B-Spline interpolation of Kirchhoff-Love space rods

Leopoldo Greco (1) , Massimo Cuomo (1)

1 Dipartimento di Ingegneria Civile ed Ambientale

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.

Domaines: Génie civil; Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Leopoldo Greco, Massimo Cuomo. B-Spline interpolation of Kirchhoff-Love space rods. Computer Methods in Applied Mechanics and Engineering, 2013, 256, pp.251-269. ⟨hal-00874611⟩