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  • 1
    Digitale Medien
    Digitale Medien
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 261-271 
    ISSN: 1069-8299
    Schlagwort(e): axisymmetric ; nonlinear ; thick shell ; buckling ; conjugate gradient like method ; semi-analytical method ; Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The paper highlights the results of numerical experimentation with a geometrically non-linear formulation of a thick axisymmetric shell element involving non-axisymmetric deformation. The formulation itself has earlier been presented in the context of a non-linear local-global analysis of shells of revolution, where very little attention was paid to an independent evaluation of the element's performance. A Fourier decomposition of the loads and the displacements has been used in the circumferential co-ordinate, in order to describe the non-axisymmetric behavior. Due to the interaction between different harmonic terms in the non-linear analysis, the tangential stiffness matrix is no longer block-diagonal. A pseudoload method and a conjugate gradient like iterative scheme have been used to overcome the problem of a large tangent stiffness matrix, and thus most of the advantages of the semi-analytical method have been retained in the non-linear analysis. The accuracy of the predictions in the study has been benchmarked by analysing the same examples using the quadrilateral shear deformable shell element available in the commercial code NISA II. A comparison with other results available in the literature hints that the effect of transverse shear deformation should not be neglected in the geometrically non-linear analysis of shells which are traditionally considered thin. © 1997 by John Wiley & Sons, Ltd.
    Zusätzliches Material: 11 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 703-712 
    ISSN: 1069-8299
    Schlagwort(e): non-linear structural analysis ; incremental-iterative solution ; conjugate gradient-like method ; arc length algorithm ; snap-through ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: A special incremental-iterative solution method for non-linear finite element structural analysis including snap-through is presented. As an alternative to the direct solution methods, a special iterative strategy along with the pseudoload method is employed within each Newton-Raphson iteration step. Two new developments concerning the pseudoload method and the special iterative strategy, which were originally conceived and applied for the non-linear analysis of shells of revolution using a semi-analytical method, are presented. Firstly, the underlying principles of the method are utilized in solving general non-linear structural mechanics problems. Secondly, the capability of the method is enhanced for tracing the load-displacement curve beyond the critical load by integrating the arc length method. Special modifications are proposed to handle situations with a non-positive-definite tangential stiffness matrix. Numerical examples with snap-through and snap-back phases in the load-deflection path are presented to demonstrate the applicability and accuracy of this approach. Results obtained from this numerical study verify the usefulness of this method as an alternative to the conventional direct methods or iterative methods of solving linearized equations in an incremental non-linear analysis.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 3
    Digitale Medien
    Digitale Medien
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3057-3074 
    ISSN: 0029-5981
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: In this paper a local-global analysis technique is presented for the non-linear analysis of shells of revolution with a localized material discontinuity in the form of a crack or a cutout. The local zone is modelled using two-dimensional general shell elements. Axisymmetric shell elements with Fourier description in the circumferential direction are used away from this local zone. In contrast to the earlier work of the authors, the geometric non-linearity is taken into account in the axisymmetric zone as well. The harmonic coupling in the axisymmetric zone is efficiently handled through the pseudo-load approach. A special preconditioned conjugate gradient iterative method is employed in conjunction with the arc length method for achieving improved convergence and negotiating the limit points. The attractive features of this methodology are that the tangential stiffness matrix of the structure is never assembled and factorized and that most of the computations are simple matrix-vector multiplications which are carried out efficiently at the element level. Numerical examples are presented to demonstrate the applicability of this method.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 4
    Digitale Medien
    Digitale Medien
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 1153-1170 
    ISSN: 0029-5981
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The mode of collapse in many metallic shells is, oftentimes, one of localized collapse, wherein severe plastic deformation and high displacement gradients are localized within some region. The combined material and geometric non-linearity emanating from this local region is the predominant cause of instability in shells of revolution. In such a situation a local-global strategy is very useful for an efficient analysis. This strategy consists of employing two dimensional degenerated isoparametric shell elements with non-linear capability in a well defined 'local' zone where all the non-linearities are expected to be localized and which also contains some form of local deviation from axisymmetry such as a circumferential imperfection, cutouts, cracks, etc. Linear elastic ring type elements are employed in the remaining axisymmetric zone and the two zones are linked through a transformation between the degrees of freedom involved. The solution of the non-linear problem is achieved by appropriate condensation procedures to reduce the number of active degrees of freedom and the load incrementation is achieved by the well known 'arc length' iterative procedure. Numerical exampies are presented to demonstrate that this strategy is very efficient and accurate for problems with well defined non-linear local zones. The capability of this strategy for treating problems with local material discontinuities such as cracks, cutouts, etc. as an efficient alternative to a complete two dimensional discretization is pointed out.
    Zusätzliches Material: 17 Ill.
    Materialart: Digitale Medien
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