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  • 1
    Electronic Resource
    Electronic Resource
    Finite element method applied to the problem of stability of a non-conservative system (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 63-87 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element method is applied to the stability analysis of structural systems subject to non-conservative forces. The development of the method is general, but the specific application considered here is the stability of thin-walled members subject to follower forces. The method predicts the type of instability, whether it be buckling or flutter. Example problems, for which exact solutions are known, illustrate the accuracy and convergence characteristic of the finite element formulation.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030110
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  • 2
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    Dynamic analysis of structures using the rank force method (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 103-117 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of the finite element rank force method for the dynamic analysis of redundant structures is presented. The applied loading consists of discrete and distributed loads. Both forced and free vibrations are considered, the latter yielding latent vectors corresponding to dynamic redundancies.It is shown that the dynamic properties of an element are given by a static flexibility matrix, an inverse mass matrix, a damping parameter and a displacement vector representing the effect of the applied distributed loading.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030112
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  • 3
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    An annular segment finite element for plate bending (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 119-129 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A stiffness matrix for a finite element having the planform of an annular segment is derived using the displacement approach. Numerical problems involved in the derivation are discussed and rapid convergence to exact solutions is demonstrated on three sample problems. It is concluded that the new element will be of great value to engineers concerned with the analysis of slabs of bridge decks curved in plan.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030113
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  • 4
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    Stress and deformation analysis of fibrous composite materials by point matching (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 89-101 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The point matching numerical method and its generalization, the method of boundary point least squares, have been successfully applied to numerous boundary value and eigenvalue problems. The present paper demonstrates the application of these techniques to problems in the micromechanics of fibrous composite materials, i.e. determination of elastic moduli and stress concentrations for parallel-fibre materials which are loaded transversely with respect to the fibres. The solution technique utilizes exact solutions of the governing equations of plane elasticity for each component fibre and its surrounding matrix material in a typical repeating section of the composite material. The continuity conditions for stresses and displacements between fibre and matrix and the repeatability conditions at the boundary of the repeating section are satisfied approximately in a pointwise manner. Some special numerical techniques which were found to be particularly useful in applying the point matching method to these problems are delineated. The method is demonstrated for composite materials having circular, elliptical and square fibres in regular, staggered arrays. Numerical results are given which show the accuracy of the method as well as stress concentration and composite elastic moduli data.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030111
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  • 5
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    Concave programming and piece-wise linear programming (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 131-144 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper discusses the mathematical foundations of a technique that has been used extensively in structural optimization.1-6 Two basic problems are considered. The first of these is the concave programming problem which consists of finding the global minimum of ‘piece-wise concave functions’ on ‘piece-wise concave sets’. Since any function can be approximated by a piece-wise concave function, this method could in principle be used to find the global minimum in non-convex optimization problems. The second one is the piece-wise linear programming problem in which the objective function is convex and piece-wise linear. The iterative method outlined for handling this problem is shown to be much more efficient than the standard simplex method of linear programming.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030114
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  • 6
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    A frontal solution program for finite element analysisB. M. Irons, ‘A frontal solution program for finite element analysis’, Int. J. num. Meth. Engng, 2, 5-32 (1970). (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 149-149 
    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.1620030116
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  • 7
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    Editorial notice (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 154-154 
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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.1620030202
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  • 8
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    Reduced integration technique in general analysis of plates and shells (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 275-290 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The solution of plate and shell problems by an independent specification of slopes and middle surface displacements is attractive due to its simplicity and ability of reproducing shear deformation. Unfortunately elements of this type are much too stiff when thickness is reduced.In an earlier paper a derivation of such an element was presented1 which proved very successful in ‘thick’ situations. Here a very simple extension is made which allows the element to be economically used in all situations.The improved flexibility is achieved simply by reducing the order of numerical integration applied to certain terms without sacrificing convergence properties. The process is of very wide applicability in improvement of element properties.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030211
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  • 9
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    Masthead (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971) 
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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.1620030301
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  • 10
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    Discussion of paperS. Gallof and B. Kaplan, ‘Numerical solution and utilization of Green's functions,’ Int. J. num. Meth. Engng, 1, 169-175 (1969). by S. Gallof and B. Kaplan (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 295-296 
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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.1620030214
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  • 11
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    A static and dynamic finite element shell analysis with experimental verification (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 299-315 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A system of finite element shell analysis codes, called SABOR/DRASTIC, is used to analyse a complex two-layered shell of revolution under static and dynamic asymmetric loads. The dynamic analysis is compared with experimentally measured response. In this linear elastic analysis, emphasis is placed on the inherent flexibility of the finite element method in modelling the complex structural geometry of a given test specimen. Static studies, which involve variations in important shell parameters, and dynamic studies, which provide a successful correlation with experiment, are used to illustrate both the detail and the generality with which shell analyses may now be performed with confidence.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030302
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  • 12
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    On the calculation of consistent stress distributions in finite element approximations (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 317-325 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The theory of conjugate approximations1 is used to obtain consistent approximations of stress fields in finite element approximations based on displacement assumptions. These consistent stresses are continuous across interelement boundaries and involve less mean error than those computed by the conventional approach.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030303
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  • 13
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    Generation of two- and three-dimensional finite elements (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 327-347 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Many of the known finite elements are based on a variational procedure in a functional basis of monomials. The present paper attempts to formulate completely a finite element procedure which is non-variational on a functional basis which is left to the choice of the user.
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    URL: http://dx.doi.org/10.1002/nme.1620030304
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  • 14
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    Discussion of paperSuryanarayan Patnaik and Pasala Dayaratnam, ‘Behaviour and design of pin connected structures’, Int. J. num. Meth. Engng, 2, 579-595 (1970). by Suryanarayan Patnaik and Pasala Dayaratnam (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 443-444 
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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.1620030312
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  • 15
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    Network-topological formulation of analysis and design of rigid-plastic framed structures (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 425-441 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A unified network-topological approach to the formulation and solution of the analysis and minimum weight design of rigid-plastic structural systems is presented. It is shown that both analysis and design can be formulated using network concepts, but that, in contrast to elastic networks, the formulation results in a mathematical programming problem. Formulations based both on the static and kinematic theorems of plasticity are presented, and it is shown that duality guarantees that the two types of formulation yield identical results. The problem is first formulated on the basis of a simple definition of yielding, and is then generalized to the case where yielding is defined in terms of a yield surface.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030311
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  • 16
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    Non-linear structural analysis by dynamic relaxation (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 463-483 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Dynamic relaxation, an iterative method for use with digital computers, is described and is shown to be suitable for the solution of a system of linear equations and in particular for such problems derived from structural frame analysis. It is further shown that the method may be modified to include non-linear equations relating to these problems.Some specific examples of linear and non-linear solutions are given and comparisons are made with another computer method which performs the same tasks.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030403
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  • 17
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    A finite-deflection analysis of shallow arches by the discrete element methodThis paper is Crown copyright and is reproduced here with the permission of the Controller, Her Majesty's Stationery Office. (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 529-552 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The discrete element displacement method is used to analyse the finite-deflection behaviour of shallow arches. The arches are idealized as assemblies of shallow curved elements and the necessary properties of the displacement patterns in these elements are discussed. Numerical solutions of the geometrically non-linear problem are obtained by directly minimizing the total potential energy of the system.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030408
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  • 18
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    Global-local finite element (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 565-574 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element procedures usually require more degrees of freedom for a specified accuracy than does a classical Ritz procedure if suitable coordinate functions are available. This paper develops a combined global and local dependent variable representation which couples the conventional and finite element Ritz methods. This hybrid method preserves much of the flexibility of the finite element method while increasing the solution accuracy for a specified system order. The method is illustrated by examination of a beam and a plate vibration problem.
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    URL: http://dx.doi.org/10.1002/nme.1620030410
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  • 19
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    A simple algorithm for the stiffness matrix of triangular plate bending elementsThe authors are indebted to the referees for many comments and suggestions. (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 553-563 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For a hierarchy of polynomials on the triangle there is derived an algorithm for computing the stiffness matrix of the plate bending element. The algorithm is easy to program and means a considerable saving of the computing time. The same approach can be used for any elliptic equation with constant coefficients.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030409
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  • 20
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    Improved numerical integration of thick shell finite elements (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 575-586 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A quadratic thick shell element derived from a three-dimensional isoparametric element was first introduced by Ahmad and co-workers in 1968. This element was noted, however, to be relatively inefficient in representing bending deformations in thin shell or thin plate applications. The present paper outlines a selective integration scheme for evaluating the stiffness matrix of the element, in which each component of the strain energy is evaluated separately using a different Gaussian integration grid for each contribution. By this procedure, the excessive bending stiffness of the element, which results from the use of me quadratic interpolation functions, is avoided.The improved performance of this element, as compared with the original thick shell element, is demonstrated by analyses of a variety of thin and thick shell problems. Editors' note: A similar development was outlined by O. C. Zienkiewicz and co-workers in lnt. J. num. Meth. Engng, 3, 275-290 (1971). Some important details differ between the two papers which are thus complementary.
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    URL: http://dx.doi.org/10.1002/nme.1620030411
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  • 21
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    An introduction to applied probability and random processes, J. B. Thomas, Wiley, New York, 1971. No. of pages: 350. Price: £6·15 (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 591-592 
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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.1620030415
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  • 22
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    Masthead (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972) 
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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.1620040101
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  • 23
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    Editorial (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 1-3 
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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.1620040102
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  • 24
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    Evaluation of orthogonal damping matrices (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 5-10 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two methods for the numerical evaluation of orthogonal damping matrices are developed. The first relates the modal damping ratios to the coefficients of the Caughey series. The second is a direct approach which expresses the damping matrix as a sum of a series of matrices each of which produces damping in a particular mode. It is found that the direct approach is more convenient to apply and is less numerically sensitive than the series approach.
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  • 25
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    A mixed finite element formulation for plate problems (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 67-84 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mixed triangular finite element model has been developed for plate bending problems in which effects of shear deformation are included. Linear distribution for all variables is assumed and the matrix equation is obtained through Reissner's variational principle. In this model, interelement compatibility is completely satisfied whereas the governing equations within the element are satisfied ‘in the mean’. A detailed error analysis is made and convergence of the scheme is proved. Numerical examples of thin and moderately thick plates are presented.
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    URL: http://dx.doi.org/10.1002/nme.1620040109
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  • 26
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    A sector element for thin plate flexure (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 133-142 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a sector shape of an element ideally suited for the analysis of sectorial and annular plates. A conforming function with twenty degrees of freedom is developed in polar co-ordinates to represent the deformation of the element in bending. The finite element method is applied to some plate bending problems to illustrate the power and efficiency of sector elements.
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    URL: http://dx.doi.org/10.1002/nme.1620040114
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    Discussion of paperJ. Robinson and M. Petyt, ‘Dynamic analysis of structures using the rank force method’, Int. J. num. Meth. Engng, 3, 103-117 (1971). By John Robinson and Maurice Petyt (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 143-144 
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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.1620040115
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  • 28
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    Discussion of papaers By R. S. Barsoum, F. Sawko and P. A. Merriman (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 144-145 
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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.1620040116
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  • 29
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    Letter to the editor (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 148-151 
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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.1620040118
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  • 30
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    Discussion of paperY. Tada and G. C. Lee, ‘Finite element solution to an elastica problem of beams’, Int. num. Meth. Engng, 2, 229-241 (1970). By Yasuo Tada and George and George C. Lee (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 145-148 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Announcements (1972)
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    International Journal for Numerical Methods in Engineering 4 (1972), S. 151-151 
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    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.1620040119
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    Numerical methods for Orr-Sommerfeld problems (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 195-206 
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    Notes: Five previously employed numerical methods for the solution of Orr-Sommerfeld problems have been compared to each other and to a new method, the differential method of near-orthonormalized integration. Brief summaries of each method are included. The comparison, based on seven factors, reflects the results of an implementation of a computer program for each method for the classic Orr-Sommerfeld problem of plane Poiseuille flow. This comparison shows that the new method and the algebraic finite difference method are currently the best available numerical solution methods for the problems in this class, with the new method being less problem dependent.
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    Numerical solution of dynamical systems by direct application of Hamilton's principle (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 207-216 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In this paper, a method is described which allows a direct derivation of a set of first-order finite difference equations to numerically compute the motion of any conservative or non-conservative dynamic system with a finite number of degrees of freedom. The derivation of the method is based on an application of Lagrangian multipliers to a functional form of Hamilton's equations, and reduces the work required to obtain the most desirable form for numerical integration from the standpoint of computational efficiency and accuracy. For systems with many degrees of freedom, the required matrix inversions produce first derivatives of the co-ordinates, instead of second derivatives, thus eliminating a potential source of error in numerical integration. Two examples are given to illustrate the method.
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    A lumped parameter element for the analysis of hyperbolic paraboloid shells (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 235-249 
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    Notes: This paper presents the derivation of the stiffness matrix for a lumped parameter hyperbolic paraboloid shell element. This element is used to obtain solutions to hyperbolic paraboloid shells with various edge conditions. Numerical example for three types of support conditions (a simple support, a clamped edge and a shell supported by concentric edge beams) are presented. To illustrate the applicability of the method, the results obtained by the lumped parameter element are compared with those obtained by well-known methods of analysis such as the variational procedure, the finite difference and the finite element method.
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    URL: http://dx.doi.org/10.1002/nme.1620040209
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    Convergence of eigenvalue solution in conforming plate bending finite elements (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 217-234 
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    Notes: The convergence proof of plate eigenvalue solution from conforming displacement finite elements is presented. The analysis is based on converting a thick plate free vibration problem in to a corresponding isoperimetric variational problem. A conforming thick, plate element is used to illustrate the mathematical development. On the basis of the derived asymptotic rate of convergence of the approximate eigenvalues, the authors propose a practical method of improving the numerical solutions. Extension of the mathematical proof to cover classical thin plate finite elements is briefly discussed.
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    Numerical solution of a separtated viscous flow problem by a non-uniform finite-difference net (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 251-260 
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    Notes: Two-dimensional stagnation point flow of a viscous fluid is modified by the introduction of a thin plate placed symmetrically at the stagnation point. Separation of the boundary layer results in back flow near the plate even at small Reynolds numbers. The Navier-Stokes equations governing the flow are replaced by finite differences using unequal net spacing which is finer in the boundary layer. The choice of finite differences guarantees convergence of the iterative procedures used. Only those relaxation parameters, which are necessary to obtain convergence and also to make the method computationally efficient, have been used. Numerical results for Reynolds numbers 9, 100 and 400 are obtained.
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    Mixed finite element method for axisymmetric shells (1972)
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    International Journal for Numerical Methods in Engineering 4 (1972), S. 261-277 
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    Notes: A mixed variational formulation is used as basis for developing a mixed finite element method for axisymmetric shell. The independent unknowns of the method are the axial and radial displacement components, the rotation of the normal to the middle surface and the meridional bending stress couple. The basic element is a frustrum of curved meridian. General advantages of the mixed method are presented, one of which is the possibility of using piece-wise linear functions of the meridional arclength to represent the basic unknowns. Test results are presented for plate bending, transverse shear deformation, membrane behaviour, edge-zone bending, bending near the junction of two shells, convergence of the method and accuracy of middle surface curvature interpolation. Shell geometries considered are cylindrical, conical, spherical and ellipsoidal. Good results are obtained which should increase interest in the relatively less known and less tested mixed method as compared to the stiffness method.
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    Numerical approximation of one-dimensional consolidation (1972)
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    International Journal for Numerical Methods in Engineering 4 (1972), S. 279-287 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A generalized finite difference scheme is developed to represent the one-dimensional consolidation process. The difference equations are derived from integral balance equations which represent the soil as a mixture of two constituents. No restrictions are placed on the soil constitutive properties or stratigraphy. An approach to stability analysis for the scheme is outlined, and an example problem is presented.
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    Propagation of transient pules from a spherical cavity in a viscoelastic medium (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 289-299 
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    Notes: The problem of an impulsively applied pressure acting on the surface of a spherical cavity in a linear viscoelastic medium is solved by an approximate inversion of the Fourier transform. The method can be applied to general models of viscoelasticity described by the Boltzmann superposition principle, with relaxation or creep functions given analytically or numerically in the time or the frequency domain.
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    A note on the estimation of critical damping in dynamic relaxation (1972)
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    International Journal for Numerical Methods in Engineering 4 (1972), S. 301-303 
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    Notes: A new way of estimating critical damping in dynamic relaxation is proposed using the concept of a mass-dependant load vector, a postulate concerning vibrations and Rayleigh's principle. The method should be particularly appealing in those not uncommon circumstances where the actual loads are approximately proportional to the masses for then the computer time required in evaluating the various constants would actually be a part of the problem-solving time.
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    Dynamic probabilistic system, R. A. Howard, Wiley, New York. Vol. 1, No. of pages: 576. Price: £7·90. Vol. 2, No. of pages: 1108. Price: £8·75 (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 303-304 
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    Keywords: Engineering ; Engineering General
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    URL: http://dx.doi.org/10.1002/nme.1620040215
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    Masthead (1972)
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    International Journal for Numerical Methods in Engineering 4 (1972) 
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    Linear algebra, vol. 2, handbook for automatic computation, J. H. Wilkinson and C. Reinsch (Editors), Springer-Verlag, Berlin, Heidelberg and New York, 1971. No. of pages: 439. Price: $19.80 (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 304-304 
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    An iterative approach to strucural optimizationResearch sponsored by the Air force Flight Dynamics Laboratory, Wright-Patterson Air Force Base, Ohio, under Contract F33615-69-C-1826. (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 331-336 
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    Notes: An iterative procedure of structural optimization is discussed that combines finite element analysis with the use of explicit optimality conditions. The procedure is illustrated by examples concerning sandwich beams with constraints on the deflection at a specified section, the maximum deflection or the sum of the maximum deflection in all spans of a continuous beam. The examples suggest that, starting from a uniform beam, by far the greatest saving in weight is obtained in the first two or three iterations.
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    The finite element method applied to ideal gaseous mixtures (1972)
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    International Journal for Numerical Methods in Engineering 4 (1972), S. 337-344 
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    Notes: The finite element technique is extended to an ideal gaseous mixture to study diffusion of several gaseous species in a carrier gas under various geometries and flow conditions. This is accomplished by obtaining the finite element analog of the balance of mass for each species, along with the corresponding equations for the balance of mass, momentum and energy for the mixture. Numerical results are obtained for a steady-state, incompressible, isothermal, viscous mixture of two gases for several boundary conditions. Favourable agreement is obtained between the finite element results and analytical solutions.
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    Errata (1972)
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    International Journal for Numerical Methods in Engineering 4 (1972), S. 452-452 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620040316
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    Optimization methods for engineering design, R. L. Fox, Addison-Wesley, Massachusetts, 1971. Price: £6·05 (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 452-452 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620040315
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    Futher limitations on general hexahedron finite elements with derivative degrees of freedom (1972)
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    International Journal for Numerical Methods in Engineering 5 (1972), S. 137-139 
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    Notes: It is shown that isoparametric finite elements with derivative degrees of freedom of second order or higher in the local curvilinear space demand an excessive number of degrees of freedom in the global space. To illustrate this limitation as it pertains to the continued development of higher order elements, discussion is centered around the general hexahedron element.
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    More on reduced integration and isoparametric elements (1972)
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    International Journal for Numerical Methods in Engineering 5 (1972), S. 141-142 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Elasto-plastic stress analysis. A generalization for various contitutive relations including strain softening (1972)
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    International Journal for Numerical Methods in Engineering 5 (1972), S. 113-135 
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    Notes: Several iterative processes for solving elasto-plastic problems are discussed in the context of a general formulation which includes: 1Associated and non-associated plasticity relations.2Strain hardening as well as strain softening behaviour.Advantages of the ‘initial stress’ process are emphasized for a wide category of problems and the isoparametric formulation is used throughout.
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    Vibration problems using isoparametric shell elements (1972)
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    International Journal for Numerical Methods in Engineering 5 (1972), S. 142-145 
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    Keywords: Engineering ; Engineering General
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    Direct finite element analysis of elastic contact problems (1972)
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    International Journal for Numerical Methods in Engineering 5 (1972), S. 145-147 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Additional Material: 6 Ill.
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    Masthead (1972)
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    International Journal for Numerical Methods in Engineering 5 (1972) 
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    Finite elements of non-linear continua, J. T. Oden, McGraw-Hill, New York, 1972. Price: $8.40 (1972)
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    International Journal for Numerical Methods in Engineering 5 (1972), S. 148-148 
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    Keywords: Engineering ; Engineering General
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    Masthead (1971)
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    International Journal for Numerical Methods in Engineering 3 (1971) 
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    Erratum (1971)
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    International Journal for Numerical Methods in Engineering 3 (1971), S. 1-2 
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    Keywords: Engineering ; Engineering General
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    Editorial (1971)
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    International Journal for Numerical Methods in Engineering 3 (1971), S. 3-3 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    The finite difference and localized Ritz methods (1971)
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    International Journal for Numerical Methods in Engineering 3 (1971), S. 155-160 
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    Notes: The conventional central finite difference equations for the plane stress extension of flat plates are derived as a localized Ritz process. A dual differential-variational discretization of this type enables common classification of the finite difference and finite element methods. Also, it provides alternative methods of establishing sufficiency conditions and relative rates of convergence for discrete systems derived from a localized Ritz process, and the existence of solution bounds for discrete systems derived using difference procedures.
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    Finite element formulation of general electrothermoelasticity problems (1971)
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    International Journal for Numerical Methods in Engineering 3 (1971), S. 161-179 
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    Notes: This paper is concerned with the development of consistent discrete models, via the concept of finite elements, of linear and non-linear electrothermomechanical behaviour of continuous bodies. In the development, general energy balances are utilized to derive equations governing electromagnetic fields over an element and coupled equations of motion and heat conduction of a typical element of the continuum. These equations make it possible to study a general class of field problems involving arbitrary geometries and boundary conditions. Sample problems are included.
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    Axial wave propagation in membrane shells of revolution (1971)
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    International Journal for Numerical Methods in Engineering 3 (1971), S. 181-198 
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    Notes: The dynamic finite element technique, which is referred to in the literature as ‘computer-analysis’, is applied to wave propagation problems occurring in finite and semi-infinite linearly elastic membranes of revolution. Both semi-infinite and finite versions of cylindrical and conical membranes are considered, and a finite membrane having a meridional curve which is parabolic is solved. The source of excitation is generally a constant velocity motion of one end of the membranes, but the results for a stress-pulse input at one end of a semi-infinite cylindrical membrane are also given. The results for the finite membranes are new, and the results for the semi-infinite problems are discussed with respect to previously published results. The two-dimensional state of stress in the membrane requires careful ordering of the calculations, and the boundary conditions for finite membranes are shown to follow logically from this ordering of the calculations. The difference in the solutions resulting from prescribing an axial or a tangential velocity excitation at the end of a conical membrane is presented, and the mesh size necessary for convergence to the solution is indicated. The graphs of the results clearly indicate regions in space and time where the membrane model should be replaced by the shell formulation to represent a realistic structure. The technique is shown to be self-contained and independent of any formal method such as the method of characteristics.
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    Dynamic programming and the solution of the biharmonic equation (1971)
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    International Journal for Numerical Methods in Engineering 3 (1971), S. 199-213 
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    Notes: The numerical solution of the biharmonic equation in a rectangular domain is presented in the context of continuous dynamic programming techniques. The equations are specialized to the solution of elastic rectangular plates. A suitable approximate expression of a certain functional equation containing derivatives only in one direction is used to derive equations for the stiffness and flexibility matrices of the plate. It is shown that those matrices satisfy matrix Riccati equations subject to suitable initial conditions. It is also shown that the condition of optimality in the Hamilton-Jacobi-Bellman equation directly expresses a classical variational principle, i.e. the principle of complementary energy. Some numerical examples are finally presented.
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    Non-linear programming for the plastic analysis of local deformations in shell structures (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 215-232 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents an analysis of the response of plastic spherical and cylindrical shells subjected to loads applied through a rigid boss. Special emphasis is placed on following the load-deflection behaviour of these structures after the application of the yield-point load in order to predict the appearance of any snapping action.The method of analysis assumes that upper bound calculations are applicable and that the associated velocity fields can be represented by a series of piecewise continuous polynomials. The internal dissipation of energy for the structures are then written in terms of the coefficients of these polynomials and the values appropriate to the solution are found by using a non-linear programming routine.The results of this analysis are correlated with a non-dimensional boss size parameter p and compared with the results of experimental investigations. Mention is also made of the possible effects of initial imperfections.
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    Trigonometric function representations for rectangular plate bending elements (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 261-273 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A study of bending of plates for small deformations by applying the finite element method is presented in this paper.A new class of displacement functions has been developed for rectangular bending elements. For the first time a method is proposed for the derivation of displacement functions in which trigonometric expressions that had apparently failed to yield satisfactory results in earlier attempts can be used along with polynomial terms.The derivation leads to conforming type of displacement functions which satisfy the convergence criterion. The approach also demonstrates how many more new displacement functions can be found.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030210
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    A steepest gradient method for optimum structural design (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 249-259 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a search procedure for finding the unconstrained maximum or minimum of a function of many independent variables. If this function represents the volume, cost, stiffness, etc. of a structure and each of the independent variables is associated with a parameter governing the geometry of the structure then designs of optimum geometry may be made in certain cases with the assistance of this search procedure. The procedure consists of steepest gradient calculations used in conjunction with a reverse Fibonacci location process. A ridge-following technique is included to speed convergence in addition to localized exploration in the region of an optimum.The search procedure has been programmed for computer use and an outline of its structural design applications is presented together with an example of its efficiency in a specific case.
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    Quadrature rules for brick based finite elements (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 293-294 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Tab.
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    A note on accuracy and convergence of finite element approximations (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 291-292 
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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.1620030212
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    Recent advances in matrix methods of structural analysis and design, edited by R. H. Gallagher, J. T. Oden and Y. Yamada, University of Alabama Press, Alabama, 1971. No. of pages: 904. Price: $32.50 (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 446-446 
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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.1620030315
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    Discussion of paperR. S. Barsoum and R. H. Gallagher, ‘Finite element analysis of torsional and torsional-flexural stability problems’, Int. J. num. Meth. Engng, 2, 335-352 (1970). by R. S. Barsoum and R. H. Gallagher (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 444-445 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Announcements (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 447-448 
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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.1620030316
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    Masthead (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971) 
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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.1620030401
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    The elasto-plastic indentation of a half-space by a rigid sphere (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 451-462 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Using the finite element method, a detailed study of the deformations and stresses produced in an elastic-perfectly plastic half-space indented by a rigid sphere was done. The analysis covers the transition region from the maximum elastic contact load to a state where this load has been increased one hundredfold. Experimental results available in the literature are in good agreement with the analysis. In solving repeatedly the large number of linear equations involved in the solution of the problem, it was found profitable, in order to save computer time, to modify the direct elimination method. This technique is described in some details in the paper.
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    A note on convergence of finite element solutions (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 485-493 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The convergence of nodal displacements obtained by the finite element method is investigated for special element patterns in plane elasticity with the aid of the differential equation derived from the equilibrium condition at each node. The convergence of strains is also discussed. It is shown that averaging is an effective tool for obtaining approximations to strain for some kinds of mesh arrangement. It is also shown that the approach becomes inaccurate along force boundaries.
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    A refined curved element for thin shells of revolution (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 495-508 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A refined axisymmetric curved finite element for the analysis of thin elastic-plastic shells of revolution is described in the paper. The improved element is obtained by employing cubic polynomials in terms of local Cartesian co-ordinates for the assumed in-plane and out-of-plane displacements. This introduces into the solution two internal degrees of freedom in the cord direction of each element. These internal degrees of freedom are removed by static condensation before assembling the individual element stiffness matrices, and are subsequently recovered after the nodal displacements are obtained. On comparison with the previous formulation, this procedure greatly improves the accuracy of the solution especially with regards to in-plane stress-resultants at discontinuities in the meridional curvature and interelement equilibrium of forces. The latter fact makes it possible to analyse shells with a discontinuous meridional slope. In using this element, improvement in the convergence of the elastic-plastic solutions has also been observed.Several examples illustrate the quality of solutions. The reported study is limited to axisymmetric loadings cum boundary conditions.
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    Numerical methods for evaluation of equilibrium composition of ideal gases (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 509-517 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper considers methods of solution of the relevant equations based on the Newton-Raphson process. Expressions are derived for calculation with both good and very poor initial guesses and for calculation of pressure, volume and temperature during an equilibrium process. A method of programming the calculations is outlined. Variations and modifications to suit specific situations are discussed.
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    An automatic mesh generation scheme for plane and curved surfaces by ‘isoparametric’ co-ordinates (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 519-528 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computer orientated method is presented which generates meshes of triangular elements in plane and curved surfaces. Depending on geometrical and material variations, the region to be discretized is divided into a number of four sided zones. By using curvi-linear co-ordinate systems, nodes within and on the boundary of each zone are automatically positioned and referenced to a global Cartesian co-ordinate system. Elements are automatically assembled from these nodes. Input data is required to specify the positions and material properties of each zone and how they are connected. Examples are given which illustrate the range of meshes that can be generated. Extension of the method to generate three-dimensional tetrahedral elements is indicated.
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    Incremental displacement in non-linear analysis (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 587-588 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620030412
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    An introduction to APL, W. Prager, Allyn and Bacon, Boston, 1971. No. of pages: 134 (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 591-591 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620030414
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    Letters to the editor (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 588-591 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620030413
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    Matrix differential equation and higher-order numerical methods for problems of non-linear creep, viscoelasticity and elasto-plasticityThis paper is largely based on the author's Report No. 68/2, Approximate Analysis of Linear and Nonlinear Creep Problems, Department of Civil Engineering, University of Toronto, December, 1968, prepared under the sponsorship of Ford Science Foundation. Further refinement was obtained in connection with the preliminary research for the National Science Foundation project, Grant No. GK-26030. (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 11-15 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The constitutive equation is assumed in a very general form which includes as special cases non-linear creep, incremental elasto-plasticity as well as viscoelasticity represented by a chain of n standard solid models. Subdividing the structure into N finite elements, the problem of structural analysis is formulated with a system of 6N(n + 1) ordinary non-linear first-order differential equations in terms of the components of stresses and strains in the elements. This formulation enables one to apply Runge-Kutta methods or the predictor-corrector methods.
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    On completeness of shape functions for finite element analysis (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 17-22 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Some elements commonly used for analysis are examined for examined for completeness of polynomial interpolation and computational efficiency. Extensions to n-dimensional space are shown to be natural consequences of the interpolation, thus all elements considered here allow for finite element approximation in higher than three-dimensional spaces (e.g. space-time interpolations). From the study it is concluded that ‘serendipity’ class elements from the most efficient elements up to third-degree polynomial approximations. The method used here to develop the serendipity shape functions allows for different orders of interpolation along each edge. Thus, in zones where high accuracy is required meshes can now be easily changed from linear to quadratic or higher-order elements. Computations on some simple problems have demonstrated this to be a superior method than using large numbers of low ordered elements.
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    Finite element analysis of plates with curved edges (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 49-65 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of the high precision triangular plate bending element to problems with curved boundaries is considered. Appropriate edge conditions for nodal points on these boundaries are derived. The error inherent in representing the shape of a curved boundary by a series of straight segments is found to be the limiting factor on accuracy, while the effect of approximations in the actual boundary conditions is minor. To overcome the first type of error, the high precision element is modified to include one curved edge. Substantial improvements in accuracy are obtained, as demonstrated in example calculations for circular and elliptical plates.
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    The application of dual minimum theorems to the finite element solution of potential problems with special reference to seepage (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 85-93 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: By formulating the potential boundary value problems in terms of physical (in contrast to purely mathematical) variables, the existence of dual energy principles may be clearly distinguished. In direct analogy with elasticity, two possible energy methods present themselves giving rise to two possible finite element procedures. General upper and lower bounds on an energy quantity may be obtained, which in the case of seepage become the total seepage rate for a certain class of seepage problem. For this case of seepage the derivation of the finite element procedure and the computing of the bounds is described.
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    Viscoelastic stress analysis (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 357-366 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper formulates the viscoelastic problem so as to allow the use of higher-order differential equation solution techniques. Viscoelastic models describing the functional relationships of stress and strain for the material are used. However, the procedure outline is valid for more general relationships. The advantages of using Runge-Kutta integration formulae are indicated and an example demonstrates the excellent results obtainable. The computational efficiency of the method is emphasized and error prediction is discussed.
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    Tetrahedral polynomial finite elements for the Helmholtz equation (1972)
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    International Journal for Numerical Methods in Engineering 4 (1972), S. 405-413 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: It is shown that the Helmholtz equation in three dimension leads to finite element approximations on tetrahedral elements that closely resemble the corresponding two-dimensional treatment on triangle. For each polynomial order, there exist two numeric universal matrices independent to tetrahedron size and shape; the element matrices are always given as linear combinations of row and column permutations of these. Numeric matrices are given up to third-order, and the permutation schemes are shown in detail. Experimental computer programs using these elements have shown fast matrix assembly times; convergence rates are essentially similar to those obtained with the corresponding triangular elements.
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    A conforming finite element with internal equilibrium for two-dimensional problemsCrown Copyright, reproduced by permission of the Controller of Her Majesty's Stationery Office. This is the first publication of this article, but since the author is a British Civil Servant his work is covered by Crown Copyright. (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 367-378 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A method is presented for the derivation of displacement fields which satisfy compatibility of normal slopes at inter-element boundaries and the condition of internal equilibrium. The displacement field is obtained by integrating the governing partial differential equation over the element, using the initial value approach. The method is applied to calculate the stiffness matrix of a triangular bending element with nine degrees of freedom. Comparison with published solutions based on various element models shows a high degree of accuracy and convergence of the method. The advantage of internal equilibrium is illustrated by an example involving slab-column interaction. The solution correlates satisfactorily with existing experimental results.
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    Solution of eigenvalue problems by sturm sequence methodThis paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration. (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 379-404 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A generalized eigenvalue algorithm is presented herein along with the complete listing of the associated computer program, which may be conveniently utilized for the efficient solution of certain broad classes of eigenvalue problems. Extensive applications of the procedure are envisaged in the analysis of many important engineering problems, such as stability and natural frequency analysis of practical discrete structural systems, idealized by the finite element technique. The procedure based on the Sturm sequence method is accurate and fast, possessing several significant advantages over other known methods of such analysis. Numerical results are also presented for two representative structural engineering problems.
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    Finite displacement plate flexure by the use of matrix incremental approach (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 415-432 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A finite element incremental stiffness formulation for determining finite displacement flexure behaviour of thin elastic plates is presented. The solution of the finite displacement problems is based on a piecewise linear incremental approach. The procedural aspects of the incremental approach, the control of incremental sizes and the accuracy of the incremental approximation are investigated. The details concerning how to obtain in-plane stresses and how to treat edge conditions are discussed. Results include rectangular plates under lateral pressure with various edge conditions and aspect ratios. The laterally loaded plate with edges movable in the plane of the plate is also treated.
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    On the principle of repeatability and its application in analysis of turbine and pump impellers (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 445-448 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Additional Material: 5 Ill.
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    Effect of shear deformation on the elastica with axial strain (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 433-444 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of the elastica is generalized to include the effect if shear as well as axial strain. This leads to a non-linear two-point boundary-value problem composed of five first-order differential equations. At first the problem is linearized to study the way in which the bucking loads are modified by the combination of effects. For a simple column, the eigenvalues are found to be zeros of a third-order polynomial, and these are evaluated by a straightforward Newton-Raphson technique using a digital computer. The postbucking behaviour is then studied by using the computer and a ‘shooting’ method to solve the non-linear problem. For the special case of the prismatic column, graphs plotted by the computer are displayed to show the variation of load with both lateral and axial deflection for various combinations of axial compressibility and shear deformability. For one particular case, the deflected center line at various load levels is shown.
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    Applied mathematics of science and engineering, Charles Dixon, Wiley, London, 1971. No. of pages: 504. Price: £8·00 (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 451-452 
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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.1620040314
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    Discussion of papers By O. C. Zienkiewicz, R. L. Taylor and J. M. TooO. C. Zienkiewicz, R. L. Taylor and J. M. Too, ‘Reduced integration technique in general analysis of plates and shells’, Int. J. num. Meth. Engng, 3, 275-290 (1971). and S. F. Pawsey and R. W. CloughS. F. Pawsey and R. W. Clough, ‘Improved numerical integration of thick shell finite elements’, Int. J. num. Meth. Engng, 3, 575-586 (1971). (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 449-451 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620040313
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    Masthead (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972) 
    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.1620040401
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  • 93
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    Optimum design of hypertatic structures (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 561-578 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The task of optimum design of structures is one that involves non-linear Programming. This is particularly the case when deflection as well as stress limitation are imposed as design criteria. In this paper a Fundamental approach is presented for the minimum weight design of statically indeterminate elastic structure subject to non-linear deflection and stress constrains.The matrix force method is adopted to formulate the problem. The constraints thus derived prove to have separable variables and therefore can be linearized in a piecewise manner. The computation aspects concerning the restricted entry in to the simplex tableau are briefly discussed and illustrative examples are given to verify the validity of the proposed method.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620040410
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    A numerical method for coupled differential equations (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 587-596 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a numerical method for solving first-order coupled matrix differential equations. Recursive equations are used to find ‘reflection’, ‘transmission’ and ‘source’ coefficients; these coefficients are then used to construct the vector solution to the differential equations. The method can be used to solve linear and non-linear differential equations with specified initial or two-point boundary values. Numerical results for several initial value problems are given in the paper.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620040413
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  • 95
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    On the rigid displacement condition (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 583-586 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper shows the importance of the rigid displacement condition when the finite element method is used for structures having little rigidity. The theoretical analysis is confirmed by numerical results obtained with a curved beam.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620040412
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    Note on the ‘Alpha’-constant stiffness method for the analysis of non-linear problems (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 579-582 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A procedure for the acceleration of convergence in non-linear analysis using the modified Newton-Raphson problem is described. The process has been found useful in plasticity and large deformation studies and its application elsewhere can be envisaged.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620040411
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    Effective quadrature rules for quadratic solid isopatametric finite elements (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 597-599 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620040414
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    Applied numerical methods, B. Carnahan, H. A. Lither and J. O. Wilkes, Wiley, New York, 1969. No. of Pages: 604. Price: £6·60 (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 599-600 
    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.1620040415
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    Simulation modeling, Forest Paul Wyman, Wiley (Series in Management and Administration), London, 1970. No. of pages: 264. Price: £3·75 (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 600-600 
    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.1620040416
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    Sparse matrices and their applications, Edited by Donald J. Rose and Ralph A. Willoughby, Plenum Press, New York, 1972. No. of pages: 215. Price: £17·50 (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 600-600 
    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.1620040417
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