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中文摘要：
针对经典“珠子”模型在计算精度和求解速度方面的不足，提出了一种基于有限单元法的高精度建模与快速求解方法。首先在考虑系绳非线性应力一应变关系的基础上，利用Hamilton原理和C—w方程推导了系统在轨道坐标系下的动力学模型，然后使用三阶的一维单元对系绳进行了离散化处理，并给出了一种利用纽马克一口法进行预估，由Newton—Raphson法进行迭代校正的高效时域求解算法，从而实现了对于系统状态的高精度快速求解。仿真结果表明：与经典的“珠子”模型相比，在分段长度相近的情况下，本文的方法不仅求解精度更高，而且计算速度能够提高至少10倍，另外还能够避免仿真过程中张力出现虚假振荡。
英文摘要：
Based on the finite element method, a method with high accuracy and great efficiency is proposed to supply the deficiency of the classical bead model. First, based on nonlinear stress-strain relation, the dynamics model under the orbit coordinate system is derived by using Hamilton principle and C-W Equation. Then, the space tether is accurately discretized by the third-order one-dimensional element. Furthermore, a new efficient time-domain solving algorithm, using the Newmark-/3 method for estimation and the Newton-Raphson iteration for correction, is proposed. Thus, the goal of quickly and accurately solving the system status is implemented. Compared with the classical lumped mass model results of the proposed algorithm demonstrate that in the case of having similar segment length, the proposed algorithm shows higher accuracy, reduces the time consumption of computation at least 10 times and avoids the pseudo oscillation in tensile stress.
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