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  • 1986  (1,506)
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  • Electronic Resource  (1,506)
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  • 1850-1859
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  • 101
    Electronic Resource
    Electronic Resource
    Spatial discretization of hyperbolic equations with periodic solutions (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1395-1406 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We investigate the Cauchy problem for hyperbolic equations for which the frequencies of the main Fourier components in the solution are located in a given frequency interval. Difference formulae for the spatial derivatives are constructed that are tuned to the given intervals of frequencies. Numerical examples illustrating these special discretizations are given both for linear and non-linear problems.
    Additional Material: 10 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230802
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  • 102
    Electronic Resource
    Electronic Resource
    Numerical solution of constrained non-linear algebraic equations (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1455-1481 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical solution of n non-linear algebraic equations with n unknowns, when any or all of the variables are subjected to constraints, is discussed. Distinction is made between physical and absolute constraints. It is shown, using a set of test problems, that solution of constrained equations does require a special approach. It is found that the step length restricted Newton's method performs best for problems with absolute constraints. Physical constraints can be best handled using a continuation method or penalty functions.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230805
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  • 103
    Electronic Resource
    Electronic Resource
    A restricted hybrid stress formulation based on a direct finite element method (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1495-1508 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A direct method, which uses stress and displacement modes obtained from the governing equations of a problem, is adopted for finite element formulation. It is shown that this method actually leads to a restricted hybrid stress formulation if the displacement modes are changed to ensure symmetry of the stiffness matrix. Through this direct method, however, the problem of selecting the appropriate number of stress modes in the regular hybrid stress model is bypassed. Only the minimum number of modes that are compatible with the number of nodal degrees-of-freedom of an element is needed in the formulation. Using more modes only leads to a combination of stress modes, and will not improve the order of performance of the element. It is shown through numerical examples that the restricted hybrid stress formulation leads to well-balanced elements.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230807
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  • 104
    Electronic Resource
    Electronic Resource
    Dynamic response of rigid strip-foundations by a time-domain boundary element method (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1547-1565 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dynamic response of rigid strip-foundations placed on or embedded in a homogeneous, isotropic, linear elastic half-space under conditions of plane strain to either external forces or obliquely incident seismic waves of arbitrary time variation is numerically obtained. The above mixed boundary-value problems are treated by the time domain boundary element method which is used in a step-by-step timewise fashion to provide the foundation response to a rectangular impulse. Numerical examples are presented in detail to demonstrate the use and importance of the proposed method. The method appears to be more advantageous than frequency domain techniques, because it provides the transient foundation response in a natural and direct way and can form the basis for extension to the non-linear case.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230810
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  • 105
    Electronic Resource
    Electronic Resource
    Announcements (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1582-1582 
    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.1620230814
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  • 106
    Electronic Resource
    Electronic Resource
    A new efficient approach to the formulation of mixed finite element models for structural analysis (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1629-1641 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new mixed finite element formulation is developed based on the Hellinger-Reissner principle with independent strain. By dividing the assumed strain into its lower order and higher order parts, the new formulation can be made much more efficient than the conventional mixed formulation. In addition the present new approach provides an alternative way of introducing a stabilization matrix to suppress undesirable kinematic modes.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230905
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  • 107
    Electronic Resource
    Electronic Resource
    Minimum weight design of cylindrical water tanks (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1679-1691 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper deals with the minimum weight design of cylindrical water tanks. The design is to conform to BS5337. The design procedure used is a combination of the finite element analysis of structures and a numerical method of optimization. In the design, the internal radius and the height of the tank are fixed and the variation of wall thickness is treated as the unknown of the design. Only piecewise linear variations of thickness are considered. Results of some examples are presented and discussed.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230908
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  • 108
    Electronic Resource
    Electronic Resource
    Finite element method for non-linear forced vibrations of circular plates (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1715-1726 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Geometric non-linearities for large amplitude free and forced vibrations of circular plates are investigated. In-plane displacement and in-plane inertia are included in the formulation. The finite element method is used. An harmonic force matrix for non-linear forced vibration analysis is introduced and derived. Various out-of-plane and in-plane boundary conditions are considered. The relations of amplitude and frequency ratio for different boundary conditions and various load conditions are presented.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230911
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  • 109
    Electronic Resource
    Electronic Resource
    Conforming versus non-conforming boundary elements in three-dimensional elastostatics (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1885-1904 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this work, we present a critical comparison of two basic ways of implementing the boundary element method in three-dimensional elastostatics. The first way is by using non-conforming elements, i.e. elements which have the collocation nodes removed from their perimeter. The number of nodes used for the collocation of the boundary tractions and displacements need not coincide with the number of nodes placed along the perimeter of the element for the purpose of describing the geometry. The second way is by placing the collocation nodes along the perimeter of the element, usually in coincidence with the geometry nodes. Thus, interelement continuity of the displacements is obtained. The basic reasons for the use of non-conforming elements in the boundary element method are twofold. First, simplification in the assembly and solution of the system equations and, secondly, easy computation of the ‘free’ and Cauchy principal value terms appearing in the integral equations. The state of the art in the boundary element method, however, has advanced in the last decade to the point where both of the aforementioned reasons are no longer problematic. As will be shown in what follows, conforming elements are able to produce more accurate results than non-conforming ones with substantial economy in the final size of the system equations.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620231008
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  • 110
    Electronic Resource
    Electronic Resource
    Derivation of Lagrangian and Hermitian shape functions for quadrilateral elements (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1939-1958 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper introduces a general theory for the derivation of the shape functions for the quadrilateral family of finite elements. The first section deals with the Lagrangian shape functions for the cases of uniform and boundary-described elements. Two basic procedures are introduced; the first by linear combinations of side-interpolations and the second by superposition. The remainder of the paper introduces a theory for the general uniform Hermitian element of any order. Details for quadrilateral elements, with first order derivatives are explained. All of the shape functions presented here were derived in the interval [0,1].The shape functions, developed by such an engineering approach, have been used successfully in the ABSEA Finite Element System of Cranfield Institute of Technology.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620231011
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  • 111
    Electronic Resource
    Electronic Resource
    Announcements (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1971-1972 
    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.1620231014
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  • 112
    Electronic Resource
    Electronic Resource
    Masthead (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986) 
    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.1620231201
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  • 113
    Electronic Resource
    Electronic Resource
    Announcement (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. I 
    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.1620231202
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  • 114
    Electronic Resource
    Electronic Resource
    Masthead (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986) 
    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.1620220101
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  • 115
    Electronic Resource
    Electronic Resource
    The patch test for elements (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 63-71 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The main purpose of this paper is to emphasize the necessity of convergence tests in general and the patch test in particular. Following a brief introduction, the patch test is described with examples. This, it is hoped, will help to remove any lingering misunderstanding of this very useful convergence test. Some positive contributions of the test in the formulation and improvement of elements are also discussed.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620220106
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  • 116
    Electronic Resource
    Electronic Resource
    An assessment of the semiloof shell element (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 133-151 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The semiloof shell element is the final product of years of research by Professor Irons and his colleagues, during which period the three-dimensional quadratic displacement isoparametric elements were successively modified into Ahmad thick shells, then eventually, using discrete Kirchhoff hypotheses, into the thin semiloof shells. The retention of curved sides and midside nodes retains the familiar appearance of the two- and three-dimensional isoparametric families, which enables ease of use with existing pre- and post-processing facilities. The element has been widely adapted and used frequently for elastic analyses of wide-ranging structures. It has also been developed for nonlinear geometric and material behaviour. However, despite the unparalleled generality in performance of this element, some unresolved problem areas still exist, particularly with use of reduced integrating rules. Such problems are highlighted in the paper and rectified where possible. A variety of problems are described to illustrate the above points and other interesting features, such as the treatment of thermal loading, and to emphasize the importance of this contribution to finite element technology by Professor Irons.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620220110
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  • 117
    Electronic Resource
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    Bruce Irons: A non-conforming engineering scientist to be remembered and rediscovered (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 1-10 
    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.1620220102
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  • 118
    Electronic Resource
    Electronic Resource
    Implicit modelling and mesh refinement for complex structures (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 17-38 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: When analysing complex structures it is rarely feasible to represent explicitly all the structural features which may contribute significantly to local or global structural performance. This paper presents a variety of methods for representing features which are below the economic analysis scale. Two approaches are described - referred to as implicit stiffness calculation and implicit mesh refinement. The former is essentially approximate and uses relatively simple formulae and computations. The latter involves quite extensive subsidiary calculation, but can lead to numerically exact simulation of fine mesh behaviour in so far as it affects neighbouring structure. Stiffness equivalence principles are stated and a number of computation schemes are presented and illustrated with simple two-dimensional examples.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620220104
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  • 119
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    A study of the influence of hierarchical nodes on the performance of selected parametric elements (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 153-171 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A number of programs have been developed and tested to enable the routine addition of elements with internal nodes into most finite element packages. A subsequent examination was carried out to assess the effect of those nodes on (a) the accuracy of the displacements and stresses using parametric elements with varying formulation complexities, and (b) the possible additional cost in processing, owing to adequacy of representation. It was found in general that, by including the internal nodes, the representation of both the displacement and the stress fields improved dramatically. It was also found that having hierarchical nodes could lead to a reduction in the processing cost.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620220111
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  • 120
    Electronic Resource
    Electronic Resource
    Numerical control of the hourglass instability (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 219-228 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620220116
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  • 121
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    Modifications to the interpretation of the stresses and strains determined using constant strain triangular elements (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 249-266 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 28 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620220119
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  • 122
    Electronic Resource
    Electronic Resource
    Improved strain interpolation for curved C° elements (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 281-288 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The strain energy of straight beam members derived from the isoparametric shape functions is known to be invariant with respect to the number of integration points as long as they exceed a minimum number. However, this invariant property is generally lost for curved members. For example, the two-point integrated, membrane strain energy of curved beams by employing the quadratic shape functions is different from the three-point integrated one. This paper presents an invariant strain interpolation scheme for quadratic curved beam elements, which can lead to improved membrane representations in curved shell elements, thus resolving the perplexing membrane-bending coupling difficulties in thin shell analysis.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620220121
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  • 123
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    Analytical tools for systematic transonic design (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 309-326 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Analytical flow models in the near sonic domain of compressible flow are discussed as a supplementary background to elliptic continuation and fictitious gas design methods, to extend shock-free design into choked flow design, shock-wave construction, with the aim of developing new analysis programs and of developing experience for three-dimensional configuration design.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620220203
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  • 124
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    Penalty-function iterative procedures for mixed finite element formulations (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 267-279 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Iterative methods for solving mixed finite element equations that correct displacement and stress unknowns in ‘staggered’ fashion are attracting increased attention. This paper looks at the problem from the standpoint of allowing fairly arbitrary approximations to be made on both the stiffness and compliance matrices used in solving for the corrections. The resulting iterative processes usually diverge unless stabilized with Courant penalty terms. An iterative procedure previously constructed for equality-constrained displacement models is recast to fit the mixed finite element formulation in which displacements play the role of Lagrange multipliers. The penalty function iteration is shown to reduce to an ordinary staggered stress-displacement iteration if the weight is set to zero. Convergence conditions for these procedures are stated and the potentially troublesome effect of prestress modes noted.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620220120
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  • 125
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    Masthead (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986) 
    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.1620220201
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  • 126
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    The design of transonic aerofoils by a well-posed inverse method (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 341-361 
    Details
    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 designing closed aerofoils that correspond to given surface speed distributions including flows with shock waves. The prescribed surface speed distribution in general contains three parameters whose values are found as part of the solution. The inverse aerofoil design problem is not well posed unless the prescribed speed satisfies three constraints that can be used to fix the value of the three adjustable parameters. The computational method is based on the numerical solution of the full potential equation in conservation form by an approximate factorization-multigrid scheme. The nature of the constraints and several strategies for introducing the necessary freedom in the prescribed speed are discussed along with typical solutions illustrating the method.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620220205
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  • 127
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    Application of elliptic continuation method for transonic aerofoil design and experimental verification (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 395-416 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: With the aid of the elliptic continuation method, transonic aerofoils for two different purposes have been optimized. The design process is described and it is shown that the optimization is more difficult for higher design Mach numbers. The results of experimental investigations confirmed the good aerodynamic performances of the designed aerofoils, although no real shock-free pressure distributions could be achieved in the experiments and the highest aerodynamic efficiencies occurred always at higher lift coefficients, with pressure distributions already having shock waves.
    Additional Material: 25 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620220208
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  • 128
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    An implicit time integration scheme for inelastic constitutive equations with internal state variables (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 533-554 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In a broad class of inelastic constitutive models for the deformation of metals the inelastic strain rates are functions of the current state of stress and internal state variables only. All known models are in some regions of application mathematically stiff and therefore difficult to integrate. The unconditionally stable implicit Euler rule is used for integration. It leads to a system of highly nonlinear algebraic equations which have to be solved by an iterative process. The general Newton-Raphson method, which converges under very broad conditions, requires repeated solution of the finite element system and is infeasible for large inelastic problems. But for the inelastic strains and internal state variables the Jacobian can be computed analytically and therefore the NRI can be used. For the stresses the Jacobian cannot be computed analytically and therefore the accelerated Jacobi iteration is used. A new method for computing the relaxation parameter is introduced which increases the rate of convergence significantly. The new algorithm is applied on Hart's model. A comparison with prior computations using an approximation is made.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230403
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    An algorithm for exact eigenvalue calculations for rotationally periodic structures (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 609-622 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An existing algorithm ensures that no eigenvalues are missed when using the stiffness matrix method of structural analysis, where the eigenvalues are the natural frequencies of undamped free vibration analyses or the critical load factors of buckling problems. The algorithm permits efficient multi-level substructuring and gives ‘exact’ results when the member equations used are those obtained by solving appropriate differential equations. The present paper extends this algorithm to cover rotationally periodic (i.e. cyclically symmetric) three-dimensional structures which are analysed by using complex arithmetic to obtain a stiffness matrix which involves only one of the rotationally repeating portions of the structure. Nodes and members are allowed to coincide with the axis of rotational periodicity and the resulting modes are classified. Rigid body freedoms are accounted for empirically, and the ‘exact’ member equations and efficient multi-level substructuring of the earlier algorithm can be used when assembling the stiffness matrix of the repeating portion.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230407
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    Exact eigenvalue calculations for structures with rotationally periodic substructures (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 695-706 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The theory presented enables rotationally periodic (i.e. cyclically symmetric) three-dimensional substructures to be included when using existing algorithms to ensure that no eigenvalues are missed when the stiffness matrix method of structural analysis is used, where the eigenvalues are the natural frequencies of undamped free vibration analyses or the critical load factors of buckling problems. A substructure can be connected in any required way to a parent structure which shares its rotational periodicity, or can be connected by nodes at each end of its axis of periodicity to any parent structure, i.e. the parent structure need not be periodic. The theory uses complex arithmetic, involves only one of the rotationally repeating portions of the substructure, allows nodes and members to coincide with the axis of rotational periodicity, permits efficient multi-level use of rotationally periodic substructures, and gives ‘exact’ eigenvalues if the member equations used are those obtained by solving appropriate differential equations. The competitiveness of the method is illustrated by approximate predictions of computation times and savings for two structures which contain rotationally periodic substructures.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230411
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    Conference diary (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 732-733 
    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.1620230417
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  • 132
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    Hybrid stress reduced-Mindlin elements for thin multilayer plates (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 555-578 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A hybrid-stress formulation of isoparametric elements for the analysis of thin multilayer laminated composite plates is presented. The element displacement behaviour is characterized by laminate reference surface inplane and transverse displacements and laminate non-normal cross-section rotations; as a result, simple Co interpolation of displacement and rotation can be used, and the number of degrees-of-freedom is independent of the number of layers. All components of stress are included and are related to a set of laminate stress parameters, the number of which is independent of the number of layers. Attention is restricted here to thin laminates, for which it is shown that the contributions of transverse shear stress and transverse normal stress to the internal complementary energy can be neglected. As a result of this reduction, a modified stiffness-formation algorithm can be used which provides a significant improvement in computational efficiency. The formulation presented is used to develop an 8-node isoparametric thin multilayer plate element. The resulting element is naturally invariant, of correct rank, and non-locking in the thin plate limit.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230404
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    Letter to the editor (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 725-730 
    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.1620230414
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    Announcement (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 734-735 
    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.1620230418
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  • 135
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    Triangular meshes for regions of complicated shape (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 751-778 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method using techniques of computational geometry for triangular mesh generation for regions with complicated polygonal boundaries in the plane is presented. The input to the method includes the desired number of triangles and a mesh smoothness parameter to be specified, as well as the polygonal curves of the region's boundary and, possibly, internal interfaces. The triangulation generated conforms to the length scales of the edges of the boundary curves, but the method can be extended to provide additional control of the triangulation by a mesh distribution function. The region is decomposed into convex subregions in two stages, such that triangles of one length scale can be generated in each subregion. This decomposition uses algorithms which run in times that are linear in the number of vertices of the input polygons. Details of two major computational experiments are provided.
    Additional Material: 21 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230503
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    Effect of rotary inertia on vibration of tapered beams (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 871-882 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Rotary inertia and dynamic-correction rotary inertia matrices for a linearly tapered beam element of any cross-sectional shape are derived in explicit form. Exact expressions for the required displacement functions are used in the derivation of these matrices. Variation of area and moment of inertia of the cross-section along the axis of the element are exactly represented by simple functions involving shape factors. Vibration analysis results of a tapered cantilever beam of I-section, obtained with and without the rotary inertia matrices are compared and effect of rotary inertia on vibration of tapered beams discussed.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230509
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    Dynamic stress intensity factors studied by boundary integro-differential equations (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 919-928 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The boundary integro-differential equation method is illustrated by two numerical examples concerning the study of the dynamic stress intensity factor around a penny-shaped crack in an infinite elastic body. Harmonic and impact load on the crack surface has been considered. Applying the Laplace transform with respect to time to the governing equations of motion the problem is solved in the transformed domain by the boundary integro-differential equations. The Laplace transformed general transient problem can be used to solve the steady-state problem as a special case where no numerical inversion is involved.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230512
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    Finite element programs for axisymmetric problems in engineerings, C. T. F. Ross, Ellis Horwood Series in Engineering Science, Chichester, 1984. No. of pages: 297. ISBN 0-85312-710-7 (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 979-979 
    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.1620230516
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    A finite element analysis of generalized Newtonian fluids through spiral mandrel dies (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1-11 
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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 described which calculates the fluid flow pattern for any generalized Newtonian fluid forced through the narrow annular space between two concentric cylindrical surfaces. The inner surface is engraved with a number of identical equally spaced spiral channels of small constant pitch angle but of varying cross-sectional area. For equal flow into the spiral passages, the pressure distribution along them is described by a quasi-linear ordinary difference-differential equation. A finite element approximation is employed to solve this equation for the pressure and resultant flow field. The method is illustrated by calculating and comparing flow patterns through two different spiral geometries.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230102
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    Elastoplastic BIE analysis of cracked plates and related problems. Part 2: Numerical results (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 439-452 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Part 1 of this paper reports on the formulation of an advanced boundary - integral equation model for fracture mechanics analysis of cracked plates, subject to elastoplastic behaviour or other, related body force problems. The basis of this formulation contrasts with other BIE elastoplastic formulations in the use of the Green's function for an infinite plane containing a stress free crack. This Green's function formulation assures that the total elastic strain field for the crack problem is accurately imbedded in the numerical model. The second part of this paper reports on the numerical implementation of this algorithm, as currently developed. The anelastic strain field (residual strains, thermal strains, plastic strains, etc.) is approximated as piecewise constant, while the boundary data is modelled with linear interpolations. An iteration solution scheme is adopted which eliminates the need for recalculation of the BIE matrices. The stability and accuracy of the algorithm are demonstrated for an uncracked, notch geometry, and comparison to finite element results is made for the centre-cracked panel. The data shows that even the crude plastic strain model applied is capable of excellent resolution of crack tip plastic behaviour.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230309
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  • 141
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    Dynamic Lagrangian computations for solids, with variable nodal connectivity for severe distortions (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 509-522 
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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 an algorithm for dynamic Lagrangian computations for solids, in plane strain geometry, with variable nodal connectivity to allow for severe distortions. The nodes are somewhat analogous to flexible circular disks. When they move closer together than their equilibrium distance they generate compressive, repulsive forces. Conversely, when they move apart, they generate tensile, attractive forces. Material strength effects are also included. Because a node can only be affected by its ‘neighbour’ nodes, the approach has been designated the ‘NABOR’ approach. The key to this approach is that it is possible to have variable nodal connectivity - a node can acquire new neighbours, thus allowing all forms of distortion. The NABOR algorithm has been incorporated as an option into the explicit finite element code, EPIC-2. By using both the NABOR grid and the EPIC-2 finite element grid together, it is possible to perform Lagrangian computations for a wide range of problems.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230313
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  • 142
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    Collocation time finite element procedures for integration of strongly nonlinear initial value problems (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 579-589 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: By use of a collocation time finite element formulation a modification of the well-known generalized midpoint method is derived. The new family possesses an additional free parameter. This allows for significant improvement of the numerical solution in strongly nonlinear situations. Numerical results show the accuracy of the proposed algorithm in comparison to the midpoint method.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230405
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    Stress analysis of filament wound tanks using three-dimensional finite elements (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 623-633 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230408
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    Solution of two-point boundary value problems using splines (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 707-710 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Cubic spline on quintic spline interpolations are used to approximate the derivative terms for use in two high order numerical schemes for the solution of two-point boundary value ordinary differential equations. The use of splines leads to solutions that reflect the smoothness of the slopes of the differential equations. Results of some computational experiments are given.
    Additional Material: 1 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620230412
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    Design and construction of concrete shells, G. S. Ramaswamy, Robert E. Krieger Publishing (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 731-731 
    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.1620230415
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    Masthead (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986) 
    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.1620230501
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    DEM: A new computational approach to sheet metal forming problems (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 847-862 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Many current approaches to finite element modelling of large deformation elastic - plastic forming problems use a rate form of the virtual work (equilibrium) equations, and a finite element representation of the displacement components. Called the incremental method, this approach produces a three-field formulation in which displacements, stresses and effective strain are dependent variables. Next, the formulation is converted to a one-field displacement formulation by an algebraic time discretization which uses a low order explicit time-stepping procedure to integrate the equations. This approach does not produce approximations which satisfy the discrete equilibrium equations at all times and, moreover, the advantage of the single-field algebraic formulation is realized at the expense of very small time steps needed to produce stability and accuracy in the numerical calculations.This paper describes a variant of the mixed method in which all three field variables (displacements, stresses and effective strain) are given finite element representations. The discrete equilibrium equations then generate a nonlinear system of algebraic equations whose solutions represent a manifold, while the constitutive equations form a system of ordinary differential equations. A commercially available, variable time step/variable order code is then used to integrate this differential/algebraic system. When applied to the problem of hydrostatic bulging of a membrane, the new approach requires far less computer time than the incremental method.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230507
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    On the performance of Mindlin plate elements in modelling plate-elastic medium interaction: A comparative study (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1229-1244 
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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 finite element analysis of the flexural interaction between an elastic plate and an elastic half-space. The applicability of certain Mindlin-type plate elements, based on reduced integration techniques, to this class of interaction problem is investigated. A series of numerical computations reveal that those elements which possess spurious zero-energy modes are deficient in modelling properly the interaction phenomenon. It is also found that the ‘heterosis’ plate element reported in the literature is capable of modelling the plate-elastic medium interaction very efficiently.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230704
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    A survey of computational efforts in the field of corrosion engineering (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1295-1311 
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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 a mathematical model governing the galvanic corrosion phenomenon and surveys the research efforts which have been applied to find a solution to the above problem. The authors classify these techniques into three categories. The first is the finite difference method (FDM), the second is the finite element method (FEM) and the last is the boundary element method (BEM).
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230708
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    Dynamic transient analysis by a mixed, iterative method (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1343-1353 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Mixed methods solved by an iterative process have been shown to provide an inexpensive procedure for improving the results of standard displacement analysis. This paper shows the possibilities present in their application to dynamic problems, where again accuracy improvement is achieved at small additional expense.The advantages of the formulation presented are particularly noteworthy in explicit forms where the difficulties of ‘hour-glass’ modes associated with minimal integration rules ae avoided without cost increase.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230711
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    Letters to the editor (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1387-1390 
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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.1620230714
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    A dynamic finite element preanalyser (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1367-1386 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In a mixed-mode dynamic crack propagation problem using remeshing, certain elements in the neighbour-hood of the propagating crack-tips may have dimensions that do not comform to the allowable limit. Hence, they need to be refined by recursively bisecting the exclusive sides until a global conformity is achieved. ADFEP (a dynamic finite element preanalyser) has been written for this purpose. Apart from this objective, ADFEP has a wide spectrum of salient applications to various discretization related problems, such as automatic irregular generation, adaptive refinement and others. A simple energy criterion to determine the cut-off frequency of a transient loading, and the concept of preprocessing the input loading using digital filters introduced by Valliappan and Murti1 are employed. They constitute the first module of ADFEP. The second (main) module consists of element splitting procedures where algorithms based on graph theory and element splitting templates have been extensively used. The notion of a ‘cross digraph’ introduced to carry a multiple ‘weights’ and to avoid duplication in node-generation, is especially useful in three-dimensional element splitting techniques. Finally, numerical inverse isoparametric mapping techniques presented by Murti and Valliappan2 are also used to interpolate the nodal quantity vectors at the newly generated nodes. These vectors are needed as initial values in subsequent iterations for a dynamic restart. This aspect, together with the node renumbering scheme, is included in the third module of ADFEP. Some illustrative examples are included to elucidate the effectiveness of ADFEP.
    Additional Material: 17 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230713
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    Computer evaluation of singular integrals and their applications (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1439-1453 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm and a standard subroutine are developed for the evaluation of singular integrals over arbitrary two-dimensional domains. The integrand is a product of a Green's function with another function having a weak singularity at the boundary of the domain. Formulae are derived for an accurate estimation of the integral in the neighbourhood of the singularities. The integral over the rest of the domain is evaluated by a library subroutine. The software developed is applied to a study of some contact problems of the theory of elasticity for non-classical domains.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230804
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    Failures of local approximation in finite-element methods (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1483-1494 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is shown that standard finite-element discretizations of second-order differential equations (i.e. Galerkin and subdomain methods) using conforming linear elements may fail to approximate the original equation locally if the finite-element grid is irregular or if subdomains are chosen improperly. This failure of local approximation can lead to spurious computational results when subdomain methods are used, but these difficulties can be averted by a judicious choice of subdomains. The conditions which the subdomains must satisfy in order for local approximation to hold are derived and used to construct an algorithm for choosing them properly. The relation of these local results to the global convergence properties of the Galerkin method is discussed.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230806
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    Improved co-ordinate transformations for finite elements: The Lagrange cubic case (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1529-1545 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A modified isoparametric co-ordinate transformation is developed for the case of Lagrange cubic finite elements. This modified transformation produces significant improvements in solution accuracy while eliminating troublesome aspects of the standard isoparametric mapping. In particular, zero Jacobians in the standard transformation, which can occur in elements having non-uniform node spacing, are completely eliminated with the new transformation. Within the analysis, the range of node locations for which the standard transformation is valid (the Jacobian does not vanish) is determined. The treatment of curved sides is discussed and illustrated. Example calculations using two-dimensional serendipity elements show that the new transformation provides solutions that are as much as several orders of magnitude more accurate than those computed using the standard formulation.
    Additional Material: 15 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230809
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    Conference diary (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1580-1581 
    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.1620230813
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    A weak variational formulation for the propagation of Love waves (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1601-1613 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes the fundamental principles of the mathematical method used by the authors in discussing the direct geophysical problem of analysing the behaviour of the Atlantic continental margin of the Iberian Peninsula as a transmission medium of seismic energy.In order to resolve this problem, a weak variational formulation is proposed, building up an approximate solution by means of a semidiscrete treatment with the finite element method.The excitation of that non-subductive ocean-continent transition zone is supposed to be caused by Love waves normally incident at the continental boundary. The physical and geometrical parameters describing the model are obtained using as a starting point the experimental data known for this zone.The work shows the main results that we have obtained, the geophysical interpretation of which can be seen in Reference 1. Finally we proposed a large variety of open problems to which analogous techniques can be applied, owing to the extended validity of the proposed method.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230903
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    Field-consistent strain interpolations for the quadratic shear flexible beam element (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1973-1984 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A shear flexible (i.e. Timoshenko) quadratic isoparametric beam element with two degrees of freedom per node is critically examined from the point of view of the consistency of the constrained strain fields that arise in the thin-beam limits. The errors, in terms of convergence of displacement fields and violent oscillations of stress fields, that emerge when exactly integrated elements are used are predicted a priori and confirmed with numerical experiments. The rationale behind the use of optimal stress sampling at Gaussian points is also derived directly from these arguments.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620231102
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    A new mode renumbering algorithm for bandwidth reduction (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1693-1704 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new algorithm is presented for automatic renumbering of systems of interconnected nodes so as to minimize the bandwidth of the connectivity matrix. This is necessary to reduce storage requirements for banded matrix solution techniques. The method is based on those due to Cuthill and McKee1 and Gibbs, Poole and Stockmeyer.2 Under test against several other algorithms on a range of 20 examples of various types it always performed at least as well as, and in most cases better than, the best of the other methods. Seven examples are given in the paper, comparing final bandwidths with those produced by seven other algorithms.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230909
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    A boundary element method for determining the effect of holes on the stress distribution around a crack (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1727-1737 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A boundary integral procedure is obtained for examining the effect of a finite number of holes on the crack tip stress intensity factors for a plane crack in a homogeneous anisotropic elastic material. Numerical results for specific examples involving a transversely isotropic material are given.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230912
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    An efficient finite-difference scheme for multidimensional Stefan problems (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1757-1771 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper the enthalpy approach for solving Stefan problems is applied to a three-dimensional situation. A novel and particularly efficient finite-difference scheme is then used to solve the resulting equations. As a starting solution for the numerical algorithm, a three-dimensional result using the heat-balance integral method is obtained for the case of heat flow in two phases with, possibly, different thermal properties.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230914
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    Letters to the editor (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1773-1775 
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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.1620230915
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    Announcements (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1779-1784 
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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.1620230917
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    Using elastic - plastic plane stress FEM programs to compute anti-plane strain (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1847-1856 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Elastic - plastic anti-plane strain problems can be solved by using FEM programs developed for plane stress. The technique does not involve any manipulations with the FEM code, but is merely a matter of specialization and of translation of notation. Two analytically solvable cases are chosen for demonstration.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620231005
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    The Lanczos algorithm applied to Kron's method (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1857-1872 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper Kron's primitive composite system matrix is shown to be reducible to a symmetric indefinite matrix. This matrix, although never formed explicitly, can then be transformed to a tridiagonal matrix of reduced order by the Lanczos algorithm. Eigenvalue solutions of this partially tridiagonalized matrix give very good approximations to the eigenvalues of the composite system. The method has multiplication counts which are over 90 per cent lower than when the (condensed) Kron matrix is solved by the Newton-Raphson iteration applied to the Kron scalar equation. Numerical examples illustrating the Kron-Lanczos method when solving for the natural frequencies of frames with large numbers of degrees of freedom are presented.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620231006
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    Conference diary (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 2170-2172 
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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.1620231115
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    Inverse design of multiholed internally cooled turbine blades (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 363-375 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A methodology is described for the inverse design and/or analysis of coolant flow passage shapes in multiholed internally cooled turbine blades. The user of this technique may specify the temperature (or heat flux) distribution along the aerofoil outer surface. In addition, the temperature on the surface of each of interior coolant flow passages (holes) may be specified. The numerical solution of the outer hot gas flow field determines the remaining unspecified aerofoil outer surface quantity - surface heat flux if temperature was originally specified or vice versa. The position and shape of each turbine blade coolant hole is then found iteratively by solving the heat conduction problem within the solid portions of the blade. This solution procedure involves satisfying the dual Dirichlet and Neumann specified boundary conditions of temperature and heat flux on the outer boundary of the aerofoil. The inner hole geometry is then modified using an optimization procedure in such a way as to minimize the error in satisfying the specified Dirichlet temperature boundary condition on the surface of each of the evolving interior holes. Results are shown for single-hole and double-hole configurations that have analytic solutions and for a realistic turbine blade design problem.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620220206
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    Optimization in design processes: An informatics point of view (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 433-450 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The purpose of this paper is to outline the optimization-system development at NLR. The paper starts with a discussion of the potential of mathematical optimization techniques in aeronautical engineering. Subsequently, the main requirements to be met by a general-purpose optimization system are given. Following this, the implementation at NLR is described, and some examples of applications are presented to illustrate the optimization capabilities.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620220210
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    Variational analysis of a slender fluid-structure system: The elasto-acoustic beam - a new symmetric formulation (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 637-647 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present a new finite element analysis of the linear dynamic responses of a slender fluid-structure system, namely the elasto-acoustic beam, neglecting flow and viscosity effects. Using one unknown field in the fluid, namely the ‘mass-flow’ corresponding to a cross-section mean value of the longitudinal displacement field component, an original symmetric formulation is derived which does not exhibit the usual spurious modes associated with the irrotationality constraint occurring in displacements formulations of fluid-structure problems.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620220309
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    A formulation of general shell elements - the use of mixed interpolation of tensorial componentsThis is an extended version of the same title paper presented at the NUMETA Conference, University College of Swansea, Swansea, England, January, 1985. (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 697-722 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We briefly discuss the requirements on general shell elements for linear and nonlinear analysis in practical engineering environments, and present our approach to meet these needs. We summarize and give further insight into our formulation of a 4-node shell element using a mixed interpolation of tensorial components, and present a new 8-node element using this approach. Specific attention is given to the general applicability of the elements and their efficient use in practice.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620220312
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    Masthead (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986) 
    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.1620230101
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    Globally convergent monotonic suppression techniques for automatic root finders in vibration analysis (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 25-34 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An examination is made of suppression techniques used to obtain global monotonicity when applying iterative processes to the determination of the zeros of residual functions in linear vibration analysis. It is shown that, when computational errors are taken into account, induced instability is a ubiquitous feature of this class of techniques. A method of inhibiting this instability behaviour is presented which at the same time avoids missing zeros between the restarting value and the last determined zero on restarting the iteration.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230104
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    A simplified finite element method for large deformation, post-buckling analyses of large frame structures, using explicitly derived tangent stiffness matrices (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 69-90 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a simplified, economical and highly accurate method for large deformation, post-buckling, analyses of frame-type structures is presented. Using the concepts of polar-decomposition of deformation, an explicit expression for the tangent stiffness matrix of a member/element of the frame, that accounts for the nonlinear bending-stretching coupling, is derived in closed form, at any point in the load-deformation path. The ranges of validity of the present simplified approach are discussed. Several example problems to demonstrate the feasibility of the present approach, over ranges of deformation that are well beyond those likely to occur in practical large frame structures, are included.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230107
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    A fast implementation of explicit time-stepping algorithms with the finite element method for a class of nonlinear evolution problems (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 155-168 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a class of nonlinear evolution problems is considered. It is shown that, under special conditions, the application of the product approximation method for nonlinear problems in the finite element method results in constant (i.e. time-independent) matrices. In those cases the amount of computing required to solve these equations with an explicit time-stepping algorithm is decreased considerably compared to the standard Galerkin formulation in which the matrices are time-dependent. The method is applied to two practical two-dimensional problems: the shallow water equations and a nonlinear heat conduction problem.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230112
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    Masthead (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986) 
    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.1620230201
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    Simply supported plates by the boundary integral equation method (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 173-191 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Plates governed by Kirchhoff's equation have been analysed by the boundary integral equation method using the fundamental solution of the biharmonic equation. In the case of supported plates, the boundary conditions permit the uncoupling of the field equation into two harmonic equations that originate, due to the nature of the fundamental solution, easier integration kernels and a simpler system of equations. The calculation of bending and twisting moments and transverse shear force can be formed, combining derivatives of the integral equation which defines the expression of the deflection on any point of the plate. The uncoupling of the biharmonic equation into two Poisson's equations involves the discretization of the domain of the studied problems. Nevertheless, the unknown quantity of the problem does not appear in the domain integrations for which a refined discretization is unnecessary. In the paper, however, a numerical alternative is considered to express the domain integral by means of boundary integrals. In this way, we need only discretize the boundary of the plate, making it necessary to solve a supplementary system of equations in order to calculate the coefficients of the approximation carried out.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230202
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    Infinite ring elements (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 385-396 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Seven infinite ring elements have been proposed for the stress analysis around opening in an infinite medium. All elements employ trigonometrical series for interpolation in the θ-direction and decaying function in the r-direction. Numerical results indicate that all of them can converge for self-equilibrating force systems, but only the element which was derived from the stress function can converge in the non-self-equilibrating external loads. The present study clearly indicates the close relationship between the semi-analytical element and closed-form solution.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230305
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    An algorithm for profile and wavefront reduction of sparse matrices (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 239-251 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm for reducing the profile and wavefront of a sparse matrix is described. The scheme is applicable to any sparse matrix which has a symmetric pattern of zeros and may be used to generate efficient labellings for finite element grids. In particular, it is suitable for generating efficient labellings for profile and frontal solution schemes. Empirical evidence, obtained from analysis of the 30 test problems collected by Everstine, suggests that the new algorithm is superior to existing methods for profile and wavefront reduction. It is fast, requires only a small amount of memory, and is simple to program.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230208
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    Boundary element analysis of a plate on elastic foundations (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 287-303 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The objective of this study is to examine the applicability of the boundary element method to analysing a plate on elastic foundation. The fundamental solution of the problem is presented as a Fourier-Bessel integral. For the computation of the values of the fundamental solution an algorithm was developed in which the Fourier-Bessel integral was decomposed into an alternative convergent sequence. Equations based on the direct and indirect boundary element method were derived for a plate situated on a one- or two-parametric elastic foundation. According to the theory presented, computer programs based on the direct and indirect boundary element method were developed. These programs can be used for examining the behaviour of a smooth-boundary plate on a one- or two-parametric elastic foundation. The computer programs were tested by several examples. The results obtained by using a small number of boundary elements compared favourably to the results obtained by a fine finite element mesh. The study shows that the boundary element method is applicable to the analysis of a plate on elastic foundation.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620230211
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    Masthead (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986) 
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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.1620230301
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    Efficient symmetrical cubature rules for complete polynomials of high degree over the unit cube (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 397-407 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The fully symmetrical cubature rules developed and presented are at present the most economically available for numerical integration over the unit cube of complete polynomial functions up to and including nineteenth order. Conventional Gaussian triple product integration formulae, by comparison, require more than twice as many integration points and weights.
    Additional Material: 1 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620230306
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    A return mapping algorithm for plane stress elastoplasticity (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 649-670 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An unconditionally stable algorithm for plane stress elastoplasticity is developed, based upon the notion of elastic predictor-return mapping (plastic corrector). Enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation. Consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm. Use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of Newton methods. The accuracy of the algorithm is assessed by means of iso-error maps. The excellent performance of the algorithm for large time steps is illustrated in numerical experiments.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620220310
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    A simple rigid body algorithm for structural dynamics programs (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 723-749 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The analysis of low velocity impacts is necessary for designing everything from safe automobiles to safe shipping casks for nuclear material. Although great strides have been made in reducing the cost of impact analysis, the cost must be reduced even more before impact analysis becomes a routine design tool. One approach replaces the mesh outside of the impact zone with a rigid body.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620220313
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  • 184
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    A faceted shell element with Loof nodes (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 49-67 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A flat shell element which utilizes the linear strain triangle (LST) for membrane representation and a plate-bending element labelled DKL (for discrete Kirchhoff element with Loof nodes) previously derived by the authors in Reference 1, is presented. This element is free from the deficiencies of displacement incompatibility, singularity with coplanar elements, inability to model intersections and low order membrane strain representation, which are associated with existing faceted shell elements. The results of the numerical examples indicate that the convergence characteristics of this element are good.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230106
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  • 185
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    Degenerated isoparametric finite elements using explicit integration (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 133-154 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The kinematics of degenerated finite elements using explicit integration are investigated, in particular for geometric nonlinear applications. Two representations of the nodal rotational degrees-of-freedom are investigated; the first adopts the infinitesimal representation of rotations, while the second uses a valid large rotation representation. A method of explicit integration is presented which satisfies rigid body rotations under arbitrary large rotations. The accuracy and convergence of these formulations are investigated.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230111
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  • 186
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    Numerical methods in heat transfer. Volume III (eds R. Lewis and K. Morgan), Wiley, Chichester, 1985, No of pages: 312. Price: £35.95 (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 169-169 
    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.1620230114
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  • 187
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    On a mixed variational theorem and on shear deformable plate theory (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 193-198 
    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.1620230203
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  • 188
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    A mesh re-zoning technique for finite element simulations of metal forming processes (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 219-228 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on some fundamental properties of finite element approximations, a mesh re-zoning scheme is proposed for finite element simulations of metal forming problems. It is demonstrated that this technique is indispensable in analysing many difficult forming processes, especially when there exist corners or very irregular shapes on the boundaries. The algorithm is tested by a backward extrusion process and direct extrusion through a square die.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230206
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  • 189
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    Derivation of Lagrangian and Hermitian shape functions for triangular elements (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 275-285 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An engineering approach to the derivation of shape functions, for Lagrangian and Hermitian, boundary-described triangular elements is introduced. The results of the special cases for the few published elements agree with the literature. This approach has been used to generate shape functions for elements of the ABSEA finite element system at Cranfield, and the results derived from the use of such elements have been shown to be reasonably accurate.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230210
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  • 190
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    Mesh grading technique using modified isoparametric shape functions and its application to wave propagation problems (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 331-348 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Mesh grading of finite element meshes is greatly simplified by allowing two or more finer elements to abut the entire straight or curved edge of a neighbouring coarser element. This paper proposes the technique by which it can be achieved while maintaining inter-element compatibility by introducing modified shape functions. The concepts and potential advantages of this technique are described in detail for two-dimensional isoparametric quadrilateral elements, although the same procedure can also be applied to other element types including three-dimensional. Implementation of this technique to existing finite element programs requires only minimal modifications. Finally, numerical examples are presented to illustrate the application of the mesh grading technique to several wave propagation problems.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230214
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  • 191
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    Announcement (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. i 
    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.1620230302
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  • 192
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    Derivation of geometrically nonlinear finite shell elements via tensor notation (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 367-384 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To develop geometrically nonlinear, doubly curved finite shell elements the basic equations of nonlinear shell theories have to be transferred into the finite element model. As these equations in general are written in tensor notation, their implementation into the finite element matrix formulation requires considerable effort. The present paper will demonstrate how to derive the nonlinear element matrices directly from the incrementally formulated nonlinear shell equations using a tensor-oriented procedure. This enables the numerical realization of all structural responses, e.g. the calculation of pre- and post-buckling branches in snap-through analysis and especially in bifurcation analysis, including the detection of critical points and the consideration of geometric imperfections. To avoid loss of accuracy care is taken for a realistic computation of the geometric properties as well as of the external loads. Finally, the developed family of shell elements will be presented and its efficiency will be demonstrated by some applications to linear and geometrically nonlinear structural phenomena.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230304
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  • 193
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    p-adaptive boundary elements (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 801-829 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the implementation of an adaptive philosophy to plane potential problems, using the direct boundary element method. After some considerations about the state of the art and a discussion of the standard approach features, the possibility of separately treating the modelling of variables and their interpolation through hierarchical shape functions is analysed. Then the proposed indicators and estimators are given, followed by a description of a small computer program written for an IBM PC. Finally, some examples show the kind of results to be expected.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230505
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  • 194
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    Predicted axial temperature gradient in a viscoplastic uniaxial bar due to thermomechanical coupling (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 903-917 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The thermomechanical response of a uniaxial bar with thermoviscoplastic constitution is predicted herein using the finite element method. After a brief review of the governing field equations, variational principles are constructed for the one-dimensional conservation of momentum and energy equations. These equations are coupled in that the temperature field affects the displacements and vice versa. Due to the differing physical nature of the temperature and displacements, first-order and second-order elements are utilized for these variables, respectively. The resulting semi-discretized equations are then discretized in time using finite differencing. This is accomplished by Euler's method, which is utilized due to the stiff nature of the constitutive equations. The model is utilized in conjunction with stress-strain relations developed by Bodner and Partom to predict the axial temperature field in a bar subjected to cyclic mechanical end displacements and temperature boundary conditions. It is found that spacial and time variation of the temperature field is significantly affected by the boundary conditions. The nomenclature used is given in an Appendix.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230511
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    Physical mathematics and nonlinear partial differential equations, J. H. Lightboure and S. M. Rankin (eds), West Virginia University. Marcel Dekker Notes in Pure and Applied Mathematics, 1985. No of pages 262 (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 979-979 
    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.1620230517
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    Announcements (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 982-984 
    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.1620230519
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  • 197
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    Solution of non-linear thermal transient problems by a reduction method (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1023-1042 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new algorithm for solving transient thermal problems in a reduced subspace of the original space of discretization is described. The basis of the subspace is formed by using the system response at the first time step (or an approximation to it) and a set of orthogonal vectors obtained by the algorithm of Lanczos. Derivatives of these vectors are included when treating non-linear cases. The method allows one to handle the sharp gradients that appear in thermally loaded structures, and the response is accurately predicted by using only a small number of degrees of freedom in the reduced system. The algorithm is specially well suited for treating large-scale problems. Examples dealing with one-, two- and three-dimensional cases of linear and non-linear conduction problems are presented.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230604
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  • 198
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    An integral formulation applied to the diffusion and Boussinesq equations (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1057-1079 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new integral method is proposed here to solve the diffusion equation (confined flow) and the Boussinesq equation (unconfined flow) in a two-dimensional porous medium. The method, based on Green's theorem, derives its integral representation from the portion of the original differential equation with the highest space derivatives so that the resulting kernel of the integral representation is not time dependent. Compared to an earlier integral formulation, namely the direct Green function, based on the same theorem, the kernel is simpler so that the present theory provides a more efficient numerical model without compromising accuracy. An iterative scheme is employed along with the theory to achieve solutions to the non-linear Boussinesq equation. Concepts used in the finite difference and finite element methods enable simplification of the temporal derivative. The method is tested with success on a number of numerical examples from groundwater flow.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230606
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  • 199
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    An efficient algorithm for the optimum design of trusses with discrete variables (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1111-1130 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method to efficiently solve the problem of minimum weight design of plane and space trusses with discrete or mixed variables is developed. The method can also be applied to continuous variables. The original formulation leads to a non-linear constrained minimization problem with inequality constraints, which is solved by means of a sequence of approximate problems using dual techniques. In the dual space, the objective function is to be maximized, depends on continuous variables, is concave and has first and second order discontinuities. In addition, the constraints deal simply with restricting the dual variables to be non-negative. To solve the problem an ad hoc algorithm from mathematical programming has been adapted.Some examples have been developed to show the effectiveness of the method.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230609
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  • 200
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    A ‘characteristic’ finite element scheme for convective-dispersive transport with non-equilibrium reaction (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1161-1178 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element method coupled with the method of characteristics is applied to the problem of convective-dispersive transport with non-equilibrium reaction. Convective terms are calculated using moving particles together with influence element meshes for particle tracking, whereas dispersion terms are calculated by means of finite element techniques. The contribution from the term of non-equilibrium reaction is incorporated into the algebraic equations by the use of analytical solutions to the equation of non-equilibrium reaction for each time step and extended Simpson's numerical integrations.Comparison of the numerical results from the proposed procedure with analytical solutions to the simultaneous partial differential equations shows good agreement for the wide spectrum ranging from dispersion- to convection-dominated transport with various reaction parameters.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230612
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