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  • 1
    Electronic Resource
    Electronic Resource
    A note on universal matrices for triangular finite elements for the quasi-harmonic equation (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 617-622 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm to generate universal matrices for plane triangular finite elements for the general ‘quasi-harmonic’ equation is presented. For every member of the triangle family three numerical universal matrices are obtained which are independent of the size, shape and ‘material’ properties of the element. Of these, two are basic and the third can be generated from one of these two. The element ‘stiffness’ matrix is conveniently generated by manipulating these two basic matrices taking into account the size, shape and material properties of the element in a simple manner.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620190410
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A field-consistent two-noded curved axisymmetric shell element (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1245-1261 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The efficiency of a field-consistent two-noded linear curved axisymmetric shear-flexible shell element is shown to be due to the removal of both shear and membrane locking. Typical applications illustrate how the field-consistent representation dramatically improves performance, and allows greater flexibility in tailoring element design to satisfy specific problem needs.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230705
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  • 3
    Electronic Resource
    Electronic Resource
    An isoparametric quadratic thick curved beam element (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1583-1600 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A three-noded curved beam element with transverse shear deformation, based on independent isoparametric quadratic interpolations, is designed from field-consistency principles. It is shown that a quadratic element that is field-inconsistent in membrane strain suffers from ‘membrane locking’ - i.e. an error of the second kind propagates indefinitely as the element length to thickness ratio and/or the element length to radius of curvature ratio increase, in nearly inextensional bending. However, field-inconsistency in shear strain does not lead to ‘shear locking’ but degrades its performance to exactly that of a field-consistent linear element. It is also seen that field-inconsistency leads to severe axial force and shear force oscillations. Error estimates for locking are derived, wherever possible, and confirmed by numerical experiments. The field-consistent element offered here is the most efficient quadratic curved beam element possible.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230902
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  • 4
    Electronic Resource
    Electronic Resource
    Field-consistent strain interpolations for the quadratic shear flexible beam element (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1973-1984 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A shear flexible (i.e. Timoshenko) quadratic isoparametric beam element with two degrees of freedom per node is critically examined from the point of view of the consistency of the constrained strain fields that arise in the thin-beam limits. The errors, in terms of convergence of displacement fields and violent oscillations of stress fields, that emerge when exactly integrated elements are used are predicted a priori and confirmed with numerical experiments. The rationale behind the use of optimal stress sampling at Gaussian points is also derived directly from these arguments.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620231102
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  • 5
    Electronic Resource
    Electronic Resource
    An alternative explicit formulation for the DKT plate-bending element (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 1289-1293 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The stiffness matrix for the DKT plate-bending element is formulated explicitly in a global co-ordinate system. This approach avoids transformations of stiffness, and elasticity properties for anisotropic materials, from local to global co-ordinates, which were required in previous formulations. A FORTRAN listing of the algorithm is appended for potential users.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620210709
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  • 6
    Electronic Resource
    Electronic Resource
    A linear thick curved beam element (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1313-1328 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Early attempts to derive curved beam and shell elements in a curvilinear system were dramatically unsuccessful. This was wrongly attributed to the failure of these elements to recover strain-free rigid body displacement modes in a curvilinear co-ordinate description. Recent evidence points to a ‘membrane locking’ phenomenon that arises when constrained strain fields corresponding to inextensional bending are not ‘consistently’ recovered. This accounts for, more completely and precisely, the failure of such elements.In this paper, a simple linear two-noded C0 continuous thick curved beam element based on a curvilinear deep shell theory is derived free from shear and membrane locking. Lack of consistency in the shear and membrane strain-field interpolations in their constrained physical limits (Kirchhoff and inextensional bending limits, respectively) causes very poor convergence due to locking and severe spurious oscillations in stress predictions. Error estimates for these are made and verified. Field-consistent strain interpolations remove these errors and produce the most efficient linear element possible.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230709
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Stress oscillations in plane stress modelling of flexure - a field-consistency interpretation (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 711-724 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Exactly integrated isoparametric plane stress elements behave poorly in flexure. The 4-noded element ‘locks’, with errors that progress indefinitely as element aspect ratio increases. Reduced integration of the shear strain energy eliminates this locking entirely. The 8-noded element does not lock, but improves in performance with reduced integration of shear strain energy. Both elements, with their original shape functions, show severe shear stress oscillations in flexure. In this paper we attribute these oscillations to the lack of ‘consistency’ of shear strain fields derived directly from independent field-variable interpolations. We derive error models for specific tractable examples which can confirm the accuracy of this conceptual scheme through digital computation using the finite element models. A field-consistent redistribution strategy for the shear strain field is offered as an elegant procedure to free the elements of spurious oscillations and give a ‘lock’-free performance.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240405
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    A field consistent three-noded quadratic curved axisymmetric shell element (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 711-723 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A curved three-noded quadratic isoparametric axisymmetric thick shell element is developed. Field-consistency interpretations allow various configurations of the element to be designed so as to satisfy specific problem needs. Typical applications demonstrate the versatility and accuracy of this element in its different problem-specific forms.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230413
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  • 9
    Electronic Resource
    Electronic Resource
    Field-consistency and violent stress oscillations in the finite element method (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 2017-2033 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The fact that finite element models can give rise to violent stress oscillations and that there are optimal locations where stresses can be correctly sampled in spite of the presence of these violent stress fluctuations has been known for some time. However, it is less well known that these oscillations arise in a specific class of problems - where there are multiple strainfields arising from one or more field-variables and where one or more of these strain-fields must be constrained in particular physical limits. In this paper, we show that unless the interpolations for these constrained strain-fields are ‘field-consistent’, violent oscillations would set in. These oscillations represent spurious self-equilibrating stress-fields generating spurious energy terms that lead to ‘locking’.The field-consistency interpretation offers a conceptual scheme to delineate these problems and an operational procedure called the functional reconstitution technique allows the errors resulting from field-inconsistency to be anticipated a priori. We demonstrate the power of this approach through an interesting example of a multi-strain-field problem - the inextensional/nearly inextensional deformation of a shear flexible curved beam.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620241013
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