Speaker
Description
Port-Hamiltonian (PH) systems modeling [1] — a framework that inherently guarantees energetic consistency and facilitates the interconnection of physical systems — is gaining increasing popularity also in computational mechanics. Structural elements such as strings [2] and beams, which often represent submodules in flexible multibody systems, are particularly well-suited for this approach [3]. This talk focuses on the application of PH modeling to the dynamics of geometrically exact beams, also known as Simo-Reissner beams or special Cosserat rods. While the linearized Timoshenko beam, that assumes small deformations and rotations, is a common application example in PH works, we focus on two aspects that are only rarely addressed: Firstly, we analyze computational aspects linked to the spatial and temporal discretization of PH beams. We demonstrate how the PH framework naturally mitigates numerical locking effects. Secondly, we present a PH formulation of the geometrically exact beam, which is amenable to large deformations and rotations. We further discuss a structure-preserving spatial discretization, using mixed finite elements. By maintaining the PH properties for the spatially discrete system, this approach provides a robust foundation for accurate and physically consistent simulations. Additionally, an appropriate time discretization ensures an exact representation of the energy balance in discrete time. Simulation results illustrate the performance of the developed approach. The gained insights highlight the potential of the PH framework for extending to more complex systems and advancing numerical treatments in structural mechanics.
References:
[1] V. Duindam, A. Macchelli, S. Stramigioli and H. Bruyninckx: "Modeling and Control of Complex Physical Systems: The Port-Hamiltonian Approach". Berlin, Heidelberg: Springer, 2009.
[2] P. L. Kinon, T. Thoma, P. Betsch and P. Kotyczka: “Generalized Maxwell Viscoelasticity for Geometrically Exact Strings: Nonlinear Port-Hamiltonian Formulation and Structure-Preserving Discretization”. In: IFAC-PapersOnLine 58(6), pp. 101–106, 2024.
[3] A. Warsewa, M. Böhm, O. Sawodny and C. Tarín: “A Port-Hamiltonian Approach to Modeling the Structural Dynamics of Complex Systems”. In: Applied Mathematical Modelling 89, pp. 1528–1546, 2021.
