AI 中文总结
研究有限应变梁动力学的两种模型，开发本征公式的结构保持离散化方法，通过混合有限元自然施加边界条件，避免代数约束，使多体系统组装更简便，且所需牛顿迭代更少，还能对封闭运动回路建模并保持能量守恒。
AI 中文摘要
Reissner-Simo模型和Hodges模型是有限应变梁动力学的两种等效连续描述。Reissner-Simo公式使用位移和旋转，而Hodges公式是本征的，避免了这两个变量。本文开发了本征公式的结构保持离散化。由于本征方程涉及线性微分算子，运动和动态边界条件都可以通过混合有限元自然施加。所得公式还使多体系统能够在没有代数约束的情况下组装，避免了运动约束通常引入的刚性微分代数方程。通过不同示例证明该方法，表明无需代数约束即可对封闭运动回路进行建模。所得互连系统保留端口哈密顿结构，所有非线性都局限于互连算子。与现有能量守恒方案相比，该方案所需的牛顿迭代更少。
英文摘要
The Reissner-Simo and Hodges models are two equivalent continuous descriptions of finite-strain beam dynamics. The Reissner-Simo formulation uses displacements and rotations, while the Hodges formulation is intrinsic and avoids both variables. Although equivalent in theory, the two approaches behave differently after discretization and offer distinct numerical advantages. In this work, we develop a structure-preserving discretization of the intrinsic formulation. Because the intrinsic equations involve linear differential operators, both kinematic and dynamic boundary conditions can be imposed naturally using mixed finite elements. The resulting formulation also enables multibody systems to be assembled without algebraic constraints, avoiding the stiff differential-algebraic equations typically introduced by kinematic constraints. We demonstrate the approach on different examples, also showing that closed kinematic loops can be modeled without algebraic constraints. The resulting interconnected systems retain a port-Hamiltonian structure,with all nonlinearities confined to the interconnection operator. This structure allows exact energy preservation when combined with implicit midpoint time integration. Furthermore the scheme appear to require less Newton iterations compared to existing energy preserving scheme.
Comments27 pages, 26 figures
