required by fixed grid domain methods. Computations are also compared to original lab data, describing two-dimensional soil freezing with a time-dependent boundary condition. Agreement between simulated and measured histories is good.
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    Masthead (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/nme.1620250101
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    Error estimation and adaptivity in flow formulation for forming problems (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 23-42 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A very simple and reliable error estimator has recently been developed for problems of linear elasticity.1 This leads naturally toa predication of an h-mesh refinement required for a given accuracy and with a suitable mesh generator2 for an efficient adaptive process. In this paper we extend the methodology developed previously to incompresible plastic flow of metals or polymers using the ‘flow formulation’ approach.3The examples of application include steady state extrusion problems for which exact solutions are available and hence allow the efficiency of the error estimates to be tested as well as more complex problems of upsetting in which the mesh is updated. It is found that the estimator performs well under various circumstances and provides an economical adaptive process.
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    Ignition phase transition of a polymer: Convective exposure (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 373-386 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The ignition of a semi-infinite solid polymer under convective exposure is investigated. A quasi-steady approximation is used for the gas phase and the transient effect is accounted for in the solid phase only. Both surface and gas phase chemical reactions are included simultaneously. The ignition mechanism is studied in terms of the concurrent heat transfer, mass transfer, mass transfer and chemical processes at the surface as well as in the gas phase. The gas phase governing equations are integrated independently from the solid phase energy equation using the Adams-Moulton subroutine. Corrections to the iterative procedure are carried out by establishing a set of perturbation equations and using the Newton-Raphson and least-squares methods. The results indicate that ignition occurs in the heterogeneous mode within a narrow range of low flow velocities and high temperatures. An ignition phase transition point exists, and within a wide range of high flow velocities, ignition switches to the homogeneous mode.
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    Shape design sensitivity analysis for non-linear anisotropic heat conducting solids and shape optimization by the BEM (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 109-120 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Shape design sensitivity analysis (SDSA) expressions have been derived for non-linear anisotropic heat conducting solid bodies by following the material derivative concept and adjoint variable method of optimal shape design given in the literature. The variation of a general integral functional has been described in terms of primary and adjoint quantities evaluated at the varying boundaries. As an example problem in shape optimization, optimal outer boundary profiles of an orthotropic solid body are obtained by the boundary element method (BEM), after reformulating the SDSA equations in a form which is most suitable for the BEM.
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    Analyses of steady-state visco-elastic fluids using the penalty function method (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 43-54 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of the penalty-function formulation of the finite element method is made possible for analysing visco-elastic fluid flows by the method which decouples the momentum and continuity equations from the constitutive equation. An upwind finite element scheme is combined with the method in order to solve the constitutive equation. As visco-elastic fluid models, Jaumann derivative, upper and lower convected derivatives are considered. The Poiseuille flow and the flow through a plane converging channel are analysed.
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    Approximate methods for analysing the cold drawing of polymeric fibres and films (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 99-112 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Approximate methods for analysing steady-state cold drawing processes in polymer forming are discussed. These methods are applied to both axisymmetric and plane-strain drawing. The cold drawing process is associated with steady-state neck propagation along the specimen. Modifications are introduced in the approximate steady-state analysis which reflect the neck initiation and localization phases prior to steady-state drawing. This is accomplished without resorting to an analysis of the entire load-deformation history of the process. Finite element results are also presented and compared with those of the proposed approximate analyses. These comparisons show the approximate analysis to be an extremely efficient and quite accurate computational scheme for the analysis of steady-state cold drawing processes.
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    Analysis of stress and strain distributions in slab rolling using an elastic-plastic finite-element method (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 55-66 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The cold rolling of rectangular section slabs is analysed for a range of width-to-height ratios (one to three) for which spread of the workpiece is appreciable. This necessitates the use of a three-dimensional model. An elastic-plastic finite-element method is used to provide a complete description of the slab rolling process.The pressure distribution at the workpiece/roll interface is found to show the typical ‘friction-hill’ observed in near-plane-strain experiments, but the pressure varies across the width of the interface. The shear-stress distribution at the roll interface provides detailed information about the ‘neutral line’ which is usually assumed to occur where the shear stress changes direction. The 3-D analysis shows clearly that there is a flow divide in both longitudinal and transverse directions.
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    Numerical simulation of the densification behaviour of metal powder during hot isostatic pressing (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 213-225 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method is introduced which is based on metal flow theory and simulates the densification of metal powder during hot isostatic pressing.The method, in which nodal velocities are variables, takes into consideration the dependence of flow stress on the temperature, strain rate and relative density of the material. The compressibility of porous metal as well as the incompressibility of fully dense metal are also taken into account.Porous specimens of the superalloy MERL76 were subjected to uniaxial compression tests at high temperature in order to determine the parameters of the equations on which the method is based. The densification behaviour of a turbine disk and two cylindrical components was numerically simulated and compared with experimental results.
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    Preface (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. i 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/nme.1620250202
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    Coarse-fine mesh method for heat and mass transfer in locally complex flows (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 347-355 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Combined forced and free convective flows having locally complicated geometries or boundary conditions were numerically studied with a finite difference method of coarse and fine meshes. The coarse-and-fine mesh method developed can be used for numerical calculations of both unsteady and steady processes of heat and mass transfer in convective and diffusion flows which are strongly influenced by locally fine flows. The method was applied to a numerical calculation of the steady flow field of a CVD (chemical vapour deposition) reactor which has locally complicated flows caused by small inlet nozzles. The results of the calculation showed a considerable contribution of locally fine flows to the overall flow field, which is well predicted with the present method.
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    Thermal analysis of human body-clothing-environment system (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 357-371 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For the solution of thermal comfort problems a coupled model is presented consisting of the thermal model of the human body and of the clothing, with boundary conditions of the third kind.For thermal modelling the human body is divided into 16 parts according to the special character of the internal heat generation, of the blood vessel system and of the sweat secretion mechanism. Part models are connected by the flow paths of arteries and veins.Transport phenomena in the clothing are treated by a coupled heat and mass transfer model which permits various kinds of clothing for the different parts of the body.The equation system of the full model has been solved numerically by using time stepping schemes. As the results of the computations an approximative temperature field of the human body is produced.Calculated results have been compared with Experimental data.
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    Finite element simulation of hot isostatic pressing of metal powders (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 191-212 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Rate form constitutive equations of elasto-viscoplastic type are expressed in a manner similar to that of classical metals, but the viscoplastic part, which is no longer incompressible, is related to the rate of variation of porosity. An incremental and implicit algorithm has been implemented in a finite element program in order to simulate hot isostatic pressing of an Astroloy powder. Temperature distributions are shown to induce strong density variations in real parts during hot isostatic pressing (HIP). For one particular turbine disk, we tested the sensitivity of the final shape to different processing parameters. Computed final shapes compare well with experimental ones.
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    Analysis of bending effects in sheet forming operations (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 253-267 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The majority of work in numerical analyses of sheet metal forming operations is based on the simple membrane-shell theory which neglects the effect of sheet bending. While useful information can be extracted from these analyses, especially for stretch-dominated operations, the membrane theory is basically inadequate for analysing the draw-type operations where sheet metal bends, slides and unbends over a draw radius.This paper presents axisymmetric and plane-strain finite element analyses of stretch/draw of sheet metal over a die corner radius. Numerical solutions obtained from a total Lagrangian formulation of a finite-strain thin shell theory are used to indicate the relative significance of including the bending effects in various simple forming operations. Comparisons of the calculated results with available experimental data are also given.
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    A finite element simulation of the sheet metal forming process (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 283-292 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element simulation code of the sheet metal forming process has been developed. This simulation code plays an important role in the computer aided engineering (CAE) system for an automobile parts forming process, which includes the pre- and post-processes. The paper presents the development of an updated Lagrangian type finite element modelling, based on the elastic-plastic (J2 flow law) membrane shell theory. An attempt is made to calculate the strain distribution incurred by peripherally clamped or non-clamped square plates when impressed by rigid punches. These are the cases of square box-shape punch drawing and arbitrary shaped panel stretch forming.
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    Punch stretching of sheet metal and differential equations on manifolds (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 269-282 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The goal of mathematical modelling of sheet metal forming processes is to provide predictive tools for use in the design of stamping processes and the selection of sheet materials. Most current approaches to finite element modelling of large deformation, elastic-plastic sheet metal forming problems use a rate form of the virtual work (equilibrium) equations, and a single-field finite element representation of the displacement components. Called the incremental method, this approach does not produce approximations which satisfy the discrete equilibrium equations at all times, and consequently it demands small time steps to insure stability and numerical accuracy. This paper describes a variant of the mixed method in which displacements, stresses, effective strain and pressures are all given separate finite element representations. The equilibrium equations in non-rate form are discretized to produce a system of algebraic equations which are coupled with the constitutive equations and then integrated using state-of-the-art numerical software. When used to model rate sensitive sheet materials in hydrostatic bulging, plane strain punch stretching and hemispherical punch stretching, the new approach proved to be between 6 and 26 times as fast as the old incremental method.
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    Buoyant flow calculations with non-orthogonal curvilinear co-ordinates for vertical and horizontal parallelepiped enclosures (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 331-345 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A control-volume-based finite-difference formulation is developed for heat transfer and fluid flow in arbitrary three-dimensional parallelepiped enclosures. The governing equations in Cartesian co-ordinates are first transformed to those in non-orthogonal curvilinear co-ordinates by tensor transformations. After introducing the properties of the parallelepiped geometry, equations are obtained in the primitive variables for which all vectors and tensors are based on the curvilinear co-ordinates. With proper treatment of the heat flux and stress tensor terms, the finite-difference equations, analogous to those in the Cartesian coordinates, are formed. Examples are utilized to show the validity of the methodology and the results are found to compare well with existing experimental data. The differences in heat transfer and fluid flow inside parallelepiped enclosures and rectangular enclosures are delineated and discussed from a physical point of view.
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    Finite element analysis of turbulent forced convection in lid-driven rectangular cavities (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 313-329 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Turbulent fluid flow and heat transfer in lid-driven rectangular cavities are analysed by a finite element procedure for the prediction of the turbulent forced convection in two-dimensional recirculating flows. The (k-ε) model is used to compute effective viscosities and thermal conductivities. The fluid flow and turbulence model parabolic equations are solved sequentially, one after the other. Then, the calculated velocity distribution is used in the solution of the steady state energy equation to yield the temperature field. Aspect ratios e=0·75, 1·0 and 1·5 and Reynolds numbers ranging from 5 × 104 to 4 × 105 are considered in the numerical examples.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620250204
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    Non-linear simulation of dendritic solidification of an undercooled melt (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 415-444 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two-dimensional finite element simulations of solidification for quiescent undercooled pure metals are presented. The full non-linear, transient heat equation is used with phase front tracking which is subject to local curvature and interfacial kinetics. During early stages of the waveform instability the simulated solutions match the linear stability analysis with fidelity. Beyond the valid range of that analysis the numerical solution continues to demonstrate the physically observed exponential growth behaviour and characteristic spacing between fingers. Whereas the simulations show the sensitivity of dendritic growth to initial conditions, as expected for an unstable process, the overall pattern formation preserves the characteristic spacing. The simulations are terminated after the onset of bifurcation. Thereafter, the numerical model is inappropriate for physical comparison owing to the planar, two-dimensional limitation.
    Additional Material: 24 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620250211
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    A regular indirect boundary element method for thermal analysis (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 495-515 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Regular Indirect Boundary Element formulation is developed following a weighted residual approach. In this formulation, the fictitious source density, which appears in the integral equations of the method, is distributed on a surface which is exteriorly separated from the physical field boundary of the problem. This approach does not require the evaluation of singular integrals and produces undeteriorated solutions at geometric discontinuities. The formulation is presented here as applied to two dimensional and axisymmetric thermal problems. It includes a different subregioning scheme which treats each subregion, of a multidomain problem, separately, thereby eliminating the need for a sophisticated reduction scheme.
    Additional Material: 24 Ill.
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    Warping torsion in thin-walled open section beams using the semiloof beam element (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 231-243 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Many structural members including metallic, reinforced polymer and concrete members must be modelled, in the simplest approximation, as thin-walled beams whose cross-sections exhibit significant, out-of-plane warping owing to torsion. The elastic capabilities of the semiloof beam element are extended to include warping torsion of thin-walled open section beams. The performance of the extended element is compared with that of the original formulation.
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    URL: http://dx.doi.org/10.1002/nme.1620260116
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    Partial eigensolution of damped structures by non-linear optimization (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 143-152 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The partial solution of damped structures involves the determination of only a few of the resonant frequencies and corresponding damping characteristics and mode shapes. The procedure outlined here uses a modification of the variable metric solution algorithm, in which the dicision variables are elements of the complex eigenvector and the eigenvalue. The quadratic eigenvalue problem is reformulated as a sequential unconstrained minimization problem. Both normality and orthogonality constraints are incorporated in the objective function. The method is compared to an adaptation of the subspace iteration technique, also applicable to the quadratic eigenvalue problem.
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    An element-by-element method for heat conduction CAE including composite problems (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 199-215 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Mechanical computer aided engineering (CAE) implies large finite element problems due to the geometric complexity of the ‘true’ 3D designs. Application of the standard finite element technique is not practical for such problems because the direct solution of the global matrix equations is too costly. This paper considers the element-by-element implicit algorithm for the CAE application of transient heat conduction. The direct solution is avoided by an operator splitting or approximate factorization technique. This results in both the execution time and storage requirements for each time step being linearly proportional to the number of elements while retaining unconditional stability. However, the approximate factorization introduces additional truncation error and incorrect jump conditions at material interfaces. Detailed analyses and numerical experiments are carried out in one dimension to assess the nature and mechanism of these inaccuracies. A three dimensional implementation is then compared with one dimensional results. The need for an additional predictor-corrector element-by-element algorithm for 3D composite problems is also presented.
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    Letters to the editor (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 281-282 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260119
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    Conference diary (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 291-292 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Plastic design. An imposed hinge-rotation approach, P. Zeman and H. M. Irvine, Allen & Unwin, London, 1986, 86, pages (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 290-290 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620260123
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    Finite elements and solution procedures for structural analysis. vol. I: Linear analysis. M. A. Crisfield, Pineridge Press, Swansea, 1986. No. of pages: 272 (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 289-289 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620260122
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    Hybrid finite element-Monte Carlo method for coupled conduction and gas radiation enclosure heat transport (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 361-378 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A hybrid two-dimensional finite element-Monte Carlo numerical solution method has been developed for solving complex transient non-linear gas radiation enclosure problems. Solid conducting media are coupled to conducting gaseous or particulate participating media and both may be internally energy generating. Bilinear isoparametric elements are used, allowing geometrically complex enclosures with internal objects to be present. Radiative energy transport within the gaseous enclosures is accounted for using a Monte Carlo method which permits a broad range of complexities. Included here are: diffuse-grey and specularly reflecting walls with temperature and spectrally dependent, and non-homogeneous emissivities or absorptivities; absorbing/emitting gases with temperature and spectrally dependent, and non-homogeneous emissivities or absorptivities; and isotropic or anisotropic scattering gases or particles. This method was verified by solving several standard steady state problems and comparing the solutions to those found using the conventional finite element, the P-N and the exchange factor methods. Solution times are comparable to those of the finite element method. A more complex transient problem solution is then given to demonstrate the versatility and power of the method.
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    Derivatives of eigenvalues and eigenvectors of a general complex matrix (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 293-311 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A survey of methods for sensitivity analysis of the algebraic eigenvalue problem for non-Hermitian matrices is presented. In addition, a modification of one method based on a better normalizing condition is proposed. Methods are classified as Direct or Adjoint and are evaluated for efficiency. Operation counts are presented in terms of matrix size, number of design variables and number of eigenvalues and eigenvectors of interest. The effect of the sparsity of the matrix and its derivatives is also considered, and typical solution times are given. General guidelines are established for the selection of the most efficient method.
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    Convergence of curved shell elements based on assumed covariant strain interpolations (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 329-347 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A C0 9-node shell element based on assumed interpolations of covariant strain components defined with respect to the element natural co-ordinate system has recently been proposed. In this formulation, the covariant strains are obtained directly from the Cartesian strains by tensor transformation without any need to compute laminar co-ordinate based strains. In the present work, the interpolated covariant strains used in this element are analysed to determine their satisfaction of the basic requirements for successful strain interpolation. These basic requirements are stated as invariance to rigid body motions and ability to represent constant and linear strain states. In the finite element formulation, the weak form of momentum balance is expressed in terms of covariant strains and contravariant stresses. The corresponding elasticity tensor is a function of the components of the metric tensor associated with the element natural co-ordinate system. The invariance properties of the metric tensor in the context of the finite element approximation are also discussed.
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    Spline collocation in the flow of non-Newtonian fluids (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 413-421 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Natural convection flow of a non-Newtonian fluid between two vertical infinite parallel flat plates forms the case study of the present work. Velocity profiles for the Prandtl-Eyring and Powell-Eyring fluid models are obtained through the method of spline collocation.The applicability and reliability of the techniques employed here are discussed in detail with a suggested error estimate and analysis. Accuracy in the successive iterations in the results is of the fourth order. To maintain this accuracy the help of a computer is not required for carrying out the calculation of velocity profiles. Thus the simplicity of the spline collocation technique is demonstrated in its application to flow problems.
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    Computation of hybrid element matrices by elimination techniques (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 423-435 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three functionals, the modified forms of the Hu-Washizu, Hellinger-Reissner, and complementary energy principles, as developed by Pian, Chen, and Kang1.2 are stated. Finite element discretization of each is presented and the ensuing computations developed, resulting in the element stiffness matrix, with displacement degrees-of-freedom only, and the stress recovery matrices. Subroutines are presented for this purpose where the close relationship of the three principles is exploited to result in a compact hybrid element technique. The techniques herein reviewed are assumed applicable at the individual element level. The usual summation over all elements in the model is implied.
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    Accuracies of numerical solution methods for the pressure-modified von Mises modelThe paper was presented at Tenth U.S. National Congress of Applied Mechanics, June 16-20, 1986, Austin, Texas, U.S.A. (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 453-465 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The accuracy of three numerical algorithms - the tangent-stiffness radial-return, secant-stiffness radial-return and simple radial-return methods - is analysed against exact solutions for the pressure-modified von Mises yield criterion with the associated flow rule. The governing equations of the exact solutions are derived using a simple and innovative geometrical approach, in terms of a pair of non-linear, first order differential equations, in rate change of the deviatoric radius and in rate change of angular locations on the deviatoric plane. For both accuracy and efficiency, and for small and large time steps, the secant-stiffness radial-return method is the best of all.
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    Three-dimensional elastic finite element study of the skid resistance of grooved pavement (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 437-452 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A three-dimensional finite element model has been developed to simulate the sliding of a rubber block over a grooved road surface. The model makes use of the symmetries of the problem to simplify the analysis, so that two-dimensional isoparametric elements of both rectangular and triangular configuration have been extended into the third dimension. A procedure for analysing the behaviour of any one groove to groove unit of the pavement is also developed, and this is extended so that the contact between the sliding rubber block and the leading edge of each raised pavement section is analysed. Preliminary comparisons between theoretical calculations and experimental measurements indicate that the finite element procedure provides an accurate and economical estimate of the behaviour of the rubber slider as it is pressed into a grooved pavement. Elastic predictions of sliding resistance seem reasonable at low sliding speeds, but viscoelastic rubber analysis appears necessary if higher speed skid resistance is to be predicted.
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    Analysis of steady free convection from an axisymmetric heat-generating body embedded in a semi-infinite porous medium (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 467-487 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An analysis is presented for the steady state free convective flow and heat transfer from an axisymmetric heat-generating body that is embedded in a fluid-saturated, semi-infinite, porous medium. The porous medium is assumed to be rigid, homogeneous and isotropic, and be in thermal equilibrium with the fluid. The fluid is assumed to be incompressible, with the density changes contributing only towards the buoyancy forces via the Boussinesq approximation. The governing equations for the fluid consist of the equation of continuity, Darcy's law and the equation of energy. After introducing the stream function concept, the equations governing the stream function and pressure are derived. Using the non-dimensional variables, the non-dimensional equations governing the non-dimensional forms of the temperature, stream function and pressure are dervied and the appropriate boundary conditions are stated. The mathematical formulation contains two parameters; D, the non-dimensional depth of the body from the surface of the porous medium, and a product Raθs of Rayleigh number (Ra) and the non-dimensional surface temperature of the body (θs). The Galerkin finite element method, with linear, isoparametric, quadrilateral elements, is used to reduce the mathematical formulation into a set of algebraic equations. The expressions to calculate the non-dimensional surface temperature and Nusselt number of the body, and the non-dimensional velocity of the fluid, are derived. A computer code has been developed to solve the algebraic equations, using Gauss elimination procedure, in a banded matrix form. The computer code, in addition to the non-dimensional temperature, stream function and pressure, calculates the isothermal lines, non-dimensional surface temperature of the body, Nusselt number of the body, velocity field and isobars.To demonstrate the application of the code, a spherical heat-generating body is considered as an example. Numerical results are obtained for D = 3 and 6, and Raθs = 0.001, 0.1, 1 and 5, and presented.
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    Masthead (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988) 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/nme.1620260301
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    Announcements (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 527-530 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620260217
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    An integrated approach to the synthesis of geometrically non-linear structures (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 555-570 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An integrated approach to the minimum weight design of geometrically non-linear three dimensional truss structures with geometric imperfections, subject to inequality constraints on static displacements, stresses, local buckling and cross sectional areas, is investigated. The integrated structural synthesis problem involves design and response quantities as independent variables and equilibrium equations, describing the finite element model, as equality constraints. The non-linear structural analysis and the optimization are thus merged together into a single process. A computer program developed to compute the contraint values and analytical gradients is coupled with a generalized reduced gradient algorithm to solve the integrated problem. Numerical results for a geometrically non-linear shallow dome example problem are presented for various types of imperfections. Furthermore, it is found that the algorithm is capable of detecting and guarding against system as well as element elastic instability using equilibrium information only, that is, without imposing system and local buckling inequality constraints.
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    Theoretical basis of the finite element iterative method for the eigenvalue problem in stationary cracks (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 531-539 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In a recently published paper a finite element based iterative method was introduced for the solution of the eigenvalue problem of stationary cracks.1 In this paper we give the theoretical basis of this iterative method and we show why it converges and how it could be extended to more complex fracture problems. The cases of cracks at interfaces are illustrated.
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    Application of the finite element iterative method to the eigenvalue problem of a crack between dissimilar media (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 541-554 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element iterative method is applied to the eigenvalue problem of a crack between dissimilar media. In this case the transfer matrix is non-symmetric, which leads to complex eigenvalues. The singularity obtained agrees with the analytical results of r(-1/2+ie). The method of evaluating the eigenfunctions is general and can be applied to more complex cases of material and geometry, which are frequently encountered in composite materials. A powerful method for evaluating stress intensities in dissimilar media is given in the Appendix. The method is also reduced for homogeneous media to give stress intensity factors for modes I, II and III.
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    Elasto-plastic large deformation analysis of space-frames: A plastic-hinge and stress-based explicit derivation of tangent stiffnesses (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 589-615 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with elasto-plastic large deformation analysis of space-frames. It is based on a complementary energy approach. A methodology is presented wherein: (i) each member of the frame, modelled as an initially straight space-beam, is sought to be represented by a single finite element, (ii) each member can undergo arbitrarily large rigid rotations, but only moderately large relative rotations; (iii) a plastic-hinge method, with arbitrary locations of the hinges along the beam, is used to account for plasticity, (iv) the non-linear bendin-stretching coupling is accounted for in each member, (v) the applied loading may be non-conservative and (vi) an explicit expression for the tangent stiffness matrix of each element is given under conditions (i) to (v). Several examples, with both quasi-static and dynamic loading, are given to illustrate the accuracy and efficiency of the approaches presented.
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    Multi-grid solutions to the elastic plastic torsion problem in multiply connected domains (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 631-646 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The elastic plastic torsion problem for an elastic, perfectly plastic cylinder with multiply connected cross section twisted around its longitudinal axis is formulated as an obstacle problem for an associated stress potential, the obstacle being defined in terms of a generalized distance function. Based upon the reformulation of the obstacle problem as an equivalent linear complementarity problem, the latter is discretized by means of finite difference techniques, and a monotonically convergent iterative scheme for its numerical solution is developed. At each step of the iteration the solution of a reduced system of discrete Poisson equations is required which is done by applying multi-grid techniques with respect to a hierarchy of grid-point sets. Combined with a suitably chosen nested iteration process this results in a computationally very efficient algorithm for the approximate solution of the elastic plastic torsion problem.
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    Application of spline strip method to analyse vibration of open cylindrical shells (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 663-676 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with the vibration of open cylindrical shells by the spline strip method based on Novozhilov's shell theory. Convergence of the solutions is investigated in a few examples and is found to be satisfactory. The accuracy of the results is compared with those calculated by other numerical methods and found to be in good agreement.The effect of inlcuded angles and inplane constraints on vibrating characteristics of simply supported cylindrical shells is shown.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260310
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    A quadrilateral finite element including vertex rotations for plane elasticity analysis (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 717-730 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element of arbitrary quadrilateral shape is presented for plane elasticity analysis. The element is derived from triangular fields of compatible quadratic displacements with vertex connectors which include rotations. All rigid body movements and constant strain states are recovered exactly. Results from several test problems demonstrate that very good numerical accuracy is obtained for both displacements and stresses, even for quite coarse finite element meshes.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260314
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  • 184
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    A numerical case study of a non-Newtonian flow problem (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 695-704 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper addresses some of the theoretical aspects involved in the numerical study of non-Newtonian flow problems. We consider the second-order Rivlin-Erickson constitutive model due to the simple differential form that emerges for the system of equations that govern the flow when expressed in stream function-vorticity variables. This model describes slightly elastic fluids that exhibit a constant viscosity behaviour. A steady two-dimensional flow is studied through a planar contraction geometry.An auxiliary variable is introduced into the problem formulation producing a non-linear system of differential equations comprising two elliptic equations and one hyperbolic equation. This system is discretized by finite difference methods and the resulting system of non-linear algebraic equations is solved iteratively by successive substitutions. The simple structure of this iteration permits a convergence analysis which is presented in Section 2. This analysis is performed prior to the spatial discretization and establishes the dependence of the iteration upon the material parameters. At the discrete linearized equation level a combination of inner iterations for elliptic equations and direct marching for the hyperbolic equation is used. The stability of the marching scheme is considered in Section 4.3 and a discussion on the results is given in Section 5.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260312
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    A nine node finite element for analysis of geometrically non-linear shells (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1945-1962 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A nine node finite element is presented for the analysis of thin shell structures undergoing large deflection. The finite element formulation is based on the concept of degenerate solid shell element and the Hellinger-Reissner principle with independent strain. Three versions of assumed independent strain are selected to suppress spurious kinematic modes. One version leads to a finite element model which is kinematically stable at element level while the other two give globally stable models. Numerical tests indicate that the finite element model which is stable at element level may reveal the locking effect in certain cases. However, the other two models are free of locking.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260905
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  • 186
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    Finite element approximations of singular parabolic problems (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1989-2007 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient implementation of finite element methods for free boundary parabolic problems in general two dimensional space domains is presented. The Stefan problem, the Hele-Shaw problem and the porous medium equation are included. Backward differences or linearization techniques are used for the time discretization of the problem. The performances of these schemes are discussed with several numerical tests.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260907
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    A new hybrid transfinite element computational methodology for applicability to conduction/convection/radiation heat transfer (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1087-1100 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes new and recent advances in the development of a hybrid transfinite element computational methodology for applicability to conduction/convection/radiation heat transfer problems. The transfinite element methodology, while retaining the modelling versatility of contemporary finite element formulations, is based on application of transform techniques in conjunction with classical Galerkin schemes and is a hybrid approach. The purpose of this paper is to provide a viable hybrid computational methodology for applicability to general transient thermal analysis. Highlights and features of the methodology are described and developed via generalized formulations and applications to several test problems. The proposed transfinite element methodology successfully provides a viable computational approach and numerical test problems validate the proposed developments for conduction/convection/radiation thermal analysis.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260507
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    A robust triangular plate bending element of the Reissner-Mindlin type (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1169-1184 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new triangular plate element is presented. This new element is based on independent interpolations for slopes, displacement and shear forces, and it is shown that it does not suffer from any defect common to other Mindlin plate elements. Several examples are presented to illustrate the behaviour of this new element.
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260511
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    Computer analysis of structures matrix structural analysis, structured programming, Siegfried M. Holzer, Elsevier, 1985, pp. 426. ISBN 0-444-00943-4 (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1235-1236 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260515
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  • 190
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    Formulation and solution of hierarchical finite element equations (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1213-1233 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a general hierarchical formulation applicable to both elliptic and hyperbolic problems. Static and eigenvalue linear elastic problems as well as convection-diffusion problems are studied. The hierarchical formulation is well suited for adaptive procedures.For the convection-diffusion problem the hierarchical approximation is made in time only. Different hierarchical functions are proposed for different types of problems. Both weighted residual and least-squares formulations are applied. A combination of these two gives a penalty method with a constraint equation corresponding to the least-squares method. A whole class of time integration formulae is obtained. These are all suitable for adaptive procedures owing to the hierarchical approximation in the time domain. If a linear discontinuous hierarchical base function is used in the Galerkin weak formulation, the method so obtained corresponds to the discontinuous Galerkin method in time and is especially suited for convection dominated problems. The streamline-diffusion method is found to be the aforementioned penalty method.This paper also examines the sequence of nested equation systems that results from a hierarchical finite element formulation. Properties of these systems arising from static problems are investigated. The paper presents some new possibilities for iterative solution of hierarchic element equations, and different procedures are compared in a numerical example. Finally, a simple ID convection-diffusion problem clearly shows that the proposed hierarchical formulation in time gives a stable and accurate solution even for convection dominated flow.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260514
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    Announcement (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1240-1240 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260518
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    Masthead (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260601
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    Exact numerical solutions for radiative heat transfer in cylindrical furnaces (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1201-1212 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Exact expressions for the distributions of the components of radiative flux density and the radiative energy source term in terms of wall and medium temperature distributions have been formulated for an emitting absorbing medium of constant properties bounded by black walls of a cylindrical enclosure. The accuracy of numerical solutions has been tested on an idealized enclosure for which exact analytical solution of the expressions is possible and shown to have six-figure accuracy. The exact expressions have then been solved numerically for an enclosure problem based on data reported previously on a large scale experimental furnace. The principal feature of the data is highly non-uniform temperature distributions which are typical of the conditions encountered in industrial furnaces. These data have been chosen because of their practical importance and the non-availability of exact solutions for such data. The resulting exact solutions have been tabulated and are intended to serve in the future as standards for testing the accuracy of the approximate predictions produced using various three-dimensional flux models in cylindrical configurations.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260513
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    On the problem of two coplanar cracks inside an infinite isotropic elastic solid (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 27-35 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is proposed for the approximate evaluation of normal displacements and normal stresses on the plane of two coplanar cracks located inside an infinite isotropic elastic solid and subjected to normal internal pressure. The formulation results in a single integral equation for the unknown normal stresses on the plane of the cracks. Numerical results are given for the stress intensity factor KI of two coplanar circular cracks and two coplanar elliptical cracks opened up under a uniform internal pressure.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620190105
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    An iterative method for finite dimensional structural optimization problems with repeated eigenvaluesResearch supported by N.S.F. Grant No. CEE 8005677. (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 93-112 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method for solving finite dimensional structural optimization problems with constraints on natural frequency and on buckling is formulated. The method treats nondifferentiable repeated eigenvalues that have been shown to systematically arise in structural optimization. Recent results on differentiability of eigenvalues are used to develop a generalized gradient projection method for structural optimization. The algorithm is shown to overcome technical difficulties associated with nondifferentiability of repeated eigenvalues. The method is used to solve buckling and vibration optimization problems in which repeated eigenvalues occur.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620190110
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    Finite element triangular meshing optimization for pure torsion (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 929-942 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a new approach to the mesh generation for torsional problems in the finite element discretization using quadratic triangular elements. A nonlinear constrained optimization program is used as a tool.As a criterion for the optimum meshing, the minimum error of second-order differential operator is adopted.An example problem is included to demonstrate the applicability of the method. Final results of the mesh distribution show significant improvements in meeting the criterion's objectives.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620190612
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    An optimally integrated four-node quadrilateral plate bending element (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 831-840 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A clearer understanding of the problems associated with reduced integration and optimum integration schemes for the development of Mindlin plate elements is presented. It is shown that an optimal selective integration rule can be found for the 4-node quadrilateral plate bending element which requires 2 × 2 Gaussian integration for bending energy and 1 × 2 and 2 × 1 rules for the shear energy terms from (θx - w,x) and (θy - w,y), respectively. This will give an element of correct rank, without any zero energy mechanisms and without shear locking in the thin plate limit, and better performance in moderately thick situations than the currently available 4-node quadrilaterals using one-point shear integration or modified one-point shear integration due to Hughes et al. The effects of arbitrary orientation of the grid and the non-rectangular form of element are discussed.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620190606
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    A decomposition procedure for large-scale optimum plastic design problemsSponsored by the United States Army under Contract Nos. DAAG29-75-C-0024 and DAAG29-80-C-0041. (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 873-889 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A decomposition procedure is proposed in this paper for solving a class of large-scale optimum design problems for perfectly-plastic structures under several alternative loading conditions. The conventional finite element method is used to cast the problem into a finite dimensional constrained nonlinear programming problem. Structures of practically meaningful size and complexity tend to give rise to a large number of variables and constraints in the corresponding mathematical model. The difficulty is that the state-of-the-art mathematical programming theory does not provide reliable and efficient ways of solving large-scale constrained nonlinear programming problems. The natural idea to deal with the large-scale structural problem is somehow to decompose the problem into a collection of small-size problems each of which represents an analysis of the behaviour of each finite element under a single loading condition. This paper proposes one such way of decomposition based on duality theory and a recently developed iterative algorithm called the proximal point algorithm.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620190609
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    Numerical methods in applied fluid dynamics, B. Hunt (Ed.), Academic Press, London, 1980 (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 949-949 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620190614
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    Three-dimensional finite element analysis of open-die forging (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 67-85 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three-dimensional finite element analysis is applied to operation sequences in open-die forging. Flat tools with rounded edges for open-die forging are geometrically modelled using Bézier curves. With this technique, the problems at the die-workpiece interface, such as the integration of frictional stress, node touching on dies and node separating from dies, can be handled effectively. It is shown that in solving general symmetric problems computation time can be saved by reducing variables and rearranging them in the stiffness matrix. One-bite operations and operation sequences for producing two-size bars and two-size pipes in several bites are investigated in regard to geometry, load, energy and deformation distribution.
    Additional Material: 15 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620250108
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