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  • 1985-1989  (613)
  • 1970-1974
  • 1920-1924
  • 1987  (613)
  • Engineering General  (448)
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  • 1985-1989  (613)
  • 1970-1974
  • 1920-1924
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  • 101
    Electronic Resource
    Electronic Resource
    On the extrusion of visco-elastic fluids subject to viscous heating (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 263-270 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The die-swell occurring during the extrusion of a visco-elastic fluid has been extensively examined in recent years, both experimentally and numerically. These investigations have been mainly confined to isothermal flows. If the material is initially relatively cool, however, viscous heating may lead to proportionally large changes in temperature and material properties, with significant effects on die-swell. An iterative computational model is presented which describes the flow of Maxwell and Oldroyed fluids subject to the effect of temperature gradients induced by viscous heating and thermal boundary conditions. Predictions are presented for extrusion from both slit and axisymmetric dies.
    Additional Material: 22 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240118
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  • 102
    Electronic Resource
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    Preface (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. i 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240121
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  • 103
    Electronic Resource
    Electronic Resource
    A block equation solver for large unsymmetric linear equation systems with dense coefficient matrices (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 289-300 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The presented solver uses the Crout L-U decomposition method. Disk memory space requirements are reduced to an absolute minimum and disk input-output is spectacularly limited. Very extensive pivoting improves numerical accuracy and stability. Experimental test runs prove the overall efficiency of the solver.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240203
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  • 104
    Electronic Resource
    Electronic Resource
    A simple error estimator and adaptive procedure for practical engineerng analysis (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 337-357 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes.The estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors. It can thus be combined with a full adaptive process of refinement or, more simply, provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials.When combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable.Estimates other than the energy norm have successfully been applied giving, for instance, a predetermined accuracy of stresses.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240206
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  • 105
    Electronic Resource
    Electronic Resource
    Treatment of material discontinuities in finite element computations (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 393-417 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider finite element analysis of problems with discontinuous material coefficients. For applications in which the material interface crosses an element, we develop special elements with an embedded flux constraint at the interface. This new procedure is compared with the standard finite element method with interface coincident with the element boundary and with an existing method proposed by Steven.1 Supporting numerical studies are conducted and rates of convergence for the solution and interface flux are examined. Some local superconvergence behaviour is observed.
    Additional Material: 23 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240209
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  • 106
    Electronic Resource
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    Conference diary (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 471-473 
    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.1620240213
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  • 107
    Electronic Resource
    Electronic Resource
    Masthead (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987) 
    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.1620240301
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  • 108
    Electronic Resource
    Electronic Resource
    Three-dimensional transient thermo-elastic analyses by the BIE method (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 25-45 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The proposed method is the direct boundary integral equation (BIE) method applied to three-dimensional transient heat transfer analyses and to corresponding elastostatic analyses under thermal loading. The mechanical and thermal problems are decoupled. For those not familiar with the BIE method, a short survey of the basic principles is given to help them understand the mathematical treatment, which is performed in the frame of distribution theory. The tempered elementary solution of the transient heat transfer problem contains time and space variables. The numerical treatment of the thermal equation is performed analytically with respect to time and numerically with respect to space in the same way as for steady state equations. Great care is paid to space integration in order to compute the values of the kernels precisely enough on the surface and inside the volume. The computational treatments of both problems are realized in such a way as to minimize computing time. Differences between transient and steady state analyses, on the one hand, and between elastostatic analyses with and without thermal loading, on the other, are emphasized. Finally, an analytical example shows the good behaviour of the proposed method to solve singular thermal problems and an industrial example shows the accuracy of the results obtained by using the BIE method to solve three-dimensional thermo-elastic problems.
    Additional Material: 23 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240103
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  • 109
    Electronic Resource
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    Thermal stress analysis of sintering using a moving grid (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 47-57 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A moving finite element method that calculates the transient temperature distribution, the density distribution and the stress distribution during the sintering cycle has been developed. Coupled two-dimensional axisymmetric energy, continuity and stress equilibrium equations along with a constraint, specifying the direction of the initial material velocity, are solved in a Lagrangian co-ordinate system. The nodes move at the same speed as the material and therefore the convective terms in the differential equations drop out. At every time step, the energy equation is solved, and the computed temperatures are then used to find the densification rate. In two-dimensional problems, the continuity equation is not sufficient to calculate the two components of material velocity. Here, it is assumed that the diffusion caused by the density gradient is the driving force. This implies that the velocity vector of the material is perpendicular to the lines of constant density. Therefore, the combination of the diffusion and continuity equations will generate the initial sintering strains. The elastic stress equilibrium equations are then solved using the thermal and initial sintering strains as the driving forces. As a result, the final shape of the material and the stresses are determined.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240104
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  • 110
    Electronic Resource
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    Numerical studies of buoyancy-driven turbulent flow in a rectangular cavity (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 89-99 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper some numerical predictions are presented for the buoyancy-driven turbulent flow and heat transfer in a large cavity using both a prescribed eddy viscosity model and a k-∊ model. The results from these models are in good agreement, although the calculations with the prescribed eddy viscosity model are considerably cheaper. The results also show the correct qualitative behaviour, but there are some differences between the predictions and the available experimental data. Possible reasons for these are discussed.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240107
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  • 111
    Electronic Resource
    Electronic Resource
    Least-squares schemes for time integration of thermal problems (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 159-175 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper proposes a generalized least-squares time finite element procedure for analysis of transient field problems. It leads to a very general four parameter and two time level family of schemes. The free parameters are optimized in terms of accuracy, stability and oscillatory behaviour of the computational algorithm. In the case of linear problems an unconditionally stable scheme of fourth-order accuracy is obtained. Special choices of the free parameters also give a number of well-known time-integration schemes, such as the Zienkiewicz-Lewis third-order algorithm, the Goodrich scheme and standard schemes such as the Crank-Nicolson and backward fully implicit schemes. The main disadvantage of the higher order algorithm is a large bandwidth of the system matrix owing to the matrix terms of the form KTK. This drawback is reduced for special choices of the parameters by forming a product formula. Somewhat more computation is required than for popular schemes such as the generalized midpoint rule, depending on the prescribed variables. Numerical comparisons are made between the proposed higher order schemes and standard schemes.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240112
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  • 112
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    Mixing and solidification of a turbulent liquid jet in a co-flowing stream (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 231-249 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mathematical model has been developed to quantify the effects of process conditions during turbulent solidification and mixing of a liquid metal jet in a confined co-flowing molten metal stream.The modelling has been split into three parts. First, a single phase model with no latent heat effects to consider the solidification potential. Secondly, a two phase model where the second phase is comprised of solid particles which solidify during mixing of the two streams. Thirdly, a two phase model where the second phase consists of the inner jet, which is assumed to break up into droplets of given size, and solid particles are allowed to form by solidification within the droplets.The results show that the thermal history (solidification path) of the solid phase formed is affected by latent heat and particle size, which implies that solidification, nucleation and jet fragmentation events should be included dynamically to ensure realistic predictions.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240116
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  • 113
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    Conference diary (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 285-287 
    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.1620240120
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  • 114
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    Masthead (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987) 
    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.1620240201
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  • 115
    Electronic Resource
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    An enthalpy method for convection/diffusion phase change (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 271-284 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An enthalpy formulation for convection/diffusion phase change is developed. The essential feature of this formulation is that latent heat effects are isolated in a source term. This formulation is applicable to a general convection/diffusion phase change, i.e. it is valid in the cases of evolution of latent heat either at an isothermal temperature or over a temperature range. Before implementation of the enthalpy formulation, a technique is required to ensure that velocities predicted to be in a solid region actually take the value zero. Three alternative schemes for achieving this are presented.The enthalpy formulation and velocity correction schemes are independent of the numerical technique. As an example of how the method can be implemented a control volume numerical discretization is chosen. This implementation is applied to two test problems: a solidification phase change in a cavity under conduction and the same phase change under conduction and natural convection. The natural convection problem is used to compare the performances of the various velocity correction schemes. The results of the problems are in good agreement with available analytical solutions and previous numerical solutions.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240119
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  • 116
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    The front-tracking scheme for the one-dimensional freezing problem (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 859-869 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The one-dimensional freezing problem can be solved numerically for the temperature distribution accompanied by explicit reference to the position of the freezing front at each time interval. A new front-tracking scheme provides accurate determination of the phase front, which is an essential requirement for the temperature distribution in the different phases of such problems. The front is made to coincide with a grid-node throughout the analysis. The scheme uses a combination of the finite difference and the finite element methods for obtaining the solution of the freezing problems.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240503
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  • 117
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    Model-size reduction for the analysis of symmetric structures with asymmetric boundary conditions (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 913-926 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple computational procedure is presented for reducing the size of the analysis model for a symmetric structure with asymmetric boundary conditions to that of the corresponding structure with symmetric boundary conditions. The procedure is based on approximating the asymmetric response of the structure by a linear combination of symmetric and antisymmetric global approximation vectors (or modes). The key elements of the procedure are (a) restructuring the governing finite element equations to delineate the contributions to the symmetric and antisymmetric components of the asymmetric response, (b) successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite element method is first used to generate a few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh-Ritz technique.A tracing parameter is introduced which identifies all the contributions to the antisymmetric response. The global approximation vectors are selected to be the solution corresponding to a zero value of the tracing parameter and the various-order derivatives of the solution with respect to this parameter, evaluated at zero value of the parameter. The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding structure with symmetric boundary conditions.The effectiveness of the computational procedure is demonstrated by means of numerical examples of linear static problems of shells, and its potential for solving non-linear problems is discussed.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240506
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  • 118
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    A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 959-973 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Almost all general purpose boundary element computer packages include a curved geometry modelling capability. Thus, numerical quadrature schemes play an important role in the efficiency of programming the technique. The present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two-dimensional, axisymmetric and three-dimensional applications. Emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of Gaussian quadrature scheme's within the near-singularity range. The procedure can easily be implemented into existing BE codes and presents the important feature of being self-adaptive, i.e. it produces a variable lumping of the Gauss stations toward the singularity, depending on the minimum distance from the source point to the element. The self-adaptiveness of the scheme also makes it inactive when not useful (large source distances) which makes it very safe for general usage.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240509
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  • 119
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    Some improvements of the finite element solution for one-dimensional problems (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 993-1014 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: New algorithms which improve the finite element solution on a fixed mesh of the domain are developed. For this, objective functions which depend on a positive parameter to be determined are proposed. These functions lead to criteria which combine in several ways the residual of the solution, the approximation in the Euclidean norm of the value of the solution at the nodes, and the approximations in the energy and Hk norms. Some aspects of optimality are studied and, finally, numerical results are given.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240511
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  • 120
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    A hybrid BEM model (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1015-1025 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The hybrid stress method is very successful for stress concentration problems.1-7 Especially for problems of fracture mechanics, procedures can be found that work efficiently for two- and three-dimensional problems. The rate of convergence with this method, evidently, is higher than that with conventional FE models. The BEM procedure, too, works more efficiently, but shows some essential disadvantages against the FEM, such as that for the direct method no symmetric positive definite matrix can be found and that there occur numerical problems at corners.8,9 This happens also when BEM and FEM are even coupled commonly.10-12. In the following, a hybrid BEM model will be described which combines the advantages of both the FEM and the BEM. It will be shown in this paper that BEM is very successful in formulating finite element functions for the hybrid assumed stress method.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240512
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  • 121
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    Conference diary (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1027-1029 
    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.1620240513
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  • 122
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    Corrections (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1029-1029 
    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.1620240514
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  • 123
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    Announcements (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1030-1030 
    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.1620240515
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  • 124
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    Masthead (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987) 
    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.1620240601
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  • 125
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    A new element used in the non-orthogonal boundary plate bending theory - an arbitrarily quadrilateral element (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1031-1042 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper develops an arbitrarily quadrilateral element to analyse bending problems of plates with non-orthogonal boundaries. A second-order Jacobian matrix for the co-ordinate transformation and an explicit form of its inverse matrix are described in detail. A shape function matrix [N] for the plate element of arbitrarily quadrilateral configuration, an equivalent load vector {R}, a strain matrix [B] and element stiffness matrix are given. Finally, four illustrated examples are given and the results of computation are compared with those from other analytical methods.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240602
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  • 126
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    Robust, geometrically based, automatic two-dimensional mesh generation (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1043-1078 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A technical description of the algorithms employed in the modified quadtree mesh generator is given. Although the basis of the mesh generator is the same as the original version developed by Yerry and Shephard,1,2 the actual algorithms on which it is built have been entirely changed for the purpose of ensuring the robustness of the technique. As demonstrated in the paper the algorithmic changes made do ensure the robustness of the approach, but introduce additional algorithmic difficulties, the solutions of which are also presented. In addition to examples showing the capability of the mesh generator, the linear computational growth rate of the mesh generator is demonstrated.
    Additional Material: 37 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240603
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  • 127
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    Sparse quasi-Newton LDU updates (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1093-1100 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Numerical solution of a given non-linear algebraic system of equations by a quasi-Newton type method requires updating the approximation to the Jacobian at each step. Two methods for large sparse systems are described. The approximation for the Jacobian is factored into an LDU form at the first step, then all the subsequent updates are made to L, D and U. Computational evidence is given exhibiting the relative efficiency of these methods over those currently available in the published literature.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240605
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    A numerical method for dynamic analysis of a general cross-section rod under combined loads (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1079-1091 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with a method for obtaining stresses in a rod of arbitrary cross-section subjected to combined loads of bending, shearing and torsion which are the complicated functions of time. In the first step, the analysis derives the bending moment, shearing force and torsional moment by use of a combination method of the Laplace transformation and Fourier series expansion. The transient stresses are obtained based on the two-dimensional theory of elasticity, but in which the Fourier expansion collocation procedure is applied to deal with the complex boundary shape of the cross-section. To affirm the validity of this analysis, experimental tests are also carried out for an oval rod subjected to the three combined transient loads.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240604
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    Norm methods and partial weighting in multicriterion optimization of structures (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1101-1121 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Methods for generating Pareto optimal solutions to a multicriterion optimization problem are considered. The norm methods based on the scalarization of the original multicriterion problem by using the lp-norm are discussed in a unified form and a parametrization suitable for different interactive design systems is suggested. In addition, an alternative approach which, instead of scalarization, reduces the dimension of the multicriterion problem is proposed. This is called the partial weighting method and it can beinterpreted as a generalization of the traditional scalarization technique where the weighted sum of the criteria is used as the objective function. The first of these two approaches (norm method) is very flexible from a designer's point of view and it can be applied also in non-convex cases to the determination of the Pareto optimal set whereas the latter (partial weighting method) is especially suitable for problems where the number of criteria is large. Throughout the article several illustrative truss examples are presented to augment the scanty collection of multicriterion problems treated in the literature of optimum structural design.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240606
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    BEM simulation of cathodic protection systems employed in infinite electrolytes (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 605-620 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes the proper external potential formulation of a cathodic protection system employed for corrosion prevention of structures in infinite electrolytes. The boundary condition associated with the mathematical formulation is not of the standard type encountered in hydrodynamic, electrostatic or heat transfer applications. The developed mathematical model is discretized by the boundary element technique, which is then solved iteratively by the Newton-Raphson method.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240310
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    Transient analysis of three-dimensional wave propagation using the boundary element method (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 621-634 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the past the time domain solution of the wave equation has been limited to simplified problems. This was due to the limitations of analytical methods and the capacity of computers to manipulate and store ‘large’ blocks of spatial information. With the advent of ‘super computers’ the ability to solve such problems has significantly increased. This paper outlines a method for transient analysis of wave propagation in arbitrary domains using a boundary element method. The technique presented will allow the definition of a domain, the input of impedance conditions on the domain's surface, the specification of inputs on the surface, and the specification of initial conditions within the domain. It will produce a complete solution of the wave equation inside the domain. The techniques are demonstrated using a program with a boundary element formulation of Kirchhoff's equation. The elements used are triangular and compatible.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240311
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    A new finite element concurrent computer program architecture (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1771-1792 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new computer program architecture for the solution of finite elemet systems using concurrent processing is presented. The basic approach involves the automatic splitting of an arbitrary spatial domain. Processors are dynamically re-assigned during the several phases of an analysis. Direct and iterative solution strategies are considered. Computational algorithms for finite element dynamic analysis of large-scale structural problems that exploit concurrent features of MIMD computers are implemented in modules around the basic architecture. Also, problems with localized non-linearities are treated. A first implementation on a 32-processor hypercube achieves efficiency rates of up to 90 per cent.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240912
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    A new node renumbering algorithm for bandwidth reduction (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1823-1824 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240915
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    An adaptive boundary element method (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1187-1202 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper explores the concept of moving singularities in the boundary element analysis. The singularities are placed on an auxiliary boundary which is located outside the domain of the problem and are allowed to move as part of the solution process. This results in a highly adaptive but non-linear method. Examples involving the two- and three-dimensional Laplace's equations are solved. Excellent agreement with exact solutions is obtained using a minimal number of singularities. Also, the trajectories of the singularity motion are plotted. The behaviour seen here is that, as the solution approaches convergence, the singularities exhibit a general trend of moving away from the domain of the problem.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240610
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    Computational methods for the solution of engineering problems, 3rd revised edn, C. A. Brebbia and A. J. Ferrante, Pentech Press, London. No. of pages: 370. Price: £15.95 (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1225-1225 
    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.1620240612
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    Navier-Stokes equations (theory and numerical analysis), 3rd edn, Roger Temam, North-Holland, 1984 (including an appendix by F. Thomasset) (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1226-1226 
    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.1620240613
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    Triangular finite element for analysis of thick laminated plates (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1203-1224 
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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 triangular C0 element, based on an assumed quadratic displacement potential energy approach, is presented for the analysis of arbitrarily laminated thick plates. The element formulation assumes transverse inextensibility and layerwise constant shear-angle. Convergence of transverse displacement, moments and stresses, the effects of two different Gauss quadrature schemes and comparison of the present solutions with the available analytical/finite-element results also form a part of the investigation. Furthermore, numerical results indicate close agreement between the LCST (layerwise constant shear-angle theory) and the three-dimensional elasticity theory with the length (or width) to thickness ratio as low as 4. Detailed comparison of the LCST-based finite-element solutions with those based on the CST (constant shear-angle theory) and the CLT (classical lamination theory) clearly demonstrates the superiority of the former over the latter two, especially in the prediction of the distribution of the in-plane displacements and stresses through the laminate thickness. This paper also introduces a new non-dimensionalized parameter, Δθ*, which is shown to be a very useful measure for classification of the laminated plates and the suitability of different plate theories over various ranges of length-to-thickness ratio.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240611
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    A numerical study of steady plane granular chute flows using the Jenkins-Savage model and its extension (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1993-2015 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The granular flow model proposed by Jenkins and Savage and extended by us is used here to construct numerical solutions of steady chute flows thought to be typical of granular flow behaviour.We present the governing differential equations and discuss the boundary conditions for two flow cases: (i) a fully fluidized layer of granules moving steadily under rapid shear and (ii) a fluidized bottom-near bed covered by a rigid slab of gravel in steady motion under its own weight. The boundary value problem is transformed into a dimensionless form and the emerging system of non-linear ordinary differential equations is numerically integrated. Singularities at the free surface and (in one case) also at an unknown point inside the solution interval make the problem unusual. Since the non-dimensionalization is performed with the maximum particle concentration and the maximum velocity, which are both unknown, these two parameters also enter the formulation of the problem through algebraic equations. The two-point boundary value problem is solved with the aid of the shooting method by satisfying the boundary conditions at the end of the soluton interval and these normalizing conditions by means of a minimization procedure. We outline the numerical scheme and report selective numerical results. The computations are the first performed with the exact equations of the Jenkins-Savage model; they permit delineation of the conditions of applicability of the model and thus prove to be a useful tool for the granular flow modeller.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620241012
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    Time-domain analysis of infinite fluid vibration (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 945-958 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A damper technique is proposed to model the effects of radiation damping in the finite element analysis of hydrodynamic pressures generated due to the vibration of a structure submerged in a compressible fluid. The proposed damper is suitable for a time-domain analysis. It is assumed that the fluid is inviscid and its vibration is of small amplitude. The structure-fluid system is assumed to be two-dimensional, and the fluid domain is considered to be unbounded along the direction of structural vibration. In the finite element analysis, pressure is assumed to be the nodal unknown, and the discretized equations of motion are solved by using a direct integration procedure. As a result of the analysis of several cases, the proposed damper is found to be very effective and efficient for a wide range of the period of excitation. The only exception is the case when the period of excitation is near the natural period of vibration of the fluid domain. For this case, the pressure becomes infinitely large and there is no requirement for any damper. The implementation of the proposed damper in the finite element analysis requires practically no extra computational effort. With the use of the suggested technique, an unbounded fluid domain may be truncated at a relatively very short distance from the structure, as compared to the distance required when the Sommerfeld damper is used. As a result of these advantages of the proposed technique, the cost of computation is greatly reduced.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240508
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  • 140
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    Least-squares finite element method and preconditioned conjugate gradient solution (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1283-1296 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A least-squares variational procedure for first-order systems of differential equations and an approximate formulation based on finite elements are developed. Error estimates, a condition number bound and analysis of weighting factors are given. Steepest descent and conjugate gradient solution procedures are examined, and an appropriate preconditioner constructed which is demonstrated to yield rapid convergence and to be insensitive to problem size. Numerical studies of rates of convergence for a test problem are given.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240705
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  • 141
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    Direct computation of Cauchy principal value integrals in advanced boundary elements (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1711-1720 
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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 new method for the direct computation of strongly singular integrals existing in the Cauchy principal value sense. It can be usefully applied in the solution by the direct boundary element method of many different problems. Initially, some considerations are provided in order to summarize the state-of-the-art on this issue. Then the features of the proposed method are reported. The procedure allows the direct calculation of Cauchy principal value integrals with first-order singularity and it is applicable even in advanced boundary element methods employing high-order elements. It requires only the use of standard Gaussian quadrature formulae plus the computation of a logarithmic term. Some examples show the effectiveness and efficiency of the procedure.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240908
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    Conference diary (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1825-1826 
    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.1620240916
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    Basis random variables in finite element analysis (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1849-1863 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Galerkin's method is applied to random operator equations. Appropriate Hilbert spaces are defined for random functions and solutions are projected into these spaces, allowing the first- and second-moment properties of the solution to be calculated. An equivalent energy-based approach similar to the Rayleigh-Ritz method is developed, from which a stochastic finite element technique is derived. Several one- and two-dimensional example problems are solved and the results discussed.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620241004
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    A posteriori estimates of the solution error caused by discretization in the finite element, finite difference and boundary element methods (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1921-1939 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A theory is described which guarantees an upper and lower bound estimate of the discretization error in numerical solutions of elliptic boundary value problems. This method gives bounded global estimates of the error in the energy norm. Pointwise estimates of the error in the solution variable or its derivatives can then be obtained if the numerical solution is exhibiting pointwise monotonic convergence.The versatility of this method is illustrated by its application to numerical solutions from finite element, finite difference and boundary element methods.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620241008
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    A finite element for edge-cracked beam columns (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1941-1950 
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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 is derived for a finite element representing a beam column with rectangular cross section and a single edge crack. The element has zero length, and the standard nodal degrees of freedom associated with beam-column elements. To illustrate its capabilities, the element is used to model propagation of multiple cracks in a self-loaded fixed beam.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620241009
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    Field-consistency and violent stress oscillations in the finite element method (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 2017-2033 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The fact that finite element models can give rise to violent stress oscillations and that there are optimal locations where stresses can be correctly sampled in spite of the presence of these violent stress fluctuations has been known for some time. However, it is less well known that these oscillations arise in a specific class of problems - where there are multiple strainfields arising from one or more field-variables and where one or more of these strain-fields must be constrained in particular physical limits. In this paper, we show that unless the interpolations for these constrained strain-fields are ‘field-consistent’, violent oscillations would set in. These oscillations represent spurious self-equilibrating stress-fields generating spurious energy terms that lead to ‘locking’.The field-consistency interpretation offers a conceptual scheme to delineate these problems and an operational procedure called the functional reconstitution technique allows the errors resulting from field-inconsistency to be anticipated a priori. We demonstrate the power of this approach through an interesting example of a multi-strain-field problem - the inextensional/nearly inextensional deformation of a shear flexible curved beam.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620241013
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    Conference diary (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 2037-2038 
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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.1620241017
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    Computational method for integral equations, L. M. Delves and J. L. Mohamed, Cambridge University Press, 1985. Price: £35.00. ISBN 0 521 26629 7 (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 2036-2036 
    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.1620241015
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    Interactive solution to multiobjective optimization problems (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1865-1877 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Sensitivity analysis is presented as a natural addition to interactive multiobjective optimization methods based on compromise programming. It is shown that useful information regarding trade-offs in the objectives can be generated effectively by means of an analysis of the sensitivity of solutions to variations in preference structures. An implementation based on sequential quadrative programming is provided and examples are given for illustration.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620241005
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    A finite element model for column-supported shells of revolution (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1951-1971 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element model suitable for the analysis of column-supported shells of revolution is presented. This model combines in a single analysis axisymmetric shell elements with nodal circles and column elements with nodal points. Thus, it takes advantage of the axisymmetry of the shell, while the non-axisymmetric nature of individual columns is fully accounted for. The compatibility between the two different types of elements is achieved through the use of a co-ordinate transformation. The accuracy of the solutions is demonstrated through numerical examples. When a shell of revolution supported on equispaced columns of the same stiffness is subjected to a harmonically varying load in the circumferential angle, it is found that the resulting displacements are associated with selective harmonic terms. An equation which precisely defines this coupling mechanism is also derived.
    Additional Material: 23 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620241010
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    Applied stress analysis, C.T.F. Ross, Ellis Horwood (Chichester), 1986. No. of pages: 322. Price £16.95/$30.75. ISBN: 74580 155 2 (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 2035-2035 
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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.1620241014
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    A turbulence model for buoyant and combusting flowsThis paper sets out and develops some of the ideas conveyed in a lecture delivered at the 4th International Conference on Numerical Methods in Thermal Problems: Swansea, 15-18 July 1984. The slide panels used in the lecture, which give a more precise idea of what was actually-said, are contained in IC CFDU Report No CFD/85/10, 1985. (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1-23 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is argued that ‘sifting’ phenomena, in which fragments of fluid subjected to larger body forces move through those subjected to smaller body forces, are prevalent in turbulent flows, and that they can be simulated by means of mathematical methods which have been developed for two-phase flows.A connection with Prandtl's mixing-length theory is established; and it is deduced from the success of that theory for shear flows that there must exist a source term in the normal-to-wall-velocity equations which is proportional to the gradient of along-the-wall velocity. This term is then included in the two-fluid-model equations.Solutions of the equations are presented for a turbulent Couette flow in which the heating of one of the walls and the presence of a gravitational field can cause ‘sifting’ phenomena to become dominant. The friction and heat-transfer coefficients, and the profiles of velocity and temperature, are computed and discussed, for flows both with and without buoyancy influences.
    Additional Material: 6 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240102
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    Experiences in non-linear analysis of temperature fields with finite elements (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 59-73 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes practical experiences in dealing with non-linearities in temperature field calculations. First the use of the load vector for representing the heat radiation on the outer surfaces is reported. However, if there are also additional non-linearities in the conductance matrix, then it may happen that because of possible counteractions of the non-linearities no convergence is achieved, at least with the direct iteration. Therefore it is more appropriate to put the radiation terms into the conductance matrix where the other non-linearities, such as temperature dependent thermal conductivity and natural convection also appear. It is shown how the Newton-Raphson iteration can be applied in an easy way. In the case of temperature dependent heat sources the load vector also needs to be considered. The appropriate special measures are described.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240105
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    An unstructured multigrid method for elliptic problems (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 101-115 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A multigrid algorithm for implementation on unstructured meshes is proposed. The algorithm uses a sequence of unnested grids and requires the development of efficient inter-grid interpolation procedures. It is demonstrated how elliptic problems can be solved in this fashion by using Jacobi smoothers.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240108
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    The effect of explosion venting in empty vessels (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 129-140 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The two-dimensional Navier-Stokes equations, suitably amplified to include the effects of chemical reactions and turbulence, are discretized by employing a finite-volume technique. A weighted upwind/central differencing scheme, the weight depending on the grid Peclet number, is used for the convection terms. Velocities are calculated on staggered grids. The source terms are treated in a quasi-implicit manner by combining linearization of these terms with an ICE procedure providing a time-advanced pressure. The effect of turbulence is included through the eddy-viscosity concept by solving equations for turbulent kinetic energy and its rate of decay. Combustion is modelled by an equation for mass fraction of fuel containing a fuel consumption term based on mixing-limited combustion.The resulting code, called FLACS-ICE, is employed in simulating the influence of confinement on flame acceleration in premixed, stoichiometric propane-air mixtures. Calculations are performed for large (425m3), medium (35m3) and small scale (0·0036m3) vessels. Satisfactory agreement with experimental data, published by Solberg1 is obtained. Some limitations of the code are also pointed out.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240110
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    Pulverized coal conversion in downflow gasifier (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 203-218 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The behaviour of coal particles undergoing pyrolysis in a downflow reactor is modelled in two dimensions using integral approximation. The governing equations are solved numerically by marching procedures using Adams-Moulton and Romberg integration methods. The conversion of coal particles is studied in terms of chemical kinetics, hydrodynamic flow of volatiles and the heat transfer mechanism at the interface. The conversion increases with decreasing velocity, solid loading, particle diameter and total pressure. Owing to large amounts of gas production, the influence of pyrolysis on the gas-particle heat transfer and drag coefficients becomes important at large particle diameters. For particle diameters less than 100 μm, such influence is minimal.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240114
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    Heat transfer in solid state laser systems: Applications of dynamic ADI methods (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 177-202 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This article describes numerical modelling of heat transfer and thermoelasticity effects that are significant in thermo-optical designs of solid state slab lasers capable of high average output power. The heat equation and equations of thermoelasticity are solved simultaneously to evaluate thermal stresses and microscopic deformations in isotropic and anisotropic laser host media. An efficient dynamic alternating-direction implicit method has been developed and applied in this work to solve the steady state heat transfer and stress potential equations in two dimensions. Numerical results are presented for some problems that arise in baseline designs of experimental slab laser systems.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240113
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    Lanczos method for heat conduction analysis (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 251-262 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An analysis technique that uses the Lanczos vectors to construct a Reyleigh-Ritz solution for the transient heat conduction problem is presented. The Lanczos vectors are derived from the heat supply vector and incorporate all the information peculiar to a given problem. They are orthonormal with respect to the heat capacitance matrix and are generated with a minimum of computational effort. Furthermore, an error bound is derived that can be used to terminate the Lanczos algorithm as soon as the number of vectors required to obtain a desired degree of accuracy has been generated. A summary of the algorithm is presented and the accuracy and efficiency of the method is illustrated using a numerical example.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240117
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    A global mapping method for improving the performance of quadratic elements (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 301-317 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple method is proposed in this paper for improving the performance (accuracy and convergence) of quadratic elements. In this the physical domain of the problem, as well as the constitutive relationships, are transformed globally by implementing a suitable co-ordinate transformation, and the problem is then solved in the mapped (transformed) domain using finite elements of the mapped space following the processes of the conventional FEM.Results show that the method significantly improves the performance of quadratic elements in both two and three dimensions. The mathematical implications of mapping in this way indicate that the method can also be applied for improved performance to higher-order elements if required.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240204
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    The method of moving asymptotes - a new method for structural optimization (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 359-373 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method for non-linear programming in general and structural optimization in particular is presented. In each step of the iterative process, a strictly convex approximating subproblem is generated and solved. The generation of these subproblems is controlled by so called ‘moving asymptotes’, which may both stabilize and speed up the convergence of the general process.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240207
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    Evaluating eigenvalues for boundary value problems of heat conduction in rectangular and cylindrical co-ordinate systems (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 419-445 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method of evaluating eigenvalues for any combination of the first, second and third boundary conditions of heat conduction in a plate, a solid cylinder or a hollow cylinder is described. Some general relationships between eigenvalues are derived. Based on these relationships a universal algorithm is developed. A list of a package of computer subroutines is included.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240210
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    One-dimensional calculations of two-phase mixing flows (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 459-469 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new algothm for the solution of two-phase fluid flow problems is presented. The algorithm consisently ensures that the evolved volume fractions are all positive and sum to unity, even in the presence of large spatial and temporal gradients of volume fraction. The momentum equations are then solved using an iterative pressure correction method. Example calculations for buoyancy driven flows, with and without phase changes, are presented.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240212
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    A finite element solution method for contact problems with friction (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 477-495 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new finite element solution method for the analysis of frictional contact problems is presented. The contact problem is solved by imposing geometric constraints on the pseudo equilibrium configuration, defined as a configuration at which the compatibility conditions are violated. The algorithm does not require any a priori knowledge of the pairs of contactor nodes or segments. The contact condition of sticking, slipping, rolling or tension release is determined from the relative magnitudes of the normal and tangential global nodal forces. Contact iterations are in general found to converge within one or two iterations. The analysis method is applied to selected problems to illustrate the applicability of the solution procedure.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240302
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    LU decomposition of matrices with augmented dense constraints (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1451-1459 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Sparse matrices composed of a central band and augmented dense rows and columns are becoming prevalent in the numerical solution of a large class of boundary and initial-value problems. A Fortran Subroutine ARROW is presented for the LU decomposition and solution of linear equation systems with such a structure. The computational speed of the program is compared in MFLOPS (millions of floating point operations per second) to the LINPACK benchmark for the solution of a dense linear system and is found to be of comparable speed on both supercomputers and minicomputers. Use of the Basic Linear Algebra Subroutines (BLAS) available on most machines significantly enhances the speed of ARROW.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240804
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    The ‘effective-stress-function’ algorithm for thermo-elasto-plasticity and creep (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1509-1532 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm for stable and accurate computations of stresses in finite element thermo-elastic-plastic and creep analysis of metals is presented. The effective-stress-function algorithm solves the governing equations of the inelastic constitutive behaviour by calculating the zero of the appropriate effective-stress-function: a functional relationship which involves as unknown only the effective stress. The derivation of the effective-stress-function for thermo-elasto-plasticity conditions, including creep, for 2-D and 3-D analysis is presented, and the algorithmic steps of the stress solution are discussed. For use in the stiffness matrix a tangent material stress-strain relationship is evaluated consistent with the effective-stress-function algorithm. The solution of some demonstrative problems shows the effectiveness of the solution procedure.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240808
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    Making the boundary element method less sensitive to changes or errors in the input data (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1533-1540 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To solve a problem by the boundary element method requires a solution of an integral equation. By discretizing the boundary, the integral equation is reduced to a set of linear algebraic equations. If the matrix in algebraic equation is not diagonal dominant or more precisely, poorly conditioned, then the accuracy of the numerical solution becomes very sensitive to small changes in the input data. Small errors in the input data or changes in the mesh description can change the solution drastically.In this paper a scheme is described which improves the condition of the matrix. Furthermore, it also reduces the sensitivity of the condition of the matrix to changes in the mesh description. The ideas described are applicable to any boundary element formulation. However, the numerical examples are from two-dimensional elastostatics solved by the indirect version of the boundary element method.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240809
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    The method of lines and exponential fitting (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 557-567 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: When the method of lines is used for solving time-dependent partial differential equations, finite differences are commonly employed to obtain the semidiscrete equations. Usually, if the solution is expected to be smooth, symmetric difference formulae are chosen for approximating the spatial derivatives. These difference formulae are almost invariably based on Lagrange type differentiation formulae. However, if it is known in advance that periodic components of given frequency are dominating in the solution, more accurate difference formulae, based on exponentials with imaginary exponent, are available. This paper derives such formulae and presents numerical results which clearly indicate that the accuracy can be improved considerably by exploiting additional knowledge on the frequencies of the solution.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240307
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    An efficient quadrilateral element for plate bending analysis (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1123-1155 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple, shear flexible, quadrilateral plate element is developed based on the Hellinger/Reissner mixed variational principle with independently assumed displacement and stress fields. The crucial point of the selection of appropriate stress parameters is emphasized in the formulation. For this purpose, a set of guidelines is formulated based on the following considerations: (i) suppression of all kinematic deformation modes, (ii) the element has a favourable value for the constraint index in the thin plate limit, (iii) element properties are frame-invariant. For computer implementation the components of the element stiffness matrix are evaluated analytically using the symbolic manipulation package MACSYMA. The effectiveness and practical usefulness of the proposed element are demonstrated by the numerical results of a variety of problems involving thin and moderately thick plates under different loading and support conditions.
    Additional Material: 19 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240607
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    Multi-objective optimization of fuzzy structural systems (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1157-1171 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is recognized that there exists a vast amount of fuzzy information in both the objective and constraint functions of the optimum design of structures. Since most practical structural design problems involve several, often conflicting, objectives to be considered, a multi-objective fuzzy programming method is outlined in this work. The fuzzy constraints define a fuzzy feasible domain in the design space and each of the fuzzy objective functions defines the optimum solution by a fuzzy set of points. A method of solving a fuzzy multi-objective structural optimization problem using ordinary single-objective programming techniques is presented. The computational approach is illustrated with two numerical examples.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240608
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    The effect of compatibility conditions on optimal design of flexural structures (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1173-1185 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In most structural optimization problems the time-consuming implicit analysis must be repeated many times during the solution process. To alleviate this difficulty, the implicit analysis equations are often neglected or replaced by explicit approximations.Assuming the force method analysis formulation, optimal solutions of two problems are studied and compared:(a)The equilibrium linear programme (ELP), where only explicit equilibrium conditions are considered in the analysis model(b)The non-linear programme (NLP), where the implicit compatibility conditions are included to obtain a complete formulation.The effect of geometrical parameters on optimal solutions of both problems is investigated and geometries with particular properties are identified. The main observations that have been made are as follows:(a)Multiple optima of the ELP have been obtained for geometries where transitions in the set of active constraints at the ELP optimum occur. The NLP optimum for such a geometry might be included in the set of ELP optima.(b)Identical optimal solutions of the two problems have been found for geometries where transitions in the set of active constraints at the NLP optimum occur.The explicit ELP can be solved instead of the implicit NLP for the two classes of transition geometries.The relationships between optimal force distributions and objective function values for the two problems are studied and examples where compatibility conditions can be neglected are illustrated.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240609
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    Dynamic response optimization using an active set RQP algorithm (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1827-1840 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A recently developed recursive quadratic programming (RQP) algorithm is applied to dynamic response design problems. The algorithm incorporates updated Hessians of the Lagrange function and uses an active set strategy in which only a subset of the constraints is included in the direction finding QP subproblem. Hessian updating with dynamic response constraints presents some difficulties. The primary difficulty is that the total number of constraints and the location of time points where they have to be imposed can change from iteration to iteration. This can cause inconsistencies in Hessian updating if proper numerical procedures are not used. A numerical procedure to handle the situation is developed, implemented and evaluated. Automatic restarting procedures are necessary for proper convergence of the algorithm. The new algorithm is robust as well as more efficient than the purely linear algorithm. The active set strategy plays an important role for application to dynamic response problems. The RQP algorithms that do not use such a strategy are not applicable to this class of problems.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620241002
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    Semiconductor device modelling from the numerical point of view (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 763-838 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper mathematical and computational aspects of device modelling are treated. Four main subjects are discussed; the analytical model, the discretizations, the non-linear and the linear systems of equations. On the one hand the most commonly used numerical techniques are described; on the other hand several new techniques are presented. Noteworthy new techniques are the generalized upwind box scheme and the mixed variable approach. Aspects such as the choice of variables and the singularly perturbed nature of the problem are treated. Properties of the matrices involved are presented in a systematic way. Throughout the paper a standard one-dimensional diode is used to illustrate the concepts involved. Finally several realistic two-dimensional examples are given.
    Additional Material: 40 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240408
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    Masthead (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987) 
    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.1620240501
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    Trefftz method: Fitting boundary conditions (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 871-891 
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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 various ways of fitting the boundary conditions in the T-complete functions method. The authors point out the distinct advantages of the orthogonal collocation in comparison to the equidistant collocation and the integral fit. The convergence of the Collatz error measures and the conditioning of the solution matrices are investigated in detail.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240504
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    Self-adaptive stress analysis based on stress convergence (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1973-1992 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new algorithm for self-adaptive stress analysis is presented. The algorithm is based on h-convergence and uses the measured stress convergence rate as an error indicator. A theoretical relation between stress convergence rate and pointwise error of stresses is derived for both the 1-D and 2-D case. Some examples are presented to illustrate the behaviour of the algorithm.
    Additional Material: 24 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620241011
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    Software for discrete manufacturing, J. P. Crestin and J. F. McWaters (eds.) (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1226-1226 
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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.1620240614
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    Numeta 85 proceedings of the international conference on numerical methods in engineering: Theory and applications, Swansea, January, 1985, J. Middleton, G. N. Pande and A. A. Balkema (eds.), 1985, 2 vols (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1226-1226 
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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.1620240615
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    An automatic design optimization procedure to minimize fillet bending stresses in involute spur gears (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 975-991 
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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 the development of an automatic design algorithm for gears. The criterion on which the design performance is assessed is the maximum tensile stress induced in the gear tooth fillet under service conditions. Starting from an initial set of design parameters the stresses in the gear tooth fillet are calculated. The maximum value of the stress is then expressed as a function of the design variables. By minimizing this function, the objective function, subject to both equality and inequality constraints a new set of design parameters, is produced. Iterative application of the analysis and minimization stages forms a sequence of non-linear optimization problems which converges to yield the optimal design.Finite element techniques employed to calculate accurately the stresses in the gear tooth are again used to compute the design derivatives. This process is very economical, owing to its efficient reuse of the factorized stiffness matrix.The algorithm is illustrated by its application to a spur gear tooth of involute profile. Both linear and non-linear forms of the objective function are used and a comparison made between the solutions obtained.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240510
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    The comparative performance of some finite difference equations for transient heat conduction (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1317-1331 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The established finite difference equations to estimate one-dimensional transient heat flow in solids are the ‘classical’ form (explicit), and the Crank-Nicolson and ‘pure-implicit’ forms (both implicit). They are all based on finite difference approximation to the Fourier continuity equation. To these are now added three more explicit forms: exponential linear, exponential inverse cosine and polynomial, which are based on exact solutions to the Fourier equation. The performance of each of the six equations is tested against the exact results of a well known step excitations problem (the Groeber model). The tests consist of examining (i) finite difference errors arising from a single implementation of each form at different stages in the transient cooling process, (ii) the errors that accumulate during part or all of the cooling process (both as regards any bias that is introduced, and also a measure of variance) and (iii) the run times in executing the various forms. The nondimensional time step r was treated as the independent variable, and can be made arbitrarily large, by use of a simple time-division procedure (otherwise r 〈 ½ for use with the classical form). It is shown that having regard to both error and run time, the polynomial form appears to be the most efficient estimator.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240708
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    Hybrid-Trefftz plate bending elements with p-method capabilities (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1367-1393 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The p-method capabilities have thus far been used only in connection with the assumed displacement model elements. When such elements are used, singular points have to be isolated by one or two layers of small elements graded in a suitable geometrical progression towards singularity. This paper presents an alternative formulation which circumvents this drawback and enables excellent solution results to be obtained with uniform FE-grids. The formulation is based on the recently presented hybrid-Trefftz FE-model and makes use of optional expansion sets for various singularities or stress concentrations. Stress concentrations due to concentrated loads are also properly accounted for. It is shown that by augmenting the order of approximation over a fixed grid of such elements rapid convergence towards the accurate solution is obtained in the most efficient way.This paper summarizes the results of a preliminary study that had been undertaken to critically evaluate the potential of the new approach as a suitable basis for subsequent developments of a fully automated adaptive process.
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240712
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    Conference diary (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1417-1419 
    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.1620240714
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    Announcement (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1419-1419 
    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.1620240715
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    Singular element construction using a mapping technique (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1305-1316 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Conformal mapping regularizes (in the new plane) the singular stress field around the crack tip. So, conventional finite elements can be used in the transformed plane. The inverse mapping of the above elements gives another class of ‘mapped elements’. The crack-tip mapped element is a singular element. Thus, using various elements (the ‘parent elements’) in the mapped plane we obtain an infinity of singular elements, the ‘product elements’. These singular elements are introduced naturally and have no defect, as many other singular elements have.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240707
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  • 184
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    An extension of the application of transmission line modelling (TLM) to thermal diffusion to include non-infinite heat sources (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1333-1341 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The modelling of heat transfer from a moving gaseous atmosphere by the TLM technique is described. For the case of very rapidly moving gas, results are compared with those derived from finite element analysis.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240709
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  • 185
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    On the preconditioned conjugate gradient method for solving (A - λB)X =0 (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1355-1366 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Classical iterative methods when applied to the partial solution of the generalized eigenvalue problem Ax =λBx, may yield very poor convergence rates particularly when ill-conditioned problems are considered. In this paper the preconditioned conjugate gradient (CG) method via the minimization of the Rayleigh quotient and the reverse power method is employed for the partial eigenproblem. The triangular splitting preconditioners employed are obtained from an incomplete Choleski factorization and a partial Evans preconditioner. This approach can dramatically improve the convergence rate of the basic CG method and is applicable to any symmetric eigenproblem in which one of the matrices A, B is positive definite. Because of the renewed interest in CG techniques for FE work on microprocessors and parallel computers, it is believed that this improved approach to the generalized eigenvalue problem is likely to be very promising.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240711
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  • 186
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    A grid generator based on 4-triangles conforming mesh-refinement algorithms (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1343-1354 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A procedure to generate 2D meshes of triangles in a quite general fashion allowing for local and selective mesh-refinement is presented and discussed. The grid generator is based on the iterative application of 4-triangles conforming mesh-refinement algorithms for triangulations, which are also introduced in this paper. These algorithms are modified versions of those proposed in Int. j. numer. methods eng., 20, 745-756 (1984), and they can be used for global refinement of a grid, as well as for local refinement. The grid generator works in the following way: given any initial coarse triangulation which properly defines the geometry of the problem, a set of user-defined refinement subregions Ri, i = 1,2,…, N, and an associated set of tolerance parameters hi, an irregular and conforming final triangulation is automatically constructed in such a way that the diameter of all the triangles contained in Ri is smaller than hi, i= 1,2,…, N. Moreover, all angles in the final triangulation are greater than or equal to half the smallest angle in the initial, coarse one. The refinement is propagated only to assure the conformity and smoothness of the grid, and consequently, the number of involved nodes will be minimized. The refinement of the final mesh will be determined by the subregions Ri and the parameters Ni and will be essentially independent of the initial coarse grid. The 4-triangles conforming mesh-refinement algorithms are presented and their properties discussed. The implementation of these techniques is discussed and examples of the application of the grid generator are given.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240710
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    On the numerical integration of a class of pressure-dependent plasticity models (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1395-1416 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An unconditionally stable algorithm for the numerical integration of elastoplastic pressure-dependent constitutive relations is analysed in detail in this paper. The application of the method to plane stress problems, in which the out-of-plane strain component is not defined kinematically, is discussed. The tangent moduli resulting from this integration algorithm are obtained by consistent linearization of the elastoplastic constitutive equations. The algorithm is applied to Gurson's constitutive model, some one-dimensional problems are solved, and comparisons with exact solutions are made. The paper closes with a numerical study of the necking of an axi-symmetric specimen using Gurson's plasticity model to describe the constitutive behaviour of the material.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240713
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    Masthead (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987) 
    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.1620240801
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    Residual flow procedure for sea water intrusion in unconfined aquifers (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1439-1450 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simplified procedure is presented for the analysis of sea water intrusion in unconfined aquifers. It involves the finite element method with a residual flow procedure which combines transformation of the salt water zone into the fresh water zone that has the same pressure distribution as that of the salt water. This procedure avoids simultaneous solutions of governing differential equations for both flow and mass transport. Numerical results are compared with laboratory observations.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240803
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  • 190
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    Numerical simulation of electrodeposition problems (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1479-1497 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The mathematical modelling of the electrodeposition phenomenon leads to a linear elliptic partial differential equation subject to non-linear mixed boundary contitions. This is complicated further by the fact that the domain under consideration is evolving with time.Owing to the nature of the mathematical model, the boundary element method is a very efficient numerical technique for the solution of such problems. The authors report their numerical simulation of the above problem which also has applications in the cathodic protection systems for corrosion prevention.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240806
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  • 191
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    An integral equation method for the solution of 3-dimensional, non-linear, magnetostatic problems (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1551-1562 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element method for computing the resultant magnetic field arising from a given source field in the presence of a magnetic material of variable permeability is described; in this method finite element approximations to the scalar potential of the resulting field and the magnetic susceptibility, in the region occupied by the magnetic material, are determined from the non-linear integral equation for the scalar potential and the constitutive susceptibility relation, using a collocation scheme.The method is used to compute the shielding effect of a thin rectangular plate of variable permeability on a given source field. The plate is subdivided uniformly into brick elements; the resulting translational invariance of the integrals required in the calculations is exploited to achieve major computational savings.A consequence of the thinness of the plate is that the calculation of the requisite integrals by analytic methods leads to considerable loss of accuracy by differencing; this difficulty is overcome by using a scheme which combines both analytic and quadrature techniques.The resulting system of non-linear algebraic equations is solved by Powell's hybrid method; an efficient scheme for calculating an initial approximation to the Jacobian, which utilizes the structure of the equations, is presented.The results of the calculations are discussed.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240811
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    Application of the finite element-difference method to vibration problems (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1581-1591 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The so-called finite element-difference method introduced in References 1 and 2 yields a continuous stress field by finite difference operations and finite element interpolations. In the present paper, applications of the method to vibration problems are discussed. The inverse iteration procedure is modified for this method. Numerical results show that the accuracy of solutions depends strongly on the type of finite difference operator chosen: for reliable and accurate solutions in modal analysis problems, element internal strains must be included in the strain field used to compute nodal forces associated with element deformations.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240813
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    CONDIF: A modified central-difference scheme for convective flows (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1593-1608 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For most practical purposes, the central-difference scheme (CDS) would be ideal only if it were unconditionally stable. It is a simple and second-order scheme which is easy to implement. It does not introduce any second-order ‘diffusion’ like truncation error. However, for grid Peclet numbers larger than 2, the CDS leads to over- and under-shoots and is unstable. This paper presents a method, called CONDIF, which eliminates this undesirable feature of the CDS. It modifies the CDS by introducing a controlled amount of numerical diffusion based on the local gradients. The numerical diffusion can be adjusted to be negligibly low for most problems.CONDIF has been used to solve a number of test problems which have been widely used for comparative study of numerical schemes in the published literature. For all these problems the CONDIF results are significantly more accurate than those obtained from the hybrid scheme when the Peclet number is very high (→∞) and the flow is at large angles (→45 degrees) to the grid. In general the computational effort for CONDIF is comparable (within 20 per cent) to that for the hybrid scheme. However, in one instance the rate of convergence was found to be significantly slower.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240814
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    Effective hybrid hierarchical element generator for vibration analysis of plates (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1615-1628 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Cost effective high precision hybrid elements are presented in a hierarchical form for vibration analysis of plates. The elements are constructed by introducing computer installed hierarchical element generator algorithms which take advantage of the exact analytical treatment of the energy integrals automatically. Additional benefits accrue from: (i) the careful selection of assumed stresses and displacements satisfying finite element requirements, and maintaining the correct stiffness rank and invariance; (ii) the ability to reduce computational costs associated with various operations and the independence with respect to element geometries, which serve to build up a methodology to handle the generation of finite elements in any general purpose finite element system efficiently. Extensive numerical studies are made to predict the natural frequencies and harmonic response of plates with different boundary conditions. Accuracy of the solutions is assessed by comparison with the well established results. The noteworthy aspects of the applications are that the proposed elements are faster than those cited previously, and show a more favourable comparison to the analytical solutions for a wider range of vibration modes by maintaining rapid convergence characteristics.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620240902
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    Finite elements in CFD: What lies ahead (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1741-1756 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The current state of the art of Finite Element Methods in Computational Fluid Dynamics is reviewed. The aim of this review is to point out what appear currently as the main shortcomings of Finite Element Methods, so as to concentrate the efforts to remove them. The analysis of flows using Finite Elements will only be successful if all steps involved in it are optimized. Therefore, I deem it necessary to describe explicit and implicit flow solvers, unstructured multigrid methods, adaptive refinement schemes, grid generation and graphics in 3-D, the effective use of supercomputer hardware and memory, as well as the combination of structured and unstructured grids.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240910
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    An expert system for the optimal mesh design in the hp-version of the finite element methodPresented at the First World Congress on Computational Mechanics, Austin, Texas, September 1986 (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 2087-2106 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper suggests a simple expert system frame and provides the domain knowledge for the optimal mesh design and the prediction of the error in the energy norm for the problem of plane elasticity using the hp-extension in the finite element method. The expert system monitors the progress of the analysis, guides the user through the various steps and is able to reason about its own advice. In an example the user-expert communication is shown and the superiority of the results is demonstrated.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620241106
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    Finite element calculation of three-dimensional hot forging (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 2107-2117 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A three-dimensional finite, element model for the simulation of isothermal hot forging is presented.The material behaviour is assumed to be incompressible visco-plastic (Norton-Hoff law), with the associated friction law. The velocity field is calculated with a finite element approximation using eight node hexahedral or six node prismatic elements. An explicit Euler scheme is used for time integration. Simulations of compression of a cubic block and horizontal cylinder are performed. The computed results are compared with experimental measurements made on special Plasticine.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620241107
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    On artificial strain of thin curved elements (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 2167-2181 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an attempt to clarify further the nature of the overstiffness of thin curved structural elements. It follows the approach presented by Ashwell and co-workers1,2 who based their study on shape functions of arch elements. Such elements display the same stiff behaviour as complex shell elements but are simpler to study and understand. An examination of several discretizations for a two-dimensional curved beam-column element for linear elastic analysis of arches is performed. This examination and the numerical results obtained from these approximations provide a new interpretation of the artificial strains based on the mapping variables of shape functions. Two new methods to reduce the artificial stiffness of the element are proposed.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620241110
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    Petrov - Galerkin method for multidimensional, time-dependent, convective-diffusion equations (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 2201-2215 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Petrov - Galerkin finite element method for two and three-dimensional time dependent convection-diffusion equations is presented in the context of two space dimensions. The method involves perturbed weighting functions in the weighted residuals formulation, that are bilinear in space and quadratic in time and depend on two parameters which are calculated according to a local analysis for the one dimensional case. The perturbations to the weighting functions can be interpreted as an added local anisotropic balancing diffusion and an added dispersion in the direction of the convective motion. The effectiveness of the method is shown through several examples involving the convective and diffusive transport of scalar distributions in known velocity fields.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620241112
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    Masthead (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987) 
    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.1620241201
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