An implicit G~1 multi patch B-spline interpolation for Kirchhoff-Love space rod

摘要

The paper presents a novel formulation for the isogeometric analysis of assemblies of Kirchhoff-Love space rod elements, introducing a multi-patch implicit G~1 formulation, so that an automatic non-singular stiffness operator is obtained without the need of adding continuity conditions. The goal is achieved using a polar decomposition of the deformation of the first and last segments of the control polygon, that allows to introduce directly the end rotations as degrees of freedom. Both parametric and geometric continuity can be obtained in this way. We use Bezier and B-spline interpolations and we show that they are able to attain very good accuracy for developing a 3D exact curve element with geometric torsion (pre-twisted rod). In the paper the performance of the multi-patch elements is examined comparing the rates of convergence of the L~2 error norm for the multi-patch and single-patch formulations. It is shown that the rate of convergence remains the same, although in certain cases the accuracy is lower for the multi-patch solutions.