Abstract:Higher-order accurate time integration methods can provide highly precise estimations for time-dependent problems, especially for complicated dynamic behavior involving abundantly high frequency contents. However, the existing higher-order accurate time integration methods generally have the drawback that they require large amount of computational efforts, which restrict their applications to linear and nonlinear dynamic response analysis of practical structures. In this article, a novel higher-order accurate and efficient time integration algorithm is proposed for structural dynamic problems. The theoretical solutions governing the state equations of the system are employed to construct the group-by-group procedure, in which a time-step group consisting of p time steps is regarded as the unknown time interval to be solved, and all p solutions within the time-step group are obtained simultaneously only by the matrix multiplications. Both numerical characteristics and test examples from linear and nonlinear dynamic problems show that, the proposed time-step group method is higher-order accurate and stable with controllable numerical dissipation, and highly accurate solutions of structural dynamic response can still be obtained stably even in the case of selecting larger time steps. Compared to traditional second-order accuracy time integration methods, the computational effort of the time-step group method has been decreased greatly.
李鸿晶, 杨寅. 结构动力问题的高阶精确时步群积分方法[J]. 振动与冲击, 2024, 43(12): 286-297.
LI Hongjing, YANG Yin. Time-step group-based higher-order accurate time integration algorithms for structural dynamics. JOURNAL OF VIBRATION AND SHOCK, 2024, 43(12): 286-297.
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