结构动力问题的高阶精确时步群积分方法

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (12) : 286-297.

论文

结构动力问题的高阶精确时步群积分方法

李鸿晶，杨寅

作者信息 +

Time-step group-based higher-order accurate time integration algorithms for structural dynamics

LI Hongjing, YANG Yin

Author information +

文章历史 +

摘要

高阶精确时间积分方法可为与时间相关的高频复杂动力行为提供高精度的预测结果，但既有高阶精确时间积分方法普遍存在计算工作量偏大的问题，难以满足实际结构线性和非线性动力分析日益增长的计算需求。本文提出了一种基于时步群的高阶精确时间积分方法，将p (p≥2) 个相邻的未知时步组成待求解的时步群，以结构动力方程积分解为基础构建逐时步群求解结构动态响应的时间积分方案。在对每个时步群进行积分的过程中，无需联立求解方程，仅通过矩阵乘法运算即可一次性地计算得到时步群内全部p个时步的动态响应。数值特性分析以及线性与非线性算例试验均表明，本文算法精度高、稳定性好、数值耗散可控，在选择较大的时间步距情形下依然能够稳定地获得高精度的计算结果。相较传统二阶精度时间积分方法，本文算法的计算效率亦有较大幅度的提高。

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.

导出引用

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[J]. Journal of Vibration and Shock, 2024, 43(12): 286-297

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