基于能量的杆体动力学建模，实现有限旋转下的保结构数值计算。
Mixed formulation and structure-preserving discretization of Cosserat rod dynamics in a port-Hamiltonian framework
- 采用独立变量混合格式，避免刚度锁定和奇异性。
- 离散后保持哈密顿结构，支持能量动量一致性积分。
- 适用于大变形、非标准驱动及耗散材料，适合仿真高精度力学系统。
提出一种基于能量的空间柯西杆非线性动力学建模框架，适用于大位移与大旋转情形。该混合形式包含独立的位移、速度与应力变量，具有客观性且无锁定问题。有限旋转通过方向矢量表示，避免奇异性并获得常数质量矩阵。系统为无限维非线性端口-哈密顿（PH）系统，由带有二次能量泛函的偏微分代数方程组描述。通过时间微分的柔度形式应力-应变关系，可自然施加几何约束（如不可拉伸或抗剪）。采用保结构有限元离散化，得到具有PH结构的有限维系统，便于设计能量动量一致的积分格式。耗散材料行为（通过广义麦克斯韦模型）及非标准驱动方式（如气室或肌腱）可自然融入该框架。多个数值算例表明，该方法为涉及有限旋转的计算力学中能量动量一致性建模提供了新途径。
原文摘要 · Abstract (English)
An energy-based modeling framework for the nonlinear dynamics of spatial Cosserat rods undergoing large displacements and rotations is proposed. The mixed formulation features independent displacement, velocity and stress variables and is further objective and locking-free. Finite rotations are represented using a director formulation that avoids singularities and yields a constant mass matrix. This results in an infinite-dimensional nonlinear port-Hamiltonian (PH) system governed by partial differential-algebraic equations with a quadratic energy functional. Using a time-differentiated compliance form of the stress-strain relations allows for the imposition of kinematic constraints, such as inextensibility or shear-rigidity. A structure-preserving finite element discretization leads to a finite-dimensional system with PH structure, thus facilitating the design of an energy-momentum consistent integration scheme. Dissipative material behavior (via the generalized-Maxwell model) and non-standard actuation approaches (via pneumatic chambers or tendons) integrate naturally into the framework. As illustrated by selected numerical examples, the present framework establishes a new approach to energy-momentum consistent formulations in computational mechanics involving finite rotations.
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