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力学学报  2014 

统一格式的显式与隐式任意混合异步算法

DOI: 10.6052/0459-1879-13-260, PP. 436-446

Keywords: 结构动力学,Newmark离散,显式算法,隐式算法,任意混合,异步积分,算法稳定性

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Abstract:

动力学问题的有限元分析需要在每一时步求解系统信息,相对于静力学问题,其计算量要大得多.因而,提高计算效率,节省计算工作量是动力学求解方法研究的主要内容.该文针对大型复杂动力学系统的高效求解问题,提出了一种基于Newmark离散格式的显式、隐式任意混合异步算法,根据整体系统不同局部的物理力学特性和求解精度要求,在空间域及时间域内对动力学系统方程进行多尺度求解.该方法根据显式、隐式算法固有的信息传递机制,采取动态的可变边界处理方法,避免了异步边界上的误差积累;并通过对整体系统能量平衡的校验,动态地确定和修正仿真计算时步,可以有效地预防不稳定性的产生和发展.数值算例表明该算法能在保持较高的计算精度的同时,极大地降低计算资源消耗,因而具有一定的实用价值.

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