Development of a Family of Unconditionally Stable Explicit Direct Integration Algorithms with Controllable Numerical Damping Using Discrete Control Theory

Abstract eng:
Integration algorithms are typically utilized to solve temporally discretized equations of motion in structural dynamics. Stability is an important property to be considered when selecting the proper integration algorithm for analysis of structures with a large number of degrees of freedom. The recent development of real-time structural testing brings more challenges to the integration algorithm. An explicit integration algorithm is more favorable in real-time structural testing because of its computational efficiency. However, the presence of numerical errors will lead to the spurious growth of high-frequency response in the dynamic analysis and the presence of inevitable experimental errors will aggravate this effect during real-time structural testing. It is therefore advantageous for an explicit integration algorithm to possess numerical damping to suppress any spurious participation of the high-frequency response while the lower modes are accurately integrated. This paper presents the development of a family of explicit direct integration algorithms with controllable numerical damping. Discrete control theory is utilized to assign proper stable poles to the discrete transfer function of the integrations algorithms to achieve unconditional stability and numerical damping. The properties of the proposed algorithm are investigated and compared with other well established algorithms such as the Newmark family of integration algorithms and the CR integration algorithm.

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