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  • 1
    Electronic Resource
    Electronic Resource
    Comment on ‘static analysis of diaphragm-supported cylindrical shells using a curved finite strip’ by D. J. DaweInt. J. Num. Meth. Engng, 11, 1347-1364 (1997). (1979)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 307-311 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620140215
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  • 2
    Electronic Resource
    Electronic Resource
    Hybrid-Trefftz plate bending elements with p-method capabilities (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1367-1393 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The p-method capabilities have thus far been used only in connection with the assumed displacement model elements. When such elements are used, singular points have to be isolated by one or two layers of small elements graded in a suitable geometrical progression towards singularity. This paper presents an alternative formulation which circumvents this drawback and enables excellent solution results to be obtained with uniform FE-grids. The formulation is based on the recently presented hybrid-Trefftz FE-model and makes use of optional expansion sets for various singularities or stress concentrations. Stress concentrations due to concentrated loads are also properly accounted for. It is shown that by augmenting the order of approximation over a fixed grid of such elements rapid convergence towards the accurate solution is obtained in the most efficient way.This paper summarizes the results of a preliminary study that had been undertaken to critically evaluate the potential of the new approach as a suitable basis for subsequent developments of a fully automated adaptive process.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240712
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  • 3
    Electronic Resource
    Electronic Resource
    Adaptivity in hybrid-Trefftz finite element formulation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 391-405 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: With the advent of computer aided design (CAD), the development of fully or semi-automated procedures by which a solution warranting the specified accuracy can most efficiently be reached has become a necessity. It is now of utmost interest to investigate finite element (FE) formulations offering a simple form of adaptivity, easy to implement.The present study (which is a sequel to an earlier paper1 on error estimation by the authors) identifies as a particularly promising approach of attaining this goal the p-method associated with the so-called hybrid-Trefftz FE model.2 Based on a simple stress error estimator1 and prior knowledge of the convergence rate, the solution warranting specified stress accuracy may be reached in a single trial by suitably respecifying just one parameter in the input data. The reported approach has successfully been implemented into the general purpose FE program SAFE3 and its high efficiency is illustrated in the paper through practical applications involving corner singularities and stress concentrations.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290212
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  • 4
    Electronic Resource
    Electronic Resource
    Dual hybrid-Trefftz element formulation based on independent boundary traction frame (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2955-2980 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents the dual hybrid-Trefftz (HT) element approach devised so as to enforce more strongly the reciprocity of boundary tractions at the element interfaces than the interelement conformity of displacements. As in the standard HT approach,1,2 a complete set of Trefftz functions is used to represent the internal displacement field of the element (and, as a consequence, the governing Navier-Lamé differential equations are a priori verified over the element). But rather than employing an auxiliary interelement displacement frame field to enforce the conformity on the internal displacements, an auxiliary boundary traction field is adopted to enforce at the element interfaces the reciprocity of tractions derived from the internal displacement field. Provided that the number of Trefftz functions is sufficiently large, this approach yields an opposite bound on the energy in comparison to the standard HT approach based on the displacement frame. As in the standard HT formulation,3 the dual HT formulation is particularly well suited for generation of highly accurate p-version elements. Although presented for solid mechanics, the formulation also holds for other problems. Numerical studies which involve comparisons of the two alternative displacement and traction frame HT element models have been performed by considering the Laplace's equation problem in two dimensions.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361707
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  • 5
    Electronic Resource
    Electronic Resource
    Improvement of computational efficiency of the 9 DOF triangular hybrid-Trefftz plate bending element (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 2167-2168 
    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.1620231113
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  • 6
    Electronic Resource
    Electronic Resource
    Hybrid trefftz plane elasticity elements with p -method capabilities (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 1443-1472 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A family of p-method plane elasticity elements is derived based on the hybrid Trefftz formulation.1 Exact solutions of the Lamé-Navier equations are used for the intra-element displacement field together with an independent displacement frame function field along the element boundary. The final unknowns are the parameters of the frame function field consisting of the usual degrees of freedom at corner nodes and an optional number of hierarchic degrees of freedom associated with the mid-side nodes. Since the element matrices do not involve integration over the element area, the elements have a polygonal contour with an optional number of curved sides. The quadrilateral element has the same external appearance as the conventional p-method plane elasticity element.2,3 But unlike in the conventional p-method approach, suitable special-purpose Trefftz functions are generally used to handle the singularity and/or stress concentration problems rather than a local mesh refinement. The practical efficiency of the new elements is assessed through a series of examples.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620350705
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  • 7
    Electronic Resource
    Electronic Resource
    A new 12 DOF quadrilateral element for analysis of thick and thin plates (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 2619-2638 
    Details
    ISSN: 0029-5981
    Keywords: Reissner-Mindlin plates ; hybrid-Trefftz elements ; shear locking ; soft and hard simple support ; h-convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a simple quadrilateral 12 DOF plate bending element based on a modified version of the hybrid-Trefftz approach. This element makes use of two independent fields of generalized displacements: ia non-conforming field (11 Trefftz terms for transverse displacement w and the corresponding rotations Θx, Θy) satisfying the governing differential equations of Reissner-Mindlin theory;iian auxiliary conforming field with displacements w̃ linked to rotations \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \Theta _x,\tilde \Theta _y$\end{document}, by the requirement of constant boundary distribution of the corresponding tangential component S̃t, of the transverse shear. This allows quadratic w̃ and linear \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \Theta _x,\tilde \Theta _y $\end{document}, at the element boundary to be obtained with only 3 DOF at the corner nodes.The resulting element, denoted by Q̃21-11, is robust and free of shear locking in the thin limit. The numerical assessment involves comparison with several recently presented 12 DOF thick plate quadrilaterals as well as with the standard 16 DOF hybrid-Trefftz quadrilateral, Q21-15S, with 15 Trefftz terms and independently interpolated w̃ and \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \Theta _x,\tilde \Theta _y $\end{document}.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620381508
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  • 8
    Electronic Resource
    Electronic Resource
    Least-squares T-elments: Equivalent FE and BE forms of a substructure-oriented boundary solution approach (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 21-32 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient solution to boundary-value problems may be based on the application of a suitably truncated T-complete set of Trefftz functions over individual subdomains and on linking the fields by a least-squares procedure. Although it yields a symmetric system of linear equations, this approach as originally presented by Zielinski and Zienkiewicz is not suited for implementation into FE codes. The present paper presents two equivalent formulations, which take respectively the form of the finite (FE) and non-conventional boundary-element (BE) approach. Both allow the resulting simultaneous equations to be assembled following the standard direct stiffness methods and can readily be implemented into existing FE codes.As in the conventional p-method, the accuracy may be controlled within large limits without increasing the number of elements. The present approach allows substantial saving in computer time in comparison with the so-called hybrid-Trefftz (HT) elements, though the assumed displacement fields are identical. The practical efficiency of the new T-element approach is assessed on the problem of stress concentration in a symmetrically compressed perforated panel.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100104
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  • 9
    Electronic Resource
    Electronic Resource
    Variational formulation of two complementary hybrid-Trefftz FE models (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 837-845 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents two complementary variational formulations of Trefftz-type elements wherein the piece-wise assumed displacement approximations a priori fulfil the governing differential equations over the element subdomain. The two formulations are such that either the displacement conformity or the reciprocity of the conjugate tractions is enforced at the element interfaces, one more strongly than the other. This is achieved through linking the piece-wise approximations either through an auxiliary displacement or a boundary traction frame. The two formulations concern solid mechanics and structures.Although for hybrid elements monotonic convergence in energy cannot be warranted, in practice the two presented formulations yield opposite bounds on the energy provided that the number of internal Trefftz functions is sufficiently large.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091007
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  • 10
    Electronic Resource
    Electronic Resource
    A family of variable section curved beam and thick-shell or membrane-stiffening isoparametric elements (1981)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 171-186 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A family of isoparametric curved beam elements of a general, compact cross-section is introduced. The formulation is based on beam theory and takes into account both transverse shear deformation and shear centre location. The elements exhibit the required displacement compatbility with Ahmad's superparametric thick-shell elements and isoparametric membrane elements. Examples presented at the end of the paper illustrate the validity of the formulation and the possibility of practical application of the elements.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620170203
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