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  • 1
    Electronic Resource
    Electronic Resource
    Vibrations of twisted cantilever plates - a comparison of theoretical results (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 1365-1380 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Previously published literature shows widely different results for the free vibration frequencies of twisted cantilever plates. Inasmuch as it is important to know the vibration characteristics of turbomachinery blades, which may have considerable twist, it would be desirable to have a comprehensive, definitive set of results, and to establish which of the numerous theoretical methods available can adequately analyse such problems. For this purpose, a joint government/industry/university research study was organized. Numerical results were obtained for a set of 20 different twisted plates having various aspect ratios, thickness ratios and pretwist angles. Nineteen distinct theoretical methods were employed, 15 using finite elements, two using shell theory, and two using beam theory. Although some of the best-known computational procedures (especially finite element codes) were used by analysts with great experience, the numerical results obtained showed considerable disagreement. The present paper describes the analytical methods used and exhibits samples of the type of results obtained.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620210802
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Vibration and buckling of beam-columns subjected to non-uniform axial loads (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1739-1755 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The small-displacement free vibration of elastic Euler-Bernoulli beams subjected to non-uniform axial forces and the buckling of elastic columns are both analysed by means of various types of beam finite elements. The procedure incorporates beams and columns of varying cross-sections, such as linear tapers, inhomogeneous beams and columns, distributed axial forces, elastic end and interior restraints and point masses with linear and rotary inertias. All of these topics individually or in some combinations have been analysed by others. The purpose of this paper is to bring together under a single umbrella the various problems studied by others, and to provide the solution to one problem apparently not yet solved - the buckling and vibration of tapered columns under non-uniform axial thrust. The mass, stiffness and geometric stiffness matrices for the standard beam element are fully written out for direct incorporation into existing finite element programs. A FORTRAN subroutine for generating these matrices, and those for various higher-order beam elements, is also provided.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230913
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Numerical analysis of a generalized plane ‘elastica’ with non-linear material behaviour (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 617-630 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This article presents a numerical procedure for the analysis of a planar, continuous, flexible member. Large displacements and rotations, non-linear material behaviour and general cross sections are admitted. A shooting method is utilized along with Newton-type iteration for improved estimates. The resulting computer program is used to compare with numerical and analytical solutions of problems solved by others, and to present the solution to a problem which brings out very clearly the effects of both geometric and material non-linearities.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260307
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Loading, unloading and reloading of a generalized plane plastica (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1645-1660 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This article presents a shooting-type numerical procedure for the analysis of a planar, continuous and flexible member where the material is permitted to unload and reload plastically. A kinematic type of strainhardening rule is employed, and large displacements, large rotations and general cross section shapes are admitted. Though numerical and semi-analytical solutions exist in the literature for specific problems where the internal and external loads increase monotonically (see, for example, References 1-4), little attention has been paid to problems where these loads (specifically internal loads) are permitted to decrease or reverse direction. In the present work a comparison is made with the solution to one such problem found in the literature, and the solution to four additional problems is given to show the versatility and usefulness of the method.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280713
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    A cubic triangular finite element for flat plates with shear (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 109-126 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the development of a straightforward displacement type triangular finite element for bending of a flat plate with the inclusion of transverse (or lateral) shear effects. The element has twenty two degrees of freedom consisting of ten for the lateral displacement of the midplane and six for rotations of the normal to the undeformed midplane of the plate. The latter are taken as independent of the slopes of the deformed midplane in order to include deformation due to transverse shear. The element is fully conforming and may be orthotropic. At interelement boundaries, the element matches adjacent elements both with respect to lateral displacement of the midplane and the rotations of the normal. The result is an efficient ‘linear moment’ triangular element but with transverse shear deformation included. Numerical computations for a number of examples are presented. The results show the element to be more flexible than most other finite element models and agree closely with those from a numerical solution of the three dimensional elasticity equations. The results also converge to those from thin plate theory when the thickness to length ratio becomes small or when the transverse shear moduli are artificially increased.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280109
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    Paper (German National Licenses)
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