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  • 11
    Electronic Resource
    Electronic Resource
    The poor bending response of the four-node plane stress quadrilateral (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 825-835 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Many plane stress finite elements which can exactly represent rigid-body and constant-strain modes are too stiff in their response to the simple flexural action of a beam. This problem has received considerable interest. In this paper we explore a new interpretation of the problem and show that the poor bending response of the original 4-node plane stress quadrilateral can be quantitatively predicted by an error model.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620210505
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  • 12
    Electronic Resource
    Electronic Resource
    The dual variable method for finite element discretizations of Navier/Stokes equations (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 883-898 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical solution of two-dimensional, transient, incompressible Navier-Stokes problems is considered. The dual variable method, originally developed in the context of a finite difference discretization, is a technique to considerably reduce the size of the linear system to be solved at each time step. The steps involved in the method are (1) the determination of the rank of the discrete divergence operator, A, (2) the determination of a basis for the null space of A, N(A), and (3) the calculation of a particular solution of the discrete continuity equation.A finite element implementation of the method is presented using quadrilateral piecewise bilinear velocity/constant pressure elements. Algorithms for the determination of a basis for N(A) and a particular solution are presented. Numerical comparisons of primitive versus dual variable formulations on several problems demonstrate the advantage of the dual variable method, in terms of both execution speed and memory requirements.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620210508
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  • 13
    Electronic Resource
    Electronic Resource
    Singularity of collapsed Q-8 finite element (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 959-965 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The ability of the collapsed Q-8 finite element to model strain singularities is studied in this paper. It is shown that its ability to model an r-1 singularity in strains depends strongly on the element size and number of Gauss points used for sampling stresses inside an element.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620210513
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  • 14
    Electronic Resource
    Electronic Resource
    An additional stiffness parameter measure of error of the second kind in the finite element method (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 1001-1012 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Conventional error analyses norms in the finite element method are based on the percentage error or its equivalent in some computed value as compared to the theoretically predicted value. In problems where two or more field variables are coupled, it is possible that if the field interpolation functions do not ‘consistently’ reproduce limiting situations of physical behaviour, there may be very large errors which are exaggerated enormously when some structural parameters become indefinitely large in a penalty limiting sense. The percentage error norms therefore saturate quickly to a value approaching 100 per cent and do not sensibly reflect the relationship between error and the structural parameter, even on a logarithmic plot.Errors due to these spurious constraints have recently been recognized as belonging to a special class described as ‘errors of the second kind’. A new error norm, called the additional stiffening parameter, helps to recognize the manner in which errors of the second kind can be blown out, of propprtion by a large variation in some structural parameter. Recent investigations in some multi-field problems are summarized here to demonstrate the usefulness of this concept.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620210603
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  • 15
    Electronic Resource
    Electronic Resource
    Finite element hourglassing control (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 1039-1048 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new hourglassing control technique for quadrilateral and hexahedral elements used in dynamic finite element codes is presented. Based on expansion of the strees in a Taylor series and retention of additional terms beyond the usual constant stress term, this technique has the advantage that actual rather than artificial material properties are used. Simplifications that render this technique competitive with artificial viscosity and stiffness procedures in terms of additional storage and computation requirements are described.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620210606
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  • 16
    Electronic Resource
    Electronic Resource
    A CAD approach to the minimum weight design problem (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 1049-1066 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A structure is defined by a set of governing points. These points can be used to define lines, surfaces and solids. A governing point can be connected to a design variable. The values of the design variables are determined in order to minimize the weight of the structure subject to a number of stress constraints. Three simple structures are then designed.
    Additional Material: 35 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620210607
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  • 17
    Electronic Resource
    Electronic Resource
    A simple plate/shell triangle (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 1149-1156 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple shear flexible triangular plate/shell element with three/five displacement degrees-of-freedom at the three corner nodes only, is identified. It does not lock or have zero-energy mechanisms. The specific geometrical configurations in which this is possible are derived through field consistency patch tests.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620210613
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  • 18
    Electronic Resource
    Electronic Resource
    Evaluation of added mass by a cloning algorithm (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 1157-1164 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In problems of structure interaction with infinite surrounding of incompressible, inviscid fluid media, added mass matrices on wet surfaces have been considered for modelling the effects of outgoing waves. For an arbitrary geometry of the wet surface, an expression for the added mass matrix is derived according to a finite element procedure which utilizes the force-displacement relations of representative elements on the boundary. In the element mass matrix a certain symmetry, which characterizes interactions between the interior and exterior surfaces, helps reduce the quadratic matrix equation of the cloning algorithm to a linear eigenvalue problem. A benchmark example is included to establish the numerical accuracy of the proposed formulation.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620210614
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  • 19
    Electronic Resource
    Electronic Resource
    Conference diary (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 1168-1169 
    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.1620210619
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  • 20
    Electronic Resource
    Electronic Resource
    Numerical differentiation of tabulated functions with automatic choice of step-size (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 1171-1185 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for determining the optimum step-size in numerical differentiation of a tabulated function is described. In test cases it gives an average error of about four times the error in the data; thus, it is more than twice as accurate as previously published methods. A Fortran program is presented.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620210702
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