Computational Technology Resources - CCP

Keywords: B-spline continuity, NURBS, Kirchhoff-Love rod theory, ribbon, curve element.

Summary

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 C^N-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.

References

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. doi:10.1016/0045-7949(95)00100-U
2: B.A. Barsky, T.D. De Rose, "Geometric Continuity of Parametric Curves: Three Equivalent Characterizations", IEEE Computer Graphics & Applications, 60-68, 1989. doi:10.1109/38.41470
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. doi:10.1016/j.cma.2009.08.013

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £65 +P&P)

	Computational & Technology Resources an online resource for computational, engineering & technology publications
	not logged in - login
Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 99 PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping Paper 222 Multi-Patch Isogeometric Analysis of Space Rods L. Greco and M. Cuomo Dipartimento di Ingegneria Civile ed Ambientale, Università degli Studi di Catania, Italy doi:10.4203/ccp.99.222 purchase the full-text of this paper Full Bibliographic Reference for this paper L. Greco, M. Cuomo, "Multi-Patch Isogeometric Analysis of Space Rods", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 222, 2012. doi:10.4203/ccp.99.222 Keywords: B-spline continuity, NURBS, Kirchhoff-Love rod theory, ribbon, curve element. Summary 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 C^N-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. References 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. doi:10.1016/0045-7949(95)00100-U 2 B.A. Barsky, T.D. De Rose, "Geometric Continuity of Parametric Curves: Three Equivalent Characterizations", IEEE Computer Graphics & Applications, 60-68, 1989. doi:10.1109/38.41470 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. doi:10.1016/j.cma.2009.08.013 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £65 +P&P)
Back to top	©Civil-Comp Limited 2023 - terms & conditions