A novel decoupling dynamic method with third-order accuracy and controllable dissipation. (June 2021) - Yuan, Peng; Li, Dejian; Cai, C.S.; Xu, Guoji
Highlights: A dynamic method with third-order accuracy and desirable dissipation is proposed. A new accuracy criterion is proposed to assess the absolute error of dynamic methods. This method can efficiently decouple complex dynamic systems in parallel. A factorization of an intricate damping matrix is not required in the method. Spurious vibrations can be strongly suppressed in high-frequency domains. Abstract: In this paper, an efficient explicit integration method with third-order accuracy and controllable dissipation properties is proposed, and a new accuracy criterion is presented to evaluate relative errors of integration methods. By using this method, a desirable accuracy for responses in the low-frequency domain can be attained, spurious vibrations in the high-frequency domain can be strongly suppressed. Moreover, for the proposed method, update values of the displacement and velocity do not depend on the new state. Hence, it is convenient for decoupling a multi-spring coupling dynamic system to achieve high computational efficiency. The standard formulations of the proposed method, including the second-order and third-order accuracy schemes, are derived by discussing the local truncation error, difference accuracy, and stability firstly. Subsequently, the accuracy properties of the proposed method, e.g., the period elongation and amplitude decay, are analyzed in comparison with other available state-of-the-art explicit integration methods. Additionally, the properties of the proposed method, including the accuracy, convergence, dissipation, efficiency, and nonlinearity, are evaluated by using three examples. More specifically, the accuracy and convergence are evaluated through an example with theoretical solutions; the dissipation and efficiency are investigated by analyzing a geodesic dome truss; and the effectiveness in terms of the nonlinearity is investigated via a typical nonlinear dynamic system.