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  • 1985-1989  (2,494)
  • 1988  (1,289)
  • 1986  (1,205)
  • Chemical Engineering  (1,399)
  • Engineering  (1,095)
  • 101
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    A numerical case study of a non-Newtonian flow problem (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 695-704 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper addresses some of the theoretical aspects involved in the numerical study of non-Newtonian flow problems. We consider the second-order Rivlin-Erickson constitutive model due to the simple differential form that emerges for the system of equations that govern the flow when expressed in stream function-vorticity variables. This model describes slightly elastic fluids that exhibit a constant viscosity behaviour. A steady two-dimensional flow is studied through a planar contraction geometry.An auxiliary variable is introduced into the problem formulation producing a non-linear system of differential equations comprising two elliptic equations and one hyperbolic equation. This system is discretized by finite difference methods and the resulting system of non-linear algebraic equations is solved iteratively by successive substitutions. The simple structure of this iteration permits a convergence analysis which is presented in Section 2. This analysis is performed prior to the spatial discretization and establishes the dependence of the iteration upon the material parameters. At the discrete linearized equation level a combination of inner iterations for elliptic equations and direct marching for the hyperbolic equation is used. The stability of the marching scheme is considered in Section 4.3 and a discussion on the results is given in Section 5.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260312
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  • 102
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    A nine node finite element for analysis of geometrically non-linear shells (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1945-1962 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A nine node finite element is presented for the analysis of thin shell structures undergoing large deflection. The finite element formulation is based on the concept of degenerate solid shell element and the Hellinger-Reissner principle with independent strain. Three versions of assumed independent strain are selected to suppress spurious kinematic modes. One version leads to a finite element model which is kinematically stable at element level while the other two give globally stable models. Numerical tests indicate that the finite element model which is stable at element level may reveal the locking effect in certain cases. However, the other two models are free of locking.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260905
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  • 103
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    Finite element approximations of singular parabolic problems (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1989-2007 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient implementation of finite element methods for free boundary parabolic problems in general two dimensional space domains is presented. The Stefan problem, the Hele-Shaw problem and the porous medium equation are included. Backward differences or linearization techniques are used for the time discretization of the problem. The performances of these schemes are discussed with several numerical tests.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260907
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  • 104
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    A new hybrid transfinite element computational methodology for applicability to conduction/convection/radiation heat transfer (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1087-1100 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes new and recent advances in the development of a hybrid transfinite element computational methodology for applicability to conduction/convection/radiation heat transfer problems. The transfinite element methodology, while retaining the modelling versatility of contemporary finite element formulations, is based on application of transform techniques in conjunction with classical Galerkin schemes and is a hybrid approach. The purpose of this paper is to provide a viable hybrid computational methodology for applicability to general transient thermal analysis. Highlights and features of the methodology are described and developed via generalized formulations and applications to several test problems. The proposed transfinite element methodology successfully provides a viable computational approach and numerical test problems validate the proposed developments for conduction/convection/radiation thermal analysis.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260507
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  • 105
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    A robust triangular plate bending element of the Reissner-Mindlin type (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1169-1184 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new triangular plate element is presented. This new element is based on independent interpolations for slopes, displacement and shear forces, and it is shown that it does not suffer from any defect common to other Mindlin plate elements. Several examples are presented to illustrate the behaviour of this new element.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260511
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  • 106
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    Computer analysis of structures matrix structural analysis, structured programming, Siegfried M. Holzer, Elsevier, 1985, pp. 426. ISBN 0-444-00943-4 (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1235-1236 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260515
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  • 107
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    Formulation and solution of hierarchical finite element equations (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1213-1233 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a general hierarchical formulation applicable to both elliptic and hyperbolic problems. Static and eigenvalue linear elastic problems as well as convection-diffusion problems are studied. The hierarchical formulation is well suited for adaptive procedures.For the convection-diffusion problem the hierarchical approximation is made in time only. Different hierarchical functions are proposed for different types of problems. Both weighted residual and least-squares formulations are applied. A combination of these two gives a penalty method with a constraint equation corresponding to the least-squares method. A whole class of time integration formulae is obtained. These are all suitable for adaptive procedures owing to the hierarchical approximation in the time domain. If a linear discontinuous hierarchical base function is used in the Galerkin weak formulation, the method so obtained corresponds to the discontinuous Galerkin method in time and is especially suited for convection dominated problems. The streamline-diffusion method is found to be the aforementioned penalty method.This paper also examines the sequence of nested equation systems that results from a hierarchical finite element formulation. Properties of these systems arising from static problems are investigated. The paper presents some new possibilities for iterative solution of hierarchic element equations, and different procedures are compared in a numerical example. Finally, a simple ID convection-diffusion problem clearly shows that the proposed hierarchical formulation in time gives a stable and accurate solution even for convection dominated flow.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260514
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  • 108
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    Announcement (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1240-1240 
    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.1620260518
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  • 109
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    Masthead (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260601
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  • 110
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    Exact numerical solutions for radiative heat transfer in cylindrical furnaces (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1201-1212 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Exact expressions for the distributions of the components of radiative flux density and the radiative energy source term in terms of wall and medium temperature distributions have been formulated for an emitting absorbing medium of constant properties bounded by black walls of a cylindrical enclosure. The accuracy of numerical solutions has been tested on an idealized enclosure for which exact analytical solution of the expressions is possible and shown to have six-figure accuracy. The exact expressions have then been solved numerically for an enclosure problem based on data reported previously on a large scale experimental furnace. The principal feature of the data is highly non-uniform temperature distributions which are typical of the conditions encountered in industrial furnaces. These data have been chosen because of their practical importance and the non-availability of exact solutions for such data. The resulting exact solutions have been tabulated and are intended to serve in the future as standards for testing the accuracy of the approximate predictions produced using various three-dimensional flux models in cylindrical configurations.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260513
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  • 111
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    Three-dimensional finite element analysis of open-die forging (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 67-85 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three-dimensional finite element analysis is applied to operation sequences in open-die forging. Flat tools with rounded edges for open-die forging are geometrically modelled using Bézier curves. With this technique, the problems at the die-workpiece interface, such as the integration of frictional stress, node touching on dies and node separating from dies, can be handled effectively. It is shown that in solving general symmetric problems computation time can be saved by reducing variables and rearranging them in the stiffness matrix. One-bite operations and operation sequences for producing two-size bars and two-size pipes in several bites are investigated in regard to geometry, load, energy and deformation distribution.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620250108
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  • 112
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    On the development of a general purpose finite element program for analysis of forming processes (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 113-131 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620250111
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  • 113
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    On the use of the boundary element method for elastoplastic, large deformation problems (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 165-176 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The boundary element method is applied to large deformation problems typical in industrial forming problems. A form of Betti's theorem relevant to an updated Lagrangian type of solution procedure is established as the basis for the boundary element formulation. Equilibrium iterations are needed in each load step. All non-linear terms are moved to the right-hand side and the boundary element method can be used. Cross-anisotropy is assumed where Hill's yield criterion is adopted together with isotropic hardening. The investigation has shown that the boundary element method is applicable to this type of problem, giving good results within reasonable computer time.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620250114
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  • 114
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    Transient analysis of forging operations by the pseudo-concentration method (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 177-189 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The pseudo-concentration method is used to follow the flow of metal during the transient analysis of an axisymmetric forging problem. The technique requires a minimum of user interaction and appears to be ideal for computer aided design of dies. An analysis of an engine disc blocker die is presented and compared with experimental results. The same problem is analysed using a Newtonian fluid which is shown to give good qualitative results which would be acceptable in the initial stages of die design.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620250115
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  • 115
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    Plastic and viscoplastic flow of void-containing metals. Applications to axisymmetric sheet forming problems (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 227-251 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A formal analogy between the equations of pure plastic and viscoplastic flow theory for void-containing metals and those of standard non-linear elasticity is presented. The formulation is particularized for the analysis of axisymmetric sheet metal forming problems using simple two node linear finite elements. Details of the treatment of friction and strain hardening phenomena, time increment computation and elastic effects are also given. Examples of the effect of void porosity on the hemispherical stretching of a circular sheet are presented.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620250118
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  • 116
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    Masthead (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620250201
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  • 117
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    Computation of low-speed compressible flows with time-marching procedures (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 293-311 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The extension of time-marching procedures to low Mach number and low Reynolds number conditions is considered. It is shown that the disparate speeds of the acoustic and particle waves prevent convergence at high Reynolds numbers, while the requirement that both the Courant and the von Neumann numbers be of order one prevents convergence in very viscous flows. A perturbation expansion is used to introduce pseudo-acoustic waves that propagate at speeds similar to the particle speed at high Reynolds numbers and that allows both the inviscid and viscous time step parameters to be of order one at low Reynolds numbers. The resulting algorithm is shown to give convergence rates that are independent of either Mach number or Reynolds number over a range of five orders of magnitude in both parameters. Results are shown for strong heat addition in low-speed flow encompassing this broad range of variables.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620250203
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  • 118
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    Optimization of actively controlled structures using goal programming techniques (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 183-197 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of design of actively controlled structures subject to restrictions on the damping parameters of the closed-loop system is formulated and solved as a multiobjective optimization problem. The purpose of control is to effectively suppress structural vibrations due to initial excitation. The cross-sectional areas of the members are treated as design variables. The structural weight and the controlled system energy are considered as objective functions for minimization. The goal programming approach is used for the solution of the multiobjective optimization problems. The procedure is illustrated through numerical simulations using two-bar and twelve-bar truss structures.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260113
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  • 119
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    A numerical study of laminar and turbulent flows in a two-dimensional bend with or without a guide vane (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 245-262 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical study of the flow in a two-dimensional 90° circular-arc bend is presented. The study is based on the solution of the governing equations using a finite volume technique. Both laminar and turbulent flows are considered. Particular attention is given to the occurrence and size of the separation regions and, in this respect, the effects of Reynolds number and bend radius to height ratio are discussed. The study includes the effect of a guide vane, placed in the bend, on the flow characteristics. It is shown that the emerging velocity distribution is more uniform than that associated with flow in a bend without a guide vane. The presence of a guide vane is shown to suppress the formation of regions of flow separation. Comparisons are made between the effects on the flow of two different designs of guide vane.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260117
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  • 120
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    Letters to the editor (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 283-287 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260120
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  • 121
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    Analysis of infilled frames using A coupled finite element and boundary element solution scheme (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 731-742 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The behaviour of infilled frames subjected to horizontal loads is analysed by an iterative numerical procedure. The stiffness of the structural system is determined with variations in geometrical and mechanical characteristics.The analysis is carried out utilizing the boundary element method (BEM) for the infill and opportunely dividing the frame into finite elements, so as to transform the mutual interactions of the two subsystems into stresses distributed along the boundary for the infill and into nodal actions for the frame.This makes it possible to take into account the separation arising between the two substructures when mutual tensile stresses are involved.At first, infills without openings are considered, using BEM with constant elements for two-dimensional problems in elasticity.The results are compared with those obtained using the simplified equivalent pin-jointed strut model, which is very common in the literature.Subsequently, using an analogous procedure, panels with openings are considered. For these systems, for which no satisfactory simplified models exist, the loss of stiffness in relation to the size of the opening is evaluated.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260315
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  • 122
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    Masthead (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260401
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  • 123
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    Announcements (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 766-767 
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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.1620260318
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  • 124
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    Generalized hybrid-combined methods for the singularity problems of homogeneous elliptic equations (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 785-803 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Combinations of the Ritz-Galerkin and finite element methods are applied to solving singularity problems of homogeneous, elliptic equations. The Ritz-Galerkin method is used in the subdomains where there exist singular points; and the finite element method is still used in the rest of the solution domains. More general coupling techniques than those of Reference 6 along the common boundary of subdomains are discussed. Numerical experiments using these kinds of coupling techniques are provided for the first time. It is interesting that the calculated results of Motz's problem have shown the simplified hybrid strategy in Reference 6 to be optimal for both error bounds and stability of numerical solutions, among all general coupling techniques.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260403
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  • 125
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    Spectral collocation methods for the primary two-point boundary value problem in modelling viscoelastic flows (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 805-813 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Expansions in terms of beam functions and Chebyshev polynomials are used to compute solutions to the primary two-point boundary value problem within a spectral collocation formulation. The performance of the methods is analysed in terms of accuracy and robustness relative to the level of non-linearity. Accurate results are obtained with Chebyshev polynomials and the performance of these trial functions is insensitive to the level of non-linearity whereas the behaviour of the beam functions shows great sensitivity to the level of non-linearity. The use of Newton's method to solve the mixed linear-non-linear system for the Chebyshev coefficients is successful for highly non-linear problems without the need for parameter continuation.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260404
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  • 126
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    The null space and non-conventional basis functions in the mixed finite element method (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 843-855 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The two matrix equations obtained from the mixed finite element method are uncoupled through the use of the QR decomposition. The procedure obtains the basis for the null space which is composed of solutions to the homogeneous flux-equilibrium equation. The result is that, even for statically indeterminate problems, stresses can be obtained without solving for the displacement field. Furthermore, the stress field can be decomposed directly into contributions from applied forces and from prescribed displacements. The appearance of kinetic modes can easily be monitored. The possibility of utilizing non-conventional basis functions for use in conjunction with the QR decomposition is explored briefly. Simple examples are given to illustrate the theoretical results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260407
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  • 127
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    A parallel householder tridiagonalization stratagem using scattered row decompositionThis paper presents one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 857-873 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Householder's method for tridiagonalizing a real symmetric matrix, a major step in evaluating eigenvalues of the matrix, is modified into a parallel algorithm for a concurrent machine of message passing type. Each processor of the concurrent machine has its own CPU, communications control and local memory. Messages are passed through connections between processors. Although the basic algorithm is inherently serial, the computations can be spread over all processors by scattering different rows of the matrix into processors, hence the term “Scattered Row Decomposition”. The steps in the serial and the parallel algorithms are identified. Expressions for efficiency and speedup are given in terms of problem and machine parameters. For a concurrent machine of ring type interconnection, a selected representative problem of large order exhibits efficiency approaching 66 per cent.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260408
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    Multi-domain BEM for two-dimensional problems of elastodynamics (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 891-911 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An advanced implementation of the boundary element technique for the periodic and transient dynamic analyses of two-dimensional elastic or visco elastic solids of arbitrary shape and connectivity is presented. For transient dynamic analysis the problem is first solved in the Laplace transform space and then the time domain solutions are obtained by numerical inversion of transformed domain solutions.The present analysis is capable of treating very large, multi-domain problems by substructuring and satisfying the equilibrium and compatibilities at the interfaces. With the help of this substructuring capability, problems related to the layered media and soil-structure interaction can all be analysed. This paper also introduces a new type of element called ‘Enclosing Element’, which has been developed and used to model the infinitely extending boundaries of a half-space or a layered medium. A number of numerical examples are presented, and through comparisons with available analytical and numerical results, the accuracy, stability and efficiency of the present analysis are established.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260410
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    A full range analysis of reinforced concrete slabs using finite elements (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 973-985 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a full range analysis of reinforced concrete slabs, which includes the effects of both geometric and material non-linearities, using the finite element method. A computer program is described which has been used to analyse slabs previously tested by a number of investigators. The comparisons between the test results and the computer program are considered to be good.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260414
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    Announcements (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1003-1003 
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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.1620260417
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    Remarks on computational magnetostatics (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 987-1000 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A two-scalar-potential formulation for magnetostatic computations has been recommended4 based on a comparative study of several different formulations in terms of their accuracy and efficiency. A different study3 challenged this recommendation. It is the purpose of this report to present results which confirm the practical necessity for the two-potential formulation.The method used for the present study was to construct a simplified computer program designed to easily compare the alternative methods. This program uses the finite element method on a geometry suited for analysis of the ‘bifiliar conductor’ problem treated in both studies mentioned above. In this program, the alternative formulations are implemented with a great deal of common code. In particular, the input, stiffness matrix, matrix solution and editing routines are common to both formulations, with differences appearing only in the source terms for the stiffness matrix equation. The known analytic solution to this particular problem provides a reference with which the computed solutions is compared. The main conclusion of this study of the ‘bifiliar conductor’ problem is that for a given choice of mesh, the two-potential formulation yields significantly more accuracy than the reduced-potential formulation.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260415
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    Finite element simulation of long and short circular die extrusion experiments using integral models (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 9-22 
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    ISSN: 0029-5981
    Keywords: Streamline Elements ; KBKZ Model ; LDPE Extrusion ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite streamline element method for use with integral type constitutive equations in viscoelastic flow simulation, including thermal effects, is presented and some new results using this method in modelling the IUPAC extrusion experiments for low-density polyethylene (LDPE), involving both long and short circular dies, are reported and discussed. It will be shown that the special streamline-based elements provide a convenient way of particle tracking and strain tensor calculation. The extrusion calculation when using a relatively realistic KBKZ type integral model with multiple relaxation times is stable, and practically important Weissenberg numbers and swelling ratios have been reached without difficulty. The agreement with experimental swelling ratios is on the whole satisfactory. In order to make the model a good fit to the Trouton viscosity experimental data of the LDPE sample, a spectrum of elongational parameters has been introduced. The second normal stress term has also been added to the integral model to examine its effect on extrusion swelling. The non-isothermal effects and the possibility of a wall slip near the die exit at high apparent shear rates are also discussed.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620250104
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    Finite-element modelling of metal flow in three-dimensional forming (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 87-97 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A fully three-dimensional elastic-plastic finite-element program for the study of metalforming operations is described. Several applications are discussed, and the finite-element (FE) predictions of metal flow, strain rate and temperature distributions, and the sites of initiation of ductile fracture are presented.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620250109
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    Finite element computation of bulging in continuously cast steel with a viscoplastic modelPresented at the 2nd International Conference on ‘Numerical Methods in Industrial Forming Processes’. Gothenburg. Sweden, 1986. (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 147-163 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The bulging of continuously cast steel between the support rolls has been computed using a viscoplastic finite element model. Both two-dimensional and three-dimensional models are based on the minimization of the functional associated with the Norton-Hoff law and use the streamlines integration to calculate the bulging. By using industrial data, the influence of both numerical parameters and process parameters on the extent of the calculated bulging values has been investigated. The comparison of our results with experimental measurements confirms the relevance of the hypothesis of viscoplastic behaviour.
    Additional Material: 15 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620250113
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    The influence of non-linear thermal parameters on moisture content distributions in unsaturated soil (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 263-279 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The influence of non-linear thermal parameters on moisture distribution predictions in an unsaturated soil is investigated. A fully non-linear numerical model of coupled heat and mass transfer is used to analyse the one dimensional drying of a stratum of loam. The distribution of moisture content in the upper 0.5 m of soil is the subject of interest. Assumed representative material parameters are used.The results show small but significant changes in moisture content variations when either the value of the thermal conductivity or the heat capacity alone is kept constant. When both are held constant, however, a cancellation of effects occurs. This is attributed to the fact that the thermal gradients in the soil remain largely unchanged when compared with fully non-linear values. Actual magnitudes of temperatures are different but the thermal gradients are not.These conclusions cannot be generalized at this stage beyond the problem dependent results achieved. The results are, however, viewed as a contribution to a greater overall understanding of the complex problem under consideration.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260118
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    Masthead (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260901
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    Conference diary (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 763-765 
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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.1620260317
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    A least squares finite element formulation for elastodynamic problems (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1883-1891 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A residual finite element formulation is developed in this paper to solve elastodynamic problems in which body wave potentials are primary unknowns. The formulation is based on minimizing the square of the residuals of governing equations as well as all boundary conditions. Since the boundary conditions in terms of wave potentials are neither Dirichlet nor Neumann type it is difficult to construct a functional to satisfy all governing equations and boundary conditions following the variational principle designed for conventional finite element formulation. That is why the least squares technique is sought. All boundary conditions are included in the functional expression so that the satisfaction of any boundary condition does not become a requirement of the trial functions, but they should satisfy some continuity conditions across the interelement boundary to guarantee proper convergence. In this paper it is demonstrated that the technique works well for elastodynamic problems; however, it is equally applicable to any other field problem.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260813
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    Reliable use of determinants to solve non-linear structural eigenvalue problems efficiently (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1825-1841 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A ‘multiple determinant parabolic interpolation method’ is described and evaluated, principally by using a plane frame test-bed program. It is intended primarily for solving the transcendental eigenvalue problems arising when the ‘exact’ member equations obtained by solving the governing differential equations of members are used to find the eigenvalues (i.e. critical buckling loads or undamped natural frequencies) of structures. The method has five stages which together ensure successful convergence on the required eigenvalues in all circumstances. Thus, whenever checks indicate its suitability, parabolic interpolation is used to obtain eigenvalues more rapidly than would the popular bisection alternative. The checks also ensure a wise choice of the determinant used by the interpolation. The determinants available are all usually zero at eigenvalues, and comprise the determinant of the overall stiffness matrix Kn and the determinants which result, with negligible extra computation, from effectively considering all except the last m (m=1, 2,…, n-1) freedoms to which Kn corresponds as internal substructure freedoms. Tests showed time savings compared to bisection of 31 per cent when finding non-coincident eigenvalues to relative accuracy ∊ = 10-4, increasing to 62 per cent when ∊ = 10-8. The tests also showed time savings of about 10 per cent compared with an earlier Newtonian approach. The method requires no derivatives and its use in the widely available space frame program BUNVIS-RG has demonstrated how easily it can replace bisection, which was used in the earlier program BUNVIS.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260810
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    Hierarchic plate and shell models based on p-extensionThis paper is dedicated to Professor Ivo Babuša on the occasion of his sixtieth birthday. A summary of the work reported herein was presented at a conference at which Professor Babuša was honoured for his numerous contributions in the fields of engineering and applied mathematics. The conference, entitled: ‘The Impact of Mathematical Analysis on the Numerical Solution of Engineering Problems’, was held at the University of Maryland, College Park, MD September 17-19, 1986. (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1855-1881 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with formulations of finite element models for beams, arches, plates and shells based on the principle of virtual work. The focus is on computer implementation of hierarchic sequences of finite element models suitable for numerical solution of a large variety of practical problems which may concurrently contain thin and thick plates and shells, stiffeners, and regions where three dimensional representation is required. The approximate solutions corresponding to the hierarchic sequence of models converge to the exact solution of the fully three dimensional model. The stopping criterion is based on (1) estimation of the relative error in energy norm; (2) equilibrium tests and (3) observation of the convergence of quantities of interest.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260812
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    Numerical simulation of the transport processes in a heat treatment furnace (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 387-399 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical simulation of the heat transfer and fluid processes in a furnace is carried out using finite difference techniques. A heat treatment furnace for the annealing of steel is considered as an example and a mathematical model of the system is obtained by simplifying the equations that govern the transport in the various components that constitute the system. The resulting set of coupled equations then governs the time-dependent temperature distribution in the furnace. Because of the complexity of the full problem, the transport processes undergone by individual components of the furnace are simulated first, using appropriate boundary conditions that decouple them from the other components. These individual simulations are considered in terms of the underlying physical mechanisms for validation. Finally, these are combined to obtain the simulation of the full, coupled problem. The temperature cycle undergone by the material is computed, along with the time-dependent temperature distributions in other components. A comparison with experimental data indicates close agreement, lending strong support to the numerical model. The relevance of these results to the design of the overall thermal system is also outlined.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620250209
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    On the numerical modelling of heat transfer during solidification processes (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 445-473 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An extensive amount of work has been published on the treatment of heat transfer associated with phase change. A few recent advances are discussed in this paper with some emphasis on the phase change of metals. The apparent capacity, effective capacity, enthalpy, post iterative, source based and semi-analytical methods are discussed and relative advantages and disadvantages of each are analysed. Recent developments in nodelling the flow during pouring and natural convection with applications of two widely used convective liffusive codes, the Los Alamos MAC and the Imperial College TEACH, are presented. An alternative tream function-vorticity approach is also discussed. Applications of these methods to turbulent convection during mould filling and continuous casting are presented. Areas of interest for further research work are identified as modelling of turbulence in liquid metals, flow through mushy regions and improvement of the performance of weak methods in multidimensional problems when the ratio of latent heat to sensible heat is large.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620250212
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    Solution accuracies of finite element reentry heat transfer and thermal stress analyses of space shuttle orbiter (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 517-543 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Accuracies of solutions (structural temperatures and thermal stresses) obtained from different finite element thermal and structural models set up for the space shuttle orbiter are compared and discussed. For studying the effect of element size on the solution accuracies of finite element heat transfer and thermal stress analyses of the orbiter, five structural performance and resizing (SPAR) thermal models and five NASA structural analysis (NASTRAN) structural models were set up for the orbiter wing midspan bay 3. The structural temperature distribution over the wing skin (lower and upper) surface of one bay was dome shaped and induced more severe thermal stresses in the chordwise direction than in the spanwise direction. The induced thermal stresses were extremely sensitive to slight variation in structural temperature distributions. Both internal convention and internal radiation were found to have equal effects on the orbiter structural temperatures. Minimum degrees of element fineness required for thermal and structural models for the orbiter to yield satisfactory solutions were established. In transient heat transfer analysis most of the computation time was consumed in the time-dependent temperature calculations and not in the radiation view-factor computations.
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    URL: http://dx.doi.org/10.1002/nme.1620250215
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    Failure of mechanically loaded laminated composites subjected to intense localized heating (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 561-570 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical procedure is presented for predicting failure in laminated composites subjected to simultaneous intense localized heating and applied mechanical loads. The method consists of a non-linear two-dimensional, axisymmetric finite difference thermal analyser which considers the effects of surface ablation, radiation and convection losses and temperature dependent thermophysical properties. The thermal results are used in conjunction with a flat plate finite element code to predict the failure of laminated composites. Predictions based on the numerical analyses are compared with experimental results obtained from mechanically loaded graphite epoxy coupons spot-irradiated at various intensities.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620250217
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    Some novel techniques for the finite element analysis of heat and mass transfer problems (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 611-624 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The coupled heat and mass transfer partial differential equations as derived by Luikov are used to analyse freezing problems in porous media. A numerical model is subsequently developed to depict the frost heave mechanism in a freezing soil system. An example is given of the application of the model and the results are compared with those achieved from field experiments.Also, a novel application of the coincident node technique is presented for the coupled heat and mass transfer problem. This circumvents the numerical problems usually associated with flow through thin layers, in this case a vapour barrier, sandwiched between materials of greater thickness.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620250221
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    Deformations and stresses in welding of shell structures (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 635-655 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The simulation of welding of shell structures is investigated in this paper. In order to verify the implementation of the shell element adopted, two different problems were studied. In the first problem the butt-welding of two plates was simulated. In the second problem the butt-welding of a thin-walled pipe was simulated. It is concluded from the analysis of the plate problem that the shell element is quite effective in the membrane state. The comparison between calculated values and experimental values for the residual stress field in the pipe shows that the shell element performs quite well in the analysis of a realistic problem.
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620250223
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    Masthead (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988) 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260101
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    Variable-order variable-step algorithms for second-order systems. Part 2: The codes (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 55-80 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In a companion paper, Thomas and Gladwell,4 the authors designed a class of multistage methods for second-order systems of ordinary differential equations (ODE's), together with local error estimators based on embedding techniques. Here we provide a set of subroutines implementing the algorithms and discuss our numerical experience with the resulting codes.
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    URL: http://dx.doi.org/10.1002/nme.1620260105
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    Preface (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. i 
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    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.1620250102
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    Practical experience with numerical simulations of plastic processes (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 1-8 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In recent years a number of programs have been developed for the calculation of plastic processes, but up to now the use of these programs in industrial practice has been limited to particular cases.On the one hand, reasons for this can be found with the users who often, not knowing the theoretical principles and the restrictions of the calculations, obtain wrong results and thus generally doubt the applicability of the program.On the other hand, in many cases calculations are only possible with low accuracy since information and data on the boundary conditions and the material behaviour are not available.This paper describes the possibilities and limits of the numerical simulations as well as the compromises which have to be accepted.
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    URL: http://dx.doi.org/10.1002/nme.1620250103
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    The structure of constitutive equations for finite deformation of elastic-plastic materials involving strain-induced anisotropy with applications (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 133-146 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Constitutive relations based on finite-deformation-valid analysis require the formulation of coupling effects that were not needed in earlier developments which included small deformation restrictions. However, the feasibility to introduce such coupling effects mathematically requires that the new terms introduced must be in accord with physically based concepts of the phenomena involved. An example came to light in which objectivity of a constitutive relation, considered to be generalized for finite deformation applications involving strain-induced plastic anisotropy, had been achieved by use of the Jaumann derivative in place of the material derivative for the growth of a tensor variable which expressed the anisotropic characteristics. The spin terms thus added to the infinitesimal displacement analogue were not in accord with a physically based assessment of the underlying micro-mechanical phenomena and in fact led to the prediction of anomalous stress response. This paper comprises comments on the subsequent development of the theory, including a tensor equation for the evolution of the anisotropy. By solving a sample test problem with different initial conditions both the numerical implementation of the constitutive relation and the response according to the proposed growth law of the anisotropy are described and discussed.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620250112
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    Oscillatory convection in liquid metals in a horizontal temperature gradient (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 401-414 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: When growing semiconductor crystals from the melt, the free convection induced in the liquid phase by the imposed thermal boundary conditions can become periodic in time. Recently, the onset of this oscillatory convection has been simulated directly through solution of the time-dependent governing equations for the particular case of an imposed horizontal temperature gradient. In this paper a new approach for detecting the oscillatory instability is presented in which the transition from steady to periodic flow is identified with a Hopf bifurcation in the solution of the steady equations. The critical Grashof number and frequency are predicted by solving an extended system of steady equations that locates exactly the Hopf bifurcation point, and the variation with aspect ratio and Prandtl number of the threshold for oscillations is obtained through continuation methods. By introducing a homotopy parameter into the boundary conditions the variation of the critical Grashof number is computed as the thermal and viscous conditions on the upper surface vary.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620250210
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    Transfinite element methodology for non-liner/linear transient thermal modelling/analysis: Progress and recent advances (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 475-494 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Recent progress and advances in the development and applicability of a novel ‘transfinite element’ computational methodology is presented for general non-linear/linear transient thermal problems. The proposed methodology and concepts are new and unique, and demonstrate the applicability to general transient non-linear/linear thermal analysis situations by combining classical Galerkin schemes and transform approaches with contemporary finite element methods to preserve the modelling versatility and numerical features-thereby, a hybrid computational methodology is proposed. Characteristic features and pertinent details of the approach are described for non-linear/linear transient thermal problems, wherein non-linearities due temperature dependence of thermophysical properties and/or general non-linear bound ary conditions to include radiation, effects due to phase change, etc., are considered. In addition, the use of high-continuity formulations in conjuction with the proposed methodology to furnish accurate temperature distributions and temperature gradients making use of a relatively smaller number of degrees of freedom is also demonstrated. Numerical test cases are presented for a variety of problems to demonstrate the fundamental features and applicability of the proposed formulations. The proposed hybrid transfinite element methodology and concepts offer significant potential for extension to several areas of mathematical physics and engineering and to interdisciplinary research areas.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620250213
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    Treating exceptionally non-linear temperature fields (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 571-580 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: By some examples it is shown how to treat non-everyday heat transfer problems which are characterized by temperature dependent heat sources and heat radiation.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620250218
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    Monte Carlo method for radiative heat transfer analysis of general gas-particle enclosures (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 581-592 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new Monte Carlo method is developed to analyse multi-dimensional radiative heat transfer in an enclosure containing grey gas with anisotropically scattering grey particles. One set of variables, called READ (Radiative Energy Absorption Distribution), is introduced to represent radiative transfer, thus appreciably reducing repeated computations required by the conventional Monte Carlo technique. A 1 m × 1 m square duct is used as the enclosure with the upper and lower walls at different temperatures in the one-dimensional case and with adiabatic specular or diffuse side walls in the two-dimensional case. Results agree well with the existing analytical solutions for one-dimensional, non-scattering cases. It is concluded that, with anisotropic scattering, an increase in the absorption coefficient and/or single scattering albedo produces adverse effects on radiative heat transfer. Anisotropic scattering effects cannot be simulated by the use of the effective absorption coefficient.
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620250219
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    Variable-order variable-step algorithms for second-order systems. Part 1: The methods (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 39-53 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We develop a new class of multistage algorithms for second-order systems of ordinary differential equations (ODE's) based on methods by Zienkiewicz et al.13 Our new methods are designed to provide a set of efficient methods which can be used with local error estimators based on embedding techniques. In a companion paper, we provide a set of subroutines implementing the algorithms derived and a discussion of numerical experience with the resulting codes.
    Additional Material: 7 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620260104
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    Stress evaluation algorithms for rate constitutive equations in finite deformation analysis (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 121-141 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The stress integration algorithm for hypoelastic constitutive equations proposed by Pinsky et al.3 is extended for the treatment of finite deformation elastoplastic constitutive relations. Another approach based on the polar decomposition of the deformation gradient tensor F = R · U is also introduced. Numerical examples and a discussion on these two approaches are given.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260109
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    Vector potential formulations and finite element trial functions (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 95-108 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In field systems containing a divergenceless vector, the problem may be posed in terms of a vector potential for convenience. For the solution of the magnetic vector potential in three dimensional problems with current sources, there exist three standard variational formulations in the literature. While all these are known to give verifiable physical solutions, there is some question as to which is to be preferred. Indeed, one of them is invalid for infinite dimensional fields in that, without the finite element trial functions, it will not give unique solutions since it does not explicitly impose the divergence of the vector potential.In this paper, we look at the formulations in the light of the restrictions imposed by the finite element trial functions for tetrahedral elements and arrive at the curious result that that formulation which is totally invalid when the vector potential is unrestricted by trial functions, is in fact valid in finite element analysis and, at the same time, is the best. We further show that this formulation yields naturally non-divergent vector potential solutions, strictly as a result of the trial functions.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260107
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    Eigenvalue reanalysis by improved perturbation (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 167-181 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new efficient method of eigenvalue reanalysis has been developed based on the perturbation method such that first the differential equations which describe the change of the eigenvalues and eigenvectors of a system being modified are derived from the perturbation method and then the solutions of these equations are obtained by following them up with the solutions of more simple equations. The special features of this method are that it can give a clear correspondence between the eigenpairs before and after system modification, and that the computer run time spent by this method is far shorter than that of revised analysis by FEM when only a few selected modes are used in the form of an approximate computation. In addition, this approximate computation can give more accurate results than the perturbation method. The efficiency of the proposed method has been verified by applying it to a simple spring-mass model as well as a 600 degrees-of-freedom model which receive structural modification.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260112
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    The numerical solution of 3-D thermoelastic problems using only Laplace operator discretization methods (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 545-559 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of potential theory to the solution of theory of elasticity problems harks back to an old tradition, witness the Boussinesq treatment of the half-space point loading.In a preceding study by the authour,1 it has been shown how plane thermoelastic problems can be solved by using only numerical methods suited to treat the Laplace operator Δ2ϕ, hence by introducing only one d.o.f. or every node of the discretization.In the present paper it is proposed to show how similar techniques can be used in a three-dimensional case. The reduction achieved in the number of nodal unknowns is from three d.o.f. to one; thus it is hoped that - notwithstanding the greater complexity of the present treatment - a computational advantage can be gained over the direct approach, at least for discretization meshes of a few thousands of nodes (which is not unusual for 3-D domains).The basic formulation draws from fairly classical works2-6 and differs from more recent ones (e.g. Goodier as quoted in Reference 7) insofar as the particular solutions of the thermoelastic problems do not ntail, in the present approach, any integration, but rather are expressed directly in terms of the thermal field.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620250216
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    A comparative investigation on recurrence formulae in finite difference methods (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 593-609 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To solve the transient heat-conduction equation, the Pade-approximation is introduced into the Finite Difference Method. But, if the time step is chosen too large relatively to the element size the Euler method (Pade (0,1) approximation) and the Crank-Nicolson solution (Pade (1,1)-approximation) lead to significant oscillations. In contrast, the Full Implicit scheme (Pade (1,0)-approximation) does not show this oscillatory behaviour, but is more inaccurate. Compared to these time stepping algorithms the presented Weighted Time Step method is seen to offer definite advantages.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620250220
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    Numerical simulation of forest fires (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 25 (1988), S. 625-633 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper reviews the work done to date on the numerical simulation of forest fires. A general model to predict forest fire spread under different conditions is presented and studied. The model is based on nth order reaction theory, and is sufficiently simple and flexible to conveniently deal with variations in wind velocity, forest properties, fire breaks and other phenomena of interest to the fire controller. The effects of changing various parameters in the equations are illustratd. Results for zero and constant wind velocity are given, together with the effect of abrupt wind changes and fire breaks.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620250222
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    Non-linear heat conduction in composite bodies: A boundary element formulation (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 19-38 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper discusses the numerical solution of steady-state non-linear heat conduction problems in composite bodies by using the boundary element method. Two kinds of non-linearities are considered: the temperature dependence of the thermal conductivity and boundary conditions of the radiative type. By introducing the integral of conductivity as a new variable the governing equation of the problem becomes linear in the transform space. Transformed boundary conditions of the Dirichlet and Neumann types are also linear but convective boundary conditions become non-linear. Also, discontinuities arise in the value of the integral of conductivity across the interface between materials with different properties since continuity of temperature is imposed. The problem is numerically solved by discretizing the external and interface boundaries of the region under consideration with constant boundary elements and applying an iterative scheme of the Newton-Raphson type.
    Additional Material: 15 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260103
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    Least-squares finite elements for first-order hyperbolic systems (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 81-93 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A class of least-squares finite element methods has been developed for first-order systems and here we study this approach for hyperbolic problems. The formulation of the least-squares method is developed in detail and compared with the Petrov-Galerkin and Taylor-Galerkin procedures. A stability analysis is carried out and the extension to the non-linear problem described. Numerical comparison studies demonstrate the performance of the method and suggest that it is a promising alternative to existing schemes. Applications considered include the convection equation, inviscid Burger's equation and shallow-water equations.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260106
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    Automatic adaptive remeshing for finite element simulation of forming processes (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1-18 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An automatic remeshing scheme has been developed to enable finite element simulation of even complicated forming processes. It has been demonstrated that for many practical applications the incorporation of this technique in the existing computer codes is indispensable not only for more accurate solutions but sometimes just for striving to obtain solutions. In order to avoid the tedious procedures of, e.g. interrupting the analysis, performing rediscretization, mapping of current state variables and preparing the new set of boundary conditions, methods for automating the remeshing procedures and the related accuracy problems have been presented. Several examples, such as a heading process, an extrusion process through a square die, and a one-blow impression-die forging process with flash have been successfully tested out with this automatic remeshing scheme.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260102
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    Generalized viscoelastic model for creep analysis coupled with plastic deformation (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 153-165 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A creep analysis capability, using a generalized viscoelastic model, is introduced to process the creep behaviour coupled with elastoplastic deformation. The formulation is based on the step-by-step time integration of the Kelvin-Maxwell rheological model with non-constant parameters.The concept of a rheological model is extended to the multiaxial stresses by the Prandtl-Reuss stress-strain relationship, from which the tangential stiffness matrix is formed for Newton's iteration. If the plastic deformation is coupled with creep, the algorithm will seek a solution in two distinct steps. Various choices of empirical creep laws are available and small variations in temperature are allowed as implemented in the general purpose finite element analysis program.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260111
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    Ill-Conditioned equations in kinematics and dynamics of machines (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 217-230 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: During mechanical system kinematic and dynamic analysis, linear and non-linear algebraic equations must be solved. Algebraic equations are often ill-conditioned, due either to physical singularities or large numerical errors, in which case solutions may have large errors or analysis methods may fail. Causes of ill-conditioned problems are studied and illustrated with examples. Ill-conditioned matrices and matrix condition numbers are discussed and an efficient and reliable indicator of ill-conditioned matrices is suggested. In constrained kinematic and dynamic analysis, equations are solved repetitively, so symbolic factorization is used. The ill-conditioning problem due to symbolic factorization is discussed and methods of detecting ill-conditioning are suggested. Three examples are studied to demonstrate the effectiveness and use of condition numbers and ill-conditioned system detection methods.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260115
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    Numerical methods in engineering and applied science - numbers are fun, B. M. Irons and N. G. Shrive, Ellis Horwood, Chichester, 1987. No. of pages: 248, 14 program listings (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 289-289 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260121
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    Masthead (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988) 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260201
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    Higher order Chebyshev basis functions for two-point boundary value problems (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 313-327 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Cubic basis functions in one dimension for the solution of two-point boundary value problems are constructed based on the zeros of Chebyshev polynomials of the first kind. A general formula is derived for the construction of polynomial basis functions of degree r, where 1 ≤r 〈 ∞. A Galerkin finite element method using the constructed basis functions for the cases r = 1, 2 and 3 is successfully applied to three different types of problem including a singular perturbation problem.
    Additional Material: 5 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620260203
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    Multi-time-step integration using nodal partitioning (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 349-359 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm is presented which integrates different groups of nodes of a finite element mesh with different time steps and different integrators. Since the nodal groups are updated independently no unsymmetric systems need be solved. Stability is demonstrated by showing that an energy norm of the solution decreases after every update if the time step is less than a given critical value. The element eigenvalue inequality theorem is used to give the critical time step in terms of element eigenvalues.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260205
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    Accuracy of a class of concurrent algorithms for transient finite element analysis (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 379-391 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The accuracy of a new class of concurrent, procedures for transient finite element analysis is examined. A phase error analysis is carried out which shows that wave retardation leading to unacceptable loss of accuracy may occur if a Courant condition based on the dimensions of the subdomains is violated. Numerical tests suggest that this Courant condition is conservative for typical structural applications and may lead to a marked increase in accuracy as the number of subdomains is increased. Theoretical speed-up ratios are derived which suggest that the algorithms under consideration can be expected to exhibit a performance superior to that of globally implicit methods when implemented on parallel machines.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260207
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    Advanced elastic and inelastic three-dimensional analysis of gas turbine engine structures by BEM (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 393-411 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The boundary element method (BEM) has been known for some time to be extremely useful for the solution of elastic stress analysis problems involving high stress/strain gradients. In particular, the method has been extensively used for the study of both two and three-dimensional fracture mechanics problems. Recent analytical and numerical developments coupled with the general availability of greatly increased computing capacity have made both elastic and inelastic three-dimensional stress analysis feasible for complex geometries such as those found in gas turbine engine components.This paper summarizes the features of an advanced stress analysis method based on BEM for elastic and inelastic analyses of multizone or substructured three-dimensional solids. The elastic analyses involve isotropic or cross anisotropic media with thermal and centrifugal loading. The inelastic analyses include isotropic plasticity with variable hardening and kinematic plasticity with multiple yield surfaces.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260208
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    Finite element analysis of plane couple-stress problems using first order stress functions (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 489-509 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A complementary energy based variational principle, using first order stress functions, is developed for plane linear elastic couple-stress problems. The principle is analogous to that used in a total potential energy based Mindlin/Reissner thick plate bending analysis and as such is a generalization of the classical analogy between plate stretching and plate bending. Traction boundary conditions are enforced using a Lagrange multiplier technique. The resulting C0 finite element ‘equilibrium stress model’ is validated by investigating the reduction of the stress concentration factor associated with a small hole in a field of uniform tension.
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260214
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    A mixed explicit-implicit (EI) algorithm for creep stress analysis (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 511-524 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mixed explicit-implicit numerical integration algorithm for creep stress analysis is presented in this paper. This method allows simultaneously use of, and thus benefit from, both these integration schemes. The continuum damage constitutive model is also implemented in this algorithm. The present method is suitable for the prediction of creep crack growth in solids using the continuum damage approach.Numerical examples using different constitutive equations have been included to demonstrate the high efficiency of the proposed algorithm.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260215
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    Conference diary (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 525-526 
    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.1620260216
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    Post-buckling analysis of shallow shells by the field-boundary-element method (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 571-587 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The non-linear field-boundary-element technique is applied to the analysis of snap-through phenomena in thin shallow shells. The equilibrium path is traced by using the arc-length method and the solution strategy is discussed in detail. The results show that, as compared to the approaches based on the popular symmetric-variational Galerkin finite element formulation, the current approach based on an unsymmetric variational Petrov-Galerkin field-boundary-element formulation gives a faster convergence while using fewer degrees of freedom. The illustrative numerical examples deal with post-buckling responses of several shallow shells with different geometries.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260305
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  • 178
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    Numerical analysis of a generalized plane ‘elastica’ with non-linear material behaviour (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 617-630 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This article presents a numerical procedure for the analysis of a planar, continuous, flexible member. Large displacements and rotations, non-linear material behaviour and general cross sections are admitted. A shooting method is utilized along with Newton-type iteration for improved estimates. The resulting computer program is used to compare with numerical and analytical solutions of problems solved by others, and to present the solution to a problem which brings out very clearly the effects of both geometric and material non-linearities.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260307
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  • 179
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    Spectral Galerkin methods for the primary two-point boundary value problem in modelling viscoelastic flows (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 647-662 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The essential character of the primary elliptic-hyperbolic operator encountered in the modelling of viscoelastic flows is encaptured in a non-linear fifth-order two-point boundary value problem in one dimension. Expansions in terms of beam functions and Chebyshev polynomials are used to compute solutions to the primary two-point boundary value problem within a spectral Galerkin formulation. An investigation of the performance of the methods with respect to the level of non-linearity is carried out. Accurate results are obtained with Chebyshev polynomials for high levels of non-linearity, whereas the behaviour of beam function expansions proves far more sensitive to the level of non-linearity.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260309
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  • 180
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    Modified shape functions for the three-node plate bending element passing the patch test (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 705-715 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A polynomial displacement basis for the three-node plate bending element (Zienkiewicz-triangle) is developed from a relaxed C1-continuity requirement called the interpolation test. The test provides a general convergence criterion for non-conforming shape functions and a practical guideline to select a proper displacement basis. The resulting simple displacement type element passes the patch test. Several reduced numerical integration schemes are discussed and numerical testing provides a comparison with the standard element formulated by Zienkiewicz.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260313
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  • 181
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    Isoparametric hybrid hexahedral elements for three dimensional stress analysis (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 677-693 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on a new functional in which displacements, strains and stresses are taken as independent variables, a set of three 8-node hexahedral hybrid elements QS11-1, QS11-2 and QS11-3 is developed. The adoption of separated stress and displacement variables proves to be effective in improving the accuracy of the elements.The new elements are all capable of yielding converging results, and they all possess the properties of having no zero energy deformation modes and of being co-ordinate invariant. From the numerical example of a beam under bending it is concluded that exact solutions can be obtained for right prism elements, while good results are still attainable for severely distorted elements.The relationship between the new hybrid elements and the conventional displacement elements is also explored in this paper.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260311
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    The identification and elimination of artificial stiffening errors in finite elements (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 743-762 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The causes of shear locking and other discretization errors are analysed using a physically interpretable notation. This analysis provides insights that allow the errors due to shear locking to be removed either directly or indirectly. St. Venant's principle is incorporated into the stiffness matrix to directly eliminate shear locking from bending elements. Rules-of-thumb are suggested by the same analysis that will insure the absence of errors due to shear locking at the cost of additional degrees of freedom. It is also shown that aspect ratio stiffening in membrane elements is partially due to the same modelling error that produces shear locking. The source of parasitic shear is also identified and a direct procedure for eliminating it is given. A two node Timoshenko beam element and a four node membrane element are fully developed in symbolic form. The procedure is directly applicable to plate bending elements.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260316
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  • 183
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    An incremental procedure for deformation analysis of elastic-plastic frames (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 769-784 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the present paper an incremental procedure is formulated for first-order elastoplastic analysis of plane frame structures discretized into a finite number of beam elements and described by piecewise linear elastic-perfectly plastic constitutive laws, under the assumption of both reversible and irreversible behaviour of material and using piecewise linear yield conditions at any desired degree of discretization in the space of the active stress resultants (axial force, shear force and bending moment).The proposed method, by using the independent elastic-plastic kinematical compatibility equations, restrains the problem sizes within not more than twice the number of the redundant unknowns in the complete elastic frame, regardless of the degree of discretization of the piecewise linear yield conditions, still maintaining the advantage exhibited by the Mathematical Programming methods of requiring only one factorization of the matrix governing the problem when no local unloading occurs. Furthermore, the outlined algorithm allows the additional computational effort to be restrained in the case of local unloading, inasmuch as it requires a new factorization to be performed of a part of the matrix governing the problem, whose size is small with respect to the total size of the matrix.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260402
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    On evaluation of the green functions for harmonic line loads in a viscoelastic half space (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 823-841 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Comparison of different quadratures for evaluation of the improper wavenumber integrals which arise in evaluation of the Green functions for a viscoelastic half space and harmonic line loadings is investigated. The model is assumed to be of the plane strain type. Extensive testing of the numerical accuracy for various quadratures is performed. A measure of numerical efficiency of the quadratures is proposed and compared for different integration formulae. It was determined that among the procedures tested the Clenshaw-Curtis quadrature offers the most efficient way of evaluating the wavenumber integrals numerically.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260406
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    Monte Carlo structural optimization in discrete variables with annealing algorithm (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 815-821 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper describes the basic ideas of Monte Carlo annealing algorithms for structural optimization with discrete design parameters. The algorithm generates randomly a set of design parameters, with probability depending on the objective function and given by the Boltzmann-Gibbs distribution. In this model the search for the global minimum is simulated by a relaxation process of the statistical mechanical system with the Hamiltonian proportional to the objective function. The rate of the convergence of the method and its dependence upon the annealing probability are discussed. Numerical implementation of the method for the weight optimization of the ten-bar planar cantilever truss is presented. The results of numerical simulation are compared with those obtained by the dual methods. The principal conjecture is that the method is fairly efficient and has great potential for applicaton in engineering design.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260405
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  • 186
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    A numerical method for computing domains of attraction for dynamical systems (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 875-890 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The backward mapping approach for computation of global domains of attraction of asymptotically stable non-critical equilibrium points of dynamical systems is presented. A basis for the proposed approach is an extension of Lyapunov's direct method due to LaSalle and Lefschetz. An iterative process that converges to the global domain of attraction of an asymptotically stable equilibrium point is formulated. The method applies to both continuous time and discrete time multidimensional systems. It is shown that the backward mapping approach proposed by C. S. Hsu for spiral equilibrium points of second order discrete time systems is a particular case of the algorithm presented here. The proposed method can be used for autonomous systems as well as for systems with periodic coefficients. When applied to discrete time formulation of dynamical systems, the method can be used to determine the regions of stability of periodic solutions. The paper concludes with a number of illustrative examples that demonstrate the usefulness of the proposed approach.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260409
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    Thin plate elements with relaxed Kirchhoff constraints (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 913-933 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An analysis of thin plates by C0 elements is presented. The fundamental part of it is the formulation of a set of constraints that relate the rotational degrees of freedom to the translational degrees of freedom and which are weaker than the usual Kirchhoff constraints. A penalty term associated with these constraints is then introduced instead of the usual expression for the shear strain energy. It is shown that the approach is effective for both quadrilateral and triangular elements.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260411
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  • 188
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    Quadratic-spline collocation methods for two-point boundary value problems (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 935-952 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new collocation method based on quadratic splines is presented for second order two-point boundary value problems. First, O(h4) approximations to the first and second derivative of a function are derived using a quadratic-spline interpolant of u. Then these approximations are used to define an O(h4) perturbation of the given boundary value problem. Second, the perturbed problem is used to define a collocation approximation at interval midpoints for which an optimal O(h3-J) global estimate for the jth derivative of the error is derived. Further, O(h4-J) error bounds for the jth derivative are obtained for certain superconvergence points. It should be observed that standard collocation at midpoints gives O(h2-J) bounds. Results from numerical experiments are reported that verify the theoretical behaviour of the method.
    Additional Material: 16 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620260412
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    A three dimensional calculation of elastic equilibrium for composite materialsWhile the authors were in residence at ICASE, NASA Langley Research Center, Hampton, VA 23666-5225, U.S.A. (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 953-971 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A compact scheme is applied to three dimensional elasticity problems for composite materials, involving simple geometries. The mathematical aspects of this approach are discussed, in particular its solution by iteration methods. A vector processor code implementing the compact scheme is presented, and several numerical experiments are summarized.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260413
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    Conference diary (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1001-1002 
    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.1620260416
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    A variable stiffness type boundary element formulation for axisymmetric elastoplastic media (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1005-1027 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new ‘direct’ elastoplastic boundary element formulation for axisymmetric bodies is developed. The procedure exploits certain features of the constitutive relationship to express the unknwon non-linear initial stress rate tensor as a scalar quantity which can then be eliminated from the boundary equation system though a back substitution of the (modified) stress rate equations.This formulation is implemented in a multi-region system that utilizes quadratic isoparametric shape functions to model the geometry and field variables of the boundary and domain of a body. The kernel functions are presented in Appendix I and the singularities associated with these kernels are discussed. New techniques are described to calculate the coefficients associated with the singular nodes.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260502
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    Masthead (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260501
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    Development of a block Lanczos algorithm for free vibration analysis of spinning structures (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1029-1037 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the development of an efficient eigenproblem solution algorithm and an associated computer program for the economical solution of the free vibration problem of complex practical spinning structural systems. Thus, a detailed description of a newly developed block Lanczos procedure is presented in this paper that employs only real numbers in all relevant computations and also fully exploits sparsity of associated matrices. The procedure is capable of computing multiple roots and proves to be most efficient compared to other existing similar techniques.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260503
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  • 194
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    Unconditionally stable staggered solution procedure for soil-pore fluid interaction problems (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1039-1055 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a simple procedure for modifying the dynamic coupled soil-pore fluid equations in a manner which allows a stable and efficient staggered solution procedure to be used. The solution method is simpler than an alternative suggested by Park15 and has a direct physical interpretation. This stabilized procedure is efficient in numerical time domain analysis of soil-pore fluid occurring in earthquake and consolidation problems. Numerical examples of one and two dimensional saturated poroelastic media demonstrate the procedure.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260504
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  • 195
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    A mixed formulation of C0-linear triangular plate/shell element - the role of edge shear constraints (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1101-1128 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple and effective linear C0-triangular element for plates and shells is developed on the basis of the Hellinger-Reissner mixed variational principle with independently assumed stress and displacement fields. Two main features are emphasized in this development concerning the assumed transverse shear stress field. Firstly, this assumption results in edge-type penalty constraints in the thin plate/shell regimes. Secondly, the element is used in the form of a four-triangle, cross-diagonal macroelement mesh. As a result, the element is shown to be free from shear locking in thin plate/shell applications, and it satisfied all the appropriate patch tests required for Kirchhoff plate models. In addition, the element exhibits good overall convergence properties in a variety of test problems for plates and shells. Finally, from the computational standpoint, the element is very efficient since all stiffness component matrices are derived in explicit forms.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260508
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    An error-based approach to complementary formulations of static field solutions (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1963-1987 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The constitutive relationship between fields in electromagnetic media is cast in error form. For well-posed static problems, the error splits systematically into complementary functionals. Error minimization provides a universal variational principle that generates complementary and dual solution formulations. The error, which is wholly attributed to the numerical constraints in approximate solutions, is always defined and computable locally and globally.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620260906
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    A rational approach for choosing stress terms for hybrid finite element formulations (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 2331-2343 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new approach for choosing the stress terms for a hybrid stress element is based on the condition of vanishing of the virtual work along the element boundary due to the stress terms higher than constant and the additional incompatible displacement. Examples using 4-node plane stress elements have shown that when the incompatible displacements also satisfy the constant strain patch test the resulting elements will provide the most accurate solutions. Advantages of this approach for the formulation of an axisymmetric solid are also indicated.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620261014
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    Three-dimensional boundary-element computation of potential flow in fractured rock (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 2319-2330 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The use of the boundary-element method (BEM) for three-dimensional potential flow problems is described herein. The specific application for which the program is designed is the flow in fractured porous media. There are several enhancements to the usual boundary-element calculations. The method uses linear elements to approximate better the boundary conditions and the solution on the surfaces as compared to constant elements; accurate integration over high-aspect-ratio triangles is achieved by computing all the integrals in closed form, as opposed to numerical cubature or mixed exact-numerical integration schemes; and the zoning for inhomogeneous regions uses an efficient method which reduces the size of the problem and avoids difficulties with singularities.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620261013
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    Conference diary (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 2347-2349 
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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.1620261017
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    A beam finite element non-linear theory with finite rotations (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 2403-2438 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620261105
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