B-Spline interpolation of Kirchhoff-Love space rods

The paper deals with the isogeometric analysis via B-splines of space rods under Kirchhoff-Love hypotheses. The approach was used by Gontier and Vollmer [12] for developing a plane curve element within the framework of the Timoshenko rod model, but they adopted only one patch to represent entirely the geometry of the rod; furthermore the authors developed their theory only for plane elements. In this work we develop an isogeometric approach for the numerical analysis of the 3D Kirchhoff-Love rod theory. We use B-splines and Bezier interpolations and we show that they are able to attain very good accuracy for rod structures, particularly for developing a 3D exact curve element with geometric torsion. The paper presents an original parametrization of the geometric torsion that proves to be very effective. The use of B-splines allows to avoid discontinuities on the geometrical quantities, and particularly on the normal fields, so that even relatively low order interpolation functions are able to yield accurate results. (C) 2012 Elsevier B.V. All rights reserved.