A partitioned combined computational method for multi-scale dynamic systems

A partitioned/combined computational method based on Newmark scheme is proposed to analyze dynamic systems with different temporal scales and element scales. To effectively filter spurious high-frequency vibration content and retain the second-order accuracy simultaneously, Generalized-α schemes are investigated and incorporated into the proposed method. The proposed method can decompose a complete domain into several independent computational subdomains (≥3), and several independent substructures can be combined into a complete computational structure. The accuracy and stability of responses in different subdomains can be ensured and adjusted by using their own integration parameters and time-step sizes. The energy conservation property is preserved in the proposed method. Only one calculation is performed at each time step for all subdomains, and computational information exchange between subdomains is only conducted at the system time step, therefore, the computational efficiency is improved significantly compared with the existing multi-time-step methods. The derivation process and theoretical demonstration of the proposed method are given in detail. Two representative examples, namely, a single degree of freedom system split into four subdomains and a sandwich beam subjected to high-frequency impact loads, are studied to systematically demonstrate the proposed method's accuracy, energy properties, and efficiency compared with the existing multi-time-step methods.