Highly-efficient dynamics simulation of flexible mechanical systems via the hyper reduction method of POD-based hybrid strains

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.