Explicit isogeometric collocation for the dynamics of three-dimensional beams undergoing finite motions

Abstract

We initiate the study of three-dimensional shear-deformable geometrically exact beam dynamics through explicit isogeometric collocation methods. The formulation we propose is based on a natural combination of the chosen finite rotations representation with an explicit, geometrically consistent Lie group time integrator. We focus on extending the integration scheme, originally proposed for rigid body dynamics, to our nonlinear initial–boundary value problem, where special attention is required by Neumann boundary conditions. The overall formulation is simple and only relies on a geometrically consistent procedure to compute the internal forces once control angular and linear accelerations of the beam cross sections are obtained from the previous time step. The capabilities of the method are shown through numerical applications involving very large displacements and rotations and different boundary conditions.