A geometrically exact isogeometric beam for large displacements and contacts

This work discusses an efficient formulation of a geometrically exact three-dimensional beam which can be used in dynamical simulations involving large displacements, collisions and non-linear materials. To this end, we base our model on the shear-flexible Cosserat rod theory and we implement it in the context of Isogeometric Analysis (IGA). According to the IGA approach, the centerline of the beam is parameterized using splines; in our work the rotation of the section is parameterized by a spline interpolation of quaternions, and time integration of rotations is performed using the exponential map of quaternions. Aiming at an efficient and robust simulation of contacts, we propose the adoption of a non-smooth dynamics formulation based on differential-variational inequalities. The model has been implemented in an open-source physics simulation library that can simulate actuators, finite elements, rigid bodies, constraints, collisions and frictional contacts. This beam model has been tested on various benchmarks in order to assess its validity in non-linear static and dynamic analysis; in all cases the model behaved consistently with theoretical results and experimental data.