Speaker
Description
In this contribution, we propose a high–order time and space–accurate isogeometric collocation (IGA-C) method for the explicit dynamics of geometrically exact beams [1]. While high–order accuracy in space is a well established feature of IGA-C for both explicit and implicit dynamics of geometrically exact beams [2, 3], time accuracy is still restricted to second–order. For some applications where temporal error is dominant, .e., impact and crash dynamics, such a lower order accuracy represents a significant drawback that prevents a fully exploitation of the high–order IGA-C potentialities. We fill this gap by proposing a high–order (up to sixth) time–accurate method based on the Runge-Kutta-Munthe-Kaas time integrator [3]. Exploiting the analogy between the dynamics of rigid bodies and shear deformable beams, we recast the classical Runge-Kutta scheme to solve the nonlinear governing equations evolving on the beam configuration manifold, IR3 × SO(3). Numerical applications to challenging benchmark problems will show the capabilities of the proposed formulation to achieve high–order time and space accuracy, while preserving computational efficiency.
References
[1] G. Ferri and E. Marino, A. Reali, G. Sangalli, Explicit high-order time and space accurate isogeometric collocation method for the dynamics of geometrically exact beams, Comput Methods Appl. Mech. Eng., Vol. 449, pp. 118495, 2026.
[2] E. Marino, J. Kiendl, L. De Lorenzis, Explicit isogeometric collocation for the dynamics of three-dimensional beams undergoing finite motions,Comput. Methods Appl. Mech. Eng., Vol. 343, pp. 530-549, 2019.
[3] E. Marino, J. Kiendl, L. De Lorenzis, Isogeometric collocation for implicit dynamics of three-dimensional beams undergoing finite motions, Comput Methods Appl. Mech. Eng.,Vol. 356, pp. 548-570, 2019.
[4] H. Munthe-Kaas, High order Runge-Kutta methods on manifolds, Applied Numerical Mathematics, Vol. 29, pp. 115–127, 1999.