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  • 1
    Electronic Resource
    Electronic Resource
    Some criteria for numerically integrated matrices and quadrature formulas for triangles (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 67-76 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For a wide calss of finite element matrices integrated numerically rather than exactly, a definable number of sampling points is found to be sufficient for keeping their theoretical properties unchanged. A systematic criterion limiting the number of possible point configurations for numerical quadrature formulas on triangles is established. Some new high order formulas are presented. Tables containing optional formulas with respect to minimum number of sampling points and required degrees of accuracy are given. They are arranged so as to assist with selection of suitable quadrature formulas for finite element computer programming.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120107
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  • 2
    Electronic Resource
    Electronic Resource
    Modification to the Suhara-Fukuda method of network generation (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 93-99 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This note describes improvements to the Suhara-Fukuda method for generating a triangular finite element network. These are based on the use of a node generation procedure which distributes nodes is a regular pattern across the network area and is sufficiently flexible to permit any variation in element density. Because of the regular node distribution, poorly shaped elements will not arise and so the procedure for connecting the nodes to form elements can be simplified. Examples of networks generaed in this way are given.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120110
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  • 3
    Electronic Resource
    Electronic Resource
    Discussion of a paper by E. O. FrindInt. J. num. Meth. Engng, 945-962 (1977). (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 183-185 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In a recent paper, Dr. Frind has formulated a two-dimensional isoparametric finite element based upon the Hermite bicubic interpolation scheme. The present discussion focuses upon certain simplifications in the derivation which appear to have diminished the accuracy of the resulting element, and suggests a simpler approach to the element formulation. This author agrees strongly with Dr. Frind's recommendation of the Hermite parametric element as an efficient and useful tool for general field problems; the present comments are offered to point out that, in fact, the accuracy comparisons presented by Dr. Frind are biased against the Hermite finite element.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120117
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  • 4
    Electronic Resource
    Electronic Resource
    Masthead (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978) 
    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.1620120201
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  • 5
    Electronic Resource
    Electronic Resource
    Construction of integration formulas for initial value problems, P. J. Van der Houwen, North-Holland Publishing Company, Amsterdam, 1976, No. of pages: 276, Price Dft. 85.00, $33.95 (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 192-192 
    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.1620120121
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  • 6
    Electronic Resource
    Electronic Resource
    The indirect design of fluid channels using a global variational method with trial functions not satisfying the prescribed boundary conditions: II cupling method (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 471-477 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A global variational method (GVM) not requiring the boundary conditions to be incorporated in the trial functions is described. The method is outlined for a linear differential equation and the extensions necessary to handle the non-linear problem of the indirect design of a compressible fluid channel described. The method requires a suitable estimate of a parameter, but the results obtained for the non-linear problem indicate that the actual value of this parameter is not critical (provided that a sufficeintly large number of trial functions is used). Comparisons are made with the results from an alternative GVM approach described in Davies and Hendry.1
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120308
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  • 7
    Electronic Resource
    Electronic Resource
    The generalized problem of confined seepage (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 479-486 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of confined seepage of water under a hydraulic structure, through a porous medium, is considered in an appropriate abstract space. Existence and uniqueness of the solution are proved. The numerical solution is derived by means of the finite element method. An error estimate is given. A sample problems in included.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120309
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  • 8
    Electronic Resource
    Electronic Resource
    Solution of water networks by sparse matrix methods (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1261-1277 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computer program for Water Network analysis has been developed usingy sparse matrix techniques for solution. The method used is the successive linearization method where the set of equations [Q]=[Y][H] is solved. In the process, two subroutines for node reordering to preserve sparsity of the Jacobian matrix and a subroutine for solving the matrix by the Doolittle method are included. The method is user oriented and requires a minimum amount of input data and effort. Networks of up to 200 nodes and 300 pipes may be analysed on an IBM 1130 computer with 16K words of memory.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120805
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  • 9
    Electronic Resource
    Electronic Resource
    A note on quarter-point triangular elements (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1333-1336 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Recently1-3 alternative methods of constructing triangular elements that reproduce strain singularities at crack-tips have been suggested. The differences and similarities between the approaches are considered in this note.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120810
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  • 10
    Electronic Resource
    Electronic Resource
    Erratum (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1492-1492 
    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.1620121003
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  • 11
    Electronic Resource
    Electronic Resource
    An iterative algorithm to build continuous stress and displacement solutions (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1493-1506 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An iterative algorithm is presented: it builds a continuous stress and displacement solution starting from the solution of a classical displacement finite element analysis. The modified solution satisfies the virtual work principle, and is much better than the starting solution. The algorithm is very easily included in existing programs. A number of examples shows the efficiency of the method.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121004
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  • 12
    Electronic Resource
    Electronic Resource
    The shear deformation of profiled metal sheeting (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1507-1541 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the stressed-skin analysis of metal structures it is vital to have a simple yet accurate treatment of the shear deformation of profiled metal sheeting. A suitable theory is developed in this paper for the two important cases of sheeting fastened to the supporting structure through every and alternate troughs of the corrugations. Various practical factors are taken into account. The results of an extensive series of numerical investigations are presented as a simple equation and a set of tables.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121005
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  • 13
    Electronic Resource
    Electronic Resource
    Application of the finite element method to an optimal control problem (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1559-1574 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element method is applied to a typical problem in the optimal control theory. A finite element formulation is first set up, and then applied, as an example, to a problem of minimizing the transfer time of a low-thrust rocket vehicle between the orbits of Earth and Mars. A procedure which combines the gradient projection technique with the Newton-Raphson method is introduced to obtain numerically the solution of the minimum time transfer problem from the discretized functional. Numerical results show that the application of the finite element method to optimal control problems seems promising as well as encouraging.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121007
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  • 14
    Electronic Resource
    Electronic Resource
    Block iterative finite element preprocessed scheme for simulation of large non-linear problems (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1543-1558 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The ‘Block Iterative Finite Element Preprocessed Scheme’ (BIFEPS) for finite element simulation combines two independent steps. In the ‘finite element preporcessing step’, spatial information about the finite element mesh is analysed and all integrals arising from the application of the Galerkin method are evaluated and stored on a permanent sequential storage unit (such as tape or disk). In the ‘block iterative step’, the preprocessed information is retrieved from permanent storage and the matrix equation is assembled and solved in an efficient manner according to a generalization of the block successive over-relaxation iterative method. Significant advantages over common finite element simulation techniques are achieved in terms of both computer core requirements and execution time. Numerical experiments show that the advantages of BIFEPS are greatest for large, non-linear simulation problems.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121006
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  • 15
    Electronic Resource
    Electronic Resource
    Stability of explicit-implicit mesh partitions in time integration (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1575-1586 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The stability of time integration for a semidiscretization of structures and continua where the mesh is partitioned into subdomains integrated simultaneously by explicit and implicit methods is considered. Stability in energy is proven for linear systems subject to the Courant condition in the explicit subdomain for a central difference explicit and trapezoidal implicit integrator. Numerical examples are presented to demonstrate the procedure.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121008
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  • 16
    Electronic Resource
    Electronic Resource
    An analysis of a cubic isoparametric transformation (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1587-1595 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The general nine point isoparametric transformation is analysed with respect to a triangle with two straight sides and one curved side. Point placements are determined on the curved side which ensure that the Jacobian of the transformation remains positive inside and on the boundary of the triangle. Special cases of the transformation are considered which lead to implied curves of the form of symmetric cubics, parabolas, and explicit cubics respectively, thus enabling isoparametric transformations to match a variety of boundary shapes.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121009
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  • 17
    Electronic Resource
    Electronic Resource
    On an elasto-plastic stress-strain relationship for multi-axial stress states (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1617-1622 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121011
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  • 18
    Electronic Resource
    Electronic Resource
    A-posteriori error estimates for the finite element method (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1597-1615 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Computable a-posteriori error estimates for finite element solutions are derived in an asymptotic form for h → 0 where h measures the size of the elements. The approach has similarity to the residual method but differs from it in the use of norms of negative Sobolev spaces corresponding to the given bilinear (energy) form. For clarity the presentation is restricted to one-dimensional model problems. More specifically, the source, eigenvalue, and parabolic problems are considered involving a linear, self-adjoint operator of the second order. Generalizations to more general one-dimensional problems are straightforward, and the results also extend to higher space dimensions; but this involves some additional considerations. The estimates can be used for a practical a-posteriori assessment of the accuracy of a computed finite element solution, and they provide a basis for the design of adaptive finite element solvers.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121010
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  • 19
    Electronic Resource
    Electronic Resource
    Announcements (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1774-1776 
    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.1620121115
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  • 20
    Electronic Resource
    Electronic Resource
    A.D.I. Methods for the solution of transient heat conduction problems in r-θ geometry (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1799-1807 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, the application of a particular class of computational methods, the alternating direction implicit methods applied to the solution of time dependent heat conduction problems in regions involving circular symmetry is presented.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121203
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  • 21
    Electronic Resource
    Electronic Resource
    A displacement method for the analysis of vibrations of coupled fluid-structure systems (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 13 (1978), S. 139-150 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A variational principle in terms of displacements in the fluid and the structure with a penalty for irrotationality of displacement in the fluid is developed for the analysis of harmonic vibrations of ideal compressible fluid and elastic structure systems. Its Discretization by the finite element method leads to an algebraic eigenvalue problem with a positive definite symmetric banded matrix. Numerical examples obtained for pure acoustic cases and coupled cases show the efficiency of the method.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620130110
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  • 22
    Electronic Resource
    Electronic Resource
    A finite element formulation for large elastic-plastic deformation analysis of polycrystals and some numerical considerations on polycrystalline plasticity (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 101-114 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation for large elasto-plastic deformation of polycrystalline materials is proposed in incremental form. The effect of rotation of crystal axes besides usual element rotaion is taken into account. Some numerical considerations on polycrystalline plasticity (i.e. stress-strain curves for several proportional loadings, effect of change of loading path on stress-strain curve, subsequent yield loci for uniaxial and equi-biaxial loadings and so forth) are given for the case of small deformation by using a plate model which consists of 121 square FCC crystals.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120111
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  • 23
    Electronic Resource
    Electronic Resource
    The solution of sparse linear equations by the conjugate gradient method (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 141-158 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The convergence properties of the conjugate gradient method are discussed in relation to relaxation methods and Chebyshev accelerated Jacobi iteration when applied to the solution of large sets of linear equations which have a sparse, symmetric and positive definite coefficient matrix. The conclusion is reached that its convergence rate is unlikely to be much worse than these methods, and may be considerably better. The conjugate gradient method may either be applied to the basic unscaled or scaled equations or alternatively to various transformed equations. Preconditioning, block elimination and partial elimination methods of transforming equations are considered, and some comparative tests given for six problems.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120114
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  • 24
    Electronic Resource
    Electronic Resource
    Closed form elastic-plastic stiffness matrix for axisymmetric finite elements (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 59-65 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This note presents the closed form equations for the stiffness terms in the elastic-plastic stiffness matrix for axisymmetric finite elements. The element considered is a triangular ring element characterized by linear displacement relationships and an averaged state of stress. The physical law is modelled by the incremental theory of plasticity utilizing the Prandtl-Reuss flow rule and von-Mises Yield Criterion. Results are presented comparing stiffness terms as computed by numerical integration to those computed from the closed form equations. Significant errors in stiffness terms arising from numerical integration are observed for axisymmetric elements located near the line of axial symmetry as a result of the logarithmic nature of some of the stiffness terms.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120106
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  • 25
    Electronic Resource
    Electronic Resource
    Certain properties of numerical schemes used to solve the blade-to-blade flow problem (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 85-92 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The compressible potential flow on a blade-to-blade surface of a turbomachine is analysed using the Thomas algorithm. The numerical properties of resulting non-linear simultaneous equations are studied with respect to grid aspect ratios and convergence. The heuristic approach has established which are the important factors that affect the flow solution in typical blade-to-blade configurations.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120109
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  • 26
    Electronic Resource
    Electronic Resource
    Periodic Galerkin finite element method of tidal flow (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 115-127 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the finite element method of the analysis of tidal flow. Assuming that tidal flow is periodic, the Galerkin approach is employed as the numerical integration procedure in time using a trigonometric function as the interpolation function. The present method has shown to be suitable for computation especially from the point of computing time and numerical stability.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120112
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  • 27
    Electronic Resource
    Electronic Resource
    The visco-plastic approach to problems of plasticity and creep involving geometric non-linear effects (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 169-181 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The visco-plastic model is used in the context of large displacement (geometrically non-linear) analysis. As the process now involves in numerical computation an updating of relevant stiffness matrices, formulation which is stable and computtionally more efficient. The applications shown demonstrate the applicability of the process to large displacement elasto-plastic shell analysis as well as to problems of creep buckling.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120116
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  • 28
    Electronic Resource
    Electronic Resource
    Finite elements in geomechanics, Ed. by G. Gudehus, Wiley, Chichester, 1977. No. of pages: 573. Price: £17, $32.50 (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 384-384 
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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.1620120217
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  • 29
    Electronic Resource
    Electronic Resource
    A finite element method for Burgers' equation in hydrodynamics (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 415-428 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Finite Element Method using rectangular elements is applied to solve Burgers' non-linear equation in one space dimension. The non-linear algebraic equations thus obtained are solved by an iteration which is equivalent to the generalized Newton method. Numerical experiments indicate that the order of accuracy is equal to 2. In two space dimensions, the method is more efficient than other methods we have tested.
    Additional Material: 7 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120304
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    Construction of triangular finite element universal matrices (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 237-244 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The various ‘universal’ matrices from which finite element matrices for triangular elements are assembled in many electromagnetics and acoustics problems, can all be derived from a basic set of three fundamental matrices. These represent, respectively, the metric of the linear manifold spanned by the triangle interpolation polynominals, the finite differentiation operator on that same manifold, and a product-embedding operator for the corresponding manifold for interpolation polynomials one order higher. Two of these have already been tabulated and published; the required method for computing the third is given in this paper, along with tables of low-order matrices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120206
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    Application of the adaptive random search to discrete and mixed integer optimization (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 289-298 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this study, a random search technique, previously applied to continuous optimization problems, is adapted and applied to discrete and mixed integer problems. The development of the method and the procedure for applying the method are discussed in detail. Three discrete and one mixed integer problems, efficiencies can be made. The radom search procedure demonstrated perfect reliability in locating the optima. Improved efficiencies resulted for each of the examples are improved optimal solutions were found in two cases.
    Additional Material: 4 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620120210
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    An advanced structural analysis/synthesis capability - ACCESSApproximation Concepts Code for Efficient Structural Synthesis. 2 (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 353-377 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An advanced automated design procedure for minimum weight design of structures (ACCESS 2) is reported. Design variable linking, constraint deletion, and explicit constraint approximation are used to effectively combine approach to structral synthesis is extended to problems involving fibre composite structure, thermal effects and natural frequency constraints in addition to the usual static stress and displacement limitations. Sample results illustrating these new features are given.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120214
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    A warning on the use of symmetry in classical eigenvalue analyses (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 379-381 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120215
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    Analysis of some dispersion corrected numerical schemes for solution of the transport equation (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 387-404 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the last decade or so finite element techniques have been applied with increased frequency to contaminant transport problems. Whereas most of the attention has focused on finite element approximations of spatial derivatives, standard finite difference techniques are generally used for approximation of the time derivative. Such an approach yields a scheme which is at best second order correct in time. In this study several higher order approximations of the time derivative are developed and analyzed using a finite difference approximation, and Galerkin-type finite element approximations in conjunction with several sets of basis functions. Results obtained with the different schemes exhibit significant improvements in the numerical solution of the convective-dispersive equation.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120302
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    A finite element for transition from a fine to a coarse grid (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 35-45 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Formulation of a transition element is presented. Such an element makes it possible to match one element with two elements side-by-side. A modified quadrature formula is used to numerically integrate discontinuous functions in the expression of the stiffness matrix. Numerical examples show the applicability of the element.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120104
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    Blending interpolants in the finite element method (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 77-83 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Blending function interpolants on rectangular elements are used to construct an overall interpolant which exactly matches function and normal derivative on the perimeter of a rectangular region. This overall interpolant is incorporated into the Ritz-Galerkin version of the finite element method and a test problem involving the biharmonic equation is solved. The numerical results obtained demonstrate the considerable increase in accuracy of the exact boundary methods as compared with the usual method using interpolated boundary conditions. A similar investigation of second order elliptic problems with Dirichlet boundary conditions where the rectangular region is divided up into triangular elements yields the perhaps surprising result that blended interpolants on triangular elements do not necessarily improve the accuracy of the Ritz-Galekin version of the Finite Element Method.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120108
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    An identification method applied to an orthotropic plate bending experiment (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 129-139 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a method of identification of material behaviour parameters. The method is applied to a simple example: the identification of orthotropic parameters using a plate bending test. A number of results are presented concerning the choice of numerical algorithm, the experimental protocole (number and locations of test points, loading) and the sensitivity of the method on experimental errors.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120113
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    Higher-order horizontally-curved beam finite element including warping for steel bridges (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 159-167 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The flexural stiffness for a horizontally curved beam element is developed for nodal parameters wi, (∂w/∂s)i, βi, (∂β/∂s)i, (∂2β/∂s2)i, (∂3β/∂s3)i by assuming a cubic displacement function for vertical deflection w, and a seventh order polynomical function for the angle of twist β, along the length of the curved beam. The element gives good accuracy with even coarse mesh for the analysis of horizontally-curved steel beam with open thin-walled bisymmetrical cross-section.Warping restraint is considered in the derivation of the stiffness matrix, which has considerable influence on the behavior and design of steel bridges curved in-plan. The results obtained from such a new element are compared with those given by a lower order finite element, developed previously by the first author, and with theoretical solutions for the particular problem.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120115
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    Reply by O. C. Zienkiewicz to comments by GartlingZnt. J. num. Meth. Engng, 12, 187-190 (1978). on Paper by Heinrich, Huyakorn, Zienkiewicz and Mitchell (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 191-191 
    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.1620120120
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    Elastoplastic thick shell analysis by viscoplastic solid finite elements (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 203-227 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Shell-like assumptions introduced in a three-dimensional isoparametric finite element provide a kinematic description of smooth thick shell structures. Elastoplastic solutions are obtained via the stationary response of an elastic/viscoplastic model. Special attention is devoted to the probem of numerical integration across the depth of the shell, as well as the applicability of the method to thin shell analysis.
    Additional Material: 19 Ill.
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    A hybrid element method for diffraction of water waves by three-dimensional bodies (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 245-266 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A hybrid element method developed recently for two-dimensional problems of water waves in an infinite fluid is extended to three dimensions. In this method only a limited fluid domain close to irregular bodies is discretized into conventional finite elements, while the remaining infinite domain is treated as one element with analytical representations of high accuracy. Continuity at the junction surface is treated as natural boundary conditions in a variational principle. Computation experience and numerical results for several ocean structures are presented.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120207
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    Optimal design of dynamically loaded continuous structures (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 299-317 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computational algorithm is developed and applied for optimization of beam and plate structures, subject to constraints on transient dynamic response. A continuous design formulation is retained, with dynamic response governed by partial differential operator equations. Adjoint equations are employed for sensitivity analysis and a function space gradient projection optimization approach is presented. Finite element analysis methods are applied for solution of the system dynamic and adjoint differential equations. Displacement constrained beam and plate minimum weight examples are solved, with a variety of boundary conditions.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120211
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    Masthead (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978) 
    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.1620120301
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    Cold rolling of a laminated composite sheet - A numerical solution (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 429-435 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of cold rolling of a composite sheet which consists of alternate layers of viscoelastic and elastic materials is studied by the finite element method. Results computed and presented graphically include the pressure distribution at the contact surface, the normal stress distribution at the middle surface and the asymmetric deformation of the surface of the sheet in contact with the roller.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120305
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    A numerical method to obtain optimal quadrature formulas (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 487-504 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper present a numerical method to obtain optimal quadrature formulas of Gauss type and Radau type in the sense of Sard. Using the relation between optimal quadrature formulas and nonospline functions, the optimal quadrature formula can be obtained by solving a set of no-linear simultaneous algebraic equations induced from the interpolatory conditions of the monospline. In attempting to solve this set of non-linear algebraic equations for numbers of knots and degrees of interpolution required in estimation problem applications insurmountable numerical errors were encountered. This paper solves the numerical problem by first reducing the number of unknowns and equations to approximately one half the original number. This is accomplished by showing and then using a symmetry property of the monospline. Second an iteration scheme which partitions the reduced order set of non-linear algebraic equations into a linear subsystem and a non-linear subsystem is developed to numerically solve the equations. This iteration algorithm provides the advantages of reducing the computational complexity, dynamically checking the convergence and explicitly evluating the resulting accuracy.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120310
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    p-convergent finite element approximations in fracture mechanics (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 551-560 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The strain energy release rate (G) converges rapidly in finite element approximations in which the finite element mesh is fixed and the order of polynomial displacement interpolations (p) is increased. Numerical experiments indicate that the error inG is very closely estimated, even for small pand very coarse finite element meshes, by an expression of the form k (NDF)-1 in which k is a mesh dependent constant and NDF is the number of degrees-of-freedom. The method provides for very efficient and accurate computation of G without the use of special techniques.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120313
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    Added mass computation by the boundary integral method (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 531-550 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Computational techniques for the treatment of fluid-structure interaction effects by discrete boundary integral methods are examinde. Attention is focused on the computation of the added mass matrix by finite element methods for a structure submerged in an infinite, inviscid, incompressible fluid. A general computational procedure is presented that is based upon a variational approach involving the assumption of constant source strength over each surface element. This is followed by an analysis of the discretization error for a spherical body that is then used to develop a hierarchy of computational schemes. These schemes are than evaluated numerically in terms of ‘fluid boundary modes’ for a submerged spherical surface. One scheme has been found to be surprisingly accurate in relation to its computational demands.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120312
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    A drafting program for isoparametric finite elements (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 505-529 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Considerable effort has been invested lately in the application of isoparametric finite elements for numerical solution of a wide range of applied mechanics problems. In fact, several general purpose computer programs are now available which are based upon such finite elements. In the present paper, a new application of the isoparametric finite element concept is introduced which significantly extends its usefulness for many practical structural configurations. In this application, final working or architectural drawings of the structure are made from the same (or similar) finite element model as was utilized in a structural integrity analysis. The hardware necessary to produce such drawing, a computer driven plotter or automated drafting machine, is available commercially or through most data centres, and the software concepts required are described herein.
    Additional Material: 18 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120311
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    Plasticity analysis by a non-conforming plane element (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 561-566 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A non-compatible rectangular element with 12 degrees-of-freedom (DF) has been developed by Wilson et at.5 for analyzing 2-dimensional problems. The superior convergence properties of this element as compared with the 8 DF element for linear elasticity problems with important bending have been demonstrated in References 2, 5. The purpose of this study is to assess the compartive efficiency of these two rectangular elements for an estimation of collapse loads in plasticity problems. For convenience, the 12 DF and 8 DF element will be represented by Q6 and Q4 respectively.
    Additional Material: 3 Ill.
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  • 50
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    Announcements (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 573-576 
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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.1620120316
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    Masthead (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978) 
    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.1620120401
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    Ritz solutions for axisymmetric temperature and stress fields in finite elastic cylinders (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 567-572 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Variational formulations are given for the stationary heat conduction and thermodelasticity problems of an orthotropic, non-homogeneous, finite length, cylinder. It is demonstrated that a single-element approach based upon Ritz approximations and the method of Lagrange multipliers offers and efficient means for computing the temperature and thermal stress distributions.
    Additional Material: 2 Tab.
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    The solution of the three-dimensional Navier-Stokes equations using a new finite difference approach (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 579-580 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 2 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620120402
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    Incompatible quadrilateral basis functions (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 589-595 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120404
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    A cost comparison of two static condensation-stress recovery algorithms (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 581-588 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider finite elements that have internal degrees-of-freedom. These d.o.f. are condensed before elements are assembled into the structure, and must be recovered later for use in element stress computation. References 1 and 2 describe two different ways to do the calculations. This paper compares the computational costs of the two methods. Test runs were made to assess costs. Relative costs depend on several factors. The factors are discussed, and suggestions are made as to the better method in various circumstances.
    Additional Material: 5 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620120403
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    Application of dynamic programming to the general inverse problem (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 613-624 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The general inverse problem is one for which measurements are made on some of the state variables and it is desired to find the forcing functions. This problem is a natural one for the method of dynamic programming. The formulation and solution of the problem are presented in matrix form, together with two illustrative examples of an inverse heat conduction problem and an inverse structural dynamics problem.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120406
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    Solution of non-linear differential equations by discrete least squares (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 597-612 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general-purpose technique has been developed for solving non-linear partial differential equations. A set of approximating functions with undetermined parameters is used to evaluate the differential equation and boundary conditions at discrete points, forming a set of residuals to be minimized. The parameters which minimize the sum of squared residuals are determined by a non-linear least-squares minimization technique. Initial value problems are solved by integrating the equations with respect to time at the fitting points by a predictor-corrector algorithm. The resulting formulation is independent of the form of the problem and the approximating functions, so that a broad class of problems may be solved with a single computer program. The technique is applied to several boundary and initial value problems in one and two spatial dimensions. The tecnique is applied to several boundary and initial value problems in one and two spatial dimensions.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120405
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    An integral method for computing the inductance and the a.c. resistance of parallel conductors (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 625-634 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In a previous paper1 a method was described for computing the current distribution and inductance of systems of infinitely-long, perfectly-conducting, straight conductors. The method relied on the solution of a Fredholm Integal equation of the first kind, and in the present paper the method is extended to equations of the second kind in order to study the inductance and a.c. resistance factor of resistive for which approximate formulas and experimental results exist, with which the method is in good agreement over a range of grequencies of particular practical practical interest. Results have also been obtained for rectangular conductors connected in parallel.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120407
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    Geometrically non-linear analysis - A correlation of finite element notations (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 635-642 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A correlation is geven between two notations currently used in the formulation of geometrically non-linear analysis in a Lagrangian co-ordinate system. The first referred to as the B-notation results in the linear elastic, initial displacement and initial stress matrices, whilst the second, here called the N-notation features matrices that repeat in the total potential energy, equilibrium and incremental equilibrium equations. An explicit example of the correlation is presented for a pin-jointed bar element.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120408
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    A non-circular arc roll force model for gold rolling (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 643-663 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A long established approximation, normally invoked in the development of classical rolling theory, is that the work roll-strip interface assumes a circular profile. Although valid for a wide range of practical rolling conditions, the approximation is definitely suspect for instance in the last and penultimate stand of a thin sheet tandem mill, and algorithms based on classical theory may fail to converge. This paper computing solutions. In deriving the algorithm it is convenient to employ the formalism of functional One notable feature is that the gradients have to be carefully defined with respect to the correct ‘space’, in order that physically inadmissible discontinuties are not introduced during the hill-climbing. Computed roll gap solutions sometimes display elastic deformation regions embedded within the normal plastic deformation zone. It is thought that this is the first time this possibility has been allowed for in the formulation, or solutions obtained exhibiting this feature.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120409
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    Finite element analysis of rubber-like materials by a mixed model (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 665-676 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Reissner type variational principle is utilized to formulate a mixed finite element model for a finite-strain analysis of Mooney-Rivlin rubber-like materials. An incremental and stationary Lagrangian formulation is adopted. The functional consists of incremental displacements and incremental hydrostatic and distortional stresses as variables. In the finite element formulation the displacements are interpolated in terms of nodal displacements while the two different strss components are approximated independently. The stress parameters for the distortional stresses are eliminated at the element level and the resulting matrix equations for each incremental solution involve the incremental nodal displacements and the average hydrostatic pressure in each element as unknowns. Four-node quadrilateral plane stain elements were used to analyze the inflation of an infinitely long thick-walled cylinder subjected to internal pressure. Both resulting displacements and stresses are found to converge to exact values as the magnitude of the loading increments is decreasing.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120410
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    Adaptive step size selection for use with the continuation method (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 677-694 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An adaptive procedure for selecting the step size when incremental or continuation methods are used to solve sets of non-linear equations is presented. The increment size is limited by requiring the corrective iteration procedure employed to reduce the drifting error to be within a contractive boundary at each level. The usefulness of the procedure is extended by the development of a set of conditions for detecting impending divergence of the corrective iteration process. These conditions, used in conjunction with the step size selection procedure permit the continuation of the solution through highly non-linear regions and also provide a simple means of isolating a limit point, if one exists. Two additional benefits of the procedure are an effective convergence criterion for terminating the iteration process and a simple means for switching between the Newton-Rephson and modified Newton-Raphson iteration procedures. The paper concludes with a number of example problems, three are hyperelastic bodies at finite strain and the final example is the large displacement analysis of an elastic beam. The results illustrate that the procedure is computationally inexpensive, using only information normally obtained in a non-linear analysis, flexible in the sense that a dense or sparse distribution of points along the total solution curve may be obtained, and effective, normally requiring less total computational effort than a constant step size procedure.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120411
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    The aperiodic behaviour of a rigid shaft in short journal bearings (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 695-702 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A study is presented of the symmetrical steady-state motion of a rigid shaft supported by two ‘short’ (Ocvirk) journal bearings. The equations of motion for a balanced or unbalanced shaft were solved using numerical ‘initial value problem’ techniques. Frequency analysis, which was used to determine the components of the steady-state motion, confirmed that, for most conditions, the motion was asymptotically periodic comprising a small number of components - principally at synchronous and half synchronous frequency. However, a region of the operating space was found, in which the motion was complex and did not settle to a limit cycle. An estimate of the extent of this region is given and the suspected cause investigated.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120412
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    A split Band-Cholesky equation solving strategy for finite element analysis of transisent field problems (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 703-710 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient strategy is outlined for out-of-core solution of the large systems of equations which specify nodal point time derivatives in finite element models of transient flow problems. The positive definiteness, symmetry, and band structure of the finite element mass matrices, as well as the nature of the equation assemblage process, is exploited by the method. Computational results are indicated for systems on the order of several thousand unknowns in size.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120413
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    An out-of-core equation solver for full, unsymmetric matrices (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 721-725 
    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.1620120415
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    Discussion of a paper by P. Friedmann, C. E. Hammond and Tye-Hsin WooThe notation in this discussion follows that of Reference 1. (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 726-728 
    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.1620120416
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    A finite difference-Galerkin finite element solution of compressible laminar boundary-layer flows (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 711-719 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite difference-Galerkinfinite element method is presented for the solution of the two-dimensional compressible laminar boundary-layer flow problem. The streamwise derivatives in the momentum and energy equations are approximated by finite differences. An iterative scheme, due to the non-linearity of the problem, in conjunction with the Galerkin finite element method is then proposed for the solution of the problem through the boundary-layer thickness. Numerical results are presented and these are compared with other numerical and analytical solutions in order to show the applicability and the effectiveness of the proposed formulation. In all the cases here examined, the results obtained attained the same accuracy of other numerical methods for a much smaller number of points in the boundary-layer.
    Additional Material: 3 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620120414
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    Authors' reply to the discussion by C. von KerczekInt. J. num. Meth. Engng, 12, 726-728 (1978). (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 728-730 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120417
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    On isoparametric elements (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 731-732 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620120418
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    Announcements (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 733-735 
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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.1620120420
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    Methods for the numerical solution of partial differential equations by Dale U. von Rosenberg. Published by Publishing Division, Gerald L. Farrar & Associates, Inc., 5536 East 35th Street, Tulsa, Okla. 74135. $12.50 (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 732-732 
    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.1620120419
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    Interpolative versus iterative solution schemes for tresca yield condition in elastic-plastic finite element analysis (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 765-777 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120503
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    Algorithms for direct-access gaussian solution of structural stiffness matrix equation (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 751-764 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on direct-access programming, algorithms have been developed for the generation, and solution by Gaussian elimination of the structural stiffness matrix equation resulted from application of the finite element method in engineering analyses. A large disk storage is used to store the rows of the stiffness matrix as directly accessible records. The developed algorithm BAND2R requires only 2Nb in-core words in implementing the Gaussian elimination where Nb is the semi-band width of the stiffness matrix. Algorithms BANDSQ and BDSQMX are presented which require N2b in-core words but minimize the number of retrieving and restoring the direct-access records during the Gaussian elimination. BANDSQ has the direct-access feature in both the elimination and backward-substitution steps whereas BDSQMX has the direct-access feature only in the backward-substitution step of the Gaussian elimination. Illustrative applications of the developed algorithms are given and the computer core and time requirements for BAND2R, BANDSQ and BDSQMX are compared to those for the conventional Gaussian elimination of using sequential, in-core storages. Methods for reducing the semi-band width Nb of the structural stiffness matrix are also discussed.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120502
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    Buckling of simply-supported skew plates (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 779-785 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The difficulties associated with the solution of the skew plate buckling problem are described, and the work of other writers is summarized.By solving a numerical example, the relative advantages of two proposed refinements to the finite element displacement method are demonstrated: A technique of boundary condition relaxation appears justified and gives favourable results compared with conventional boundary condition specification. A mesh grading technique, which is simple to apply, results in a marked improvement in convergence to a solution.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120504
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    Yielding of plates with hardening and large deformations (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 739-750 
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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 technique is used to study the influence of yielding on buckled plates. Orthogonal anisotropic hardening is determined solely by a yield condition, which is introduced into a mixed functional for the elastic plate by Lagrange Multipliers. The Euler equations of the constrained functional include Prager's normality rule.Numerical results are given for rectangular plates of different size calculated for various material properties.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120501
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    Finite elements of C1-class on a tetrahedron (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 787-793 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes two finite elements of C1-class defined on a tetrahedron. In order to define these elements we give the corresponding function spaces in explicit form.
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    URL: http://dx.doi.org/10.1002/nme.1620120505
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    An accelerated automatic root search algorithm for iterative methods in vibration analysis (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 809-820 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents an accelerated version of an automatic root searching technique developed by the authors for application to residual function iterative methods in vibration analysis.The power and generality of the accelerated method is demonstrated by application to (i) an 8 rotor torsional vibration system, and (ii) a 15 rotor torsional vibration system specially synthesized so as to have an uneven root distribution including clusters of close frequencies.
    Additional Material: 3 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620120507
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    On suitable formulations of the method of modal analysis for numerical calculations (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 795-808 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The method of modal analysis is a method widely used in structural analysis of linear systems. After a short introduction two step by step formulations for modal calculations are discussed. One of them is of more theoretical interest, the other is recommended for practical calculations for multi-degree-of-freedom systems because it is efficient in computing time. The first is formulated for the whole system the latter for each mode. Likewise a combination of the method of modal analysis and the LAPLACE transformation is established. The numerical calculation of the LAPLACE transformation is done by using the algorithm of the Fast FOURIER transformation. The advantages of the different formulations for numerical calculations are discussed.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120506
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    Solution of fixed cost trans-shipment problems by a branch and bound method (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 837-851 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Varied problems in the fields of operation, scheduling, allocation and design in power systems analysis can be formulated as fixed cost trans-shipment problems. This paper indicates possible areas of application of such formulations, and by exploiting specific characteristics of certain power systems problems presents an efficient branch and bound method for solving them.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120509
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    Application of the initial stress method to soil-structure interaction (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 873-880 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general method is presented for the analysis of soil-structure interaction problems using the initial stress finite element approach. The soil and structure will be treated as separate bodies related only by nodal forces at the soil-structure interface. Provision is made for plastic failure of both soil and structure, shear failure at the interface, and breakaway of the structure from the soil.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120511
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    Geometrically similar elements (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 881-884 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element analyses sometimes involve elements that are simple rescalings of each other. A useful relation is derived between the stiffness matrices of elements which differ by the same scaling factor in all co-ordinate axes and an application is illustrated.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120512
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    Finite element method for spectral modelling of tides (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 853-871 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A spectral method for modelling of tides is proposed and applied to the calculation of the M2 component of the tide in the English Channel. The classical non-linear hyperbolic problem of long wave propagation in shallow waters is transformed into a sequence of elliptic problems by looking at a multiperiodic solution the frequencies of which are previously known. The method is based upon a perturbation technique, but the principal difficulties arise from the non-analytical form of the quadratic friction term: the main conclusions of the corresponding study only are given here, because the purpose of this paper is to present a practical application of the method to the calculation of a tidal component by the finite element method. The variational formulation of the problem is presented, and the finite element package used is described. Some results are given for the M2 tide in the English Channel: cotidal maps and current fields.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120510
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    A rayleigh-ritz determination of upper and lower bounds for the deflection of orthotropic cantilever beams (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 885-890 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical scheme based on polynomial approximation is presented for the caluclation of upper and lower bounds for the flexibility coefficient of end-loaded orthotropic cantilever beams in a state of plane stress, through use of the principles of minimum potential energy and of minimum complementary energy. The degree-of-freedom of the two-dimensional polynomials employed along with the elastic constants and the depth-to-span ratio of the beam are external parameters of the problem.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620120513
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    A historical note about ‘hybrid elements’ (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 891-892 
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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.1620120514
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    Announcements (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 893-896 
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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.1620120515
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    Masthead (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978) 
    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.1620120601
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    Errata (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 898-898 
    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.1620120602
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  • 88
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    Iterative procedures for improving penalty function solutions of algebraic systems (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 821-836 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The standard implementation of the penalty function approach for the treatment of general constraint conditions in discrete systems of equations often leads to computational difficulties as the penalty weights are increased to meet constraint satisfaction tolerances. A family of iterative procedures that converges to the constrained solution for fixed weights is presented. For a discrete mechanical system, these procedures can be physically interpreted as an equilibrium iteration resulting from the appearance of corrective force patterns at the nodes of ‘constraint members’ of constant stiffness. Three forms of the iteration algorithm are studied in detail. Convergence conditions are established and the computational error propagation behaviour of the three forms is analysed. The conclusions are verified by numerical experiments on a model problem. Finally, practical guidelines concerning the implementation of the corrective process in large-scale finite element codes are offered.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120508
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  • 89
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    Analysis of explicit difference methods for a diffusion-convection equation (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 899-916 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider the numerical solution of a model one-dimensional diffusion-convection equation by a variety of explicit finite difference methods including conventional central and upwind replacements of the convection terms. We discuss commonly observed phenomena such as instability, unwanted oscillations in the numerical solution, and numerical diffusion and we present an analysis of these effects by simple mathematical techniques.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120603
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  • 90
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    Contcat stress minimization by contour design (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 917-930 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A sequential linear programming method is developed for contour design of elastic bodies to minimize contact stresses when two bodies are pressed together by extrenally applied loads. Constraints on the amount of acceptable contour modification are imposed, based on kinematic functions to be performed by the two mating bodies. The teachique is illustrated through solution of a simple example and a more practical bearing contact design problem.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120604
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  • 91
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    Convective difference schemes and Hermite interpolation (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 931-940 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method for numerically solving the convection equation is presented. The reduction of numerical errors is achieved by introducing an auxiliary variable and solving an auxiliary equation for the latter. The method is based on a Hermite interpolation of the convected quantity. Three explicit numerical versions of the method are investigated and compared with some of the most widely used schemes, and it is shown that the new method gives better physical results. Arguments are given that the usual mathematical series expansions do not work sufficiently well in that context. Instead of using linear stability analyses the quality of the method is investigated by numerical experiments.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120605
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  • 92
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    The numerical solution of the dynamic response of helical springs (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 949-961 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120607
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  • 93
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    Application of displacement and hybrid strees methods to plane notch and crack problems (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 963-975 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For calculating stress concentration factors at plane notches and stress intensity factors at plane cracks a system of finite elements is proposed which uses specially developed triangular hybrid stress elements at the notches and cracks and combines them with triangular elements acording to the displacement method. In formulating the stresses at the notches the Fade-away Law formulated by Neuber has been taken into consideration; for the cracks, formulations are used which exactly contain the stress distribution of Irwin's equations. The quick convergence and high degree of accuracy of this approach are demonstrated by way of test examples.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120608
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  • 94
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    Hierarchal finite elements and precomputed arrays (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 977-999 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two-dimensional C° finite elements of arbitrary polynomial order are developed for a general functional which includes a least squares or potential energy functional as special cases. The elements are ‘hierarchal’ in the sense that the nodal variables for polynomial order p constitute a subset of the nodal variables for order p+1. It is shown that the elemental arrays for high polynomial order may be efficiently computed by using hierarchal elements together with precomputed arrays - i.e., arrays which are computed once, stored on permanent file, and then re-used in all subsequent applications of the program. A number of example problems are solved. Comparisons are made of the relative efficiency of finite element convergergence with mesh refinement (polynomial order held fixed) and with increasing polynomial order (mesh held fixed). The latter approach is found superior.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120609
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  • 95
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    The finite element solution of rapid cycling creep problems (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1001-1024 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper describes a simplified finite element method for high temperature creep problems involving cyclic load and temperature. The principal assumptions, that the cycle time is small compared with characteristic material time scales, is appropriate for the moderate load levels which occur when structures are designed for life times measured in years and decades. Because of the simplicity of the method, thermal loading problems may be studied in some detail. A parametric study of a plane stress problem is presented. Characteristic deformation rates are related to reference stress and timperature quantities, thereby reducing the main features of the solution to a few important structural and material parameters.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120610
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  • 96
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    On a numerical solution of the plastic buckling problem of structuresThis paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology. (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 941-947 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An automated digital computer procedure is presented for the accurate and efficient solution of the plastic buckling problem of structures. This is achieved by a Sturm sequence method employing a bisection strategy, which eliminates the need for having to solve the buckling eigenvalue problem at each incremental (decremental) loading stage that is associated with the usual solution techniques. The plastic bucking mode shape is determined by a simple inverse iteration process, once the buckling load has been established.Numerical results are presented for plate problems with various edge conditions. The resulting computer program written in FORTRAN for the JPL UNIVAC 1108 machine proves to be most economical in comparison with other existing methods of such analysis.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120606
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  • 97
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    Numerical solutions for a class of multi-part mixed boundary value problems (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1025-1030 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper proposes a procedure for the extension of a widely used numerical method1-4 for the solution of systems of singular integral equations, from mixed boundary value problems with two or three parts to those having many parts. The procedure is applied to three previously solved mixed boundary value problems and the result are presented in graphical form. The effectiveness of the given procedure is observed through the results for some limiting and special cases found in the literature.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120611
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  • 98
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    Transition elements to be used with quarter-point crack-tip elements (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1031-1036 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A generalization of the (r-1/2) strain or stress singularity capability of the quadratic isoparametric element is presented. It is shown that, by variable placement of the side-nobe between quarter- and mid-point, the point of singularity sensed by the element can be controlled. By using eight-noded quadrilateral isoparametric elements with appropriately placed side-nodes as transition elements between the quarter-point crack-tip trinagular and remaining non-singular elements, stress intensity factors may be computed with higher accuracy.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120612
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  • 99
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    Specification of skew conditions in finite element formulation (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1037-1041 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Fields exhibiting skew symmetry occur frequently in structural problems. There are many situations where non-skew-symmetric functions are conveniently used to analyse these skew fields. Specification of force and displacement conditions on the skew axis reduces the analysis to a half of the domain. The difficulty in using such conditions in an FEM analysis is their non-explicit nature. A method of overcoming this difficulty is developed using concept of generalized forces and displacements.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120613
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  • 100
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    Finite element solution of spherically symmetric elasticity problems using general purpose structural analysis programs (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1044-1048 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120615
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