The paper deals with the isogeometric analysis via B-splines of space rods under Kirchhoff-Love hypoth- eses. 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 the- ory. We use B-splines and Bezier interpolations and we show that they are able to attain very good accu- racy 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 nor- mal fields, so that even relatively low order interpolation functions are able to yield accurate results.
B-Spline interpolation of Kirchhoff-Love space rods
GRECO, LEOPOLDO VINCENZO;CUOMO, Massimo
2013-01-01
Abstract
The paper deals with the isogeometric analysis via B-splines of space rods under Kirchhoff-Love hypoth- eses. 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 the- ory. We use B-splines and Bezier interpolations and we show that they are able to attain very good accu- racy 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 nor- mal fields, so that even relatively low order interpolation functions are able to yield accurate results.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.