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©2012 Civil-Comp Ltd |
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L. Greco and M. Cuomo
Dipartimento di Ingegneria Civile ed Ambientale, Università degli Studi di Catania, Italy
Keywords: B-spline continuity, NURBS, Kirchhoff-Love rod theory, ribbon, curve element.
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The paper deals with the isogeometric analysis using B-splines of space rods subject to Kirchhoff-Love hypotheses. The approach was used by Gontier and Vollmer [1] for developing a plane curve element within the framework of the Timoshenko rod model, but they adopted only one patch to represent the entire geometry of the rod; furthermore the authors developed their theory only for plane elements.
In this work a multi-patch isogeometric approach is developed for for the numerical analysis of the three-dimensional Kirchhoff-Love rod theory. Bezier and B-splines interpolations are used and it is shown that they are able to attain very good accuracy for rod structures, particularly for developing a three-dimensional exact curve element with geometric torsion.
The patches in general present a CN-continuity in the interior and are joined with C0-continuity, so that the global tangent stiffness operator in general is singular. In order to avoid the singularity in the stiffness operator several continuity conditions at the joints of the patches are required. Either parametric continuity (C2 or C3) or geometric continuity (G1 or G2) conditions can be imposed [2].
The geometric continuity conditions are weaker than the parametric conditions. The continuity conditions in the CAD literature are known as the beta-constraints and represent constraint conditions for the displacements of the control points where the scalar beta-quantity represents additional unknowns [3]. In this paper, the continuity conditions are not imposed using beta-constraints but directly by means of the Lagrange multiplier method.
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- 1
- C. Gontier, C. Vollmer, "A large displacement analysis of a beam using a CAD geometric definition", Computer and Structures, 57, 6, 981-989, 1995.
- 2
- B.A. Barsky, T.D. De Rose, "Geometric Continuity of Parametric Curves: Three Equivalent Characterizations", IEEE Computer Graphics & Applications, 60-68, 1989.
- 3
- J. Kiendl, Y. Bazilevs, M.-C. Hsu, R. Wuchner, K.-U. Bletzinger, "Isogeometric shell analysis with Kirchhoff-Love elements", CMAME, 198, 3902-3914, 2009.
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