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<p>We propose a new, port-Hamiltonian formulation for the highly nonlinear dynamics of planar geometrically exact beams, which are amenable to arbitrary large deformations and rotations. A structure-preserving spatial and temporal discretization procedure&#xa0;- using mixed finite elements and second-order time-stepping methods&#xa0;- is proposed. It is observed that the present approach is objective, locking-free and provides an exact discrete representation of the energy and angular momentum balance. By comparing the approach to a classical displacement-based scheme from the literature it is shown that the port-Hamiltonian formulation paves new ways for the design of energy-momentum schemes in computational mechanics. Numerical examples underline the applicability to flexible multibody systems and beneficial numerical performance.</p>

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Energy-momentum-consistent simulation of planar geometrically exact beams in a port-Hamiltonian framework

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月16日

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  • Philipp L. Kinon,
  • Peter Betsch,
  • Simon R. Eugster

摘要

We propose a new, port-Hamiltonian formulation for the highly nonlinear dynamics of planar geometrically exact beams, which are amenable to arbitrary large deformations and rotations. A structure-preserving spatial and temporal discretization procedure - using mixed finite elements and second-order time-stepping methods - is proposed. It is observed that the present approach is objective, locking-free and provides an exact discrete representation of the energy and angular momentum balance. By comparing the approach to a classical displacement-based scheme from the literature it is shown that the port-Hamiltonian formulation paves new ways for the design of energy-momentum schemes in computational mechanics. Numerical examples underline the applicability to flexible multibody systems and beneficial numerical performance.