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  • 1985-1989  (2,531)
  • 1975-1979  (946)
  • 1830-1839
  • Engineering  (3,477)
  • 101
    Electronic Resource
    Electronic Resource
    New techniques for fast hybrid solutions of systems of equations (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 455-467 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A fast analogue solver with limited precision is used as a preconditioner in an iterative process which develops full digital precision. This hybrid process is highly parallel, and, in principle, it can be faster than digital computations alone. A problematic feature of this process is that the low analogue precision can adversely affect convergence speed. New techniques are introduced to address this limitation. A partial separation of analogue imprecision and poor problem condition is made. Fully parallel digital (smoothing) iterations are introduced to eliminate the effect of random errors which accompany analogue-digital conversion. Application is made to the problem of repeated summation.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270303
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  • 102
    Electronic Resource
    Electronic Resource
    The D1/2-norm of the SOR and Cyclic Chebyshev Semi-Iterative (CCSI) methods for a class of non-symmetric matrices (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 547-557 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Successive Overrelaxation (SOR) and the Cyclic Chebyshev Semi-Iterative (CCSI) methods are considered for solving the non-symmetric linear systems Ax = b when A has the form \documentclass{article}\pagestyle{empty}\begin{document}$$ {\bf A} = \left({\begin{array}{*{20}c} {{\bf D}_1} & {\bf F} \\ {-{\bf F}^{\rm T}} & {{\bf D}_{\rm 2}}\\ \end{array}} \right) $$\end{document} with D1 and D2 symmetric positive definite (SPD).The D1/2-norms of both methods are determined and it is shown that, though the SOR method is better based on the spectral radius, the CCSI scheme is far better than SOR according to the D1/2-norm.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270308
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  • 103
    Electronic Resource
    Electronic Resource
    A mixed finite element formulation for the boundary controllability of the wave equationDedicated to David Young for his 65th birthday (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 623-635 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270313
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  • 104
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    Electronic Resource
    Masthead (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989) 
    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.1620280101
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  • 105
    Electronic Resource
    Electronic Resource
    Modal solution of transient heat conduction utilizing Lanczos algorithm (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 13-25 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this work, a modal solution method for transient heat conduction utilizing a co-ordinate transformation matrix generated by the Lanczos algorithm is presented. The special characteristics of this co-ordinate transformation are also discussed. The comparisons made in the NASA Insulation Test problem analysis shown that this approach is more cost-effective than direct solutions, without loss of accuracy.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280104
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  • 106
    Electronic Resource
    Electronic Resource
    Sensitivity analysis and shape optimization of axisymmetric structures (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 95-108 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient method is developed for sensitivity analysis in shape optimization of axisymmetric structures. The technique of isoparametric mapping is used to generate the finite element mesh from a small set of master elements and master nodes. Co-ordinates of selected master nodes are used as design variables. Shape function values of master elements at derived finite element nodes obtained during the isoparametric mapping process are utilized to calculate the gradients of weight and response of the structures with respect to the design variables. Analytic formulations of the gradients are developed for sensitivity analysis of axisymmetric structures. An optimization procedure using a sequential linear programming method is applied to effectively utilize the calculated gradients. Numerical examples of optimum design of disks subject to thermo-mechanical loadings are presented.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280108
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  • 107
    Electronic Resource
    Electronic Resource
    Benchmark computation and performance evaluation for a rhombic plate bending problem (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 155-179 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper addresses the question of the accuracy and reliability of the computational analysis of the rhombic plate problem. The Kirchhoff model has a large error (measured in the energy norm) in comparison with the three dimensional solution with a soft simple support; also for very thin plates (t = 1/100a) and all angles (up to α = 90°). The Reissner-Mindlin model gives results 3-5 times better and is less sensitive to the change of the plate angle. The Kirchhoff model is a relatively good approximation of three dimensional setting for a hard simple support. The paradoxical (polygon) behaviour of the simply supported Kirchhoff plate extends to the Reissner-Mindlin model with a hard support. The finite element solution of the Kirchhoff model is addressed in detail. It is shown that higher degree methods are clearly preferable and that the skewness of the elements does not influence essentially the accuracy of the method; the singularity of the solution, which strongly depends on the skewness of the plate, is the primary cause of the deterioration of the performance of the FEM.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280112
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  • 108
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    Electronic Resource
    A simple stress error estimator for Hybrid-Trefftz p-version elementsA preliminary version1 of this paper has been presented at NUMETA 87 Conference, The University of Swansea, 6-10 July 1987 (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 211-236 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An a posteriori error estimator is presented which allows a good pointwise evaluation of the error in predicted stresses and can easily be implemented in existing FE codes. Although this estimator has especially been developed for and tested on p-version Hybrid-Trefftz (HT) elements, it is anticipated that it can also be applied to conventional conforming p-version elements. The practical efficiency of the estimator is illustrated through the solution of various plate bending problems by using the HT p-version Kirchhoff plate elements.2
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280115
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  • 109
    Electronic Resource
    Electronic Resource
    A moving boundary circulation model for regions with large tidal flats (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 245-260 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical model is developed for computing two-dimensional circulation in coastal regions dominated by large tidal flat motion. This model is based on the shallow water momentum and continuity equations being operated upon by the Galerkin finite element method. The particular advantage of the model lies in its ability to accommodate a changing domain boundary. This is accomplished by adopting finite elements that change shape so as to consistently move with the water's edge. Application of the model to the Kuwait Bay is described, and the associated results on circulation are given.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280202
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  • 110
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    A boundary element method analysis of electrostatics in a tank during filling operations (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 315-329 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Electrostatic charging inside a tank is analysed numerically using the boundary integral method. The electrostatic charge is transmitted to the tank through a charged liquid. Profiles for the charge density and potential are obtained in the tank during the filling operation. The analysis is based on the equation governing the transport of charge and Poisson's equation. The results are characterized by two dimensionless parameters, the dimensionless Debye length given by the Debye length divided by the height of the tank, and the number Pe defined as a Peclet number. The results show where the maximum charge density and potential occur and give a prediction of when during the filling operation a hazardous situation may occur.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280206
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  • 111
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    Electronic Resource
    Assumed strain stabilization procedure for the 9-node Lagrange shell element (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 385-414 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An assumed strain (strain interpolation) method is used to construct a stabilization matrix for the 9-node shell element. The stabilization procedure can be justified based on the Hellinger-Reissner variational method. It involves a projection vector which is orthogonal to both linear and quadratic fields in the local co-ordinate system of each quadrature point. All terms in the development involve 2 × 2 quadrature in the 9-node element. Example problems show good accuracy and an almost optimal rate of convergence.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280210
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  • 112
    Electronic Resource
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    A consistent characteristic length for smeared cracking models (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 461-474 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical scheme for crack modelling by means of continuous displacement fields is presented. In two-dimensional problems a crack is modelled as a limiting case of two singular lines (with continuous displacements, but discontinuous displacement gradients across them) which tend to coincide with each other. An analysis of the energy dissipated inside the band bounded by both lines allows one to obtain an expression for the characteristic length as the ratio between the energy dissipated per unit surface area (fracture energy) and the energy dissipated per unit volume (specific energy) at a point. The application of these mathematical expressions to the finite element discretized medium allow one to obtain a general spatial and directional expression for the characteristic length which guarantees the objectivity of the results with respect to the size of the finite element mesh. The numerical results presented show the reliability of the proposed expressions.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280214
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  • 113
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    Computational methods for non-linear problems, edited by C. Taylor, D. R. J. Owen and E. Hinton, Pineridge Press, Swansea, 1987 (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 476-476 
    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.1620280216
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  • 114
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    Superconvergent derivatives: A Taylor series analysis (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 489-509 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An analysis, based on the use of Taylor series expansions, is developed to determine accuracy estimates for derivatives in one and two dimensions computed by differentiation of a finite-element interpolant or approximation. The analysis clarifies some issues concerning special points at which the derivatives are believed to be exceptionally accurate with higher convergence rates (superconvergence). Moreover, it leads directly to a class of post-processing strategies for the derivatives and offers a more direct constructive approach to the subject.
    Additional Material: 7 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280302
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  • 115
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    Application of differential quadrature to static analysis of structural components (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 561-577 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical technique of differential quadrature for the solution of linear and non-linear partial differential equations, first introduced by Bellman and his associates, is applied to the equations governing the deflection and buckling behaviour of one- and two-dimensional structural components. Separate transformations are used for higher-order derivatives, as suggested by Mingle, thus extending the method to treat fourth-order equations and to include multiple, boundary conditions in the respective co-ordinate directions. Results are obtained for various boundary and loading conditions and are compared with existing exact and numerical solutions by other methods. The application of differential quadrature to this class of problems is seen to lead to accurate results with relatively small computational effort.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280306
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  • 116
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    A Schwarz alternating procedure using spline collocation methods (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 621-627 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A collocation method is described which obtains an approximate solution to Poisson's equation, δu = f, on an L shaped region. The L shaped region is viewed as the union of two overlapping rectangles. The Schwarz alternating procedure may be employed to reduce the problem to one in which collocation techniques are used on each rectangle. The convergence of the alternating scheme depends upon a discrete maximum principle for collocation methods. Several sample problems are presented to illustrate the order of convergence of this method and to compare it with several existing numerical methods for the L shaped region.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280310
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  • 117
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    Weighted residual solutions in the time domain (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 679-685 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Galerkin and subdomain forms of the weighted residual method are used to generate recursive equations in time for the numerical solution of a system of ordinary differential equations. The single-step methods that result from a linear interpolation equation match currently available methods whose stability and oscillation properties are known. A three-level scheme developed by combining two linear elements is shown to be unconditionally unstable. Two of the three schemes obtained using a quadratic interpolation equation and quadratic weighting functions are also shown to be unconditionally unstable. The third scheme is unconditionally stable, but the calculated values for a numerical solution of u̇ + u = 0, u(0) = 1 are not as accurate as the values obtained using the single-step central difference method.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280314
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  • 118
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    Computational mechanics '88, theory and applications, S. N. Atluri and G. Yagawa (eds.), Springer-Verlag, New York, 1988. No. of pages: 1260 approx (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 726-726 
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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.1620280318
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  • 119
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    Finite element formulation for non-steady-state large deformations with sliding or evolving contact boundary conditions (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 753-768 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method using a material description of the instantaneous configuration, valid for viscoplastic material with large deformations, is presented. In view of numerical tests which were carried out, this material formulation, associated with an implicit integration scheme which proved to be numerically accurate and reliable, is shown to be preferable.An algorithm is developed for resolution of sliding or evolving contact condition problems.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280403
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  • 120
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    A new method for modelling reinforcement and bond in finite element analyses of reinforced concrete (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 833-844 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method of representing the steei in finite element analyses of reinforced concrete structures is described in which the steel and the concrete are analysed separately. The forces between the steel and concrete are used In an interative method which brings the two solutions together. The method converges very rapidly and it is shown that the computational effort is principally dependent on the mesh chosen for the concrete. All the steel in a reinforced concrete structure may be easily included without affecting the layout of the concrete mesh. Results, which are given for three practical problems, include detailed steel and bond stresses for all bars.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280408
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  • 121
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    Crypto-DOF finite elements (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 943-954 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: New finite elements, called crypto-DOF elements, are introduced, utilizing degrees of freedom that satisfy the differential equation but do not appear explicitly in the discrete equations. The crypto-DOF elements can be advantageous in adaptive finite element techniques, and to approximate singular-type eigensolutions (e.g. in convective diffusion or stress concentration problems) without altering the original mesh or introducing new degrees of freedom. In this paper the crypto-DOF elements, the construction of crypto-DOF element families and selected numerical results are presented.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280415
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  • 122
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    Virtual crack extension methods for non-linear materials (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 929-942 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The virtual crack extension technique is a very efficient and accurate approach to fracture mechanics calculations in the numerical analysis of bodies containing cracks using the finite element method. A few variations of the technique have been described in the literature, and have been extensively used in linear elastic fracture mechanics, where good validation has frequently been available with accepted alternative solutions for standard tests. However, for non-linear materials extra complications arise in the technique, particularly in describing material response in a compatible manner. It is shown that, using few assumptions, a very competitive virtual crack extension technique based, on a direct minimization of potential energy is available for elastic non-linear elastic materials. Such materials can be closely approximated to elastic-plastic behaviour for monotonically increasing loads including mechanical, thermal and body force forms. The technique is described and demonstrated via examples to be in good agreement with alternative fracture parameter evaluations when evaluated in the same computer system, BERSAFE.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280414
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  • 123
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    Numerical methods in transient and coupled problems, R. W. Lewis, E. Hinton, P. Bettess and B. A. Schrefler, Wiley (Chichester) 1987. No. of pages: 350. ISBN: 0 471 91200X (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 979-979 
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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.1620280419
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  • 124
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    Masthead (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989) 
    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.1620280501
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  • 125
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    A numerical model for the thermo-elasto-plastic behaviour of a materialThis paper presents results of research performed for the FSA project, Jet Propulsion Laboratory, California Institute of Technology sponsored by the U.S. Department of Energy through an interagency agreement with NASA (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1103-1114 
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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 numerical model for the thermo-elasto-plastic behaviour of an isotropic material. The model is based on the assumption that the yielding of the material obeys von Mises distortion energy theory and the material exhibits isotropic strain hardening. This unique model can be used both for isothermal and non-isothermal cases. The original formulation for the non-isothermal three-dimensional case has been specialized for plane stress conditions and the equations for the computation of warping and thickness change are provided. The finite element implementation of this model is also outlined.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280508
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  • 126
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    Duality and symmetry in mixed integral methods of elastostaticsDedicated to the memory of Professor John Munro. (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1161-1179 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Mixed formulations for integral methods of elastostatic analysis of structures are presented. Both finite and boundary element approaches are considered. A governing system exhibiting symmetry is obtained in both cases by preserving duality in the descriptions of equilibrium and compatibility and reciprocity in the elastic constitutive relations. The theorems of virtual forces and displacements are interpreted as the energetic representation of static-kinematic duality. The quadratic programs associated with the governing system are identified as the theorems of minimum potential energy and co-energy. Mathematical programming theory is used to establish conditions for the existence and uniqueness of solutions.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280512
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  • 127
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    Numerical solution of linear two-point boundary problems via the fundamental-matrix method (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1205-1216 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method is presented for the-solution of linear systems of differential equations with initial-value or two-point boundary conditions. For y′(x) = A(x)y(x) + f(x) the domain of interest [a,b] is divided into an appropriate number L of subintervals. The coefficient matrix A(x) is replaced by its value Ak at a point xk within the Kth subinterval, thus replacing the original system by the L discretized systems yk(x) = Akyk(x) + fk(x), k = 1,2,…, L. The fundamental matrix solution Φk(x, xk) over each subinterval is found by computing the eigenvalues and eigenvectors of each Ak. By matching the solutions yk(x) at the L - 1 equispaced grid points defining the limits of the subintervals and the boundary conditions, the two-point problem is reduced to solving a system of linear algebraic equations for the matching constants characterizing the different yk(x). The values of y1(a) and yL(b) are used to calculate the missing boundary conditions. For initial-value problems this method is equivalent to a one-step method for generating approximate solutions. By means of a coordinate transformation, as in the multiple shooting method,1 the method becomes particularly suitable for stiff systems of linear ordinary differential equations. Five examples are discussed to illustrate the viability of the method.
    Additional Material: 8 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620280514
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    Coupled bending-torsional dynamic stiffness matrix for beam elements (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1283-1298 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Explicit expressions for the coupled bending-torsional dynamic stiffness matrix of a uniform beam element are derived in an exact sense by solving the governing differential equation of the beam. Implementation of the derived dynamic stiffness matrix in a space frame computer program is discussed with particular reference to an established algorithm to enable vibration analysis of coupled systems to be made. The application of the theory is demonstrated by an illustrative example wherein the results for a cantilever beam with a substantial amount of coupling between bending and torsion are highlighted. The correctness of the theory is confirmed to a high degree of accuracy by computed results and numerical checks.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280605
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    On a mixed finite element method for clamped anisotropic plate bending problems (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1351-1370 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper deals with a new mixed finite element method of solution of the bending problem of clamped anisotropic/orthotropic/isotropic plates with variable/constant thickness. This new mixed method gives simultaneous approximations to displacement u and bending and twisting moment tensor (ψij)1 ≤ i, j ≤ 2. Computer implementation procedures for this mixed method are given along with results of numerical experiments on a good number of interesting problems.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280609
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    A parallel mesh generation algorithm based on the vertex label assignment scheme (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1429-1448 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this article a new mesh generation algorithm is presented. The algorithm is based on a new approach called the vertex label assignment scheme to provide the information for the mesh generation so that parallel processing becomes possible. The algorithm generates 2D meshes of quadrilaterals on the basis of individual faces; conformity and smoothness of the resultant mesh are automatically assured. Local and selective mesh-refinements are also supported. A regular quadrilateral network which defines the geometry of the problem and an associated subdivision level assignment which specifies mesh density data on the network are the only input information.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280613
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    Book received (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1477-1478 
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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.1620280619
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    Computational fluid dynamics, by T. K. Bose, Wiley (New York), ISBN 0-470209534, 1988. No. of pages: 226. Price: £19.50 (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1476-1476 
    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.1620280617
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    Announcement (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. ii 
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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.1620280702
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  • 134
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    A comparison between isoparametric Lagrangian elements in 2D BEM (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1539-1555 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A comparison between a family of isoparametric C°-continucus elements in the context of two-dimensional elastostatics using the direct boundary element method is presented. The elements studied use Lagrangian shape functions of orders quadratic, cubic and quartic. The relative efficiencies of these elements from the viewpoint of accuracy of solution as well as cost effectiveness are examined through certain selected problems. It emerges from the present study that the quartic element is more reliable in accuracy than the lower members of the family without being necessarily more expensive.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280706
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    Assumed stress function finite element method: Two-dimensional elasticity (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1577-1598 
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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 finite element formulation, using assumed stress functions as the approximating functions, is developed for the linear elastic two-dimensional stress analysis. It features the use of blending function interpolants, enabling the convenient representation of traction boundary conditions, which in the past have posed difficulties. A family of rectangular elements is constructed. Numerical results assessing the behaviour of these elements are presented. An advantage of this approach is in the accurate prediction of stress distributions.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280709
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    Reusable intrinsic sample point (RISP) algorithm for the efficient numerical integration of three dimensional curved boundary elements (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1661-1676 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an algorithm that provides an order of magnitude gain in the computational performance of the numerical integration of the boundary integral equations for three dimensional analysis. Existing algorithms for numerical integration have strategically clustered integration sample points based on the relative proximity of the load points to the boundary element being integrated using element subdivision or element co-ordinate transformation. The emphasis in these techniques has been on minimizing the number of sample points required to obtain a given level of accuracy. The present algorithm, while closely following the spirit of these earlier approaches, employs a discrete number of sets of predetermined, customized, near-optimum, sample point quantities associated with the intrinsic boundary element. The ability created by this approach to reuse sample point geometric information of the actual element allows for the realization of substantive computational economy. This algorithm provides accurate and efficient numerical results both when load points are far from, and when they are on the boundary element being integrated. Numerical results are provided to demonstrate the substantial economy achieved through the use of the present algorithm.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280714
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    Editorial (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1731-1731 
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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.1620280802
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    An assumed strain finite element model for large deflection composite shellsModified version of a paper presented at the 29th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, Williamsburg, VA, U.S.A., April 18-20, 1988 (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1749-1768 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A nine node finite element model has been developed for analysis of geometrically non-linear laminated composite shells. The formulation is based on the degenerate solid shell concept and utilizes a set of assumed strain fields as well as assumed displacement Two different local orthogonal co-ordinate systems were used to maintain invariance of the element stiffness matrix. The formulation assumes strain and the determinant of the Jacobian matrix to be linear in the thickness direction. This allows analytical integration in the thickness direction regardless of ply layups. The formulation also allows the reference plane to be different from the shell midsurface. The results of numerical tests demonstrate the validity and the effectiveness of the present approach.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280804
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    Symmetry-preserving return mapping algorithms and incrementally extremal paths: A unification of concepts (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1839-1853 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this work we seek to characterize the conditions under which an elastic-plastic stress update algorithm preserves the symmetries inherent to the material response. From a numerical standpoint, the aim is to determine under what conditions a stress update algorithm produces symmetric consistent tangents when applied to materials obeying normality. For the ideally plastic solid we show that only the fully implicit or closest point return mapping algorithm is symmetry preserving. For hardening plasticity, symmetry cannot be preserved in general unless suitable restrictions are imposed on the constitutive equations. We show that these restrictions amount to the existence of a pseudo-internal energy function acting as a joint potential for both the direction of plastic flow and the hardening moduli. In view of the fact that holonomic methods based on incrementally extremal paths also result in update rules possessing a potential structure and, hence, in symmetric tangents, we address the question of whether any connections exist between the two approaches. We show that holonomic methods and the fully implicit algorithm may indeed be brought into correspondence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280810
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  • 140
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    Coupled use of reduced integration and non-conforming modes in quadratic Mindlin plate element (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1909-1928 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The applications of the reduced integration technique, and the addition of non-conforming modes and their coupling to Mindlin plate elements to improve their basic behaviour are reviewed and the establishment of a series of new plate elements by combined use of these schemes is presented in this paper. The element formulation is based upon the quadratic Mindlin plate concept. The results obtained by new elements converge to the exact solutions very rapidly as the mesh is refined and show reliable solutions even for severely distorted meshes. The new elements have the requisite numbers of zero eigenvalues associated with rigid body modes to avoid spurious zero energy modes. These elements are shown to solve the shear locking problem completely so that they are applicable to a wide range of plate problems, giving a high accuracy for both thick and thin plates.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280814
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    Combined effect of shear and large deformation on stress intensity factors (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1951-1964 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An attempt has been made to study the influence of large deformation on the stress intensity factor in a cracked plate subjected to bending including shear deformation. It is assumed that singular terms for stress resultants and strains in the case of large deformation have the same angular distribution and order of singularity as in the case of a linear problem. With this in view the small deformation singular element has been used at the crack tip region surrounded by large deformation plate bending elements. The finite element analysis, based on total Lagrangian formulation combined with the modified Newton-Raphson technique, has been used to get numerical results. Several examples connected with large deformation of cracked plates subjected to bending are studied. Using the above technique stress intensity factors for linear and non-linear cases have been compared.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280816
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  • 142
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    Free and forced vibrations of plates by boundary and interior elements (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1977-1994 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A direct boundary element method is developed for the dynamic analysis of thin elastic flexural plates of arbitrary planform and boundary conditions. The formulation employs the static fundamental solution of the problem and this creates not only boundary integrals but surface integrals as well owing to the presence of the inertia force. Thus the discretization consists of boundary as well as interior elements. Quadratic isoparametric elements and quadratic isoparametric or constant elements are employed for the boundary and interior discretization, respectively. Both free and forced vibrations are considered. The free vibration problem is reduced to a matrix eigenvalue problem with matrix coefficients independent of frequency. The forced vibration problem is solved with the aid of the Laplace transform with respect to time and this requires a numerical inversion of the transformed solution to obtain the plate dynamic response to arbitrary transient loading. The effect of external viscous or internal viscoelastic damping on the response is also studied. The proposed method is compared against the direct boundary element method in conjunction with the dynamic fundamental solution as well as the finite element method primarily by means of a number of numerical examples. These examples also serve to illustrate the use of the proposed method.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280902
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    Conference diary (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2219-2222 
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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.1620280916
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    Correction (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. ii 
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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.1620281002
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    Three-dimensional crack analysis using singular boundary elements (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2257-2273 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A multi-domain method of solving three-dimensional elastic crack problems in an infinite elastic body using the boundary element method is proposed. The \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt r $\end{document} displacement and \documentclass{article}\pagestyle{empty}\begin{document}$ 1/\sqrt r $\end{document} traction behaviours near a crack front are incorporated in special crack elements. The elimination of singularities arising from the \documentclass{article}\pagestyle{empty}\begin{document}$ 1/\sqrt r $\end{document} term combined with Kelvin's kernel for displacement in the integrals is discussed in detail. Stress intensity factors of modes I, II and III are obtained directly from crack-front nodal values, without any extrapolation as in some other methods. No differentiation of conventional boundary integral equations (with Kelvin's tensor kernels) is necessary in the current approach. This method is applicable to cracks of arbitrary shape. Infinite bodies are modelled precisely as such, not approximated as large finite bodies. Numerical solutions of stress intensity factors are given for several problems involving a penny-shaped crack.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620281005
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    On updating the structure of sparse matrix factors (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2339-2360 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Structural analysis often involves the solution of a sparse system of linear equations using matrix factorization. For structural reanalysis problems, the system of equations is progressively changing and matrix factorization is required at each iteration step. In this paper, we study the problem of updating the structure of sparse matrix factors using an ordered-tree model. The ordered-tree model provides the information needed to symbolically compute the non-zero structure of the matrix factor of a sparse matrix. Furthermore, for matrix factor modification problems, this tree model can be used to determine the numerically modified entries in the matrix factor. Examples for modification of a structure and h-adaptive refinement of a finite element model are given to illustrate the potential application of the procedures developed in this study.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620281010
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    A time domain boundary element method for poroelasticity (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2423-2449 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The development of a general boundary element method (BEM) for two- and three-dimensional quasistatic poroelasticity is discussed in detail. The new formulation, for the complete Biot consolidation theory, operates directly in the time domain and requires only boundary discretization. As a result, the dimensionality of the problem is reduced by one and the method becomes quite attractive for geotechnical analyses, particularly those which involve extensive or infinite domains.The presentation includes the definition of the two key ingredients for the BEM, namely, the fundamental solutions and a reciprocal theorem. Then, once the boundary integral equations are derived, the focus shifts to an overview of the general purpose numerical implementation. This implementation includes higher-order conforming elements, self-adaptive integration and multi-region capability. Finally, several detailed examples are presented to illustrate the accuracy and suitability of this boundary element approach for consolidation analysis.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620281014
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    On the problem of modelling for parameter identification in distributed structures (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2451-2463 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Structures are often characterized by parameters, such as mass and stiffness, that are spatially distributed. Parameter identification of distributed structures is subject to many of the difficulties involved in the modelling problem, and the choice of the model can greatly affect the results of the parameter identification process. Analogously to control spillover in the control of distributed-parameter systems, identification spillover is shown to exist as well and its effect is to degrade the parameter estimates. Moreover, as in modelling by the Rayleigh-Ritz method, it is shown that, for a Rayleigh-Ritz type identification algorithm, an inclusion principle exists in the identification of distributed-parameter systems as well, so that the identified natural frequencies approach the actual natural frequencies monotonically from above.
    Additional Material: 2 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620281015
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    Treatment of corners in BIE analysis of potential problems (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2569-2581 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: At corners or edges in the boundary of the domain of a potential problem the local normal gradient of potential is double-valued. When Dirichlet boundary conditions are specified there are thus two unknowns at a single nodal point, and the sets of equations resulting from the usual BIE discretization are rendered indeterminate. We discuss here earlier approaches to the resolving of this problem, and describe a further approach which appears to offer some advantages. Both normal gradients can be approximated directly from local potential boundary conditions, showing the problem indeed to be formally overdetermined. This ability is discarded, in favour of yielding a robust and well-conditioned relationship between the two gradients. This, in conjunction with the BIE analysis, permits solutions of considerable accuracy to be found, including the gradients at such corner nodes. Illustrative calculations are presented for rectilinear and curvilinear domains. These show that, even with as few elements as there are corners, and thus one and a half times as many unknowns as there are nodal points, good approximations to the gradients can be obtained. The need for progressively finer discretization as a corner is approached is thus much reduced.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620281107
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    Process modelling of metal forming and thermomechanical treatment, C. R. Boer, N. Rebelo, H. Rydstad and G. Schroder, Springer-Verlag, Berlin, 1986. No. of. pages: 410. ISBN 3-540-16401-4 (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2710-2711 
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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.1620281116
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    Computational structural mechanics and fluid dynamics CASV 30/1-2H, edited by A. K. Noor, ISBN 008 0371973, Pergamon Press, Oxford OX3 OBW, U.K., 1988. Price: £70.00 $125.00 (hardback). No. of pages: 465 (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2711-2711 
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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.1620281117
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    An efficient through-thickness integration scheme in an unlimited layer doubly curved isoparametric composite shell element (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2777-2793 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an efficient numerical integration scheme for evaluating the matrices (stiffness, mass, stress-stiffness and thermal load) for a doubly curved, multilayered, composite, quadrilateral shell finite element. The element formulation is based on three-dimensional continuum mechanics theory and it is applicable to the analysis of thin and moderately thick composite shells.The conventional formulation requires a 2 × 2 × 2 or 2 × 2 × 1 Gauss integration per layer for the calculation of element matrices. This method becomes uneconomical when a large number of layers is used owing to an excessive amount of computations. The present formulation is based on explicit separation of the thickness variable from the shell surface parallel variables. With the through-thickness variables separated, they are combined with the thickness dependent material properties and integrated separately. The element matrices are computed using the integrated material matrices and only a 2 × 2 spatial Gauss integration scheme. The response results using the present formulation are identical to those obtained using the conventional formulation. For a small number of layers, the present method requires slightly more CPU time. However, for a larger number of layers, numerical data are presented to demonstrate that the present formulation is an order-of-magnitude economical compared to the conventional scheme.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620281205
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    On the rotation of conductors of finite torsional stiffness by eccentric snow loading and control of rotation using counterweights (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2829-2838 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the prevention of snow loading on an overhead conductor caused by the mechanism of cylindrical-sleeve growth. The eccentric snow loading on the windward side of the conductor, having finite torsional stiffness, causes the conductor to rotate and a theoretical study of how this rotation can be controlled on attaching counterweights along the span of the conductor is presented. In the absence of counterweights, the non-linear rotation equation is solved analytically in terms of elliptic functions, simulating ice loading by a uniform torque density; for large torque density an asymptotic solution is obtained using matched asymptotic expansions. In the rotation equation the counterweights producing torque at discrete points are incorporated as delta functions which enable the discontinuity in the twisting couple at such locations to be accounted for by means of an integral moment balance. A simple algorithm is then presented for integrating the equation of rotation as an initial value problem which can deal with any distribution of counterweights along the span of the conductor. Illustrative numerical results are presented for zero, one, two, three and four counterweights per span; in the absence of counterweights analytical and numerical solutions are in exact agreement.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620281208
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    Fast algorithm for assembling blocks of global equations in FE programs (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2907-2922 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method for assembling blocks of global equations in FE programs is presented. The method has been implemented in SAP IV, the well-known FE program.The new assembling process consists of two phases. First, for each pair of blocks, the numbers of active elements are determined in ascending order. Then, from the sequential file containing element matrices, active records only are read and processed, the non-active ones being skipped.The most important features of the new method as compared to the method previously used are the following: (i) it saves up to 2/3 of the CPU-time for assembling, (ii) the amount of data on an auxiliary file is negligible, (iii) it does not require any additional high speed storage, (iv) it can be directly applied in any FE program with blocks using the constant bandwidth row storage scheme, (v) after some modifications it can be applied also in FE programs with blocks using the skyline column storage scheme.The full source code in FORTRAN IV is given in Appendix II.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620281213
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    Some recent developments in numerical modelling of fracture toughness in brittle matrix composites (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 233-255 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element analysis was used to study the fracture toughening of a ceramic by a stress induced dilatant transformation of second phase particles. The finite element method was based on a continuum theory which modelled the composite as subcritical material. Transient crack growth was simulated in the finite element mesh by a nodal release technique. The crack's remote tensile opening load was adjusted to maintain the near-tip energy release rate at the level necessary for crack advance. The transformation zone surrounding the crack developed as the crack propagated through the composite. Resistance curves were computed from the analysis; and the results show that during crack advance maximum toughness is achieved before a steady state is reached.The toughening effect of a crack-bridging ductile phase in a brittle material may be predicted if ligament deformation is characterized. A plastically deforming ligament constrained by surrounding elastic matrix material is modelled using finite elements and the relevant toughness enhancement information extracted. Comparison is made to model experiments as well as to toughness measured for technologically important materials. The results suggest that debonding along the interface between the ligament and the matrix may enhance the toughening effect of a ductile phase.
    Additional Material: 21 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620270203
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    Fatigue life estimation of graphite/epoxy laminates under consideration of delamination growth (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 323-341 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A closed form approach to the assessment of the fatigue life of graphite/epoxy laminates under cyclic tension-compression loading has been developed. The model is mechanistic and uses cyclic energy release rates for prediction of delamination growth and of critical delamination sizes which induce buckling and the final failure of the laminates. Tests performed with graphite/epoxy specimens of stacking order [0n, φm]s with severed central plies [φ], and of stacking order [02, +45, 02, -45, 0, 90]s with a central unloaded hole, indicate good correlation between estimated values and observed delamination growth, critical buckling strength of separated plies and load cycles to failure.
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620270208
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    Analysis of viscoelastic structural elements in the frequency domain (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 429-436 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a formulation in the frequency domain for the viscoelastic material behaviour of structural elements. This approach is equally valid for deterministic forces, but also in the case of probabilistic descriptions of those forces. The method takes advantage of readily available experimental data and shows how to introduce them in e.g. finite element formulations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270213
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    Conference diary (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 449-452 
    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.1620270215
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    A dual adaptive procedure for the automatic determination of iteration parameters for Chebyshev acceleration (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 483-499 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Chebyshev acceleration for a symmetrizable basic iterative method u(n+1) = Gu(n) + k; requires estimates of the extreme eigenvalues m(G) and M(G) of the iteration matrix G. Adaptive procedures are often used in order to obtain good estimates for m(G) and M(G). Some existing adaptive procedures are able to give an estimate of either m(G) or M(G) but not both on any given iteration. In this paper we present an adaptive procedure which can estimate both m(G) and M(G) at the same time and which has other useful properties. Numerical results are given which show the new procedure usually requires fewer iterations than previous procedures.
    Additional Material: 3 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620270305
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    Experience with the conjugate gradient method for stress analysis on a data parallel supercomputer (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 523-546 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The storage requirements and performance consequences of a few different data parallel implementations of the finite element method for domains discretized by three-dimensional brick elements are reviewed. Letting a processor represent a nodal point per unassembled finite element yields a concurrency that may be one to two orders of magnitude higher for common elements than if a processor represents an unassembled finite element. The former representation also allows for higher order elements with a limited amount of storage per processor. A totally parallel stiffness matrix generation algorithm is presented. The equilibrium equations are solved by a conjugate gradient method with diagonal scaling. The results from several simulations designed to show the dependence of the number of iterations to convergence upon the Poisson ratio, the finite element discretization and the element order are reported. The domain was discretized by three-dimensional Lagrange elements in all cases. The number of iterations to convergence increases with the Poisson ratio. Increasing the number of elements in one special dimension increases the number of iterations to convergence, linearly. Increasing the element order p in one spatial dimension increases the number of iterations to convergence as pα, where α is 1·4-1·5 for the model problems.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620270307
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    On an SSOR matrix relationship and its consequences (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 559-570 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A matrix relationship connecting the Jacobi and the Symmetric Successive Overrelaxation (SSOR) matrices associated with a k-cyclic consistently ordered matrix A is presented. Next the equivalence of the SSOR method and a certain monoparametric k-step one for the solution of the linear algebraic system Ax = b is established. The aforementioned equivalence can be exploited to derive regions of convergence, optimum parameters involved, etc. of the two iterative methods above. This is done by studying the simplest of the two methods that is the monoparametric k-step one. To show how the idea works the case k = 2 is very briefly discussed.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620270309
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    On a class of preconditioned iterative methods on parallel computers (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 637-654 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The standard implementations of iterative solvers for finite element and finite difference methods frequently use a diagonal (Jacobi) preconditioner, particularly for element-by-element schemes. However, for such methods the actual order of the condition number with respect to mesh size is not reduced by the preconditioner. In the present paper we describe an iterative method where, in addition, the condition number is reduced by an order of magnitude. Moreover, the scheme may also be implemented as an element-by-element method. The method uses a generalized SSOR preconditioner and a wave front or multi-frontal ordering of the mesh nodes. For a general irregular finite element mesh a striped irregular wave front ordering may be used. The performance of the method as well as various iterative acceleration techniques for a parallel computer are examined in the numerical studies.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620270314
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    A partially bonded beam element model for superconducting magnet pancakes (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 299-321 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The stiffness matrix of a beam made of composite superconductor elements is derived. The effects of friction between conductors through the insulation layers are taken into account. Furthermore, the effects of strand transposition of the wires, already studied by the authors, are included in the model.Some applications of the proposed approach to superconductor layouts proposed for the NET (Next European Torus) toroidal and poloidal field coils are shown. These indicate that the effects of slip are not negligible and should be taken into account in a more reliable structural analysis of the coil system. Parametric studies with varying width and heights of the insulation layer have been also carried out and the corresponding diagrams are shown here.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620270207
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    Buckling and postbuckling analyses of laminated anisotropic structures (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 383-401 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A review is given of recent advances in two aspects of the numerical simulation of the buckling and postbuckling responses of composite structures. The first aspect is exploiting non-traditional symmetries exhibited by composite structures; and strategies for reducing the size of the model and the cost of the buckling and postbuckling analyses in the presence of symmetry-breaking conditions (e.g. asymmetry of the material, geometry, and/or loading). The second aspect pertains to the prediction of onset of local delamination in the postbuckling range and accurate determination of transverse shear stresses in the structure. The accuracy and effectiveness of the strategies developed are demonstrated by means of a numerical example.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620270211
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    Preface (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 453-453 
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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.1620270302
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    Masthead (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989) 
    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.1620270301
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    Fully vectorizable block preconditionings with approximate inverses for non-symmetric systems of equations (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 501-522 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We used a conjugate gradient type method, with preconditioning, to solve the sparse linear systems arising from the discretization of PDEs. With such methods, the main obstacles for complete vectorization have been the preconditioning calculation and its application step within the iteration: for the matrices obtained using 5- or 9-point discretization operators, some well known existing preconditionings (like ILU) require a block-recursive procedure which prevents vectorization. Preconditioners based on nested incomplete factorization, which require the calculation of approximate inverses of tridiagonal matrices, allow complete vectorization of the application step. We present a formulation of such a preconditioning, using a Frobenius norm minimization to calculate the inverses, which also allows complete vectorization of the inverses' calculation, thus making the iterative solver completely vectorizable. Numerical experiments show that the method is robust over a range of symmetric and non-symmetric problems, and up to 4 times faster than other existing methods, such as ILU, depending on the computer and compiler being used. We also show the importance of diagonal scaling used in conjunction with other preconditionings and present some theoretical results concerning the approximate inverses of tridiagonal matrices, calculated using the Frobenius norm minimization.
    Additional Material: 19 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620270306
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    The vectorization of ITPACK 2C (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 571-588 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: ITPACK 2C14 is a package of seven iterative algorithms for solving sparse linear systems represented by Au = b, where A is symmetric and positive definite or mildly non-symmetric. This paper describes the techniques used to vectorize the iterative algorithms in the ITPACK 2C package for the Cyber 205 and Cray X-MP vector computers. The resulting package was named ITPACKV 2C.15 The basic iterative methods in ITPACK 2C are described in terms of matrix-vector multiplications and forward and backward solutions, and the techniques used in the vectorization of these and other computational kernels are given. Results of experiments using ITPACK 2C and ITPACKV 2C are given, including a comparison of megaflop rates and timings for two model problems.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620270310
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    An introduction to the NSPCG software package (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 589-608 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: NSPCG is the most recent research-oriented software package developed as part of the ITPACK Project at the Center for Numerical Analysis of The University of Texas at Austin. It is designed to solve large sparse systems of linear equations by a variety of different non-symmetric preconditioned conjugate gradient methods. Several different sparse data storage schemes are available for storing the coefficient matrix of the linear system. Matrices with a wide range of structures from highly structured to completely unstructured can be accommodated. To limit memory requirements, the accelerators in the package can be called directly with the matrix stored in a user-defined sparse data storage format (for example, from a particular application) by supplying some user-written routines for certain matrix-vector operations.The main entry point into the package is through a single subroutine call. The various methods are accessed by using a particular naming convention for the first two parameters that in turn selects a preconditioner, an accelerator and a data storage scheme. Some of the basic preconditioners that are available are Jacobi, Incomplete LU Decomposition and Symmetric Successive Overrelaxation as well as block preconditioners. The user can select from a large collection of accelerators such as Conjugate Gradient (CG), Chebyshev (SI, for semi-iterative), Generalized Minimal Residual (GMRES), Biconjugate Gradient Squared (BCGS) and many others. The package is modular so that almost any accelerator can be used with almost any preconditioner. One of the main purposes for the development of the package was to provide a common modular structure for research on iterative methods. The entire package is written in Fortran 77 with vectorization in mind for applications on supercomputers.
    Additional Material: 2 Tab.
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    A decomposition method for the integration of the elastic-plastic rate problem (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1-11 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical integration of the rate equation of an elastic-plastic material is considered. Special attention is focused on the discretization via the fully implicit backward Euler method in the small strain case with linear elasticity and the yield function a general quadratic in stress space. Here the calculation of the plastic (Lagrange) multiplier reduces to the computation of the smallest positive root of a polynomial in one variable. Explicit formulae are given for some special cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280103
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    The mode-decomposition, C° formulation of curved, two-dimensional structural elements (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 145-154 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on purely kinematical considerations the possibility of inextensional bending is introduced to isoparametric curved C° elements, which, otherwise, are plagued by severe membrane (and shear) locking. The analysis is restricted to arches and axisymmetric deformations of shells, i.e. kinematically two-dimensional problems. The results show exceptionally good accuracy. High reliability of the approach is guaranteed by absence of spurious kinematic modes on the element level, which complements its ability to bend inextensionally (in the case of arches).
    Additional Material: 5 Ill.
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    Phase increment analysis of damped Duffing oscillators (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 193-209 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A phase increment method is introduced to construct the response curves for the damped Duffing oscillator in primary, superharmonic, and subharmonic resonances. Non-linear parameters can be arbitrarily large. The algorithm is numerically stable. All resonance response curves are constructed in a unified manner. Closed loop curves are obtained in subharmonic resonances as opposed to open ended ones predicted by the perturbation method. Higher order resonances are constructed without difficulties. Loops are also observed in superharmonic resonances when non-linearity is not small.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280114
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    Conference diary (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 241-244 
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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.1620280118
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    The FDM in arbitrary curvilinear co-ordinates - formulation, numerical approach and applications (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 261-277 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The basic concept, formulation and numerical application of a fully automatic version of the finite difference method (FDM) on a two-dimensional manifold embedded in three-dimensional Euclidean space are presented. This version of the FDM was developed in order to enable automatic solution of problems formulated in arbitrary curvilinear co-ordinate systems in terms of covariant derivatives (e.g. shell equations).In the classical version of the FDM all operations in the curvilinear co-ordinates (the derivation of base vectors, curvature tensors and so on) have to be performed manually. The goal of the present work was to transfer this job to a computer, in order to minimize the user's effort during the numerical formulation of the physical problem. The relevant version of the fully automatized program FIDAMF, based on the FDM on arbitrary irregular grids,1,2 has been worked out. This code performs automatically all stages of the numerical analysis, starting from the mesh generation and approximation of the shape of the manifold, through computation of necessary objects on this manifold, to the solution of linear or non-linear problems formulated in terms of covariant derivatives.The method has been extended to the analysis of problems in which the co-ordinate system changes during the computation (e.g. the analysis of large deformations in the convectional description). This version of the curvilinear FDM was applied to the analysis of large deformations of hyperelastic membrane shells.The approach and the numerical routines, although used here with the FDM, can be combined with any other approximation method, in particular the finite element method.
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    URL: http://dx.doi.org/10.1002/nme.1620280203
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    Approximate direct-search minimax circuit optimization (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 359-368 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A direct-search optimization strategy, involving pattern-searches, pattern-moves and a simplex algorithm, has been applied to a number of frequency-domain circuit problems. We show that an approximate minimax result can be obtained with our simple approach, which includes using a modified minimax error function. In the examples attempted, the method comes quite close to the accuracy, if not the efficiency, of true minimax optimizers, and yields an accuracy as good as or better than a least-pth (p = 10) gradient optimizer. The method is broadly appropriate wherever it is difficult or inconvenient to calculate the gradients required for conventional minimax optimization.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280208
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    Implementation of curvilinear geometry into p-version HT plate elements (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 431-443 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The formulation of the recently presented hybrid-Trefftz (HT) p-version elements1 has thus far been restricted to straight-sided polygonal elements. The present paper removes this limitation. Two alternative formulations are studied. In the first one any curvilinear geometry is represented accurately but the rigid body modes are recovered only in the limit as the p-refinement level is increased. In contrast, the second formulation represents the rigid modes exactly while the actual curvilinear geometry is approached with increasing accuracy as the p-refinement level is increased. The practical efficiency of the two alternative approaches is studied and assessed on pertinent examples of thin plates in bending.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280212
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    Books received (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 477-478 
    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.1620280217
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    Conference diary (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 483-487 
    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.1620280220
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  • 179
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    A discrete shear triangular nine D.O.F. element for the analysis of thick to very thin plates (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 533-560 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with the formulation and the evaluation of a new three node, nine d.o.f. triangular plate bending element valid for the analysis of thick to thin plates. The formulation is based on a generalization of the discrete Kirchhoff technique to include the transverse shear effects. The element, called DST (Discrete Shear Triangle), has a proper rank and is free of shear locking. It coincides with the DKT (Discrete Kirchhoff Triangle) element if the transverse shear effects are not significant. However, an incompatibility of the rotation of the normal appears due to shear effects. A detailed numerical evaluation of the characteristics and of the behaviour of the element has been performed including patch tests for thin and thick plates, convergence tests for clamped and simply supported plates under uniform loading and evaluation of stress resultants. The overall performance of the DST element is found to be very satisfactory.
    Additional Material: 19 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280305
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  • 180
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    Efficient optimization of integrated aerodynamic-structural design (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 593-607 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The introduction of composite materials is having a profound effect on the design process. Because these materials permit the designer to tailor material properties to improve structural, aerodynamic and acoustic performance, they require a more integrated multidisciplinary design process. Because of the complexity of the design process numerical optimization methods are required.The present paper is focused on a major difficulty associated with the multidisciplinary design optimization process - its enormous computational cost. We consider two approaches for reducing this computational burden: (i)development of efficient methods for cross-sensitivity calculation using perturbation methods; and (ii) the use of approximate numerical optimization procedures. Our efforts are concentrated upon combined aerodynamic-structural optimization. Results are presented for the integrated design of a sailplane wing. The impact of our computational procedures on the computational costs of integrated designs is discussed.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280308
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  • 181
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    Structural modifications simulated by virtual distortions (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 645-666 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical strategy for the simulation of structural modifications by virtual distortions is proposed. Two cases of structural modification are considered: the first concerns modifications of material distribution, and the second modifications of local constitutive relations (e.g. unilateral constraints for stresses or deformations). A formaulation of the fundamental equations of the simulation method is presented. These equations are applicable to the general structural modification problem of a truss-like structure. Then numerical algorithms which refer to particular applications, such as progressive collapse analysis or the analysis of structures with gaps, are discussed.The versatility of the method is illustrated with a number of examples, and the computational advantages of structural modification by the virtual distortion method are discussed.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280312
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  • 182
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    Computational plasticity, Edited by D. R. J. Owen, E. Hinton and E. Oñate, Pineridge Press, Swansea, U.K., 1987. No. of pages: 1865. ISBN 0-906674-61-1 (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 725-726 
    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.1620280317
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  • 183
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    First-order design sensitivities for transient conduction problems by an adjoint method (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 733-752 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An adjoint approach is presented for the design sensitivity analysis of transient conduction problems. Variations of a general design functional are expressed in explicit form with respect to all design quantities, i.e. material properties, shape, applied thermal loads including convection, and initial conditions. The methodology incorporates the mutual energy between the real and adjoint thermal problems and a geometric mapping to describe shape variations. Finite element implementation of the method is discussed and an example is provided. Some potential difficulties that might be encountered when using the adjoint method with the finite element method are addressed. These involve the application of impulse loadings and Dirac temperature fields in the adjoint loadings.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280402
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  • 184
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    Conference diary (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1229-1232 
    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.1620280516
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  • 185
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    A numerical integration approach by weight factors and its accuracy (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1217-1228 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new parabolic approach for numerical integration using weight coefficients is proposed.Several basic approaches for integration have been analysed: linear (trapezoidal), parabolic (new form), Simpson's, Newton-Cotes and Gaussian. The weight coefficients are transformed into the same form for all methods. Simpson's and Newton's formulas (for n = 3) are obtained as special cases of the general parabolic formula. A simple procedure to estimate the accuracy of the integral for final intervals is given.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280515
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  • 186
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    A mixed finite element model for the elastic contact problem (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1249-1264 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The static elastic contact problem is approached using Lagrange multipliers, leading to a mixed finite element problem. A non-linear friction law is introduced explicitly and the non-local character of the friction phenomena is implicitly assumed. In order to avoid stress oscillations near singular points, a perturbed Lagrangian functional is considered. The algorithms herein proposed do not impose nodal dependencies over the contact surfaces, allowing for the independent discretization of both bodies. The method is able to model simultaneous contact over different regions of any geometrical shape. Computer code, examples and results presented here are restricted to axisymmetrical and bidimensional cases.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280603
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  • 187
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    On linear constraints for Newton-Raphson corrections and critical point searches in structural F.E. problems (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1317-1334 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper discusses the introduction of constraining equations in the tangential stiffness relation used to calculate the responses to different load cases in solution algorithms for non-linear mechanical Finite Element (F.E.) problems. An alternative to the normal two-phase solution method is discussed. This method is used to represent different iteration constraints, and in conjunction with the search for critical solution points. Numerical tests are presented, evaluating the efficiency of different iteration constraints for a model problem. Practically useful criteria for critical points are discussed. The basic methods for search of such points and some numerical aspects are discussed and evaluated for three different problems.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280607
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  • 188
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    Boundary integration and interpolation procedures for plate bending (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1389-1408 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the direct boundary element method (DBEM) for thin plate bending analysis, the integration of the kernel-shape-function products can lead to complications due to a combination of factors. The first is the existence of a singularity at the source point, leading to the singular kernel, which increases in strength as the integral equation is differentiated once for rotation, again for moment and yet again for shear. The second factor arises from the use of piecewise interpolation polynomials.In the first part of the DBEM analysis where the unspecified boundary values are computed, the numerical procedures are fairly straightforward. It is found in this paper that special care must be taken in calculating internal actions at domain points. The problems which can be encountered are demonstrated, and a modified boundary interpolation procedure is described. Examples are given which show the superiority of the recommended approach.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280611
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    Letter to the editor (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1485-1485 
    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.1620280621
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  • 190
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    More on optimal stress points - reduced integration, element distortions and error estimation (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1487-1504 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The presented work addresses the relationships between optimal sampling points, reduced integration and geometric distortion with the objective of estimating errors in terms of those considerations. Isoparametric quadratic plane and solid elements are used as a vehicle for the study. Geometric distortion measures and evaluation conditions, based on convergence requirements, are first defined in terms of the polynomial orders of the geometry and applied strain. Using these, the concept of optimal stress sampling, already established for undistorted elements, is extended to distorted geometry and shown to be effective over a range of geometries and strains. Errors in the strain-displacement relationship and numerical integration of the strains are used to estimate the total response error and to rationalize the connection between optimal stress points and reduced integration. Enhanced convergence, by extension to the representation of linear strains in elements with quadratic geometry, is identified as the main advantage of reduced integration. The applicability of the proposed, and other, distortion parameters to vetting of element geometry and error prediction is discussed.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280703
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  • 191
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    An operator-splitting algorithm for two-dimensional convection-dispersion-reaction problems (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1023-1040 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An operator-splitting algorithm for the two-dimensional convection-dispersion-reaction equation is developed. The flow domain is discretized into triangular elements which are fixed in time. The governing equation is split into three successive initial value problems: a pure convection problem, a pure dispersion problem and a pure reaction problem. For the pure convection problem, solutions are found by the method of characteristics. The solution algorithm involves tracing the characteristic lines backwards in time from a vertex of an element to an interior point. A cubic polynomial is used to interpolate the concentration and its derivatives on an element. For the pure dispersion problem, an explicit finite element algorithm is employed. Analytical solutions are obtained for the pure reaction problem. The treatment of the boundary conditions is also discussed. Several numerical examples are presented. Numerical results agree well with analytical solutions. Because cubic polynomials are used in the interpolation, very little numerical damping and oscillation are introduced, even for the pure convection problem.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280504
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  • 192
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    Numerical differentiation for use in integrating unified constitutive equations (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1115-1129 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The NONSS method for numerically integrating time-dependent constitutive equations requires evaluation of the partial derivatives of the constitutive equations. A numerical method for evaluating these partial derivatives has been developed, thus avoiding the cumbersome task of analytically re-deriving the partial derivatives when improvements to the constitutive model are evaluated. This method is based upon the adaptive finite-difference algorithm published by Stepleman and Winarsky. Modifications of their algorithm are described that allow its efficient use within an extended version of NONSS, called NONSS-ND.Using the MATMOD constitutive equations, the capabilities of NONSS-ND are demonstrated by comparing the results of a wide variety of deformation simulations with those of NONSS, for which the derivatives are computed from analytical solutions. The numerical differentiation within NONSS-ND is shown to be sufficiently accurate for use in integrating time-dependent constitutive equations, but results in a 30-100 per cent increase in computation time. Multi-element structural calculations are therefore found to be uneconomical, but NONSS-ND is well suited for testing alternative constitutive models owing to its accuracy and its general applicability to highly non-linear systems of differential equations.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280509
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  • 193
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    The application of symbolic computing to the hierarchical finite element method (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1181-1204 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: One difficulty associated with the hierarchical finite element method is that of accurately determining the integrals necessary to establish the stiffness and mass matrices of arbitrarily high order elements. This paper describes how such integrals can be calculated exactly using symbolic computing.Results are presented which permit the construction of high order hierarchical finite elements applicable to a variety of problems involving two-dimensional elasticity, and plate and shell bending. Three-dimensional solid or brick elements are not considered.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280513
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  • 194
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    Masthead (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989) 
    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.1620280601
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  • 195
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    A dynamic programming method for analysis of bridges under multiple moving loads (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1265-1282 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A dynamic programming (DP) method is presented for analysis of statically determinate and indeterminate bridges subjected to moving loads such as those specified by the American Association of State Highway and Transportation Officials (AASHTO) specifications. These loads consist of uniform lane loading, two-axle truck loading and two-axle truck plus one-axle semitrailer loading. The solution of the DP problem is based on the use of influence line diagrams and extremum functions. Recurrence formulae have been developed for various types of AASHTO live loads. The procedure presented in this article is quite general and can be applied to any type of structures with linear behaviour and any type of moving loads. Six examples are presented: a simply-supported beam, a simply-supported Pratt truss, an arch bridge, a continuous Pratt truss, a continuous frame and a cable-stayed bridge.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280604
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  • 196
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    Adaptive h-, p- and hp-versions for boundary integral element methods (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1335-1349 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Recently very promising results in a so-called hp-version of the finite element method have been obtained. The basic idea is a balanced combination of mesh refinement and increase of the polynomial degree of the shape functions. This idea is applied to a boundary collocation method in this paper. The new method is compared with adaptive h- and p-versions and it is shown in numerical examples that even in the presence of singularities in the exact solution exponential convergence is obtained.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280608
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  • 197
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    Adaptive 2D finite element simulation of metal forming processes (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1409-1428 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The development and integration of available current methods and the development of new methods for an adaptive finite element analysis of metal forming processes are presented. The analysis includes large-strain, elastic-plastic, and thermal effects. Many numerical methods such as mesh generation, simulation of the contact between the workpiece and tool and die, and optimization of the finite element mesh are integrated and incorporated. In addition, an algorithm is developed which can detect certain severely distorted elements where the area of integration is approaching zero. The advantage of correcting these regions of locally distorted elements is demonstrated. These numerical methods are implemented in a finite element program developed for simulating metal forming processes, with the emphasis on automating the analysis. Examples include an axisymmetric stress simulation of a coldheading process, a plane strain simulation of an extrusion process and a plane strain simulation of orthogonal metal cutting, all with noticeable thermal effects. The orthogonal cutting forces and feed forces calculated are compared with two sets of experimental data, with good agreement.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280612
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  • 198
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    Engineering quality software, David J. Smith and Kenneth B. Wood, Elsevier, Amsterdam, No. of pages: 209. ISBN 1-85166-074-7 (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1476-1477 
    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.1620280618
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    Conference diary (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1479-1483 
    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.1620280620
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  • 200
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    Some acceleration methods for iterative computer of derivatives of eigenvalues and eigenvectors (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1505-1519 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The performance of an iterative method for computing partial derivatives of eigenvalues and eigenvectors of parameter dependent matrices may be improved dramatically by various extrapolation methods proposed here. With exact computation, all these extrapolation methods yield the exact solution with a finite number of iterations. Two of these methods, which have not been used before for this problem, are compared with the ∊-algorithms. Numerical examples are given. The methods suggested may be used to obtain either highly accurate estimates or cheap estimates of modest accuracy.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280704
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