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  • Electronic Resource  (927)
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  • 1990-1994  (927)
  • 1990  (927)
  • Engineering General  (524)
  • Computational Chemistry and Molecular Modeling  (403)
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  • Electronic Resource  (927)
  • Loose Leaf
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  • 1990-1994  (927)
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  • 1
    Electronic Resource
    Electronic Resource
    Modeling of real 20-component protein chains: Determination of the electronic density of states of aperiodic seven-component polypeptide chains containing strongly different amino acid residues (1990)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 38 (1990), S. 573-583 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: To model a real 20-component protein chain, the results of the electronic density of states (DOS) of seven-component periodic and aperiodic polypeptide chains calculated on the basis of ab initio matrix block negative factor counting method are presented. The seven amino acid residues taken into account are rather different: glycine, serine, cysteine, asparagine, histidine, aspartic acid, and tryptophane. In the case of aperiodic chains, the energy states are found to be distributed over a much wider range of energy than in the corresponding periodic chains. In the intrinsic state, both periodic and aperiodic polypeptide chains are predicted to be insulators. The effect of the block copolymerization on the DOS distribution and the band gap values of both periodic and aperiodic polypeptide chains has been also investigated. Finally, the methods to calculate from the DOS curves hopping conductivities and the possibilities to compare them with experiment are outlined.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560380407
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  • 2
    Electronic Resource
    Electronic Resource
    Masthead (1990)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 38 (1990) 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560380501
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  • 3
    Electronic Resource
    Electronic Resource
    Methods for electron correlation on large molecules (1990)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 38 (1990), S. 641-652 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: High-quality ab initio calculations, i.e., calculations including electron correlations with large atomic basis sets, have been restricted to relatively small systems due to their excessive demand on computer facilities. To extend these methods to large systems, one is faced with two problems: the steep (6 power) increase of the computational task with the molecular size, and the large number of electron repulsion integrals that must be stored and retrieved. We have recently introduced new computational methods where both these problems have been addressed. The local correlation method reduces the steep dependency of computational effort with molecular size without significant loss of accuracy by taking advantage of the localizability of the electronic structure. For electron correlation calculations integrals in the MO basis are needed in addition to the two electron integrals in the AO basis, and the only way electron correlation can be applicable to large systems is by a direct approach in the spirit of Almlof's direct SCF. We have recently extended the direct approach to post Hartree-Fock methods. Description of both these methods including their supercomputer implementations are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560380506
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  • 4
    Electronic Resource
    Electronic Resource
    A combined octree/delaunay method for fully automatic 3-D mesh generation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 37-55 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Fully automatic three-dimensional mesh generation is a fundamental requirement for automating the numerical solution of partial differential equations. Two techniques in particular - the octree and Delaunay approaches - have been used towards this end. A method that combines both approaches to fully automatic mesh generation is presented here. The resulting algorithm provides the linear growth rate and divide-and-conquer approach of the octree method with the simplicity and optimal properties of the Delaunay triangulation.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290105
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  • 5
    Electronic Resource
    Electronic Resource
    Axisymmetric contact of an elastic layer underlain by rigid base (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 57-72 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Axisymmetric contact problems of an elastic layer are studied in this paper. The lower surface of the layer is either bonded to or in smooth contact with a rigid base. The upper surface is in tensionless smooth contact with a rigid flat cylinder, a rigid sphere, an elastic sphere or a circular plate, respectively. A general method is developed so that all these related problems are treated in a straightforward and like manner. In comparison to the other methods used in previous papers, the simplicity and high numerical accuracy are the major advantages of this method. The convergence is proved by comparing the numerical values to some available analytical solutions. Extensive numerical results for contact radii, displacements and contact pressures are provided.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290106
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  • 6
    Electronic Resource
    Electronic Resource
    An alternative numerical procedure for simulating the dynamical response of non-linear elastic rods (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 123-139 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper there is presented an alternative numerical procedure for obtaining approximations to non-linear conservation laws like those that describe the dynamical behaviour of elastic rods (composed of materials whose stress-strain relation is non-linear). The above-mentioned procedure consists of approximating the solution of the Riemann problem (associated with the considered conservation law) by a piecewise constant function (satisfying the jump conditions) and using Glimm's scheme for advancing in time, step by step. The proposed numerical approach eliminates the necessity of solving (in a complete way) the associated Riemann problem, easing and cheapening its computational implementation. This procedure is employed for simulating the dynamical response of an elastic-non-linear rod, fixed at its edges, that is left in a non-equilibrium state. There is presented a comparison between results obtained through a classical procedure and through the procedure proposed in this work.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290109
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  • 7
    Electronic Resource
    Electronic Resource
    Formulation of implicit finite element methods for multiplicative finite deformation plasticity (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 483-514 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Some constitutive and computational aspects of finite deformation plasticity are discussed. Attention is restricted to multiplicative theories of plasticity, in which the deformation gradients are assumed to be decomposable into elastic and plastic terms. It is shown by way of consistent linearization of momentum balance that geometric terms arise which are associated with the motion of the intermediate configuration and which in general render the tangent operator non-symmetric even for associated plastic flow. Both explicit (i.e. no equilibrium iteration) and implicit finite element formulations are considered. An assumed strain formulation is used to accommodate the near-incompressibility associated with fully developed isochoric plastic flow. As an example of explicit integration, the rate tangent modulus method is reviewed in some detail. An implicit scheme is derived for which the consistent tangents, resulting in quadratic convergence of the equilibrium iterations, can be written out in closed form for arbitrary material models. All the geometrical terms associated with the motion of the intermediate configuration and the treatment of incompressibility are given explicitly. Examples of application to void growth and coalescence and to crack tip blunting are developed which illustrate the performance of the implicit method.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290304
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  • 8
    Electronic Resource
    Electronic Resource
    Model reduction for thermal diffusion: Application of the Eitelberg, Marshall and aggregation methods to a heat transmission tube model (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 599-617 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This study, dealing with model reduction for thermal diffusion, describes the numerical techniques used: the Eitelberg, Marshall and aggregation methods. The non-linear model of a heat transmission tube, to which these methods are applied, is then described, pointing out the necessary initial algebraic treatment for reduction. Finally the outputs of the complete model and of several reduced ones are compared for some characteristic variations of the inputs. For this problem, the Eitelberg and Marshall methods, which can be used with a high coefficient of reduction, are well adapted.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290309
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  • 9
    Electronic Resource
    Electronic Resource
    Hybrid method for transient response of circular pins (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 303-314 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The combined application of the Laplace transform and the finite element method is used to analyse the transient response of circular pins. The present method removes the time-dependence terms from the governing differential equations and boundary conditions using the Laplace transform and then the eigenfunction expansion method is applied to reduce the two-dimensional boundary value problem to that of one dimension. Accordingly, the final transformed equation can easily be solved by the finite element method. The transformed temperature is inverted to the physical quantity numerically. The present results agree well with analytical solutions. In addition, it is seen that the results of axisymmetric transient heat conduction problems with the central node at r = 0 can accurately be obtained using the present method.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290207
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  • 10
    Electronic Resource
    Electronic Resource
    Adaptivity in hybrid-Trefftz finite element formulation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 391-405 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: With the advent of computer aided design (CAD), the development of fully or semi-automated procedures by which a solution warranting the specified accuracy can most efficiently be reached has become a necessity. It is now of utmost interest to investigate finite element (FE) formulations offering a simple form of adaptivity, easy to implement.The present study (which is a sequel to an earlier paper1 on error estimation by the authors) identifies as a particularly promising approach of attaining this goal the p-method associated with the so-called hybrid-Trefftz FE model.2 Based on a simple stress error estimator1 and prior knowledge of the convergence rate, the solution warranting specified stress accuracy may be reached in a single trial by suitably respecifying just one parameter in the input data. The reported approach has successfully been implemented into the general purpose FE program SAFE3 and its high efficiency is illustrated in the paper through practical applications involving corner singularities and stress concentrations.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290212
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  • 11
    Electronic Resource
    Electronic Resource
    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990) 
    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.1620290301
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  • 12
    Electronic Resource
    Electronic Resource
    Automatic step size correction for non-associated plasticity problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 579-598 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element method is used in calculating accurate collapse loads. The behaviour of granular materials is described by the non-associated Mohr-Coulomb model. The load-displacement path is traced up to and beyond limit points using an accelerated initial stiffness method. The convergence properties of this method are examined, both for associated and non-associated plasticity.Step sizes in the incremental iterative procedure are adapted during the iteration process, depending on an estimated number of iterations. The automatic step size control thus obtained proves to be robust and particularly appropriate for non-associated plasticity. Some soil collapse calculations are discussed to demonstrate the practical application of the method.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290308
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  • 13
    Electronic Resource
    Electronic Resource
    A surface fitting method for three dimensional scattered data (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 633-645 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is presented that may be used to empirically establish the type of relationship that is present between a response variable and its influencing factors, by fitting a mathematical model to three dimensional scattered data. The generated response surface is composed of continuous triangular planes that are fitted to the corresponding data in the least squares sense. The method may be easily implemented. It requires some fairly large number of scattered data, two initial boundary conditions and a desired accuracy for the band-wise partitioning of the data. The proposed surface fitting technique has been successfully applied to solar radiation modelling for a number of different data combinations.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290311
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  • 14
    Electronic Resource
    Electronic Resource
    The multigrid method in solid mechanics: Part II - Practical applications (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 739-753 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The performance of the multigrid algorithm is investigated by solving some large, practical, three dimensional solid mechanics problems. The convergence of the method is sensitive to factors such as the amount of bending present and the degree of mesh non-uniformity, as was also observed in Part I for two dimensional problems. However, in contrast to Part I, no proportionality is observed between the total number of operations to convergence and the problem size. Despite such behaviour, the multigrid algorithm proves to be an effective matrix equation solver for solid mechanics poblems. It is orders of magnitude faster than a direct factorization method, and yields converged solutions several times faster than the Jacobi preconditioned conjugate gradient method.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290405
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  • 15
    Electronic Resource
    Electronic Resource
    Some observations on time domain and frequency domain boundary elements (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 785-800 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical solution of problems in elastodynamics involving infinite media calls for the use of discrete techniques such as the boundary element method and the finite element method. These techniques can, in turn, be formulated in the time or frequency domains, and have each relative merits and drawbacks. This paper presents a comparative study of the accuracy and limitations of three different implementations of these methods.The problem studied is that of transient loads on the surface of homogeneous elastic halfspaces, and of finite depth strata. In each case, the response is computed first for an uninterrupted (continuous) medium, and then for a medium that includes a trench (or cavity).Three independent computer programs were used that incorporated the following methods: (i) frequency domain boundary element method (FD-BEM), using a discrete fundamental solution; (ii) time domain boundary element method (TD-BEM) using an analytical fundamental solution; and (iii) a coupled time domain boundary element-finite element model (BEM/FEM).It is found that for convex domains (halfspace or stratum without a trench) the three independent implementations are in excellent agreement, while for non-convex domains (trench in the path of the waves), numerical errors associated with non-causal behaviour become evident in some cases.
    Additional Material: 23 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290408
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  • 16
    Electronic Resource
    Electronic Resource
    A non-Jacobian numerical quadrature for semi-infinite integrals (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 833-846 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A non-Jacobian numerical quadrature is proposed for evaluating improper integrals over a semi-infinite range. The quadrature first transforms the semi-infinite integration limit into a finite limit between - 1 and 1. Standard numerical integration procedures such as Gauss-Chebyshev or Gauss-Legendre schemes can then be used to obtain the integral value. Unlike traditional methods using Laguerre or Hermite polynomials, numerical results show that no specific weight function is required for the proposed quadrature to converge as long as the integral exists. The transformation also includes a scale parameter which effectively expands the numerical-integration sampling points along its original semi-infinite integration path. Numerical examples shows that selection of the scale parameter is rather flexible and convergence can always be achieved within a wide range of parameter values. Several applied mechanics problems are also illustrated to validate the proposed numerical scheme. The quadrature can be easily incorporated into finite element or boundary element schemes for the evaluation of semi-infinite integrals.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290411
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  • 17
    Electronic Resource
    Electronic Resource
    Data structures and algorithms for the finite element method on a data parallel supercomputer (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 881-908 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This article describes a formulation of the finite element method and its implementation on a data parallel computing system. The Connection Machine® system, CM-2, has been used as the model architecture. Data structures, storage requirements, communication and parallel arithmetic complexity are analysed in detail for the cases when a processor represents an unassembled finite element and when a processor is assigned to an unassembled nodal point. Data parallel algorithms for the grid generation, the evaluation of the elemental stiffness matrices and for the iterative solution of the linear system are presented. The algorithm for evaluating the elemental stiffness matrices computes the matrix elements concurrently without communication. This concurrency is in addition to the inherent parallelism present among different finite elements. A conjugate gradient solver with diagonal pre-conditioner is used for the solution of the resulting linear system. Results from an implementation of the three-dimensional finite element method based on Lagrange elements are reported. For single-precision floating-point operations, the measured peak performance is approximately 2·4 G flops s-1 for evaluating the elemental stiffness matrices and approximately 850 M flops s-1 for the conjugate gradient solver. On a Connection Machine system with 16K physical processors, the time per conjugate gradient iteration for an application with 400 000 degrees of freedom is approximately 0·13 s for double-precision floating-point operations.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290414
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  • 18
    Electronic Resource
    Electronic Resource
    A fixed grid finite element technique for modelling phase change in steady-state conduction-advection problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 969-984 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new fixed grid finite element technique for modelling phase-change effects in steady-state conduction-advection problems is described. The method is appropriate for materials that transform at a fixed critical temperature and is based on the assumption that the enthalpy experiences a jump discontinuity at this temperature, yielding a singular specific heat. This singularity is described using a Dirac delta function and the appropriate finite element matrix equations are developed for isoparametric elements. A simple first order upwinding scheme is used to avoid numerical oscillations in advection dominated problems. The utility of the method is illustrated through the solution of a one-dimensional test problem using eight-node hexahedral isoparametric finite elements. The technique may be applied to a wide range of finite element types and offers a number of advantages over other schemes for modelling phase-change effects.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290505
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  • 19
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    Finite element analysis of multiconductor printed-circuit transmission-line systems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1033-1047 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper the finite element method (FEM) is used to analyse general, multiconductor transmission-line systems of arbitrary cross-section. The per-unit-length matrices of capacitance, inductance, conductance and resistance, which characterize a multiconductor transmission line, are obtained from the FEM analysis. Numerical results are presented and compared both with experimental results and other available data.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290509
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  • 20
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    Advanced time-domain formulation of BEM for two-dimensional transient elastodynamics (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1421-1440 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a new formulation for two-dimensional time-domain transient elastodynamic analysis by the Boundary Element Method (BEM) is presented. The traction kernel is derived by using the causality of the waves and the resulting kernel is explicit and much simpler than the ones that have appeared in the recent literature. An appropriate set of linear time interpolation functions together with quadratic spatial variations are incorporated. Moreover, the algorithm has a capability of handling problems with multiply connected regions. All of these advanced features have resulted in an efficient formulation capable of producing very accurate results and represent significant improvements over the present level of sophistication in this area. This above algorithm is now a part of the general purpose BEM code known as GPBEST.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290704
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  • 21
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    A finite element model for non-linear shells of revolution with finite rotations (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1455-1471 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The axisymmetric behaviour of geometrically non-linear elastic shells of revolution with finite rotations is discussed. In contrast to the approach of Reissner and to standard classical shell theories a new straightforward strategy is derived for the formulation of fully non-linear strain measures in the axisymmetric case. Within this approach the computation of the deformed director vector d is a main assumption which is essential to describe the fully non-linear bending behaviour. A Total Lagrangian Description is chosen to represent the large displacements. As an illustrative example the finite element formulation for a simple two-node conical element is given. A consistent linearization of the weak form leads to a quadratically convergence behaviour. The discussed shell examples under proportional loading show the good performance of the derived finite element formulation.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290706
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  • 22
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    The numerical simulation of electron transmission through a two-dimensional quantum device by the finite element method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1527-1537 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we present a method for numerically solving the Schrödinger equation for the problem of electron transmission through a quantum device defined on a two-dimensional domain. An important aspect of our formulation is the treatment of the boundary conditions at the contact-device interfaces, allowing the problem to be discretized on the device domain only. With the FEM aproach that we employ, the nature of the potential field does not effect the computational expense (for smoothly varying fields). We examine a sample problem of a symmetric cavity in a wave-guide structure.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290710
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  • 23
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    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990) 
    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.1620290801
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  • 24
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    Natural approach for thin-walled beam-columns with elastic-plasticity (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1653-1679 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In a realistic analysis of thin-walled steel frames the warping of beam-columns of open cross-section must be considered. To model the behaviour of these structures up to collapse load, the plasticity of the material also has to be included in the analysis. This work presents the derivation of a new finite element for three-dimensional non-linear analysis of steel frames with bi-symmetrical cross-sections that models warping and elastic-plasticity. The displacement field is described by the Principle of Sectorial Areas and is modelled with Hermitian functions. For the material non-linearity the Incremental Plasticity Theory in a concentrated plasticity model has been used. The yield surfaces based on the natural stress resultants which include torsion and bimoment are used in the formulation of the element. The matrices of the proposed element are derived explicitly and implemented in a computer program which uses the Natural Approach. The implemented stress recovery process is insensitive to rigid-body motions. The accuracy of the finite element and the efficiency of the implementation are illustrated through examples.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290804
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    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990) 
    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.1620300101
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    Finite element solution of two-dimensional inverse elastic problems using spatial smoothing (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 57-75 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element method (FEM) is presented for calculating the surface tractions on a body from internal measurements of displacement at discrete sensor locations. The solution algorithm employs a sensitivity analysis which minimizes the difference between the calculated and measured displacements at each sensor location. Spatial regularization is one technique employed to stabilize the minimization process by imposing various degrees of smoothness on the solution. It also allows the problem to be solved with fewer sensors than traction boundary nodes. As an alternative to spatial regularization, a method based on ‘keynodes’ is introduced which assumes that each component of the boundary traction distribution can be described by a polynomial of specified order. The methods are applied to several two-dimensional examples including a rolling contact problem. The effects of parameters such as the number of sensors, the location of the sensors and the error in the sensor displacements are discussed.
    Additional Material: 19 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300105
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    Finite element/Newton method for the analysis of Czochralski crystal growth with diffuse-grey radiative heat transfer (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 133-154 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A quasi-steady-state, integrated system model describing high temperature heat transfer, solidification and the action of capillarity in the Czochralski crystal growth process is solved by a finite element/Newton method. The numerical analysis couples the calculation of the temperature field in all phases and the determination of the melt/crystal and melt/gas interfaces and the crystal radius free boundaries. The analysis includes conductive heat transfer in the melt, crystal, crucible, pedestal, heater and the surrounding insulation and diffuse-grey radiation, which couples the heat transfer between surfaces, the crystal radius and the melt/gas free boundary through the view factors. Finite element approximations are used to reduce the entire problem to a coupled set of non-linear algebraic equations. These are solved simultaneously by Newton's method with the Jacobian matrix computed by a combination of closed form expressions and finite difference approximations. Quadratic convergence of the Newton iteration is demonstrated along with a factor of four increase in computational efficiency over a successive iteration procedure that decouples the calculation of radiation from the rest of the heat transfer model.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620300109
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    A Petrov-Galerkin/modified operator formulation for convection-diffusion problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 331-347 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new Petrov-Galerkin method to deal with convection-diffusion problems is presented. The formulation is derived from the concept of using a modifying function to make the differential operator self-adjoint. The so-called ‘optimal upwind’ parameter (α) arises naturally from the process of approximating the modifying function. Transient and steady-state examples on uniform and non-uniform meshes are shown.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300208
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    A unified numerical integration formula for the perfectly plastic von Mises model (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 491-504 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The accuracy of numerical integration of the perfectly plastic constitutive equation of von Mises is examined. Based on the analysis of the three existing numerical integration schemes a unified numerical integration formula (UNIF) is derived, which encompasses the three existing schemes as special cases and allows one to integrate the constitutive equation more accurately. According to the UNIF there are, in fact, many integration schemes depending on the direction of the trial stress. The validity of the UNIF is verified by presenting ten contours of constant angular error calculated with the UNIF. We then come to the conclusion that the three widely used schemes are by no means the most accurate ones. Some other schemes with better accuracy are thereby suggested. The determination of the number of substeps is also discussed in conjunction with the UNIF, when a multi-step method is used.
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300308
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    The finite element method Vol. 1: Basic formulation and linear problems, Fourth Edition by O. C. Zienkiewicz and R. L. Taylor, McGraw-Hill, Maidenhead, England, 1989. No. of pages: 648. Price (cloth): £25.00 ISBN: 0-07-084174-8 (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 565-567 
    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.1620300312
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    Biharmonic analysis of rectilinear plates by the boundary element method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 517-539 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An improved boundary element formulation (BEM) for two-dimensional non-homogeneous biharmonic analysis of rectilinear plates is presented. A boundary element formulation is developed from a coupled set of Poisson-type boundary integral equations derived from the governing non-homogeneous biharmonic equation. Emphasis is given to the development of exact expressions for the piecewise rectilinear boundary integration of the fundamental solution and its derivatives over several types of isoparametric elements. Incorporation of the explicit form of the integrations into the boundary element formulation improves the computational accuracy of the solution by substantially eliminating the error introduced by numerical quadrature, particularly those errors encountered near singularities. In addition, the single iterative nature of the exact calculations reduces the time necessary to compile the boundary system matrices and also provides a more rapid evaluation of internal point values than do formulations using regular numerical quadrature techniques. The evaluation of the domain integrations associated with biharmonic forms of the non-homogeneous terms of the governing equation are transformed to an equivalent set of boundary integrals. Transformations of this type are introduced to avoid the difficulties of domain integration. The resulting set of boundary integrals describing the domain contribution is generally evaluated numerically; however, some exact expressions for several commonly encountered non-homogeneous terms are used. Several numerical solutions of the deflection of rectilinear plates using the boundary element method (BEM) are presented and compared to existing numerical or exact solutions.
    Additional Material: 15 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300310
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    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990) 
    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.1620300401
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    The numerical simulation of heat conduction in irregularly-shaped materials of thermally-dependent properties (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 679-696 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical simulation of conduction heat transfer in arbitrarily-shaped regions is relevant to many engineering applications including the casting of plastics and metals, cold region problems and latent heat storage. This class of problem offers its particular challenges. The accurate computational simulation of conduction with thermally-dependent properties requires a solution technique with good conservation properties. The boundary-fitted co-ordinates of an arbitrary solution domain typically yield grids which are non-orthogonal and which, consequently, make energy conservation difficult to model.In the current article, a technique is described to simulate accurately the conduction heat transfer in materials of thermally-dependent properties in irregular domains. The method combines boundary-fitted co-ordinates with the finite volume method, FVM, to produce a numerical technique which will accurately solve this non-linear conduction problem using a grid which may be highly skewed. This capability is achieved through a unique treatment of the cross-derivative terms that arise when the heat conduction equation is transformed to a non-orthogonal grid. The cross-derivative terms represent the non-normal components of the heat fluxes into the skewed control volume. The tangent components of the heat fluxes are interpreted in a special way to produce finite difference expressions which accurately model the cross-derivative partial.The numerical procedure is validated by comparing it against a purely analytical mathematical method. Although the numerical results have been obtained using a highly skewed grid, they exhibit close agreement with the analytically-derived solution.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300409
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    Recent advances, trends and new perspectives via enthalpy-based finite element formulations for applications to solidification problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 803-820 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper describes recent advances and trends in finite element developments and applications for solidification problems. In particular, in comparison to traditional methods of approach, new enthalpy-based architectures based on a generalized trapezoidal family of representations are presented which provide different perspectives, physical interpretation and solution architectures for effective numerical simulation of phase change processes encountered in solidification problems. Various numerical test models are presented and the results support the proposition for employing such formulations for general phase change applications.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300415
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    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990) 
    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.1620290101
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    Total Lagrangian formulation for the large displacement analysis of rectangular plates (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 73-103 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a method for the non-linear dynamic analysis of rectangular plates that undergo large rigid body motions and small elastic deformations is presented. The large rigid body displacement of the plate is defined by the translation and rotation of a selected plate reference. The small elastic deformation of the midplane is defined in the plate co-ordinate system using the assumptions of the classical theories of plates. Non-linear terms that represent the dynamic coupling between the rigid body displacement and the elastic deformation are presented in a closed form in terms of a set of time-invariant scalars and matrices that depend on the assumed displacement field of the plate. In this paper, the case of simple two-parameter screw displacement, where the rigid body translation and rotation of the plate reference are, respectively, along and about an axis fixed in space, is first considered. The non-linear dynamic equations that govern the most general and arbitrary motion of the plate are also presented and both lumped and consistent mass formulations are discussed. The non-linear dynamic formulation presented in this paper can be used to develop a total Lagrangian finite element formulation for plates in multibody systems consisting of interconnected structural elements.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290107
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    Contact problems of kinked cracks modelled by a boundary integral method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 847-860 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on the integral equation for the resultant forces along a crack, a numerical method is developed for the solution of two dimensional kinked crack problems taking crack contact into account. The method is demonstrated by a consideration of an elastic half-plane containing a piece-wise straight line crack. Two numerical examples are presented and compared to finite element calculations. The numerical results indicate that the present method can be an effective and reliable tool for investigations of kinked crack problems associated with crack contact.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290412
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  • 38
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    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990) 
    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.1620290501
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    A truncated Newton-Lanczos method for overcoming limit and bifurcation points (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1065-1077 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this study procedures for overcoming limit and bifurcation points in large-scale structural analysis problems are described and evaluated. The methods are based on Newton's method for the outer iterations, while for the linearized problem in each iteration the preconditioned truncated Lanczos method is employed. Special care is placed upon line search routines for accelerating the convergence properties and enhancing the stability of the outer method. The proposed methodology retains all characteristics of an iterative method by avoiding the factorization of the current stiffness matrix. The necessary eigenvalue information is retained in the tridiagonal matrix of the Lanczos approach.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290511
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    Prediction of thermal stress and deformations due to phase change in solidifying objects via flux/stress based finite element representations (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1473-1485 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents numerical simulations for the prediction of thermal-stress and deformation fields resulting from phase change in solidifying bodies employing new finite element representations. The formulations developed in this paper provide different perspectives and physical interpretation for the modelling/analysis of thermo-mechanical problems and possess several inherent advantages. In comparison to traditional approaches for solving similar problems, the paper employs new computational architectures in conjunction with flux/stress based representations to enhance the overall effectiveness. Comparative numerical applications validate applicability of the formulations for predicting the temperature induced deformations and stresses resulting from effects due to phase change.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290707
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    A numerical integration scheme for finite element method based on symbolic manipulation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1539-1549 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the improvement of the efficiency and accuracy of the usual numerical integration procedures for the finite element method. A modified numerical integration scheme based on both the symbolic manipulation system and the numerical integration formula is proposed. Its efficiency for the integration of complicated rational or irrational expressions is demonstrated through several numerical examples. To verify its effectiveness in the calculation of the finite element stiffness matrix, a simple numerical example is also presented.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290711
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  • 42
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    Inverse finite element techniques for the analysis of solidification processes (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1569-1587 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper provides a finite element methodology (FEM) for the solution of several one-dimensional inverse solidification problems. In particular two design related problems will be addressed. The first one uses an inverse technique to calculate the boundary heat flux history that will achieve a specified velocity and flux at the freezing front. This front velocity and flux history can be appropriately selected so that the cast structure is controlled. The second problem is the calculation of the boundary heat flux and freezing front position, given appropriate estimates of the temperature field in a specified number of sensor locations (thermocouples) inside a solidifying body.Front fixing and front tracking FEM techniques are used for the solution of the first problem, while a fixed domain finite element formulation (enthalpy method) is used for the solution of the second one. The ‘future information technique’ is employed in both problems. A detailed analysis of the effect on the solution of the error in the data, amount of future information used, time step, number of sensors and their location and of other parameters in the solution will be examined via several numerical tests. Finally, further applications of such inverse methodologies on the control of casting processes will be mentioned.
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290713
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    Two-level approximation concept in structural synthesis (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1681-1699 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new concept for complex structural optimization problems is presented. Based on investigation of the mechanical nature of the studied problem, a set of basic mechanical characteristics can be introduced as the generalized variables. A high-quality explicit first-level approximate problem FA is formed by first-order Taylor series expansion of the behaviour constraints in terms of the generalized variables. The FA is explicit but highly non-linear with respect to design variables. Therefore, a second-level approximation is introduced to solve the FA by considering a sequence of second-level approximate problems SA in the design variable space. This approach is a Two-Level Approximation Concept. Its application to space frame synthesis shows its good grasp of the mechanical nature of the problem. The computational results for several examples show that the method presented in this paper is very efficient.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290805
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    Free-vibration analysis of three-dimensional solids by BEM (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1737-1757 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In practical applications, it is often necessary to determine the natural frequencies and mode shapes of a solid, in addition to the static response under a variety of loading conditions. This paper discusses the calculation of natural frequencies and mode shapes of three-dimensional solids using the boundary element method. The method developed is based on the use of particular integrals of the elastic equilibrium equations, and employs only real arithmetic. It represents an extension to three dimensions of work previously carried out for two-dimensional problems in References 1 and 15. The method has been incorporated, for multiregion analysis, in the BEST3D (Boundary Element Solution Technology - Three Dimensional) computer program.Much of the work described in this paper was carried out under the support of National Aeronautics and Space Administration Contract NAS3-23697, ‘3D Inelastic Analysis Methods for Hot Section Components’. The program managers at the NASA-Lewis Research Center are Dr C. C. Chamis and Mr Dale Hopkins. The program manager at Pratt & Whitney is Dr E. S. Todd Results of the boundary element calculations are compared with analytical, finite element and experimental results.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290809
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    Numerical analysis of three-time-level finite difference schemes for unsteady diffusion-convection problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 307-330 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For the linear diffusion-convection model problem, this paper develops the numerical analysis of two classes of three-time-level second order finite difference schemes: weighed schemes similar to two-step schemes for differential equations and LF schemes based on the classical conservative approximation of the wave equation. As in our paper devoted to two-level schemes, Fourier Analysis is an essential tool which yields several key properties (stability, dissipation, numerical diffusion and dispersion). It also permits the analysis of parasitic solutions characteristic of three-level schemes and their control in terms of the starting scheme.The analysis is completed by giving results on the accuracy, positivity and parabolicity of the numerical schemes.The main conclusions are the expected superiority of these schemes over two-level schemes when the diffusion phenomenon is not negligible (cell Reynolds number less than 1) and the very limited possibilities of obtaining satisfactory numerical results (even with upstream differencing) when convection is strongly predominating.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300207
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    Towards adaptive mesh refinement: Application of new rectangular hybrid finite elements in 2D elasticity problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 473-489 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A modified global approach to choosing stress terms for hybrid finite elements in plane stress problems is based on the known requirement of minimum number of stress parameters. Let nβ be the number of independent β-stress parameters, nq the number of nodal displacements and nR the number of rigid body degrees of freedom, then the satisfaction of the criterion nβ ≥ nq - nR of the assembled structure instead of the individual element enables the reduction of nβ. New rectangular hybrid transition elements applied in adaptive mesh refinement and a new eight node rectangular invariant element including only 12 β parameters, based on the modified criterion, are presented here.The new elements, which are used in order to analyse the stress singularity of two bonded elastic plates of different materials, yield reliable results compared with results based on classical hybrid elements, displacement elements and the analytic solution.
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300307
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    Conference diary (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1131-1134 
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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.1620290515
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    Erratum (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. ii 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290602
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    Tangent constitutive matrices for inelastic finite element analysis (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1193-1203 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general formulation is presented for the tangent constitutive matrices of rate-independent material models which assume that the strain increment consists of two components. One component is related to the stress increment through a known constitutive matrix, while the other component results from deformation mechanisms not reflected in the constitutive matrix. The procedure to modify the known matrix for these additional strains is specified. The formulation is a generalization of the well-known procedure used in plasticity to modify the elastic constitutive matrix for plastic deformation. Application to both the classical and endochronic theories of plasticity and to a smeared crack theory is illustrated.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290606
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    Error indicators for adaptive mesh refinement in the boundary element method - a new approach (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1247-1269 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a new approach to the development of a posteriori error indicators for the direct boundary element method (BEM) is presented. It takes advantage of a unique opportunity offered by the collocation BEM, that is the possibility of obtaining more than one numerical solution from a given boundary element mesh. Unlike other approaches, the error indicator introduced in the present paper does not require any explicit evaluation of the residual of the approximate solution. In order to test the capability of the proposed error indicators to actually control a selective mesh refinement process, an h-adaptive refinement strategy is also described, together with the criteria for refinement and for the termination of the adaptive process. Full details on the whole numerical implementation for two-dimensional problems are provided. In particular, there is described a direct method for the numerical evaluation of Cauchy principal value integrals. Numerical examples show that pointwise convergence is always obtained in a few steps and the final meshes look nearly as if they were designed by an expert analyst.
    Additional Material: 17 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290610
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    A boundary element algorithm using compatible boundary displacements and tractions (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1323-1341 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: With the aid of Muskhelishvili's complex plane elasticity solution representation compatible displacement and stress fields are constructed. The complex functions in these formulas are represented by Cauchy integrals, which are discretized along the boundary with the aid of complex shape functions for each boundary element. The constructed displacement and stress functions satisfy the Navier equations and the equilibrium equations, respectively. The use of fifth order complex basis functions with continuous second complex derivatives gives numerical results of high accuracy.
    Additional Material: 17 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290614
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    Boundary elements in zoned media: Direct and indirect methods (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1727-1735 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Several formulations of the Boundary Element Method (BEM) are examined herein in the context of heterogeneous media. A strong singularity develops at re-entrant interzonal corners and its effect is made more acute by large differences in the material properties. The effects of this singularity on the performance of the various BEM formulations are illustrated with examples. It is concluded that the direct BEM, either in the collocation or Galerkin formulations, is unable to give good results in zones of low conductivity. On the other hand the indirect BEM does not adequately reproduce the behaviour of the flow field near boundaries. A multi-step version of the direct BEM is formulated to eliminate the difficulties introduced by the interzonal singularities.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290808
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    Gauss quadrature rules for finite part integrals (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 13-26 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We construct a set of polynomials ϕn(x,ζ) which are orthogonal with respect to w(x)/(x - ζ)2, where w x is a weight function. These polynomials can be used for the definition of a Gauss quadrature formula for the finite part integral The process is exactly the same as the one used for the extraction of the classical Gauss formula for the Riemann integrals. Three different methods are derived.The first and most accurate quadrature formula is successfully tested in some numerical examples. The proposed quadrature formulas have many applications in problems of mathematical physics, mechanics, etc.
    Additional Material: 3 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620300103
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    Dynamics of general flexible multibody systems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 77-97 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general treatment is presented for modelling the dynamics of a flexible multibody system, using a lumped mass finite element approach. The system topology considered here is defined as an arbitrary combination of both rigid and flexible bodies, connected together by joints that permit translation and compliance, in a general tree configuration. An extension to handle closed loop kinematic chains is also indicated. Kane's theory of generalized speeds, which is based on the Lagrange-D'Alembert principle, is used to derive the equations of motion, and this results in a very efficient computer oriented methodology for solving the dynamics of such large mechanical systems. To facilitate numerical computations, these dynamical equations are transformed into a system of first-order differential equations for an explicit formulation of the problem. The accuracy of the proposed formulation is assessed via three examples with known solutions. The results obtained indicate the method is accurate, efficient and versatile for the analysis of a general, flexible multibody system.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300106
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    A general procedure for the direct computation of turning and bifurcation points (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 155-176 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300110
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    Books received (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 389-390 
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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.1620300212
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    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990) 
    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.1620300301
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    Non-diffusive N + 2 degree Petrov-Galerkin methods for two-dimensional transient transport computations (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 397-418 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new non-diffusive Petrov-Galerkin type finite element method which uses test functions two polynomial degrees higher than the trial functions is developed for the transient convection dominated transport equation in two dimensions. The scheme uses bilinear quadrilateral finite elements for the spatial discretization and Crank-Nicolson finite differencing for the time integration. The standard product extension of very successful one-dimensional N + 2 degree upwinding functions to two dimensions is ineffective for general 2-D flow problems, especially at higher Courant numbers where cross-derivative truncation terms become important. Therefore effective N + 2 degree test functions are developed through an analysis by which the truncation error terms in the discrete nodal equation are eliminated up to fifth order. The new scheme is very effective for general 2-D flows over a wide Courant number range and eliminates the troublesome cross-derivative truncation terms. The scheme is simple and robust in that the upwinding coefficients are readily defined and only dependent on Courant number. Numerical examples illustrate the excellent behaviour of the new scheme.
    Additional Material: 15 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300302
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    An implementation of the hp-version of the finite element method for Reissner-Mindlin plate problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 459-471 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Reissner-Mindlin plate theory is still a topic of research in finite element analysis. One reason for the continuous development of new plate elements is that it is still difficult to construct elements which are accurate and stable against the well-known shear locking effect. In this paper we suggest an approach which allows high order polynomial degrees of the shape functions for deflection and rotations. A balanced adaptive mesh-refinement and increase of the polynomial degree in an hp-version finite element program is presented and it is shown in numerical examples that the results are highly accurate and that high order elements show virtually no shear locking even for very small plate thickness.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300306
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    Thermo-mechanical finite element model of casting systems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 579-599 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A coupled finite element model is developed to simulate the metal casting process. We present a new method for capturing the solidification zone and obtaining the corresponding rate of phase change. The latent energy release is predicted by the heat conduction rate and introduced by following the enthalpy-temperature curve. The influence of mould-metal contact is considered in calculating the heat flux through the mould-metal interface. A viscoplastic model is employed to predict the gap opening and evolution of plastification.Four examples are presented to demonstrate certain numerical aspects and the capability of the model for industrial applications.
    Additional Material: 20 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300403
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    Monte Carlo simulation of indoor radiant environment (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 615-627 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a numerical method of radiant environment analysis in a complicated enclosure containing human bodies and furniture. An arbitrary configuration expressed in a three-dimensional co-ordinate system can be treated by this method. A unique space index and another surface index are proposed to specify the geometry of solid body and surface in the enclosure. The Monte Carlo method is used to determine direct interchange areas, which are then transformed into total exchange areas using the zone method. Energy balance equations accounting for thermal radiation, convection, wall conduction and air ventilation are then formulated for each solid surface segment in the enclosure. A human body model with skin temperatures and clothing is also proposed to simulate its heat release and to predict local thermal sensation around the body. As a practical application, this method is applied to the analysis of the radiant environment in a floor-heated meeting room with eight people seated around a table.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300405
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    F.E.M. in steady MHD duct flow problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 647-659 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The governing equations and the boundary conditions of steady incompressible magnetohydrodynamic (MHD) problems are adapted to the case of steady MHD flow in simply connected cross sections with arbitrary wall conductance. The problem is then solved numerically by means of the finite element method based on the weighted residual approach, and solutions for industrially relevant Hartmann numbers and non-symmetric kinetic fields are presented.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300407
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    A conservative algorithm for multidimensional conduction phase change (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 697-709 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a generally applicable version of an algorithm, for multidimensional phase change conduction, is presented which bridges the gap between ‘full enthalpy’ and ‘equivalent heat capacity’ methods. In the text the problem is formulated first with reference to the three-time-level method for the FE analysis of non-linear heat conduction. Then the suggested algorithm is utilized as a ‘corrector’ which can be activated for the analysis of isothermal phase change problems. In the corrector step the enthalpy balance is recovered from the standard formulation, and temperatures are post-calculated by means of the inverse temperature vs. enthalpy function. The algorithm is verified in one-dimensional situations by comparing the results obtained with available analytical and numerical solutions for boundary conditions of the first kind (temperature) and of the third kind (convection). Finally, as a 2-D test problem, a solution is presented for inward solidification in a cylinder, using Cartesian co-ordinates to demonstrate robustness with respect to space deformation of the mesh.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300410
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    Computer simulation of salami drying (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 767-777 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Salami sorts are made of special meat pastes filled in hygroscopic casing and preserved by drying.The characteristic features and the time of drying are greatly affected by the operational conditions. Factories are interested in reducing the time of the drying treatment. To determine a reliable and economic drying schedule a physical-mathematical model has been elaborated and used. The system of equations has been solved numerically by using the FDM technique for the determination of the temperature, concentration and stress fields as a function of the time. Computed results have been verified by experiments.By the numerical analysis it has been proved that the maximum rate of drying to be permitted is limited by the danger of possible deformations and inner fissures caused by tensile stresses occurring if shrinkage is prevented.On the basis of the proper drying schedule an algorithm and a strategy of the microprocessing operational control has been elaborated.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300413
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    Letter to the editor (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 211-215 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290114
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    Conference diary (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 219-222 
    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.1620290116
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    A boundary-integral formulation for complex three-dimensional geometries (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 263-273 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new boundary-integral formulation is proposed to analyse the heat transfer in complex three-dimensional geometries. One example of such geometry is the die sets in the injection moulding process. Networks of cooling conduits within the mould and the closely spaced die surfaces require special attention both in formulation and numerical treatment of the integral equations. The proposed formulation couples the boundary formula, the gradient of the boundary formula and the exterior formula. The derivation of the integral equations is presented here along with an efficient method for integration of some of the kernels in these equations and a semi-analytical procedure for the integration of the highly singular integrands which result from differentiating the boundary formula. Although the techniques introduced here are applied to a particular problem in heat transfer, their potential application is much broader.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290204
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    The effect of temperature and total gas pressure on the moisture content in a capillary porous body (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 357-369 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element method is used for the solution of two dimensional heat, mass and pressure transfer problems in capillary porous bodies. This paper demonstrates a practical solution to Luikov's three degree of freedom system of partial differential equations where, previously, only an analytical solution in one dimension was feasible.
    Additional Material: 12 Ill.
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    Mathematical modelling of creep and shrinkage of concrete, edited by Z. P. Bazant, Wiley, Chichester, 1988. ISBN 0 471920576 (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 447-447 
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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.1620290214
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    Magnetostatic field computations in terms of two-component vector potentials (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 515-532 
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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 the magnetostatic problem is stated in terms of two-component electric and magnetic vector potentials. An associated numerical method, based on the adoption of edge elements, is proposed. This procedure overcomes the cancellation problems and the complexity of the interface conditions encountered by similar approaches in the presence of magnetic inhomogeneities and discontinuities of currents and magnetic fields.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290305
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    Computer simulation of turbulent swirling flows (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 533-557 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Simulation of turbulent swirling flows has been carried out to provide insight on streamline curvature effects. Numerical calculations were based on the control-volume method. Turbulence effects were represented by two-equation turbulence models. The analysis of steady flow between two concentric rotating cylinders showed that the most promising model which incorporates curvature effects is that based on mixing energy developed by Wilcox and Chambers, as opposed to the ad hoc modification to the standard k-∊ model. This model has also been used to simulate the decay of turbulent swirling flow in a short cylinder. A comparison between calculations and experimental results for such flow fields has been presented.
    Additional Material: 19 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290306
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    Parallel multisplitting, block Jacobi type solutions of linear systems of equations (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 619-632 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three parallel iterative schemes to solve banded systems of equations are presented in this study. The techniques are special implementations of the theory of matrix multisplitting. The resulting algorithms are implemented on a Multiple Instruction Multiple Data (MIMD) grid architecture using 16 Transputer processors. Parametric analyses are performed to develop convergence criteria and examine the speed-up of solution. It is concluded that the algorithms make very efficient use of the parallel computer architecture, especially if this consists of a large number of nodes.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290310
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    A finite-element model of two-layer ocean circulation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 665-678 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mixed finite-element formulation is applied to solve the quasi-geostrophic equations in a two-layer ocean domain enclosed by solid boundaries. A combination of leap-frog and θ-schemes is used to integrate the equations in time. Wood's formula of the wall vorticity is derived in our formulation for the case of square elements adjacent to the boundaries. Long-term computations with and without lumping have been carried out.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290313
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    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990) 
    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.1620290401
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    The multigrid method in solid mechanics: Part I - Algorithm description and behaviour (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 719-737 
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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 is described that can be used to obtain the finite element solution of linear elastic solid mechanics problems. The method is applied to some two dimensional problems to evaluate its strengths and weaknesses. Extensive studies are made to determine the convergence behaviour of the method. In general, this depends on many factors: the number of degrees-of-freedom in the discretization, characteristics of the algorithm, Poisson's ratio when it is close to 0·5, the amount of bending deformation in the problem under consideration, and the degree of non-uniformity in the mesh. Only certain values of the multigrid parameters allow a converged solution to be obtained with a computational effort proportional to the number of degrees-of-freedom. These values include the optimum ones, i.e. those that lead to convergence with the least computational effort. The constant of proportionality is only independent of the number of degrees-of-freedom and still depends on the other factors listed above.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290404
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    Partial hybrid stress element for transient analysis of thick laminated composite plates (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1787-1796 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The variationally consistent partial hybrid stress element proposed by the authors is extended to transient analysis of thick laminated composite plates in this paper. Through dividing six stress components into flexural (σx, σy, τxy, σz) and transverse shear (τxz, τyz) parts, the corresponding dynamic version of the modified Hellinger-Reissner principle is presented. By assuming stress parameters for transverse shear only, the partial hybrid stress element can be used to solve transient problems without any contradiction. The mass matrix derived is a simply consistent mass regardless of the assumed stress field. Comparisons are made with results available in the literature. Through thickness variations of all the six stress components for a dynamic version of Pagano's example are also presented for the first time. These results can serve as a reference source for future comparisons.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290811
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    Transient finite element computations on 65536 processors: The connection machine (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 27-55 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper reports on our experience in solving large-scale finite element transient problems on the Connection Machine. We begin with an overview of this massively parallel processor and emphasize the features which are most relevant to finite element computations. These include virtual processors, parallel disk I/O and parallel scientific visualization capabilities. We introduce a distributed data structure and discuss a strategy for mapping thousands of processors onto a discretized structure. The combination of the parallel data structure with the virtual processor mapping algorithm is shown to play a pivotal role in efficiently achieving massively parallel explicit computations on irregular and hybrid two- and three-dimensional finite element meshes. The finite element kernels written in C*/Paris have run with success to solve several examples of linear and non-linear dynamic simulations of large problem sizes. From these example runs, we have been able to assess in detail their performance on the Connection Machine. We show that mesh irregularities induce an MIMD (Multiple Instruction Multiple Data) style of programming which impacts negatively the performance of this SIMD (Single Instruction Multiple Data) machine. Finally, we address some important theoretical and implementational issues that will materially advance the application ranges of finite element computations on this highly parallel processor.
    Additional Material: 20 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300104
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    Generalized axisymmetric elastodynamic analysis by boundary element method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 115-131 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The boundary element formulation for three-dimensional problems of steady state (periodic) dynamic analysis has been cast into the generalized axisymmetric form by expressing the boundary tractions and displacements in terms of a Fourier series expansion. The resulting formulation has been developed for the dynamic analysis of axisymmetric geometries subjected to non-axisymmetric loading. The analysis has been implemented in a large general purpose analysis capable of analysing both finite as well as semi-infinite domains and a series of examples has been shown to demonstrate the versatility of the implementation.
    Additional Material: 15 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300108
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    Analysis of locking and stress oscillations in a general curved beam element (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 177-200 
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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, we have attempted to provide new insights into the phenomenon of shear and membrane locking in a general quadratic curved beam element. Locking is seen to be accompanied by significant quadratic oscillations in the axial force and cubic oscillations in the shear force. The functional reconstitution technique is applied to derive accurate error estimates for the manner in which locking is relieved and for the magnitude of the stress oscillations. The orthogonally correct field-consistent interpolations are determined for the optimal form of the element using an elegant concept of expanding strain interpolations in terms of Legendre polynomials. The popular two-point Gaussian integrated version of the element is shown to be non-orthogonal, resulting in a cubic oscillation in the shear force that curiously vanishes at the Barlow points.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300111
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    Iterated θ-method for hyperbolic equations (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 271-290 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The iterated θ-methods employing residue smoothing for finding both steady state and time-accurate solutions of semidiscrete hyperbolic differential equations are analysed. By the technique of residue smoothing the stability condition is considerably relaxed, so that larger time steps are allowed which improves the efficiency of the method. The additional computational effort involved by the explicit smoothing technique used here is rather low when compared with its stabilizing effect. However, in the case where time-accurate solutions are desired, the overall accuracy may be decreased. This paper investigates the effect of residue smoothing on both the stability and accuracy, and presents a number of explicitly given methods based on the iterated implicit midpoint rule (θ = 1/2). Numerical examples confirm the theoretical results.
    Additional Material: 12 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620300205
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    Announcement (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. ii 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290102
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    A full tangent stiffness field-boundary-element formulation for geometric and material non-linear problems of solid mechanics (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 15-35 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The field-boundary-element method naturally admits the solution algorithm in the incompressible regimes of fully developed plastic flow. This is not the case with the generally popular finite-element method, without further modifications to the method such as reduced integration or a mixed method for treating the dilatational deformation. The analyses by the field-boundary-element method for geometric and material non-linear problems are generally carried out by an incremental algorithm, where the velocities (or displacement increments) on the boundary are treated as the primary variables and an initial strain iteration method is commonly used to obtain the state of equilibrium. For problems such as buckling and diffused tensile necking, involving very large strains, such a solution scheme may not be able to capture the bifurcation phenomena, or the convergence will be unacceptably slow when the post-bifurcation behaviour needs to be analysed. To avoid this predicament, a full tangent stiffness field-boundary-element formulation which takes the initial stress-velocity gradient (displacement gradient) coupling terms accurately into account is presented in this paper. Here, the velocity field both inside and on the boundary are treated as primary variables. The large strain plasticity constitutive equation employed is based on an endochronic model of combined isotropic/kinematic hardening plasticity using the concepts of material director triad and the associated plastic spin. A generalized mid-point radial return algorithm is presented for determining the objective increments of stress from the computed velocity gradients. Numerical results are presented for problems of diffuse necking, involving very large strains and plastic instability, in initially perfect elastic-plastic plates under tension. These results demonstrate the clear superiority of the full tangent stiffness algorithm over the initial strain algorithm, in the context of the integral equation formulations for large strain plasticity.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290104
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    A new implementation of the Lanczos method in linear problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 141-159 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Lanczos algorithm has proved to be a powerful solution method not only for finding the eigenvalues but for solving linear systems of equations. In this work a new implementation of the algorithm is presented for solving linear systems of equations with a sequence of right-hand sides. The versions of the method proposed in the past treat the right-hand side vectors successively by keeping the tridiagonal matrix and the orthonormal basis in fast or secondary storage. The new technique handles all approximations to the solution vectors simultaneously without the necessity for keeping the tridiagonal matrix or the orthonormal basis in fast or secondary storage. Thus, when the first solution vector has converged to a required accuracy good approximations to the remaining solution vectors have simultaneously been obtained. It then takes fewer iterations to reach the final accuracy by working separately on each of the remaining vectors.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290110
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    A non-proportional loading finite element analysis of continuum damage mechanics for ductile fracture (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 197-209 
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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 a finite element analysis based on an anisotropic model of continuum damage mechanics theory proposed recently by the authors for ductile fracture under non-proportional loading. The condition of non-proportional loading is formulated by introducing a dynamic co-ordinate system of principal damage allowing the principal direction of damage during the loading to rotate accordingly.The finite element analysis developed under non-proportional loading is applied to predict the crack initiation load of a centre-cracked plate under uniform loading. The predicted load agrees satisfactorily with those determined experimentally with centre-cracked thin plates made of aluminium alloy 2024-T3. The analysis also reveals under non-proportional loading the hysteresis effect of the principal directions of damage and stress. In addition, the influence of varying anisotropic damage coefficients on the crack initiation load and the crack tip displacement profile is also examined. The larger the degree of the anisotropy, the higher the crack initiation load. The magnitude of the crack tip displacement profile is found to be proportional to the degree of material anisotropy.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290113
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    Element by element a posteriori error estimation and improvement of stress solutions for two-dimensional elastic problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 223-244 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A quantitative method of a posteriori error estimation based on finite element solutions is developed. The proposed method can estimate the error of solutions obtained by the finite element method for two-dimensional elastic problems with 4-node elements. Since the error is estimated element by element, the proposed method does not require a large memory or long computing time. Not only rectangular elements but also arbitrarily shaped 4-node elements can be used in this method for estimating the error in the finite element computation with high accuracy. The finite element solutions are improved by adding the estimated errors onto the original solutions. The proposed method can be utilized for any type of linear problem if an isoparametric finite element method is used.
    Additional Material: 27 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290202
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    Higher derivative explicit one step methods for non-linear dynamic problems. Part II: Practical calculations and comparisons with other higher order methods (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 291-301 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A generalized explicit one step alogorithm developed in Part I of this paper is presented in the form of a predictor-corrector scheme suitable for arbitrary non-linear analyses of structural dynamics problems. Convergence results are checked through practical calculations on linear and non-linear systems. The generalized algorithm proposed is compared with other recently developed higher order one step algorithms. The slight amount of additional computational effort compared to second order methods pays off in linear and weakly non-linear systems. The behaviour of the methods is also tested on extreme stiffening and softening systems to investigate reliability and robustness of the algorithm.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290206
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    Non-linear vibration of frames by the incremental dynamic stiffness method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 337-356 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dynamic stiffness method is extended to large amplitude free and forced vibrations of frames. When the steady state vibration is concerned, the time variable is replaced by the frequency parameter in the Fourier series sense and the governing partial differential equations are replaced by a set of ordinary differential equations in the spatial variables alone. The frequency-dependent shape functons are generated approximately for the spatial discretization. These shape functions are the exact solutions of a beam element subjected to mono-frequency excitation and constant axial force to minimize the spatial discretization errors. The system of ordinary differential equations is replaced by a system of non-linear algebraic equations with the Fourier coefficients of the nodal displacements as unknowns. The Fourier nodal coefficients are solved by the Newtonian algorithm in an incremental manner. When an approximate solution is available, an improved solution is obtained by solving a system of linear equations with the Fourier nodal increments as unknowns. The method is very suitable for parametric studies. When the excitation frequency is taken as a parameter, the free vibration response of various resonances can be obtained without actually computing the linear natural modes. For regular points along the response curves, the accuracy of the gradient matrix (Jacobian or tangential stiffness matrix) is secondary (cf. the modified Newtonian method). However, at the critical positions such as the turning points at resonances and the branching points at bifurcations, the gradient matrix becomes important. The minimum number of harmonic terms required is governed by the conditions of completeness and balanceability for predicting physically realistic response curves. The evaluations of the newly introduced mixed geometric matrices and their derivatives are given explicitly for the computation of the gradient matrix.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290209
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    Conference diary (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 449-452 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290215
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    Non-linear optimization technique for partial solution of generalized eigenvalue problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 473-482 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an alternative to the subspace iteration and Lanczos techniques, both of which are now used to solve partial eigenvalues and eigenvectors of large generalized linear first order symmetric matrix systems. It is based on non-linear optimization of a modified Rayleigh quotient. The elements of the eigenvector are the decision variables. Orthogonality constraints with respect to the two matrices are incorporated in the sequential unconstrained optimization scheme. By imposing normality with respect to one of the matrices, the Hessian matrix reduces to a much simpler form for which the Woodburry transformation may be used. This, in combination with the fact that the banded structure of the matrices is maintained, results in a number of operations of the same order as the two standard methods. Shifting is readily integrated. Numerical comparison with existing techniques demonstrate the practicality of this method.
    Additional Material: 7 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620290303
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    Importance and use of rigid body mode in boundary element method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 453-472 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The superposition of a rigid body mode on a body should result in a corresponding change in displacement values but should not affect the stresses. However, in the numerical solution by the boundary element method (BEM) large errors may be obtained for displacements and stresses if a rigid body mode is present in the input data. To eliminate the effects of the rigid body mode on the numerical accuracy of the solution, the fundamental solutions for displacements must be correctly interpreted and used. The rigid body mode may be unknowingly present in the boundary condition data. It may be present because the boundary data are not known accurately. Or it may be present if the displacement values at the support have been computed from a separate analysis. A rigid body mode may arise due to the collocation nature of satisfying the boundary conditions. The point values of the applied load at the collocation point may not satisfy equilibrium. Or the point values of the specified displacements may not satisfy the condition of zero translation and rotation. For bodies under pure traction, we know that the analytical solution can contain an arbitrary amount of rigid body mode. Numerically, however, some unknown value is assigned to this rigid body mode. It might be desirable (for example in limit analysis) to eliminate the rigid body mode from the displacements to obtain deformation of a point with respect to a point on the body. In addition, knowledge and elimination of the rigid body mode is necessary for the implementation of a scheme described by this author in an earlier work. The importance of the earlier work is that it reduced the sensitivity of the BEM to changes and errors in the input data. In this paper the causes, and the effects of the rigid body mode on the BEM, the correct interpretation of the fundamental solution for displacements and an algorithm for determining and accounting for the rigid body mode are discussed. A numerical example validates the ideas in this paper for the indirect version. The algorithm for the direct version is presented without a numerical example in the Appendices.
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    A panel method computation for oscillating aerofoil in compressible flow (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 559-578 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A panel method using source and doublet singularity has been proposed to solve for subcritical aerodynamics of a two dimensional steady and unsteady aerofoil. The source singularities are placed on the aerofoil surface. The doublet singularity is distributed by a function along the chordline of the aerofoil; this distribution is further projected downstream into infinity.The aerodynamics of an oscillating aerofoil is investigated. The governing unsteady linearized potential equation has a Hankel function as its fundamental solution, which is a source type function. A combination of source and doublet singularity is therefore used for solving the unsteady compressible problem by means of the panel method, this methodology being an extension of a steady aerofoil formulation. Incremental effects of profile change in aerofoil and wake geometry are accounted for. A surface boundary condition is applied on the stationary mean aerofoil surface with time dependent geometrical changes accounted for. An unsteady Kutta condition of equal pressure across the trailing edge is assumed. Results are presented on the aerodynamic influence of Mach number, oscillating frequency parameter, angle of incidence and change of pivoting point. Results are also compared with linear theory, a subsonic experimental result and a subcritical solution of a transonic model.
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290307
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    A new approach in non-linear mechanics: The large time increment method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 647-663 
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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 family taking into account the entire loading process in a single large time increment is proposed to compute structures with physical non-linearities and is tested on some examples in elastoplasticity. The method considerably reduces the number of transfers between local and global levels, hence the numerical cost of calculation is also diminished.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290312
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    Vibration analysis of fluid-solid systems using a finite element displacement formulationThis research was sponsored by the Lawrence Livermore National Laboratory under contract CERDA LLNL-1513603. This support and the interest of Dr G. L. Goudreau are gratefully acknowledged. (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 683-698 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This report presents a finite element solution for the vibration interaction between an inviscid fluid and a solid. The equation of motion governing the inviscid fluid is expressed in terms of the displacements. This ensures that compatibility and equilibrium will be satisfied automatically along the interface of the coupled systems. To suppress circulation modes with non-zero energy, reduced integration is used when computing the element stiffness matrix contributed by the fluid. In addition, a projection is used on the element mass matrix in order to remove the spurious modes which result from the use of reduced integration. Numerical examples for both fluid and coupled fluid-solid systems are performed and the results are shown.
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    URL: http://dx.doi.org/10.1002/nme.1620290402
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    A dynamic contact buckling analysis by the penalty finite element method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 755-774 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper deals with the application of the finite element method to dynamic contact buckling problems. The penalty function method is applied to incorporate the contact conditions in the equation of motion and a trial-and-error method is employed to obtain the converged contact state. Numerical examples are analysed to show the effectiveness and the validity of the method, and it is applied to a dynamic buckling problem involving contact phenomena.
    Additional Material: 23 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290406
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    The dynamic response of compliant materials to an impulsive pressure field (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 811-831 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dynamic interaction between a compliant material and an impulsive pressure field, periodic in space and instantaneous in time, was examined as a first step at modelling the interaction between organized structures in a turbulent boundary layer and a compliant surface. The interaction, modelled two-dimensionally, was treated dynamically by matching the pressure forces to the surface stresses in the compliant material at each instant of time. A new boundary element method was formulated to model the compliant material which was treated as a linear isotropic material, elastic in dilatation and viscoelastic (Standard) in shear. The inertial forces and viscoelastic creep stresses have been included in this formulation as transient body forces. The elastic interaction was characterized by a non-dimensional threshold velocity, above which the elastic instabilities grew temporally and spatially in the downstream direction to produce a non-linear breakdown of the interaction. Freestream velocities as high as 9CT (shear wave speed) were found to produce stable elastic interactions. Thinner materials produced smaller amplitude waves of higher frequencies that grew more rapidly than those in thicker materials. The stability characteristics were independent of the location of the compliant material with respect to the spatial distribution of the pressure pulse. For viscoelastic interactions, the stability curve, which serves as a bound on the types of materials capable of producing drag reduction, shows distinct regions of elastic types of interactions (Class B) and damping dominated interactions (Class A) as a function of the constants of the rheological model describing the compliant material. Class A disturbances in these interactions show slower growth or decay than Class B disturbances.
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    URL: http://dx.doi.org/10.1002/nme.1620290410
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    Conference diary (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 909-912 
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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.1620290415
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  • 97
    Electronic Resource
    Electronic Resource
    A finite element formulation for the coupled thermoviscoelastic response of solid-fluid systems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 953-968 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The coupled thermoviscoelastic response of a solid-fluid system is computed by a finite element formulation which involves only temperature and displacement fields. The Laplace transform with respect to time is applied to the coupled equations. This results in a global matrix in the transform domain that is symmetric and banded and the time response is obtained by numerical inversion of the transformed solution. Also, this formulation permits the use of fractional derivatives to model viscoelastic material behaviour.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290504
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  • 98
    Electronic Resource
    Electronic Resource
    A subspace forward iteration method for solving the quadratic eigenproblem associated with the FDE formulation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 935-951 
    Details
    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 efficient and numerically stable algorithm for accurately computing the eigensolutions of the quadratic real symmetric eigenproblem arising in the finite dynamic element (FDE) formulation. Closely related to the subspace forward iteration method, the proposed scheme is well suited to extracting the lowest natural frequencies and associated mode shapes of large practical eigenproblems, takes full advantage of the banded configuration of the stiffness, inertia and dynamic correction matrices involved in the eigenproblem and ensures a monotonic convergence from above to the required eigenpairs. A shifting technique for convergence acceleration and an eigenpair verification scheme are also presented. Numerical examples are shown demonstrating the excellent performance of the solution procedure.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290503
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  • 99
    Electronic Resource
    Electronic Resource
    Application of the boundary element method to non-linear diffusion with reaction problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1021-1031 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An integral solution method based on the concept of the direct boundary element technique has been applied to develop a solution procedure for problems of diffusion with a non-linear reaction in one dimension. The non-linearity is handled by a process of quasi-linearization over subintervals or elements in the main domain of integration. The weighting functions are defined for each subinterval such that the discretization is exact for the corresponding linear problem. This leads to a new powerful and simple method for the solution of this class of problems. A banded global matrix is obtained with both the concentration and its gradient as the unknown variables, and the problem is solved in an iterative manner. Illustrative results are presented for a test problem of diffusion with a second order reaction in an infinite slab, an infinite cylinder and spherical geometries. The accuracy of the method for situations with a sharp concentration gradient is demonstrated. The technique can also be used to numerically compute the solution in the boundary layer for fast reactions.
    Additional Material: 5 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290508
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  • 100
    Electronic Resource
    Electronic Resource
    Flow through fissured porous media with deformable matrix (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1079-1094 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An approach, which is based on the double porosity concept and takes into account pore deformation, has been presented to derive a set of coupled differential equations governing the behaviour of fissured porous media. This approach has resulted in a set of non-linear (variable coefficient) differential equations. Various coefficients involved in the formulation have been explicitly defined in terms of measurable physical parameters. The finite element technique has been employed as the numerical tool for the solution of these equations. The results based on the proposed non-linear formulation have been compared with those of previously presented linear (constant coefficient) formulations. It is found that, in relatively rigid formations, the linearity assumption is quite reasonable and can successfully model the behaviour of fissured porous media. However, in very deformable formations, the linearity assumption could lead to a significant level of error in the numerical solutions.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290512
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