Model order reduction approaches such as proper orthogonal decomposition (POD) can be used to model and simulate mechanical systems with geometric nonlinearity in high efficiency. However, the complexity of a POD-based reduced-order model (ROM) in online computation is still related to the dimension of its full order model (FOM). In this work, the POD-based hybrid strain method is proposed for the hyper reduction of flexible mechanical systems. This method distinguishes the strain compositions evaluated from the POD modes of high or low energies (i.e. singular values of data). The quadratic terms of Green-Lagrange strain calculated from the low-energy modes are removed such that the computational complexity of the generalized internal forces and their Jacobians are greatly reduced. Then the invariant stiffness coefficients of hybrid strains formulated by the POD modes are deduced to remove the dimension effect of FOM, thus greatly enhancing the computational efficiency of the ROM in online stage. Afterwards, dynamics simulations of a mechanical system with internal resonance, a rotating slender beam and a paraboloid truss space structure are presented to verify the accuracy and efficiency of the proposed hyper-reduction model and to validate its robustness.

中文翻译：

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通过基于 POD 的混合应变的超还原方法对柔性机械系统进行高效动力学仿真


模型降阶方法，如适当的正交分解 （POD），可用于高效地对具有几何非线性的机械系统进行建模和模拟。然而，在线计算中基于 POD 的降阶模型 （ROM） 的复杂性仍然与其全阶模型 （FOM） 的维度有关。在这项工作中，提出了基于 POD 的混合应变方法，用于柔性机械系统的超还原。该方法将评估的应变组成与高能或低能的 POD 模式（即数据的奇异值）区分开来。去除了从低能模式计算的格林-拉格朗日应变的二次项，从而大大降低了广义内力及其雅可比矩阵的计算复杂度。然后，推导了POD模式公式化的混合应变的不变刚度系数，消除了FOM的维数效应，从而大大提高了在线阶段ROM的计算效率。然后，对具有内共振的机械系统、旋转细长梁和抛物面桁架空间结构进行了动力学仿真，验证了所提出的超还原模型的准确性和效率，并验证了其鲁棒性。