AI 中文总结
本文针对弹性动力学保结构离散化中Dirichlet边界速度施加的精度问题，提出连续层面的加性运动学分解，推导强施加边界速度的提升端口-哈密顿系统模型，经数值模拟验证其能量平衡特性与计算性能。
AI 中文摘要
在端口-哈密顿弹性动力学的有限元模型中，边界速度的施加通常依赖拉格朗日乘子，会产生微分-代数方程（DAEs）。另一种弱施加方法虽能保持常微分方程（ODE）结构，但在Dirichlet边界处精度往往较差。为解决这些局限，本文在连续层面引入加性运动学分解，将位移和速度场拆分为在边界处消失的相对动态分量，以及延伸至内部域的规定提升函数。该分解诱导出分布式端口，将边界驱动的效应映射至域内。通过将此映射融入合适的虚功率原理，我们推导出提升后的端口-哈密顿系统（PHS）模型，经有限元离散后可简化为强施加Dirichlet边界速度的ODE系统。该框架被用于推导适用于不同PHS几何表示的2场和4场格式。此外，我们证明在特定形函数下，标准有限元（FEM）格式可被恢复，表明离散模型中的提升框架等价于计算力学实践中的经典代数矩阵划分。数值模拟验证了所提方法的能量平衡特性和计算性能。
英文摘要
The imposition of boundary velocities in finite element models of port-Hamiltonian elastodynamics typically relies on Lagrange multipliers, yielding Differential-Algebraic Equations (DAEs). Alternatively, weak imposition methods that maintain an Ordinary Differential Equation (ODE) structure often exhibit poor accuracy at Dirichlet boundaries. To address these limitations, this paper introduces an additive kinematic decomposition at the continuous level, splitting the displacement and velocity fields into a relative dynamic component that vanishes on the boundary and a prescribed lifting function extending into the interior domain. This decomposition induces a distributed port that maps the effects of the boundary actuation inside the domain. By incorporating this mapping into suitable virtual power principles, we derive lifted port-Hamiltonian system (PHS) models that, upon finite element discretization, reduce to ODE systems in which Dirichlet boundary velocities are strongly imposed. The framework is applied to derive 2-field and 4-field formulations suited to distinct PHS geometric representations. Furthermore, we show that under specific shape functions, standard FEM schemes are recovered, demonstrating that the lifting framework in the discrete models is equivalent to the classic algebraic matrix partitioning in computational mechanics practice. The energy-balance properties and computational performance of the proposed methodology are verified through numerical simulations.
Comments36 pages, 9 figures
