Extensions of the Generalized-Alpha Method to Multi-Time-Step Integration in Structural Dynamics

Abstract eng:
We present an implicit-explicit multi-time-step method for structural dynamics using the family of Generalized-α methods. With the proposed partitioned method, one can divide a complex structural domain into several subdomains and solve the individual subdomains separately. The solution of the original global problem is retrieved by enforcing the prescribed velocity continuity at subdomain interfaces like the method of Gravouil and Combescure (GC method). For large-scale simulations, e.g., to solve a global-local Finite Element model with a coarse global model of the whole structure and several refined local models of parts of the structure, the proposed scheme can be effective. In order to implement the Generalized-α method to the multi-time-step integration, first we derive a new predictor-corrector form of the implicit Generalized-α method from the implicit method previously introduced by Arnold and Br¨uls. Secondly, we propose a new predictor-corrector form of the explicit Generalized-α method. Both the implicit method and the explicit method are the one-step four-stage variants of the Generalized-α methods. Finally, we built our partitioned scheme with the extended Generalized-α methods. The multi-time-step method is obtained based on the Prakash and Hjelmstad’s method (PH method). We study the convergence of the current multi-time-step method by examining a single degree of freedom model problem. It is found that the current multi-time-step method maintains second-order accuracy, both with a unique time scale and with different time scales in each subdomain. Moreover, the current multi-time-step method is not dissipative at subdomain interfaces. Its numerical dissipation is solely introduced by the Generalized-α methods in each subdomain.

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